decision support tool to optimize the operation of … · and lake tana, which is the largest fresh...

Decision Support Tool to Optimize the Operation of Multi-Purpose Reservoirs: A Case Study in the Lake Tana Catchment, Ethiopia Entscheidungsunterstützungswerkzeug zur Optimierung des Betriebs von Mehrzweckspeichern: Eine Fallstudie im Einzugsgebiet des Lake Tana, Äthiopien

By

Alemayehu Habte Saliha (M.Sc)

Dissertation

submitted to Faculty of Civil Engineering of

Technical University of Dresden

in partial fulfilment of the requirements

for the degree of

Doctor of Engineering

(Dr.-Ing.)

Supervisor: Prof. Dr.–Ing. habil. Hans-B. Horlacher

Co-supervisor: Prof. Dr.-Ing. Markus Disse

Local supervisor: Dr.-Ing. Seleshi Bekele Awulachew

Technical University of Dresden

November 2012, Germany

Acknowledgement

I

Acknowledgement

First and for most I thank my Almighty God, for through Him I had my well being and passed every hurdle in my study time and in my life.

My sincere and special thanks indebted to my supervisor Prof. Dr.-Ing. habil. Hans-B. Horlacher for his supervision, encouragement and guidance he has provided me throughout my study. His critical comments and helpful guidance gives me a chance to explore further. I have learned a lot from him. My deepest gratitude goes to my second supervisor Prof. Dr.-Ing. Markus Disse and local supervisor Dr.-Ing. Seleshi Bekele. Their kind support and encouragement gives me strength right from the start to the last minute of the research work.

My special thanks and appreciations go to Dr. Johannes Cullmann and Dr. Niels Schütze for their special kind of support and encouragement at the time when I needed them most. I have equally learned a lot from them.

I would like to extend my appreciation and many thanks to Mr. Ulf Möricke and Dr. Torsten Heyer for their support, socialization and easing my life in Dresden from the first day till this time. I equally appreciate Mr. Matthias Lehmann and Thomas Wagner for their technical support.

I would also like to gratefully acknowledge ArbaMinch University, the Ethiopian Ministry of Water and Energy (MoWE), Challenge Program on Water and Food (CPWF), the former German Technical Cooperation (GTZ) and the International Water Management Institute (IWMI) for their financial and technical support. Many thanks to the Ethiopian Ministry of Water and Energy (MoWE) and the National Meteorological Service Agency (NMSA) for providing me the hydro-meteorological data for the case study area.

I am very grateful to my beloved wife Hermon Abraham, her parents, my parents and my friends back home for their consistent encouragement through out my study. I would like to thank my friends in Dresden, Dr.-Ing. Negede, Dr.-Ing. Abrehet, Mr. Anteneh, Mr. Taddele and colleagues in the Institute for Hydraulic Engineering and Technical Hydromechanics for their support and made my life in Dresden easy and comfortable. My appreciation and many thanks go to Mr. Gerhard Strigel, Mr. Philipp Saile, Mr. Ulrich Schroeder, Dr. Johannes Cullmann, Ms. Ana Maria Conde Corral, Ms. Andrea Weßler, Ms. Dagmar Kronsbein, Dr.-Ing. Mandy Cullmann, Ms. Solveig Schartl and colleagues in Bundesanstalt für Gewässerkunde who made my life in Koblenz much easier and enjoyable. I, apologize, those whom I did not mention the names for acknowledgment. I equally appreciate and acknowledge all of you.

Dedication

II

Dedication

This dissertation is dedicated to my wife Hermon Abraham Tesfamariam

and to my mother Alemnesh Keraga Andnew

Abstract

III

Abstract

This dissertation presents the work of developing decision support tools for the management of multi-purpose multi-reservoir systems in hydro-meteorological data scarce areas. In the planning and design of water resource systems comprising a large number of reservoirs, it is necessary to optimize simultaneously the operation of the entire system rather than to consider the reservoirs separately. One of the basic input variables in reservoir operation is inflow to each reservoir. Predicting runoff in ungauged basins is still a big challenge in the field of hydrology. Despite the lack of sufficient hydro-meteorological information, water resources development particularly in developing countries is crucial. Therefore, this research proposes two methods: (1) Building a regional model to estimate runoff for ungauged catchments by coupling artificial intelligence and a watershed model and (2) developing a method to generate optimal operation rule curves of multi-objective multi-reservoir systems by integrating a reservoir simulation model and an optimization algorithm.

The proposed tools were tested to generate optimal operating policies for a multi-objective multi-reservoir system in the Lake Tana sub-basin of the Blue Nile river basin and to estimate runoff from ungauged catchments of the Blue Nile river basin, Ethiopia. At first, a self-organizing map (SOM) was used to group hydrological homogeneous catchments. Then, the water balance model WaSiM-ETH was used to generate daily flow for the ungauged catchments in the respective group identified by SOM. The reservoir system was set up using the reservoir simulation model HEC-5 to guide the releases of the reservoir system. The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) was adopted for optimizing the rule curves of the multi-objective multi-reservoir system.

SOM identified five hydrological homogenous groups of catchments in the case study area. The regional model, which is the coupled SOM and WaSiM-ETH models, was able to transfer hydrological information from a data rich catchment to a data poor (ungauged) catchment. The regional model generally overestimates the low flows. For some catchments, the regional model underestimates the daily peak flows but fits very well on the 10-day and monthly peak flows. Considering the Nash-Sutcliff (N-S) and coefficient of determination (R2) efficiency criteria, the validation results for sub-catchments whose flow data have never been involved during calibration showed that the regional model is promising and quite satisfactory.

The integrated reservoir simulation and optimization (single and multi-objective CMA-ES and HEC-5) model was demonstrated by considering the existing development situation and future water resources development scenarios in four artificial reservoirs and Lake Tana, which is the largest fresh water lake in Ethiopia. The competing water sectors considered were irrigation, domestic water supply, environmental flows for ecosystems and flows that are needed to maintain the aesthetic value of the Tis-Issat waterfall, navigation and hydropower production. Thus, the objective function was set to minimize the water shortage for the domestic water supply, the environmental flows, irrigation and hydropower generation and to keep the best possible water level for navigation. Comparison has been done between single objective CMA-ES (SO-CMA-

Abstract

IV

ES) and multi-objective CMA-ES (MO-CMA-ES) for the multi-objective multi-reservoir system. In the case of SO-CMA-ES, an approximate pareto-curve was generated by running the model for several times with different combinations of priorities given to each demand. However, the choice of priorities is subjective. Moreover, it was found that the performance of MO-CMA-ES as compared to SO-CMA-ES was superior in terms of finding pareto-optimal solutions for the operating rule curves. Therefore, for the case study considered in this dissertation, the MO-CMA-ES was chosen to investigate different future water resources development scenarios in the Lake Tana sub-basin and a clear trade-off amongst demands was observed. Results for optimal reservoir operation under full water resources development scenario showed that 90% of the total water supply and 91% of hydropower demands can be met with Lake Tana navigation level kept as high as 1784.8 m a.s.l. For the same scenario, 91% of the total water supply and 88% of hydropower demands with navigation level of 1784.6 m a.s.l. were obtained for reservoir operation in favour of total water supply.

The stand-alone developed tools, i.e. the regional and integrated reservoir simulation-optimization models, enable decision makers and planners to choose an optimal operation policy amongst competing water uses in existing and planned multi-objective multi-reservoir systems in hydro-meteorological data scarce areas.

However, it further needs a graphical user interface to link all the inputs and outputs of the regional and the reservoir simulation-optimization models to the database and vice versa. Generally, the results highlighted a paramount importance of the proposed regional model and an integrated reservoir simulation-optimization model to support decision makers and planners.

Zusammenfassung

V

Zusammenfassung

In der Dissertation werden Instrumente zur Unterstützung von Entscheidungen für die Bewirtschaftung von Mehrzweckspeicher-Verbundsystemen in Gebieten entwickelt, in denen nur wenige hydrometeorologische Daten vorhanden sind. Bei der Planung und Konstruktion von wasserwirtschaftlichen Systemen mit einer Vielzahl von Speichern ist es eher erforderlich, den Betrieb des Gesamtsystems zu optimieren, anstatt die Speicher getrennt zu betrachten. Eine der grundlegenden Eingangsgrößen beim Betrieb von Speichern ist der Wasserzufluss zu jedem Speicher. Die Vorhersage des Abflusses in unbeobachteten Einzugsgebieten gehört immer noch zu den großen Herausforderungen der Hydrologie. Obwohl keine ausreichenden hydro-meteorologischen Informationen vorhanden sind, ist die Erschließung der Wasserressourcen in Entwicklungsländern von äußerster Wichtigkeit. In dieser Forschungsarbeit wird folgendes Vorgehen vorgeschlagen: (1) Die Erstellung eines regionalen Modells durch die Kopplung von künstlicher Intelligenz mit einem Einzugsgebietsmodell zur Abfluss-Abschätzung in unbeobachteten Einzugsgebieten sowie (2) die Entwicklung einer Methode zur Ermittlung optimaler Speicherinhaltskurven für Mehrzweckspeicher-Verbundsysteme durch die Einbindung eines Speicher-Simulationsmodells und eines Optimierungsalgorithmus.

Die vorgeschlagenen Instrumente wurden zur Ermittlung der optimalen Speicherinhaltskurven für Mehrzweckspeicher im Lake Tana-Teileinzugsgebiet des Blauen Nil eingesetzt sowie zur Schätzung des Abflusses in unbeobachteten Einzugsgebieten des Blauen Nils in Äthiopien. Zuerst wurden mit Hilfe von Selbstorganisierenden Merkmalskarten (SOM) Gruppen hydrologisch homogener Einzugsgebiete bestimmt. Im Anschluss wurde das Wasserhaushaltsmodell WaSiM-ETH zur Berechnung der Tagesabflussmengen von unbeobachteten Einzugsgebieten angewendet, die zu einer der von der SOM zuvor bestimmten Gruppen gehören. Mit Hilfe des Reservoir-Simulationsmodells HEC-5 wurde das aus dem Speichersystem abgegegebene Wassers gesteuert. Die Covariance Matrix-Adaptation Evolution Strategy (CMA-ES) wurde zur Optimierung der Speicherinhaltskurven des Mehrzweckspeicher-Verbundsystems angewandt.

Mit Hilfe der Merkmalskarten wurden fünf Gruppen hydrologisch homogener Einzugsgebiete für die Fallstudie ermittelt. Mit dem regionalen Modell, bei dem SOM mit WaSiM-ETH gekoppelt wurde, konnten hydrologische Informationen aus einem Einzugsgebiet mit vielen Daten auf ein (unbeobachtetes) Einzugsgebiet mit wenigen Informationen übertragen werden. Das regionale Modell neigt generell zu einer Überschätzung der Niedrigwasserabflüsse. Bei einigen Einzugsgebieten werden mit dem regionalen Modell zu geringe Tages-Abflussspitzen ermittelt, während die 10-Tages- und monatlichen Abflussspitzen gut abgebildet werden. Basierend auf dem Nash-Sutcliff Koeffizienten und dem Bestimmtheitsmaß, zeigen sich in der Validierung für diejenigen Teileinzugsgebiete, die während der Kalibrierung nicht berücksichtigt wurden, vielversprechende und sehr gute Ergebnisse.

Zusammenfassung

VI

Das integrierte Speichersimulations- und Optimierungsmodell (Einzweck- und Mehrzweck-CMA-ES und HEC 5) wurde für den gegenwärtigen Zustand und für zukünftige wasserwirtschaftliche Entwicklungsszenarien für vier Speicher und den größten See Äthiopiens, Lake Tana, eingesetzt. Die konkurrierenden Wassersektoren sind Bewässerung, kommunale Wasserversorgung, ökologischer Mindestabfluss, Erhalt des ästhetischen Werts des Tis-Issat Wasserfalls, Schifffahrt und Wasserkrafterzeugung. Daher wurde die Zielfunktion so gewählt, dass die Summe der Wasserdefizite bei der kommunalen Wasserversorgung, den ökologischen Mindestabflüssen, der Bewässerung und der Wasserkrafterzeugung minimiert und der für die Schiffbarkeit bestmögliche Wasserstand eingehalten werden. Dabei wurde für das Mehrzeckspeicher-Verbundsystem CMA-ES mit einer und mit mehreren Zielgrößen (SO-CMA- ES bzw. MO-CMA-ES) miteinander verglichen. Bei SO-CMA-ES wurde eine Pareto-Kurve approximiert, indem den Zielgrößen in mehreren Modellläufen unterschiedliche Gewichtungsfaktoren zugeordnet wurden. Jedoch ist die Auswahl der Gewichtungsfaktoren subjektiv. Außerdem erzielte MO-CMA-ES höhere Güten bei der Ermittlung pareto-optimaler Lösungen für die Speicherinhaltskurven. Daher wurde in der betrachteten Fallstudie MO-CMA-ES für die Untersuchung verschiedener zukünftiger wasserwirtschaftlicher Entwicklungsszenarien im Lake Tana Teileinzugsgebiet verwendet und es konnte ein eindeutiger Kompromiss für die konkurrierenden Zielgrößen ermittelt werden. Bei einer vollständigen Nutzung der Wasserressourcen und einer optimalen Bewirtschaftung können bei einem Füllstand des Lake Tana von 1784.8 m 90% der gesamten Wasserversorgung und 91% der Wasserkraftnutzung realisiert werden. Wird die Wasserversorgung beim Speicherbetrieb bevorzugt, so können bei einem Füllstand von 1784.6m 91% der gesamten Wasserversorgung und 88% der Wasserkraftnutzung erfüllt werden.

Die entwickelten Instrumente, d.h. das regionale und das integrierte Speichersimulations-Optimierungs-Modell, können von Entscheidungsträgern und Planern in anderen Einzugsgebieten mit wenigen hydro-meteorologischen Daten für die Auswahl einer optimalen Bewirtschaftungsstrategie bei konkurrierenden Wassernutzungen in bestehenden und geplanten Mehrzweckspeicher-Verbundsystemen genutzt werden.

Jedoch ist hierfür eine grafische Benutzeroberfläche erforderlich, um alle Inputs und Outputs der regionalen und Speicher-Simulations-Optimierungsmodelle mit der Datenbank zu vernetzen. Die Ergebnisse heben die besondere Bedeutung des vorgestellten regionalen Modells und integrierten Speichersimulations-Optimierungsmodells zur Unterstützung von Entscheidungsträgern und Planern hervor. Die Instrumente ermöglichen ihnen, optimale Strategien unter konkurrierenden Wassernutzungen bei bestehenden und geplanten Mehrzweckspeichersystemen in Regionen mit geringen hydro-meteorologischen Datenbeständen zu ermitteln.

Table of contents

VII

Table of contents ACKNOWLEDGEMENT ......................................................................................................................... I DEDICATION...........................................................................................................................................II ABSTRACT ............................................................................................................................................. III ZUSAMMENFASSUNG...........................................................................................................................V TABLE OF CONTENTS.......................................................................................................................VII LIST OF FIGURES................................................................................................................................. IX LIST OF TABLES..................................................................................................................................XII LIST OF ABBREVIATIONS................................................................................................................ XV LIST OF NOMENCLATURES AND SYMBOLS .............................................................................XVI 1 INTRODUCTION ............................................................................................................................1

1.1 BACKGROUND OF THE STUDY.....................................................................................................2 1.1.1 Decision Support System ......................................................................................................2 1.1.2 Reservoir operation ..............................................................................................................3 1.1.3 Estimation of flow for ungauged river basins.......................................................................4

1.2 OBJECTIVE OF THE RESEARCH ....................................................................................................6 1.3 CONTENT AND STRUCTURE OF THE THESIS .................................................................................7

2 DESCRIPTION OF THE CASE STUDY AREA...........................................................................9 2.1 ETHIOPIA....................................................................................................................................9 2.2 THE BLUE NILE RIVER BASIN ..................................................................................................11

2.2.1 Hydro-Meteorological stations...........................................................................................13 2.2.2 Land use and soil................................................................................................................14

2.3 LAKE TANA SUB-BASIN............................................................................................................19 2.3.1 General ...............................................................................................................................19 2.3.2 Climate ...............................................................................................................................19 2.3.3 Geology ..............................................................................................................................20 2.3.4 Soil and land use ................................................................................................................21 2.3.5 Navigation ..........................................................................................................................21 2.3.6 Tourism...............................................................................................................................21 2.3.7 Hydropower generation......................................................................................................22 2.3.8 Lake Tana hydrology ..........................................................................................................22

2.4 PLANNED AND EXISTING ARTIFICIAL RESERVOIRS IN LAKE TANA SUB-BASIN..........................25 2.4.1 Koga Reservoir ...................................................................................................................27 2.4.2 Ribb Reservoir ....................................................................................................................29 2.4.3 Megech reservoir................................................................................................................31 2.4.4 Gumera reservoir ...............................................................................................................33 2.4.5 Tana-Beles basin transfer...................................................................................................35

3 STATE OF THE ART AND PROPOSED DECISION SUPPORT TOOL ...............................37 3.1 PROPOSED FRAMEWORK OF DST .............................................................................................37 3.2 DATA BASE COMPONENT..........................................................................................................40 3.3 REGIONAL MODEL COMPONENT ...............................................................................................41

3.3.1 General background ...........................................................................................................41 3.3.1.1 Regionalization ....................................................................................................................... 41 3.3.1.2 Rainfall-runoff model.............................................................................................................. 42 3.3.1.3 Cluster analysis ....................................................................................................................... 44

3.3.2 Proposed method of regionalization to the case study area ...............................................45 3.3.2.1 Water balance simulation model (WaSiM-ETH) .................................................................... 47 3.3.2.2 Self-organizing maps or Kohonen networks ........................................................................... 60

3.3.3 Working principle of coupled WaSiM-ETH and NeuroShell ..............................................64 3.4 RESERVOIR SIMULATION-OPTIMIZATION MODEL COMPONENT .................................................68

3.4.1 General ...............................................................................................................................68

Table of contents

VIII

3.4.2 Definition and formulation of Multi-objective optimization problems ...............................69 3.4.3 Solution methods for multi-objective reservoir operation problems ..................................71

3.4.3.1 Conventional method .............................................................................................................. 71 3.4.3.2 Evolutionary algorithms (EAs) method................................................................................... 73

3.4.4 Proposed coupled reservoir simulation-optimization model to the case study area ..........76 3.4.4.1 HEC-5 reservoir simulation model.......................................................................................... 77 3.4.4.2 Optimization of reservoir operation ........................................................................................ 79

3.4.5 Formulation of coupled simulation-optimization model.....................................................84 3.4.5.1 Coupled single objective CMA-ES (SO-CMA-ES) algorithm and HEC-5 ............................. 84 3.4.5.2 Coupled multi-objective CMA-ES algorithm and HEC-5....................................................... 89

3.5 DECISION MAKING COMPONENT...............................................................................................90 4 APPLICATION OF THE METHODOLOGY TO THE CASE STUDY AREA ......................91

4.1 REGIONAL MODEL....................................................................................................................91 4.1.1 Identification of hydrological homogeneous groups ..........................................................91 4.1.2 WaSiM-ETH model setup ...................................................................................................95

4.2 OPTIMIZATION OF MULTI-RESERVOIR USING SINGLE OBJECTIVE CMA-ES...............................96 4.2.1 Reservoir model setup ........................................................................................................96

4.2.1.1 Input Data to HEC-5 ............................................................................................................... 96 4.2.1.2 Schematization of HEC-5 and CMA-ES model .................................................................... 101

4.2.2 Existing condition and scenarios......................................................................................105 4.2.2.1 Existing condition: sectoral approach ................................................................................... 105 I. Tis-Abay I and II hydropower production ....................................................................................... 105 II. Tana-Beles hydropower production at different navigation level .................................................... 105 4.2.2.2 Scenario 1: reservoirs optimized individually (sectoral approach)........................................ 105 4.2.2.3 Scenario 2: SO-CMA-ES for full water resources development of Lake Tana sub-basin (integrated approach).................................................................................................................................. 105

4.3 OPTIMIZATION OF MULTI-RESERVOIR USING MO-CMA-ES...................................................106 4.3.1 Multi-reservoir model setup .............................................................................................106

4.3.1.1 Scenario 3: MO-CMA-ES for partial water resources development of Lake Tana sub-basin106 4.3.1.2 Scenario 4: MO-CMA-ES for full water resources development of Lake Tana sub-basin.... 106

5 RESULTS AND DISCUSSIONS .................................................................................................107 5.1 ESTIMATIONS OF FLOW IN UNGAUGED CATCHMENT ...............................................................107

5.1.1 Ungauged tributaries of the Blue Nile river basin............................................................107 5.1.2 Ungauged catchments in Lake Tana sub-basin ................................................................111

5.2 DERIVED OPTIMUM RULE CURVE............................................................................................114 5.2.1 Results of coupled SO-CMA-ES algorithm and HEC-5....................................................114

5.2.1.1 Existing condition: sectoral approach ................................................................................... 114 I. Optimized hydropower productions of Tis-Abay hydropower plant ............................................... 114 II. Optimized hydropower production of Tana-Beles hydropower plant .............................................. 114 III. Tana-Beles hydropower production at different navigation level .................................................... 115 5.2.1.2 Scenario 1: reservoirs optimized individually (sectoral approach)........................................ 117 I. Megech, Ribb, Gumera and Koga reservoirs for irrigation.............................................................. 118 II. Lake Tana reservoir for hydropower production ............................................................................. 121 5.2.1.3 Scenario 2: full water resources development of Lake Tana sub-basin using SO-CMA-ES (integrated approach).................................................................................................................................. 122

5.2.2 Results of coupled MO-CMA-ES algorithm and HEC-5 (integrated approach) ..............123 5.2.2.1 Scenario 3: partial water resources development of Lake Tana sub-basin using MO-CMA-ES 123 5.2.2.2 Scenario 4: full water resources development of Lake Tana sub-basin using MO-CMA-ES 125

6 CONCLUSIONS AND RECOMMENDATIONS......................................................................135 7 REFERENCES..............................................................................................................................139 APPENDIX A. HYDRO-METEOROLOGY.......................................................................................148

A.1 HYDROLOGY..................................................................................................................................148 A.2 METEOROLOGY .............................................................................................................................161

APPENDIX B. RESERVOIRS..............................................................................................................166

List of figures

IX

List of figures Figure 2-1: Mean annual distribution of rainfall and approximate boundary of 12 major basins of

Ethiopia.............................................................................................................................................10 Figure 2-2: Location of the Blue Nile river basin and its 14 major sub-regions ........................................12 Figure 2-3: Location of the hydro-meteorological stations in the study area .............................................13 Figure 2-4: Soil map of the Abay river basin .............................................................................................15 Figure 2-5: Land use of the Abay river basin .............................................................................................17 Figure 2-6: Location of Hydro-meteorological stations, mean monthly rainfall histogram and drainage

map of Lake Tana sub-basin .............................................................................................................20 Figure 2-7: Tis-Issat waterfalls a) before and b) after the completion of Tis-Abay Hydropower station II

(Phote source: [29]) ..........................................................................................................................22 Figure 2-8 Locations of the proposed reservoirs around Lake Tana ..........................................................26 Figure 2-9 Schematics of Tana-Beles basin transfer for hydropower generation (Adopted from EEPCO,

Beles Multipurpose Project) .............................................................................................................36 Figure 3-1 General framework of DSS for water resources .......................................................................38 Figure 3-2 Conceptual framework of the proposed structure of decision support tool...............................40 Figure 3-3 Structure of the proposed regionalized model ..........................................................................45 Figure 3-4 Structure of the hydrologic model [WaSiM-ETH] (Modified from [80]).................................48 Figure 3-5 Comparison of daily ETP computed using Penman-Monteith and Hamon methods................50 Figure 3-6 Gilgel Abay observed and simulated daily discharge for calibration and validation period.....59 Figure 3-7 Gilgel Abay observed and simulated 10 days discharge for calibration and ............................59 Figure 3-8 Gilgel Abay observed and simulated monthly discharge for calibration and validation period60 Figure 3-9: Structure and basic principle of rectangular topology of SOM ...............................................61 Figure 3-10 The decrease in neighbourhood radius over time ...................................................................63 Figure 3-11 (a) initial iteration, (b) after 100 iteration, (c) after 200 iterations and (d) after 500 iterations

..........................................................................................................................................................64 Figure 3-12 Framework of the coupled WaSiM-ETH and SOM models ...................................................65 Figure 3-13 Input form of the coupled program.........................................................................................67 Figure 3-14 Typical pareto front for two objective functions.....................................................................71 Figure 3-15 Simple structure of evolutionary algorithm ............................................................................74 Figure 3-16 Structure of the proposed reservoir simulation and optimization models for multi-purpose

multi-reservoir system operation ......................................................................................................76

List of figures

X

Figure 3-17 Different storage zone used in HEC-5 reservoir simulation model ........................................78 Figure 3-18 Framework of combined single objective CMA-ES and HEC-5............................................88 Figure 3-19 Framework of the combined multi-objective CMA-ES and HEC-5.......................................90 Figure 4-1 Architecture of the unsupervised SOM network in NeuroShell2 .............................................92 Figure 4-2 Five hydrologically homogeneous groups in the case study area .............................................93 Figure 4-3 Box plots showing the distribution of 16 catchment characteristics in each group ..................94 Figure 4-4 Cropping pattern for non-rice crops (CP1) ...............................................................................98 Figure 4-5 Schematics of Megech reservoirs used in HEC-5 simulation model ......................................102 Figure 4-6 Schematic of Lake Tana and four upstream reservoirs used in HEC 5 simulation model ......104 Figure 5-1 Tana-Beles mean annual hydropower production at different navigation ..............................117 Figure 5-2 Sample simulated water level for 1993 and 1994, upper and lower rule curve for Ribb

irrigation reservoir. .........................................................................................................................119 Figure 5-3 Evaluation of model performance during optimization ..........................................................119 Figure 5-4 Upper and lower rule curves for Megech reservoir ................................................................120 Figure 5-5 Approximate pareto-curve using coupled SO-CMA-ES and HEC-5......................................123 Figure 5-6 An approximate pareto-front for partial WRD scenario using MO-CMA-ES........................124 Figure 5-7 An approximate pareto-front for full WRD scenario using MO-CMA-ES.............................125 Figure 5-8 Approximate pareto-front for full WRD generated using SO-CMA-ES and MO-CMA-ES ..126 Figure 5-9 An approximate pareto-front for different water resources development scenarios ...............128 Figure 5-10 An approximate pareto curve at different navigation levels using MO-CMA-ES................129 Figure 5-11 Percentage demand met for each reservoir at selected navigation levels..............................131 Figure 5-12 Observed and simulated Lake Tana water levels for navigation level fixed at 1784.8 m a.s.l.

for reservoir operation in favour of TWS .......................................................................................132 Figure 5-13 Extracted non-dominated points for navigation level fixed at 1784.8 and 1785.0 m a.s.l. ...133 Figure A- 1 Formats of Hydro-meteorological time series data for WaSiM-ETH ...................................148 Figure A- 2 Measured and WaSiM-ETH model out put of Uke river after calibration in group 1...........150 Figure A- 3 Measure and regional model out put of Dembi river (validation of group 1) .......................150 Figure A- 4 Measured and WaSiM-ETH model out put of Buno Bedelle river after calibration in group 2

........................................................................................................................................................151 Figure A- 5 Measure and regional model out put of Ardy river (validation of group 2)..........................151 Figure A- 6 Measured and WaSiM-ETH model out put of Dura river after calibration in group 3 .........152

List of figures

XI

Figure A- 7 Measure and regional model out put of Lower Fetta river (validation of group 3)...............152 Figure A- 8 Measured and WaSiM-ETH model out put of Gilgel Abay river after calibration in group 4

........................................................................................................................................................153 Figure A- 9 Measure and regionalized model out put of Gilgel Beles river (validation of group 4)........153 Figure A- 10 Measured and WaSiM-ETH model out put of Sibilu river after calibration in group 5......154 Figure A- 11 Measure and regionalized model out put of Robi Jiga river (validation of group 5) ..........154 Figure A- 12 Mean monthly aerial precipitation and mean daily open water evaporation of Lake Tana.161 Figure A- 13 Mean monthly aerial precipitation and mean daily open water evaporation.......................162 Figure A- 14 Mean monthly aerial precipitation and mean daily open water evaporation.......................162 Figure A- 15 Mean monthly aerial precipitation and mean daily open water evaporation of Gumera

reservoir ..........................................................................................................................................163 Figure A- 16 Mean monthly aerial precipitation and daily open water evaporation of Koga reservoir ...163 Figure B- 1 Sample HEC-5 reservoir simulation model’s control file .....................................................166 Figure B- 2 Matlab programme used to handle physical reservoir constraints.........................................173 Figure B- 3 Matlab programme used to handle physical reservoir constraints.........................................173 Figure B- 4 Perl computer programme used to couple single CMA-ES with HEC-5 for sigle reservoir .174 Figure B- 5 Perl computer programme used to couple SO-CMA-ES with HEC-5 for multi-reservoir

multi-objective problems ................................................................................................................175

List of tables

XII

List of tables Table 2-1: Selected hydro-meteorological characteristics of the 12 major drainage basins of Ethiopia ....11 Table 2-2: Percentages of major soil types of the Abay river and its sub-basins .......................................15 Table 2-3: ID and soil group names of major soil types of the Abay river and its sub-basins ...................16 Table 2-4: Percentage of major land use of the Abay river basin and its sub-basins..................................17 Table 2-5: Major land use types of the Abay river basin............................................................................18 Table 2-6: Characteristics of major rivers around Lake Tana ....................................................................23 Table 2-7 Planned irrigation schemes in the Lake Tana sub-basin (Source: [21], [22] and [24]) ..............25 Table 2-8: Koga Dam Irrigation Scheme....................................................................................................28 Table 2-9 Ribb Dam Irrigation Scheme (construction in progress)............................................................30 Table 2-10 The Proposed Megech Dam Irrigation Scheme........................................................................32 Table 2-11 The Proposed Gumera Dam Irrigation Scheme........................................................................34 Table 2-12 Main dimension of the powerhouse of Tana-Beles multipurpose hydropower station ............36 Table 3-1 Default (northern Switzerland) and modified (case study area) monthly correction factors fi of

Hamon method..................................................................................................................................50 Table 3-2 Two years daily mean monthly potential evapotranspiration using Penman-Monteith method

and modified Hamon method............................................................................................................50 Table 3-3 WaSiM-ETH model parameters used during calibration ...........................................................56 Table 3-4 Optimized WaSiM-ETH soil model (Topmodel) parameters after calibration ..........................58 Table 3-5 Performance of the WaSiM-ETH, the HBV [33] and the SWAT2005 [95] hydrological models

for two rivers in the Lake Tana sub-basin.........................................................................................58 Table 4-1 Unique catchment characteristics in each group ........................................................................94 Table 4-2 Monthly total gross irrigation water requirement in mm for Megech (Source: This study and

[24]) ..................................................................................................................................................98 Table 4-3 Minimum environmental flow downstream of Lake Tana reservoir (Source: [145] and [146])99 Table 4-4 Characteristics of Tis-Abay I, II and Tana-Beles hydropower plants ......................................101 Table 4-5 Lower boundary (top of inactive zone) and upper boundary (bottom of flood level) for each

reservoirs.........................................................................................................................................103 Table 5-1: Model performance for sub-catchments in group 1 ................................................................108 Table 5-2: Model performance for sub-catchments in group 2 ................................................................108 Table 5-3: Model performance for sub-catchments in group 3 ................................................................109 Table 5-4: Model performance for sub-catchments in group 4 ................................................................110

List of tables

XIII

Table 5-5: Model performance for sub-catchments in group 5 ................................................................110 Table 5-6 Mean monthly (1986-2005) inflow to each artificial reservoirs in Lake Tana sub-basin ........112 Table 5-7 Mean monthly (1986-2005) inflow to Lake Tana at selected junctions in Lake Tana sub-basin

........................................................................................................................................................113 Table 5-8 Optimized power production for Tis-Abay hydropower station ..............................................114 Table 5-9: Optimized hydropower production for Tana-Beles hydropower station.................................115 Table 5-10 Tana-Beles hydropower production at different navigation levels.........................................116 Table 5-11 Monthly irrigation water demand and irrigation deficit in 106 m3 for both lower rule curves121 Table 5-12 Tana-Beles hydropower production at different CMA-ES population size ...........................122 Table 5-13 Deficits in total water supply and hydropower production at different priority level ............123 Table 5-14 Comparision of deficits in total water supply and hydropower production for two partial

WRD scenarios ...............................................................................................................................124 Table 5-15 Comparison of SO-CMA-ES and MO-CMA-ES for multi-objective problems ....................127 Table 5-16 Comparison of different water resources development of Lake Tana sub-basin ...................128 Table 5-17 Percentage demand met of mean annual total water supply and hydropower production at

different navigation levels of Lake Tana using MO-CMA-ES .......................................................130 Table 5-18 Percentage demand met at selected points of pareto-front for navigation level of 1784.8 m

a.s.l. .................................................................................................................................................133 Table 5-19 Monthly deficit in total water supply and hydropower production for all reservoirs at

navigation level of 1784.8 m a.s.l. ..................................................................................................134 Table 5-20 Monthly upper target reservoir level for all reservoirs for navigation level of 1784.8 m a.s.l.

........................................................................................................................................................134 Table A- 1 Catchment characteristics used in SOM................................................................................149 Table A- 2 Estimated monthly inflow to Lake Tana at junction Gilgel Abay (106 m3)............................155 Table A- 3 Estimated monthly inflow to Lake Tana at junction Ribb (106 m3) .......................................155 Table A- 4 Estimated monthly inflow to Lake Tana at junction Megech (106 m3) .................................156 Table A- 5 Estimated monthly inflow to Lake Tana at junction Gumera (106 m3) ..................................156 Table A- 6 Estimated monthly inflow to Lake Tana at junction Gelda (106 m3)......................................157 Table A- 7 Estimated monthly inflow to Lake Tana at junction Gemero (106 m3) ..................................157 Table A- 8 Estimated monthly inflow to Lake Tana at junction Garno (106 m3) .....................................158 Table A- 9 Estimated monthly inflow to Koga reservoir (106 m3) ...........................................................158 Table A- 10 Estimated monthly inflow to Gumera reservoir (106 m3) .....................................................159

List of tables

XIV

Table A- 11 Estimated monthly inflow to Ribb reservoir (106 m3) ..........................................................159 Table A- 12 Estimated monthly inflow to Megech reservoir (106 m3) .....................................................160 Table A- 13 Meteorological data used for evapotranspiration computation.............................................164 Table B- 1 Elevation-Area-Volume relations of Koga reservoir..............................................................167 Table B- 2 Elevation-Area-Volume relations of Gumera reservoir..........................................................167 Table B- 3 Elevation-Area-Volume relations of Megech reservoir..........................................................167 Table B- 4 Elevation-Area-Volume relations of Ribb reservoir...............................................................168 Table B- 5 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement

for Koga reservoir ...........................................................................................................................169 Table B- 6 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement

for Megech reservoir.......................................................................................................................170 Table B- 7 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement

for Gumara reservoir.......................................................................................................................171 Table B- 8 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement

for Ribb reservoir............................................................................................................................172

List of abbreviations

XV

List of abbreviations

ANN Artificial Neural Network a.s.l. Above Sea Level BMU Best Matching Unit CMA Covariance Matrix Adaptation CMA-ES Covariance Matrix Adaptation Evolutionary Strategy CP1 Cropping Pattern 1 CP6 Cropping Pattern 6 CRBDSS Colorado River Basin Decision Support System CROPWAT A computer program to calculate crop water requirements CSA Central Statistics Authority CTIWM Cooling Technology Institute Water Management DBS Database System DEM Digital Elevation Model DP Dynamic Programming DSS Decision Support System DST Decision Support Tool EAs Evolutionary Algorithms ELECTRE ELimination Et Choix Traduisant la REalité

(Elimination and Choice Expressing Reality) EP Evolutionary Programming EEPCO Ethiopian Electric Power Corporation EPLAUA Environment Protection, Land Administration and Use Authority ES Evolutionary Strategy ETP Potential evapotranspiration ETR Real evapotranspiration FAO Food and Agriculture Organization of the United Nations GA Genetic Algorithm GDP Gross Domestic Product GIWR Gross Irrigation Water Requirement HBV Hydrologiska Byråns Vattenbalansavdelning HDP Hydropower production HEC-5 Hydrologic Engineering Center series 5 IAHS International Association of Hydrological Sciences IRAS Interactive River-Aquifer Simulation Kc Crop coefficient KNN Kohonen Neural Network LAI Leaf area index LP Linear Programming MBS Modal Base Subsystem MIT Massachusetts Institute of Technology MOEA Multi-objective Evolutionary Algorithms MO-CMA-ES Multi-Objective Covariance Matrix Adaptation Evolutionary

Strategy MOO Multi-Objective Optimization MOO-EALib Multi-Objective Optimization Evolutionary Algorithm Library MOP Multi-Objective Problem MoWE Ministry of Water and Energy

http://www.google.de/url?sa=t&rct=j&q=iahs&source=web&cd=4&ved=0CEMQFjAD&url=http%3A%2F%2Fwww.iugg.org%2Fassociations%2Fiahs.php&ei=fGFnT5LCFMKm0QWNk5G0CA&usg=AFQjCNFqHfK_9x_uxRI_Hb2ZPmnydXMrsg�

List of nomenclatures and symbols

XVI

N-S Nash-Sutcliffe NSGA-II Non-dominated Sorting Genetic Algorithm version II OMP Optimized Model Parameter OWP Optimized WaSiM-ETH parameter PEST Parameter Estimation Technique PMF Probable Maximum Flood RA Reservoir area RD Reservoir diversion RE Reservoir elevation REW Representative Elementary Watershed RL Reservoir level (rule curve) RQ Reservoir outlet capacity RS Reservoir storage SA Simulated Annealing SAC-SMA Sacramento Soil Moisture Accounting SCE-UA Shuffled Complex Evolution-University of Arizona SHE Systéme Hydrologique Européen SMAR Soil moisture Accounting and Routing SO-CMA-ES Single objective Covariance Matrix Adaptation Evolutionary

Strategy SOM Self-organizing Map SWAT Soil and Water Assessment Tool SWM Stanford Watershed Model TANALYS Topographical ANALYSis TERRA Tennessee Valley Authority Environment and River Resource

Aid TWS Total water supply (irrigation, domestic water supply,

environmental flow) UIS User Interface Subsystem UNESCO-ISRIC United Nations Educational, Scientific and Cultural Organization

International Soil Reference and Information Centre USACE U.S. Army Corps of Engineers USBR United States Bureau of Reclamation WaSiM Water Balance Simulation Model WWDSE Water Work Design and Supervision Enterprise List of nomenclatures and symbols

C positive definite matrix cmelt fraction of snow melt to surface runoff [0… 1]

sC topographic index [-] dci distance between map units c (BMU) and i on the map grid. EI interception evaporation [mm] es saturation vapour pressure at temperature T [hPa] ƒ function fi empirical factor, monthly value [] Fs amount of infiltrated water up to saturation g acceleration due to gravity [m/s2]


XVII

g generation number h gross head [m]

( )cih k neighbourhood function which is valid for the actual BMU hd day length [h] hSI maximum height of water at the leaf surfaces [mm] i time step i [month]

)j(I inflow for reservoir j ]/sm[ 3 j reservoir j ][− k denotes the iteration step of a training procedure, kD single linear recession constant for surface runoff [h] kf saturated hydraulic conductivity [mm/h] kH single linear recession constant for interflow [h] Kkorr correction factor for vertical percolation [-] Ks saturated hydraulic conductivity [mm/h] ls saturation depth [mm] m total number of reservoirs ][− m recession model parameter [mm] m matrix mean n total number of months ][− N normal distribution na porosity [-] Ni the neighbourhood relationship P power [W] Pgren precipitation intensity threshold for generating preferential flow into

the saturated zone [mm/h] PI precipitation intensity [mm/h]

)j(Pi power production for month i and reservoir j [MWh] q discharge [m3/s]

(j)minq minimum downstream release for reservoir j [ 3m /s ] (j)maxq maximum downstream release for reservoir j [ 3m /s ]

QB base flow [mm/time step] QD,I surface runoff [mm/time step] QD,i transformed surface runoff in time step i [mm/time step]

DQ∧

surface runoff in the time step i within the lowest flow time zone [mm/time step]

(j)iQ downstream release of reservoir j [ 3m /s ]

Qobs,i observed discharge at time step i

obsQ mean observed discharge Qruck capillary rise as a mean value for the (sub-) catchment in the actual time

step [mm/time step] QSH,in interflow into the interflow storage [mm/time step] Qsim,i simulated discharge at time step I [mm/time step] QSUZ groundwater recharge from the unsaturated zone as a mean value for the

(sub-) catchment [mm/time step] qv vertical flow rate [mm/time step]


XVIII

R2 coefficient of determination rk scaling of the capillary rise/refilling of soil storage from interflow [0..1] S saturation deficit SB actual content of the soil water storage [mm] SBmax maximum capacity of the soil water storage [mm] SImax maximum interception storage capacity [mm] SHmax maximum storage capacity of the interflow storage [mm] SI content of the interception storage [mm] Si local saturation deficit [mm]

),( jirriS demand for irrigation for month i and reservoir j [ 3Mm ]

),( jpubiS demand for for public water supply for month i and reservoir j [ 3Mm ]

),(ˆ jpubiS release for public water supply for month i and reservoir j [ 3Mm ]

),(ˆ jirriS release for irrigation for month i and reservoir j [ 3Mm ]

Sm mean saturation deficit for a (sub-) basin [mm] SUZ content of the storage of the unsaturated zone [mm] T temperature [oC] Th local hydraulic transmissivity [m2/s] To saturated local hydraulic transmissivity [m2/s] ts saturation time from the beginning of the time step [h] Tkorr correction factor for the transmissivity of the soil [-]

)( jmaxz top of flood control zone for reservoir j [m]

)( jminz buttom of buffer zone for reservoir j [m]

),( jbufferiZ target level of the buffer zone for month i and reservoir j [m]

),( jconsiZ target level of the conservation zone for month i and reservoir j [m]

ρ density [Kg/m3] ta specific catchment area per unit length of a grid cell [m2/m]

( )s kα the learning rate at step k ( )kσ neighbourhood radius at k βt slope angle [m/m] λ offspring γ mean topographic index of the (sub-) catchment μ population

fψ suction at the wetting front ( ≈ 1000 na) [mm] ∆t time step [h] υ degree of vegetation covering [m2/ m2]

s ,Θ Θ saturated and actual water content [-]

iw weights

1ω weight for shortage term in the objective function ][−

2ω weight for energy production term in the objective function ][−

Introduction

1

1 Introduction The provision of adequate water supply is of fundamental importance to social and economic security worldwide. The rapid population growth in large parts of the world and the general increasing demand for water of sufficient quantity and quality makes the development and reservoir operation of sustainable water resources systems and related management strategies continuously more important. The development of water resources systems, however, has major impacts on socio-economy and the environment. In some cases, such impacts only become visible after several years or decades of reservoir operation. Thus, it is important to avoid negative long term impacts already during the planning stages or to adjust systems and their operation rules after these impacts have become visible.

Ethiopia’s vast water resources have not yet been effectively developed. Though, Ethiopia gets plenty of annual rainfall, most of the time it either falls ahead of time or beings late or even stops short in mid-season. That means the right amount of rainfall is not available at the right time. In order to alleviate the problems on agricultural outputs and other water users, sustainable and reliable development and proper use of the water resources becomes an imperative. The government’s Millennium Development Goals strategy calls for a rapid up scaling of existing irrigation development plans. The need for investments in multi-purpose water infrastructure in combination with the market infrastructure investments needed to fully leverage their growth potential is clearly demonstrated in [1].

The Lake Tana sub-basin contains the largest natural fresh water lake in Ethiopia called Lake Tana. Given the sub-basin’s significant water resources, rich cultural and natural assets, relatively developed urban centres, good road and air connectivity and dense settlements, has a potential for growth in multiple sectors with strong multiplier effects, particularly commercially oriented smallholder agriculture, agro-industry and export, tourism, fisheries and energy. Consequently, it can serve as a stimulus to national economic growth [2]. Amongst others, the main sectors associated with water resources development in the sub-basin includes fishing, irrigation, hydropower production, navigation and tourism. Despite the enormous untapped water resources, the water level of the lake fell to a historic low level ( 1784.39 m a.s.l.) in 2003. As a result, the navigation activities on the lake had to cease for a couple of months. On top of this, the water resources of the Lake Tana area are highly vulnerable to climate change, especially concerning the distribution of runoff throughout the year. With climate change, the seasonal distribution of runoff might become much more pronounced and as a result, small streams may dry up completely for part of the year [3].

Background of the study

2

1.1 Background of the study

1.1.1 Decision Support System

The use of mathematical models in water resources research and management has been constantly increasing since the 1960’s [4]. The reason for this is that models are the easier means of gaining insight into the planning, operation and policy formulation of systems that have some degree of complexity. Besides, the use and development of a model is of great help for increasing knowledge of the system and organizing the data [5]. Model is a representation of a system within a defined mathematical framework. A good model captures the key characteristics of the system under study so that the system can be better understood and hence better decisions can be made about it. Because the model is merely an abstract representation of the actual system, it is always an approximate to and simplification of reality. However, the mathematical analysis of a good model can be very effective at investigating the properties of the system and forecasting or simulating system behaviour.

The concept of Decision Support System (DSS) has been made very attractive in the sense that it facilities the use of a set of models and data in an interactive way. Analysis to support planning for water resources development and management has a simple aim: to provide (preferably quantitative) information to decision makers to enable a better selection from alternative measures (strategies) [6].

There have been a number of basin-wide water resources management tools that include a module for reservoir simulation. However, most of those are generalized packages for simulation purposes with limited capabilities to develop optimal operation policies and water allocation schemes for site-specific systems [7]. Apart from the above general packages, a number of investigators have developed decision support systems/ tools for site-specific reservoir operation planning. Most of these packages employ search and optimization algorithms that have been developed for single-objective optimization problems whereas many optimization problems naturally involve multiple objectives. Almost all previous general DSS packages or decision support tool (DST) have been developed for gauged rivers. Hence, a more flexible and general methodology, which combines a watershed model with reservoir simulation and optimization models for planned and existing multi-purpose multi-reservoir systems in ungauged rivers with decision-making procedures, is vital.

Introduction

3

1.1.2 Reservoir operation

As demands on reservoir systems increase and diversify, reservoir system operations become a more pressing and controversial issue. A methodology is required to resolve the conflicting demands that invariably arise when resources are limited. Reservoir is one of the major surface water storages. Optimally, the operation of single and multi-reservoir network systems form an integral part of water resources management. Reservoir operation rules are intended to guide and manage the reservoir system so that the release made is in the best interests of the system objectives, consistent with certain inflow and existing storage levels. Once, a reservoir system has been developed as a physical system, future structural changes are often technically or financially infeasible.

Reservoir operation, one of the challenging problems for water resources planners and managers, is a complex problem that involves many decision variables, multiple objectives as well as considerable risk and uncertainty. In addition, the conflicting objectives lead to significant challenges for operators when making operational decisions. The optimal use of the available limited resources requires a scientific approach to plan and operate new and existing reservoir systems. Literature review of reservoir operations reveals that no general optimization strategy exists. It is impossible to develop a single objective satisfying all interests, all adversaries and all political and social viewpoints [8].

Generally, most reservoir systems are still managed based on fixed, predefined rules that are typically derived in the design stages through simulation techniques. However, these techniques can be very time-consuming and do not always lead to best results. These predefined rules are usually presented in the form of graphs or tables [9] that guide the release of a reservoir system based on current storage level, hydro-meteorological conditions, and time of a year. Nevertheless, reservoir operators still have to manually adapt the rules to the actual circumstances.

Despite the fact that reservoir simulation models are effective tools for studying the operation of complex physical and hydrological characteristics of a reservoir, they are limited to predict the performance of a reservoir for a given operation policy. Optimisation models have an advantage of being able to search for the optimum policy from an infinite number of feasible operation policies that are defined through decision variables. In recent years, incorporation of an optimisation technique into a simulation model to execute a certain degree of optimisation has been advocated [10].

Traditional optimization approaches, including linear programming and dynamic programming, for solving large-scale mathematical programs applied to complex reservoir operations involve decomposition, partitioning, aggregation and various successive approximation techniques. When dynamic programming is applied to a multi-reservoir system, it involves a major problem of the curse of dimensionality, with the increase in the number of state variables. Techniques like linear programming and non-linear programming have essential approximation problems in dealing with discontinuous, non-differentiable, non-convex multi-objective functions [10].

Background of the study

4

In addition to the above limitations, most traditional algorithms are meant for single-objective problems whereas many real-world search and optimization problems are bound by multiple objectives. Thus, new and more robust optimization techniques, capable of handling complex and multi-objective problems, are needed. In the field of water resources engineering, particularly reservoir operations, evolutionary algorithms have been proved computationally superior to traditional methods.

1.1.3 Estimation of flow for ungauged river basins

In order to create an initial model for reservoir operation or design, records of stream flow data are needed as an input. Therefore, this inflow time series data should be available in both appropriate quantity and quality. Such inflow time series data is missing in ungauged river basins. An ungauged basin is one with insufficient records (in terms of both data quantity and quality) of hydrological observations to enable computations of hydrological variables of interest (both water quality and quantity) at the appropriate spatial and temporal scales and to the accuracy acceptable for practical applications [11].

In seeking to address the challenges of water resources and water-environmental degradation issues across a basin, a major difficulty is encountered with those basins for which little or no hydrometric data is available. These basins are predominantly in developing country regions where basin developments are undertaken with limited data. This frequently led to the depletion of water resources, ecosystem degradation and poor quality of life [11].

Specific to most rivers in Africa, either they are ungauged or they have limited hydro-meteorological data due to poorly developed hydrometric networks and lack of human and financial resources to develop and maintain such networks. While the needs for hydrological information for Africa are increasing, technical and human capacities are declining as noted from the reduction in the number of meteorological stations in Africa during the last 30 years [12] and [14].

As watershed models become increasingly sophisticated and useful, there is a need to extend their applicability to locations where they cannot be calibrated or validated (ungauged catchments). Transfer of hydrologic characteristics of watersheds from data rich or ‘donor’ catchments to data poor environments is one of the most fundamental challenges in the field of hydrology. [14] argues that the new International Association of Hydrological Sciences (IAHS) decadal initiative on “Predictions in Ungauged Basins’ [15] represents a grand challenge for the field of hydrology that forces us to deal with questions that are ‘deep, grand and practical’. [14] further argues that ‘prediction in ungauged basins, sans calibration, remains a difficult, unsolved problem, demanding urgent resolution and requiring significant new breakthroughs in data collection, process knowledge and understanding’.



Introduction

5

There are plenty of hydrologic models from a simple black box model to more complex physically based models. However, none in practice can be applied to ungauged catchments because all black box models, conceptual models and even physically based models to date need stream flow data for calibration. In the past decade, there has been a significant increase in research relating to the regional calibration of watershed models to enable their use at ungauged sites. Regionalization techniques enable the extrapolation of properties of flow across homogeneous regimes and the estimation of flow statistics at ungauged sites [16]. This technique is the most widely used method to date, which relates the parameters of watershed models with catchment characteristics. Even when one attempts to regionalize a very reasonable and parsimonious watershed model, results are still mixed [17]. [19] further demonstrated that a very large number of watersheds are necessary to obtain a meaningful relationship between watershed model parameters and watershed characteristics.

Selection of watershed models for regionalization is also a difficult task due to the existence of hundreds of watershed models and different models towards regionalization give mixed results. Moreover, past studies on this technique showed good results in calibration but poor results on validation of the model to ungauged catchments or to catchments where their flow data never involved during calibration. Despite the difficulty encountered due to limited or no hydrological data, planning and design of water resources projects has inevitably to be undertaken for ungauged basins.

Objective of the research

6

1.2 Objective of the research Based on the problems stated above, a decision support tool for multi-purpose multi-reservoir systems in hydro-meteorological data scarce area was proposed by combining watershed model, reservoir simulation model, optimization model and artificial intelligence. Each model is developed as stand-alone model and applied as independent decision support tool. It involves the integration of a rainfall runoff model, to generate runoff in ungauged catchments that are flowing into reservoirs, and reservoir simulation-optimization models to come up with the best optimal operating policies (ruling curves) for decision makers. The stand-alone decision support tool was demonstrated on existing and proposed multi-purpose multi-reservoir systems around Lake Tana sub-basin, Ethiopia. It is a useful tool to foresee the potential impacts of water resources development of Lake Tana before the realization of the schemes. Consequently, decision makers have a chance at least to make wise decisions, which minimize both conflicts among water users and adverse environmental effects. The proposed general framework is applicable not only in the case study area but also to other basins. Although the proposed decision support tool was tested in multi-purpose multi-reservoir system in the Lake Tana sub-basin, the regional model was developed to estimate flow from ungauged catchments in the whole Blue Nile (Abay) river basin taking into account of future and current water resources development plan in the basin.

General objective of the research includes:

• To propose a new approach on the method of regionalization instead of following the traditional two-step procedure to estimate stream flow for ungauged rivers. The approach will be verified by validating the regional model in gauged catchments within the case study area that their flow data has never been involved in deriving the regional watershed model parameters.

• To develop reservoir simulation-optimization models that are capable of

generating optimal reservoir operating policy (ies) for multi-objective multi-reservoir systems. And then the application of the proposed optimized strategies derived from evolutionary algorithm in the case study. The trade-off between conflicting objectives such as irrigation, drinking water supply, navigation and hydropower generation will particularly be emphasized in determining the control strategies of the reservoirs.

Specific objective to Lake Tana sub-basin includes:

• To assess available surface water resources in Lake Tana sub-basin including flows from the ungauged catchments.

• To evaluate the impact of existing and proposed reservoirs on Lake Tana. • To produce joint multi-objective multi-reservoir systems operation rules for

existing and proposed reservoirs in Lake Tana sub-basin under different scenarios.

Introduction

7

1.3 Content and structure of the thesis This dissertation is organized into six chapters. Chapter 2 provides general catchment characteristic of the study area where the proposed methodology in chapter three is going to be tested. The chapter begins with general description of Ethiopia and its major drainage basins. The second section of this chapter presents different catchment characteristics like climate, topography, land use and soil of the Blue Nile river basin (locally called Abay river basin), which by most criteria is the most important river basin in Ethiopia. Section three focuses on Lake Tana sub-basin, which is one of the large-scale sub-basins of the Abay river basin. In this section different water resources development in Lake Tana sub-basin and its current socio-economic situation will be discussed. Physical characteristics of planned and existing artificial reservoirs and the Lake Tana itself are described in the same section.

Chapter 3: The purpose of this chapter, which is the heart of the dissertation, and its accompanying appendix, is to provide in more detail procedures/ methodologies to be followed in the development of decision support tool for existing and planned multi-objective multi-reservoir in ungauged catchments. This chapter presents a general conceptual framework of the proposed methodology of the research, which combines watershed model, artificial intelligence, reservoir simulation model and optimization model. The second sub-section of the second section will brief general theoretical background of a regional model followed by step-by-step development of a regional model for the case study area. Reservoir simulation-optimization component of the proposed decision support tool is presented in the third section of this chapter. This section describes the proposed combined reservoir simulation and optimization models. A proposed technique on multi-objective multi-reservoir operation problems to derive optimum rule curves (monthly target reservoir storage/ level) in the case study area are outlined on sub-section 3.3.4 and 3.3.5. The same section presents details of the selected reservoir simulation model (HEC-5), optimization model (single and multi-objective Covariance Matrix Adaptation Evolutionary Strategy) and the combination of these two models.

Chapter 4: Chapter 4 explains how models are setting up in order to apply the selected models in chapter 3 to the case study area in chapter 2. The first sub-section of the first section outlines model set-up to estimate flow in ungauged catchment, which is one of the input data to reservoir and in between flows for reservoir systems in Lake Tana sub-basin. Detail procedures on how to use a self-organizing map (SOM) to identify hydrological homogeneous groups of catchments and how the combined watershed model (WaSiM-ETH) and SOM are used to estimate flow in the case study area are presented in the second sub-section of section 4.1. Section 4.2 explains model set-up of single and multi-reservoir systems in the sub-basin and the application of the combined simulation-optimization models under existing and different future water resources development scenarios.

Content and structure of the thesis

8

Chapter 5: This chapter provides main results from the combined watershed and SOM model to estimate flow and the combined reservoir simulation-optimization model to generate optimal rule curves of multi-purpose multi-reservoir systems in the case study area. Comparison of results from single objective Covariance Matrix Adaptation Evolutionary Strategy (sectoral approach) and multi-objective Covariance Matrix Adaptation Evolutionary Strategy (integrated approach) for multi-objective multi-reservoir systems are presented in the same section. Most tabular and graphical results are attached to appendix.

Chapter 6 presents main conclusions drawn from the proposed methodologies, the application of the proposed methodology to the case study area and some recommendations.

Description of the case study area

9

2 Description of the case study area 2.1 Ethiopia Ethiopia is located between approximately 3° to 15° N latitude and 33° to 48°E longitude. The country covers a land area of about 1.12 million km2, occupying a significant portion of the Horn of Africa. It shares boundaries to the east and southeast with Djibouti and Somalia, to the north with Eritrea, to the south with Kenya, to the west with Sudan and to the southwest with South-Sudan. The altitude ranges from the highest peak at Ras Dashen (4620 m a.s.l.), in Gonder, down to the Danakil depression (120 meters below sea level), one of the lowest dry land points on the earth, in the Northeast part of the country.

The climate of Ethiopia is mainly controlled by the seasonal migration of the Intertropical Convergence Zone and associated atmospheric circulations as well as by the complex topography of the country. It has a diversified climate ranging from semi-arid desert type in the lowlands to humid and warm (temperate) type in the southwest. Mean annual rainfall distribution has maxima (>2000 mm) over the South-western highlands and minima (<300 mm) over the South-eastern and North-eastern lowlands. Figure 2-1 shows contours of mean annual rainfall distribution using inverse distance method. In terms of rainfall occurrence one can generally identify three seasons in Ethiopia namely; Bega: - dry season (October- January), Belg: - short rainy season (February- May) and Kiremt: - long rainy season (June- September). Mean annual temperature ranges from < 15oC over the highlands to > 25oC in the lowlands.

Although Ethiopia is endowed with large amount of water resource potential, between 80-90 % of its water resources is found in the four river basins namely, Abay (Blue Nile), Tekeze, Baro-Akobo and Omo-Gibe (see Figure 2-1) in the west and south-western part of Ethiopia where the population is no more than 30 to 40 %. On the other hand, more than 60 % of the populations are residing in the east and central river basin system where the availability of the water resources is only 10-20 % [19]. Much of the river systems are transboundary in nature.

Ethiopia

10

Figure 2-1: Mean annual distribution of rainfall1 and approximate boundary of 12 major basins of Ethiopia

As is shown in Figure 2-1, the country is hydrologically divided into 12 basins; eight of these are river basins, one lake basin and three dry basins. Four of the river basins namely Abay, Baro-Akobo, Mereb and Tekeze are part of the Nile river system, flowing generally in the western direction towards Sudan and then to Egypt which eventually entering in the Mediterranean Sea. Five basins namely, Omo-Gibe, Awash, Rift-valley lakes, Denakil and Aysha, can be categorized as the Rift-valley system as all of them drain their water in the great East African Rift-valley. The remaining three, Genale-Dawa, Wabishebelle and Ogaden are part of the eastern Ethiopian basin that generally flows in the south-easterly direction toward the Somalia and then to the Indian Ocean. Table 2-1 presents selected hydro-meteorological characteristics of major drainage basins of Ethiopia.

1 Data source: NMSA and Climwat (FAO)

Ogaden Wabi-shebele

Denake

Abay Awash

Genale Dawa

Baro-Akobo

Tekeze

Omo-Gibe

Aysha

Mereb

Rift-valley


11

Table 2-1: Selected hydro-meteorological characteristics of the 12 major drainage basins of Ethiopia2

Rainfall (mm) Water resources (109 m3) Basin

Area (km2)

max

imum

m

inim

um

a

vera

ge

No.

of o

pera

tiona

l ga

ugin

g st

atio

ns

surf

ace

grou

nd

stor

ed

Irrig

atio

n po

tent

ial

(103 h

a)

Hyd

ropo

wer

firm

en

ergy

(GW

h)

Awash (R) 11000 1600 160 557 72 4.9 0.8 2.2 206 5589 Abay (R) 199000 2220 800 1420 131 54.4 Na 30 1800 55000 Wabi-shebelle(R) 202220 1563 223 425 30 3.4 2.3 1.1 2093 7457 Genal-Dawa (R) 172259 1200 200 528 36 6 Na - 1070 9270 Rift-valley(L) 52000 1800 300 Na 54 5.64 Na 56.6 131 12240 Omo-Ghibe(R) 79000 1900 400 1140 46 16.6 1.0 Na 90.4 26026 Baro Akobo(R) 75912 3000 600 1419 32 23.23 1.0 Na 631 19826 Tekeze (R) 82350 1200 600 39 8.2 Na - 186.9 8384 Denkile (D) 64380 1500 100 Na 11 0.86 Na Na - - Ogaden (D) 77120 800 200 400 - 0 Na - - - Aysha (D) 2223 500 120 Na - 0 Na - 0 - Mereb (R) 5900 2000 680 Na 3 0.72 0.11 - 5 - R- River D- Dry L- Lake Na- data not available 2.2 The Blue Nile River Basin The area of the Blue Nile locally called the Abay river basin is about 200,000 km2 and the total perimeter is 2440 km. The basin is located in the centre and west of Ethiopia. It lies approximately between latitude 7°45’N and 12°46’ N and longitude 34°06’E and 40°00’E, being generally rectangular in shape, and extending about 400 km from north to south, and about 550 km from east to west.

Although there are several feeder streams that flow into Lake Tana, the source of the river is generally considered a small spring at Gish Abbai at an altitude of approximately 2744 m a.s.l. This stream, known as the Gilgel Abay, flows north into Lake Tana. The Abay river rises in the centre of the catchments and develops its course in a clockwise spiral in a deep gorge, collecting tributaries along its 922 km length from Lake Tana to the Sudan border, by which point it is only know as the Blue Nile. After flowing past Er-Roseires reservoir inside Sudan, and receiving the Dinder on its right bank at Dinder, the Blue Nile joins the White Nile at Khartoum and, as the Nile, flows through Egypt to the Mediterranean Sea at Alexandria. In this dissertation, both names (Abay and Blue Nile) are used interchangeably.

The elevation of the basin ranges from 490 m a.s.l. at the Sudan border to 4230 m a.s.l. at the summit of mountain Guna. Within Ethiopia, there is a traditional distinction made between highland and lowland, with the division being at about 1500 m altitude. Within the basin, about 62 % of the land falls above an altitude of 1500 m and which can be considered as highland, while the remaining 38 % is lowland [20]. Figure 2-2 depicts 14 sub-regions of the Abay river basin and the Dinder and the Rahada sub-basins. The

2 Collected from different tables in http://www.mowr.gov.et as visited in Sept, 2010

http://en.wikipedia.org/wiki/Gish_Abay�

http://en.wikipedia.org/wiki/Er_Roseires�

http://en.wikipedia.org/wiki/Dinder_River�

http://en.wikipedia.org/wiki/Dinder,_Sudan�

http://en.wikipedia.org/wiki/White_Nile�

http://en.wikipedia.org/wiki/Khartoum�

http://en.wikipedia.org/wiki/Nile_River�

http://en.wikipedia.org/wiki/Egypt�

http://en.wikipedia.org/wiki/Mediterranean_Sea�

http://en.wikipedia.org/wiki/Alexandria�

The Blue Nile River Basin

12

Dinder and Rahad sub-basins, which are directly crossing the Ethio-Sudan border, are excluded from the main Abay river basin system considered in this study.

Figure 2-2: Location of the Blue Nile river basin and its 14 major sub-regions

The Blue Nile river basin is perhaps, the most important basin in Ethiopia. It accounts for about 17.1% of Ethiopian land area (see Table 2-1 above), 25% of its population and 50% of its annual average surface water resources [21]. The Blue Nile river runs from its origin, Lake Tana, to the Sudanese border and eventually meets the White Nile river at Khartoum, Sudan (see Figure 2-2 above).

The climate of the basin varies from humid to semiarid. Most precipitation occurs in the wet season locally called Kiremt (June through September), and the remaining precipitation occurs in the dry season locally called Bega (October through January or February) and in the mild season locally called Belg (February or March through May). The annual precipitation has an increasing trend from northeast to southwest. The estimated annual precipitation ranges from 1200 mm to 1600 mm depending on the estimation method and the period used in the previous studies of the basin. The mean annual temperature from 1961 to 1990 was estimated at about 18.3 °C with a seasonal variation of less than 2°C and the annual potential evapotranspiration was estimated at about 1100 mm [22].


13

2.2.1 Hydro-Meteorological stations

Figure 2-3 shows the location of meteorological stations and gauging stations of tributaries of the Blue Nile river basin collected from National Meteorological Service Agency (NMSA) and Ethiopian Ministry of Water and Energy (MoWE) respectively. There are more than 100 gauging stations in the Blue Nile river basin that have daily runoff records. However, 7 years (1993-1999) daily runoff records from 40 gauging stations (see Figure 2-3) were collected from the MoWR for this study. Additional daily runoff data for some gauging stations in Anger and Dedessa sub-basins (1986-1999), gauging stations in South-Gojam sub-region (1986-2005) and Lake Tana sub-basin (1986-2005) were collected from the same Ministry.

Figure 2-3: Location of the hydro-meteorological stations in the study area

Almost all operational gauging stations of the tributaries are located along the main road from Addis Ababa, the capital city of Ethiopia, to different routes of cities of Bahir Dar, Gonder, Jimma, Assosa etc and are located upstream of the main rivers, which capture small portion of the sub-basin flow. From its accessibility point of view, their locations are very suitable. From the hydrological point of view, however, some of the gauging stations are located on unstable section of the river. For some gauging stations, the carrying capacities of the channel are limited to hold above average flows. Such phenomena like deposition of debris and siltation on the vertical staff gauge and inadequacy of tandem vertical staff gauge to measure low flow were observed during field visit of some gauging stations in the Lake Tana sub-basin. The qualities of

Lake Tana sub-basin

Jemma, Guder, Muger sub-basins

Anger, Dedessa sub-basins

Dabus sub-basin

South Gojam sub-basin


14

measured hydrometric data from such gauging stations are questionable. Detail assessment and recommendations of the gauging stations in the Blue Nile river basin can be found in [20]. After visiting most gauging stations in the Abay river basin, [20] concluded that the measured flow from some gauging stations can only give rough values and cannot be used for precise discharge series. For example the present gauging station on Ribb River, after 35 years of continuous operation, is only able to give rough values of discharge [20], as will be presented latter, this is proved in this research as well. Like Ribb near Addis Zemen, Megech gauging station at Azezo is not adequate for the establishment of any precise discharge series and will only yield very rough values [20].

2.2.2 Land use and soil

Figure 2-4 shows soil map of the Blue Nile river basin, which was collected from Ethiopian MoWR. The classifications of the soils were based on the revised FAO-UNESCO-ISRIC legend to Soil Map of the World 1988. This classification system, which is widely used in Ethiopia, was chosen mainly because of its universality and simplicity. The FAO-UNESCO-ISRIC legend contains 28 major soil groupings at the highest level and 153 soil units, which are subdivisions of the soil groupings, at the second level [23].

Table 2-2 presents percentage of sub-divisions of the major soil types, which its percentage cover is greater than 2 %, of the Blue Nile river basin. The percentages of second level sub-divisions in each sub-basin of the river basin were computed from the soil map (Figure 2-4) using Arc-GIS. Accordingly, about 21 % of the basin is constituted by Haplic Alisols and 17 % by Eutric Leptosols. Percentages and characteristics of the second level subdivision of major soil type of the Abay river basin were used for the selected watershed model in chapter 3 and chapter 4. With respect to major soil type division, about 21% of the basin is constituted by Alisols and 20 % by Leptosols.


15

Figure 2-4: Soil map of the Abay river basin3

Table 2-2: Percentages of major soil types of the Abay river and its sub-basins

Percentage of major and second level soil groups of the Abay basin Soil Basin A1 A2 B1 B2 C1 D1 E1 E2 F1 G1 H1

2.7 17.3 4.14 4.91 4.46 5.72 6.62 8.92 8.56 8.62 20.71 Abay 20.00 9.05 4.46 5.72 15.54 8.56 8.62 20.71Sub-basin Percentage of second level soil groups for each sub-region of the Abay basin

Tana --- 4.8 20.6 15.9 --- 9.8 --- 12.4 11.8 1.3 --- Beles --- 7.1 5.4 3.9 7.5 9.79 3.19 44.6 15.8 0.62 1.98 Beshil 0.4 80.3 4.2 0.0 --- --- --- --- 5.94 6.01 --- N.Gojam 4.4 40.9 8.6 3.8 --- 0.8 --- 0.65 1.32 27.4 9.69 Dabus --- 2.3 --- --- 4.5 3.3 32 16.7 0.52 6.34 28.75S.Gojam 3.3 12.7 2.3 0.4 1.6 2.72 1.82 4.95 17.3 6.54 44.34

3 Source: Ethiopian Ministry of Water and Energy (MoWE)


16

Jimma 5.4 35.1 0.1 0.6 --- 2.46 0.98 0.47 7.1 28.9 --- Welaka 8.7 52.0 --- --- --- 11.3 --- --- 8.15 3.73 --- Wonbera --- 1.1 --- 0.0 7.2 --- 17.9 25.9 26.6 0.11 20.34Fincha 0.0 0.2 1.0 2.6 --- --- 8.41 --- 21 0.92 42.13Anger --- 2.3 --- --- 26.5 --- 16.5 3.67 --- 0.10 38.27Muger 30 18.3 6.4 8.4 --- 3.34 1.38 2.59 3.64 11.5 7.99 Table 2-3: ID and soil group names of major soil types of the Abay river and its sub-basins

ID Soil group ID Soil group ID Soil group A1 Rendzic Leptosols C1 Haplic Acrisols F1 Eutric Cambisols A2 Eutric Leptosols D1 Eutric Fluvisols G1 Eutric Vertisols B1 Haplic Luvisols E1 Rhodic Nitisols H1 Haplic Alisols B2 Chromic Luvisols E2 Haplic Nitisols

Figure 2-5 depicts land use distribution of the Abay river basin. Large proportion of the basin’s land use is dominated by three land use categories namely Agricultural, Agro-pastoral and Traditional (descriptions are found on Table 2-5). Table 2-4 presents the relative percentage distribution of these dominant land use categories, which was computed using ARC-GIS, for each sub-basins of the Abay river basin.


17

Figure 2-5: Land use of the Abay river basin4

Table 2-4: Percentage of major land use of the Abay river basin and its sub-basins

Percentage of major land use groups Land use Basin A T P U AP AS M SF S SP N WAbay 20.0 21.8 7.3 0.1 27.8 7.8 0.3 0.5 3.7 8.7 0.4 1.8Sub-basin Tana 51.4 0 5.6 0.1 22.0 0.4 0.1 0 0.2 0.03 0 20Beles 7.0 40.9 7.3 0 17.3 6.1 0 0 10.9 10.5 0.1 0Beshilo 28.9 0 3.3 0 66 0 0 0 0 0 1.3 0N.Gojam 29.6 0 6.3 0.0 58.5 1.9 0 0 0 0 3.6 0.0Dabus 0 34.1 18.7 0.0 10.8 26.1 2.7 0 2.2 5.5 0 0S.Gojam 29.3 0.0 6.2 0.1 44.4 0.8 0 1.0 1.1 17.1 0 0.01Jimma 42.8 0 9.0 0.2 42.8 1.9 0 0 0.8 2.6 0 0Welaka 35.9 0 15.6 0 48 0 0 0 0 0 0 0Wonbera 0.15 44.7 1.4 0 0.69 19.5 0 0 6.36 27.3 0 0Fincha 27.4 0.3 16.7 0.1 41.3 0 0.5 1.3 0 1.5 0 11.0Anger 0.3 29.3 4.4 0.0 3.7 13.3 0 5.8 13.2 30.1 0 0Muger 43.4 0 5.9 0.0 45.9 4.3 0 0 0.41 0 0 0.01Guder 15.9 0 6.9 0.1 73.2 1.6 0.5 0 0 1.6 0 0.1Dedessa 16.2 18.6 2.8 0.1 8.7 18.5 0 1.5 13.0 20.7 0 0

4 Source: Ethiopian Ministry of Water and Energy (MoWE)


18

Table 2-5: Major land use types of the Abay river basin

ID Land use type Explanation A Agriculture T Traditional Semi-nomadic pastoralism, which covers most of the

lowlands. Mostly grasslands are mixed with woodlands in this category. (Shrubby grassland).

P Pastoral These are the grassland areas, generally above an altitude of 1500m

AP Agro-pastoral Covers moderately cultivated areas, which are normally associated with various types and degrees of stress/ limitation on cultivation, mixed with grassland at significant level.

AS Agro-silvicultural These are moderately cultivated areas mixed with significant forest, plantation or woodland or forest/ woodland areas with extensive cultivation.

M Marsh and perennial or seasonal swamp

SF State farm Same as agriculture with totally different management System and incorporates both rain fed and irrigated state farms.

S Silvicultural Forest areas, plantations and highland woodlands. SP Woodland, bush land

and shrub land Generally above 1,500m. These areas provide both grazing and wood resources.

W Open water Lake Tana is the dominant open water in the basin. U Urban N Unusable land Most are rock land area.


19

2.3 Lake Tana sub-basin

2.3.1 General

Lake Tana sub-basin, which is located in northern part of the Abay river basin, is one of the 14 large-scale sub-catchment of the Abay river basin. The sub-basin contains the country’s largest fresh water lake called Lake Tana and the third largest in the Nile basin. It is the headwater of Abay river with a contribution of around 7 % of the total flow at Ethio-Sudan border. Geographically, the sub-basin is located between 10.95°N to 12.78°N latitude and between 36.89°E to 38.25°E longitude.

2.3.2 Climate

Based on the climatic zones classification, the Lake Tana sub-basin falls within the cool semi-humid zone that represents altitudes of 1800-2400 m a.s.l. with mean annual temperature of 17-20°C and the cool and humid zones that represents altitudes of 2400-3200 m a.s.l. with mean annual temperature of 11.5-17°C [24]. The average rainfall is highest in the southern and south-eastern part and strongly decreases towards the northern and north-western part of the basin as is shown in Figure 2-6. The northward and southward movement of the Inter Tropical Convergence Zone controls its seasonal rainfall distribution. Wet air masses are driven from the Atlantic Ocean and Indian Ocean during main rainy season (June to September). Small rains also occur sporadically during April and May. The mean annual rainfall at Gonder Airport, at Delgi, at Bahir Dar and at Dangla meteorological stations are 1176 mm, 784 mm, 1400 mm and 1544 mm respectively. Daily rainfall data for each meteorological station in Figure 2-6 were collected from Ethiopian NMSA. Figure 2-6 also depicts mean monthly distribution at these meteorological stations.

Lake Tana sub-basin

20

Figure 2-6: Location of Hydro-meteorological stations, mean monthly rainfall histogram and

drainage map of Lake Tana sub-basin

2.3.3 Geology

Lake Tana basin is a junction point of three grabens centring Lake Tana, which were active in the mid tertiary and quaternary and run from Gonder, Dengel Ber and Debre Tabor [25]. The lake is dammed by dyke swarms that run NW-SE, NE-SW, ESE –WNW and a 50 km lava flow cut off at the outlet of the Blue Nile river to a possible depth of 100 m [25]. Quaternary lacustrine sediments and alluvial deposits are evident at the head and toes of the basin namely Chilga, Debretabor and Fogera flood plains overlain on basalts. The simplified geological cross-section by [26] shows that the underlying formations beneath the 250 m thick basaltic grabens are Adigrat and Nile Gorge sand stones and Ashengi, Aiba and Tarma Ber formations that go 1-2 km deep. The underlying basaltic graben serves as a cut off against seepage loss from the lake as it is confirmed upon the absence of geochemical mixing outside of the basin [27].


21

2.3.4 Soil and land use

Referring to Table 2-2 above, seven second level major soil groupings were identified in Lake Tana sub-basin. These include Eutric Leptosols, Haplic Luvisols, Chromic Luvisols, Eutric Fluvisols, Haplic Nitisols, Eutric Cambisols and Eutric Vertisols. About 16 % of the Lake Tana sub-basin is constituted by Chromic Luvisols and about 12 % each by Eutric Cambisols and Haplic Nitisols. Haplic Luvisols cover 21 % of the sub-basin. Based on major soil groupings at highest level, about 37 % of the sub-basin is constituted by Luvisols.

Around nine major land uses were identified in Lake Tana sub-basin (see Table 2-4 above), of which Agriculture, Agro-pastoral and water covers more than 90 % of the sub-basin. Other major land use of the sub-basin includes pastoral, Agro-sylvicultural, Silvicultural, Urban and Marshy area with percent coverage ranging from 6 % to 0.1 %.

2.3.5 Navigation

Lake Tana is one of the country’s inland freshwater resources that provide intensive transportation for the public, goods and tourists. The presence of different historical and cultural tourist attractions on the islands and islets, and adjacent terrestrial areas, together with the occurrence of villages/ towns at its peripheries make transportation an important sector in Lake Tana. According to Lake Tana Transport Enterprise, the minimum operation level for the boats on the lake is 1785 m a.s.l. However, [24] suggested the minimum operation level for the navigation as 1784.75 m a.s.l. The effect of varying minimum operational navigation level of Lake Tana on planned and existing hydropower production and vice versa was investigated in chapter 5 of this dissertation.

2.3.6 Tourism

Lake Tana region with a population of about 3 million, of which majority of the population resides in rural areas is endowed with many cultural and natural assets. There are, about 37 islands in the lake, up on which some 20 monasteries from the 16th and 17th century exists with several historical monasteries and churches having religious and cultural interests [28]. The famous Tis-Issat waterfall of the Blue Nile, which is 45 m high, is located about 40 km downstream of Lake Tana. Some wetland areas of the sub-basin have abundant bird and fish species. Owing to this fact, the region is one of the best tourist destinations in the country. According to [29] an average of 27,189 people per year (both domestic and foreign) visits the area. From these tourists an average of 2,221,533 Ethiopian Birr was collected yearly (1996-2005) from the Tis- Issat waterfalls alone. Figure 2-7 shows the Tis-Issat waterfalls before and after the operation of Tis-Abay hydropower plant II. Unless proper reservoir operation policy is in place, further water resources development in the region may significantly distort the spectacular view of the waterfall, which may reduce the number of tourists visiting the area.

Lake Tana sub-basin

22

Figure 2-7: Tis-Issat waterfalls a) before and b) after the completion of Tis-Abay Hydropower station II (Phote source: [29])

2.3.7 Hydropower generation

Before 2010, the two important water resources development around Lake Tana include the water level regulation weir (635 m long and 6 m high) called Chara Chara weir constructed at the mouth of the lake in 1996 and Tis-Abay I and II hydropower plants with installed capacity of 11.4 MW and 73 MW respectively at 35 km downstream of the lake. The Chara Chara weir is equipped with seven radial gates, two of which were completed in 1996 and the remaining five gates were completed in 2001, which allow the release of water from Lake Tana to be controlled as long as the water level of the lake remains lower than the elevation of the spillway at 1787 m a.s.l. The construction of the weir was intended to augment the dry season outflow to supply water regularly to the hydropower plants and to Tis-Issat waterfall, a national identity symbol and international tourist attraction. Currently, Tana-Beles hydropower project, having a total installed capacity of 460 MW, is completed and operational. This project, which is based on inter-basin transfer from Lake Tana to Beles river basin, is discussed in section 2.4.5 of this dissertation.

2.3.8 Lake Tana hydrology

The catchment area of Lake Tana sub-basin is about 15,320 km2 and surface area of the lake itself is 3,060 km2, which is about 20 % of the lake’s catchment area [30]. The lake is characterized by a flat bottom and rapid drop in depth at its edges. A bathymetric survey conducted by [30] revealed that the deepest point of the lake is at an elevation of 1772 m a.s.l., which is about 14 m below the average water level (1786 m a.s.l.). The average depth of the lake is about 9.5 m. The lake is about 76 km long and 67 km wide. The natural sill level prior to the construction of Chara Chara weir in 1996 was 1785 m a.s.l. However, after the construction of the weir, the natural sill level was lowered by 1m (i.e. at 1784 m a.s.l.).

(a) (b)


23

The lake is fed by relatively five large perennial rivers, Gilgel Abay, Koga, Gumera, Ribb and Megech and many (gauged and ungauged) seasonal streams and has only one natural outlet called Abay at BahirDar. Table 2-6 presents catchment characteristics of the main perennial rivers, which are flowing towards Lake Tana. According to [31] four major rivers namely Gilgel Abay, Gumera, Ribb and Megech contribute 93 % of the inflow and only 7 % of the lake’s inflow is from ungauged catchments. [24] indicates that some 29 % of the lake’s inflow is from ungauged catchments where, contrary to [31], Koga river is considered gauged with some 4 % of the total river inflow. [32] compared three methods to estimate inflow to Lake Tana from ungauged catchments. [32] have estimated inflow from ungauged catchment as high as 42 %, 47 % and 46 % of the total inflow to Lake Tana using regression, proximity and catchment size methods of parameter transfer respectively. Total inflow to the lake from gauged and ungauged catchments was estimated in this dissertation as well and presented in chapter 5.

Table 2-6: Characteristics of major rivers around Lake Tana

River Gauging site near

Catchment area (km2)

Average slope (%)

Maximum length (km)

Average elevation (m)

Mean annual rainfall (mm)

Mean annual flow (m3/s)

Gilgel Abay

Merawi 1664 0.90 83.7 2284 1675 54.35

Ribb Addis Zemen 1592 1.18 97.0 2433 1350 12.60

Gumera BahirDar 1394 0.88 82.9 2270 1300 30.19 Megech Azezo 462 1.70 42.0 2540 1095 6.03 Upper Ribb

DebreTabor 844 1.70 60.0 2635 1450 8.42

Koga Merawi 244 0.67 49.1 2083 1580 5.06

The only river that drains Lake Tana is the Blue Nile river (Abay river at BahirDar) with a natural outflow that ranges from a minimum of 6101075 ⋅ m3 (1984) to a maximum of 6106181⋅ m3 (1964). For the period from 1976 to 2006, the average outflow is estimated to be 6103732 ⋅ m3 [33]. The lake has a storage capacity ranging between 91023⋅ m3 at minimum operation level of 1784.0 m a.s.l. and 91032 ⋅ m3 at maximum storage level of 1787.0 m a.s.l. The lake is regulated by Chara Chara weir aiming at a controllable storage of 9101.9 ⋅ m3 between elevations of 1784 m a.s.l. and 1787 m a.s.l. [35], which represents approximately 2.4 times the average annual outflow of the lake [35]. However, this storage will reduce by about 25 % if the minimum operation level is increased to 1784.75, which is set by EEPCO to allow a minimum draught needed for navigation in Lake Tana [24].

Lake Tana sub-basin

24

Lake level fluctuations primarily respond to seasonal influences by the rainy and dry season and reaches maxima around September and minima around June with historic maximum and minimum water levels of 1788.02m (September 21, 1998) and 1784.46m (June 30, 2003) [33]. It was observed from the hydrological records that the long-term mean water level of the lake fluctuates seasonally between 1.86m in June and 3.39m in September above the datum point, i.e. 1783.515 m a.s.l. Flooding in lake Tana sub-basin, like for other major river basins in Ethiopia with heavy rain and mountainous topography, is a common phenomena. Although the country experiences two common types of floods i.e. flash floods and river floods, flooding problems in lake Tana sub-basin are attributed to rivers that overflow or burst their banks. This exacerbated by back water flow of lake Tana and inundate flood plains upstream of the lake. Fogera flood plain, which is located between Ribb and Gumera catchments, is one of the most affected areas by flood. According to the UN Office for the Coordination of Humanitarian Affaires5 report in 2006, flooding in Fogera has affected 43127 and displaced 8728 people. The other important hydrological variable in the planning, design and operation of a reservoir is the accumulation of sediment. Many type of sediment-related problems can occur both upstream and downstream of dams and sediment entrainment can also interfere with the beneficial use of diverted water. Like other existing reservoirs in Ethiopia, for instance, Koka, Legedadi, Geferesa and Angereb, the planned reservoirs in the Lake Tana sub-basin may also be threatened by reservoir sedimentation problems due to accelerated soil erosion. Amongst sediment related problems, the accumulation of sediment in a reservoir reduces the storage capacity and affect the flow regulation of the reservoir. As a result, the reservoirs will fail to fulfill supplying water for domestic water supply, flood control, hydropower, navigation, environmental and other benefits that depend on releases from the storage. Reservoirs have been planned, designed and operated over the design life of the project. Operation may continue with revised project demand and with some remedial measures until the design life of the reservoir, which will eventually be terminated by sediment accumulation. Therefore, sediment data is required in order to foresee the potential loss of capacity due to sedimentation over the design life of the project during planning and design stage. Suspended sediment rating equations have been developed for existing and planned reservoirs in the Lake Tana sub-basin by [39], [40], [41] and [42]. [40] and [41] have developed regional suspended sediment rating equation that relate suspended sediment mass transport rate in ton per day and discharge in cumec using the Megech, Ribb, Gumera and Gilgel Abbay suspended sediment rate and discharge data. The bed loads for upper Ribb watershed and Megech watershed were taken as 10% of the respective suspended loads that were estimated using the regional rating equation by [40] and [41]. Accordingly, the total mean annual sediment load entering the Ribb and Megech reservoirs are thus estimated as 531,371 ton (743 ton/km2/year) and 481,183 ton (1,135 ton/km2/year) respectively. For Gumera reservoir, [42] estimated total mean annual sediment load as 638,000 ton (1,643 ton/km2/year) assuming that the bed load accounted 15% of the suspended load. Based on the rating equation developed by [39], sediment load at Koga dam estimated as 57,665 ton/year (350 tons/km2/year). 5 http://reliefweb.int/sites/reliefweb.int/files/reliefweb_pdf/node-5468.pdf


25

2.4 Planned and existing artificial reservoirs in Lake Tana

sub-basin Agriculture is the dominant sector in the Ethiopian economy, accounting for 52 % of gross domestic product (GDP), 60 % of export earnings and 80 % of total employment. Over 95 % of all cereals, oilseeds, and pulses are produced by smallholders. Industrial production and services, on the other hand, comprise 11 and 37 % of GDP respectively.

Lake Tana sub-basin is one of the major agricultural areas of the country. The livelihood of most of the inhabitants in the sub-basin is rain fed agriculture. Major crops growing in the area include cereals (rice, wheat, barely, maize, teff, millet), beverages (coffee) and vegetables. Out of the total grain crops produced in Amhara Region, where the sub-basin is found, 64 % is for consumption, 20 % for sale, 13 % for seed and 3 % for others [36]. In addition to crop production, livestock raising is also an integral part of the agricultural system. The land and water resources in the area are suitable for irrigation development. Experience from small-scale irrigation schemes has demonstrated that a range of crops could be grown profitably during the dry season, without affecting the production of staple food crops during the rainy season.

Table 2-7 presents planned irrigation schemes for rice (cropping pattern 6) and non-rice (cropping pattern 1) cereals in the lake Tana sub-basin with an overall gross water requirement greater than 610600 ⋅ m3/year. This will be accomplished by constructing 6 artificial reservoirs and 3 pumping station. The proposed large-scale irrigation schemes on rivers flowing to Lake Tana include Gilgel Abay, Koga, Jema, Megech, Ribb and Gumera with annual gross water requirement greater than 610500 ⋅ m3. The introduction of these large-scale irrigation schemes will make farmers feel more secure about their basic food supply and enable them to diversify their crops based on local market demand and export opportunities.

Table 2-7 Planned irrigation schemes in the Lake Tana sub-basin (Source: [20], [21] and [23])

Annual gross water requirement (106 m3)

Net water demand (106 m3)

Irrigation project

Irrigable area (ha)

CP1 (non-rice) CP6 (rice) CP1 CP6 Gilgel Abay B 12852 103.7 141.9 88.1 120.6 Gumara A 14000 - 114.8 - 97.6 Ribb 19925 172.1 220.0 146.3 187.0 Megech 7300 63.3 98.1 53.8 83.4 Jema 7800 56.8 - 48.3 - Koga 6000 61.6 - 52.4 - NE Lake Tana 5745 50.3 61.8 42.8 52.5 NW Lake Tana 6720 53.6 - 45.6 - SW Lake Tana 5132 42.3 - 35.9 -

Planned and existing artificial reservoirs in Lake Tana sub-basin

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The possibility of irrigating agricultural land by impounding water from rivers flowing into Lake Tana had been studied at different stages of planning for more than the last four decades. Section below summarizes characteristics of under construction large-scale irrigation schemes and irrigation schemes, which their final design are approved by the Ethiopian MoWE. These include Megech, Ribb, Gumera and Koga reservoirs respectively (see Figure 2-8 for their locations). Jema and Gilgel Abay irrigation project were not included in this study due to lack of data. The three pumping station on lake Tana were included under full future water resources development scenario of this study. Except Megech reservoir, which is designed for irrigation and for Gonder city public water supply, the other three reservoirs considered in this dissertation are designed mainly for irrigation purpose. Technical data for each artificial reservoir were taken from their design report as:

• Koga Irrigation project report, 2006 • Ribb Dam feasibility report, 2007 • Megech Dam Final feasibility report, 2008 • Gumera Irrigation project report, 2008

Figure 2-8 Locations of the proposed reservoirs around Lake Tana


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2.4.1 Koga Reservoir

Koga dam is located on the Koga river, on the southern side of Lake Tana. The dam is designed to irrigate 7000 ha of land that intends to improve rain fed agriculture. Main and saddle dams are semi-homogeneous earth fill with comprehensive filter and drainage systems. The saddle dam is located on the north end of the reservoir to prevent water flowing over. The source of the Koga river is close to Wezem, at an altitude of about 3200 m. The river is 64 km long; flowing into the Gilgel Abay river after it crosses the Debre Markos - BahirDar road, downstream of the town of Wetet Abay, at an altitude of 1985 m [38].

Using Thiessen polygon method, the mean annual areal rainfall on the reservoir for a period of 1985 to 1999 was estimated as 1450 mm. As the case for most areas in the Lake Tana sub-basin, the rainfall in the Koga catchment area has uni-modal characteristics with one rainy and one dry season. The rainy season extends from May to October and dry season from November to April. A high concentration of rainfall occurs in July and August. 95 % of the annual rainfall occurs in the wet season months of May to October. [38] estimated mean annual open water evaporation using the Penman method as 1542 mm.

The Koga river at the Wetet Abay gauging station drains a catchment of 250 km2. The average discharge in the 44 year of record (1959-2002) is 4.76 m3/sec (equivalent to

610151⋅ m3/year), representing 607 mm depth over the catchment. The average annual rainfall for Merawi is 1566 mm, giving a catchment runoff coefficient of 38 % [38]. In the same report, flow at the Koga dam site was synthesized from records of Wetet Abay flows and its mean annual flow at the dam site was estimated as 61098.112 ⋅ m3. According to the regional model proposed in this dissertation, the mean annual flow at the Koga dam site was estimated as 61008.105 ⋅ m3. Table 2-8 summarizes the main characteristic of Koga reservoir.


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Table 2-8: Koga Dam Irrigation Scheme6

6 Source collected from Koga Irrigation project report

Features Unit Value Hydrology

Catchment area Mean annual rainfall Mean annual evaporation Mean annual inflow Spillway design inflow flood is 2 day ½ PMF Spillway design routed outflow flood

km2

mm mm 106 m3 m3/s

m3/s

165 1450 1542 112.98 335.4 760

Storage Dam Dam crest level Full supply level Minimum draw off Dead storage level Crest length Maximum Height (above river bed level) Maximum storage Effective/Live storage Maximum Submergence

m m m m m m 106 m3 106 m3 ha

2019 2015.25 2005.16 2005 1730 21 83.1 82.6 1856

Spillway Type of spillway Ungated chute spillway Location Left abutment Crest elevation Crest length of the spillway

m m

2015.25 21.5

Inlets-Outlets (Intake structures) Centre line of irrigation outlet level 2.26 m above the inverted level of bottom outlet for irrigation Bottom outlet for emergency release for flushing sediment and for environmental release Max. discharge capacity of bottom outlet Max. discharge capacity of irrigation off take

m m m m3/s m3/s

2005.4 2004.2 2001.9 31 9.1

Saddle Dam Location Right flank Type Earth fill dam with clay core Crest elevation Crest length of the saddle Maximum height

m m m

1933 1162 9


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2.4.2 Ribb Reservoir

The Ribb river, which is some 130 km long, has a drainage area of about 1790 km² and an average annual discharge of 11.6 m³/s. The catchment area at the dam site is 685 km2. The river, which flows generally in a westerly direction and empties into Lake Tana, is one of the main streams flowing into Lake Tana from the east. The Upper Ribb watershed is characterized as a mountainous, wedge-shaped and steep-sloped (3.6 %) watershed. The highest elevation of the watershed is about 4100 m in its south-eastern part. The lowest topography land is at the dam site, which is at an altitude of 1873 m.

The climate of the Ribb basin is marked by a rainy season from May to September, with monthly rainfall varying from 65 mm in May to 411 mm in July. Mean annual precipitation is about 1400 mm in the upper part and about 1200 mm in the lower part. The dry season, from October to April, has a total rainfall of about 8 % of the mean annual rainfall. Temperature variations throughout the year are minor (19ºC in December to 23ºC in May), with maximum and minimum temperatures of 30°C and 11.5°C, respectively. Mean annual potential evapotranspiration at Ribb dam site was computed on a daily basis using modified Hamod method (see section 3.3.2.1), which requires only temperature data, as 1437 mm. Mean annual open water evaporation from the reservoir was calculated by multiplying the mean annual evapotranspiration with an aridity correction factor, which was estimated for Ethiopia as 1.2 [40]. Accordingly, the mean annual open water evaporation from the reservoir was estimated as 1724 mm. The value was compared to other evaporation estimates of Ribb reservoir by [40] and other studies near the project area. The Netherlands Engineering consultants cited on [40] estimated potential evapotranspiration at Gondor as 1538 mm with open water evaporation of 1845 mm. Mean annual potential evapotranspiration at BahirDar was estimated by [24] as 1428 mm with open water evaporation value of 1714 mm.

The Ribb dam project [39] consists of an earth-rock fill dam with maximum reservoir capacity of 610234⋅ m3 of water. Saddle dam is located southwest of the left abutment of the main dam where the topography deepens. The lowest elevation of the saddle dam is 1933.0 m a.s.l. The saddle dam, maximum height of about 13.6 m, prevents water flowing through the lowest point. The axis of the saddle dam is located to the left side of the spillway bridge and ends where the ground elevation is 1945.50 m .

The intake tower is situated at the toe of the main dam, which will be used for both environmental flow and irrigation needs, as well as drawdown of reservoir, as necessary. The octagonal cross-section intake tower is founded on the bedrock, and its height from bottom floor to entrance floor will be 53.5 m. On each of six of the walls, an external inlet gate: 2.5 m wide and 4 m high (net opening size), will be accommodated. On one of the walls, the 3.0 m diameter water supply conduit and its internal regulating gate (3.0 m x 3.0 m) are situated. Another wall will support the edge of the Pedestrian Bridge, where the entrance of the tower is situated. The inlet gates are arranged in two groups of three gates, with each group having a common sill elevation for its three gates. The water supply conduit, about 222 m long from the intake tower to its outlet, will convey the irrigation water supply at a maximum discharge of 40 m3/sec (monthly maximum), where the water will be at elevation of some 2.17 m below the lower gates' side elevation (1893.83 m). At the end of the conduit, there will be an outlet


30

pipe chute that will serve to break up the flow and dissipate energy before discharging to the river [39]. Table 2-9 presents characteristics of Ribb reservoir.

Table 2-9 Ribb Dam Irrigation Scheme (construction in progress)7

7 Source collected from Ribb Dam feasibility report


Catchment area Mean annual rainfall Mean annual evaporation Mean annual inflow Spillway design inflow flood is 1 day ½ PMF

km2

mm mm 106 m3 m3/s

715 1487 1800 225 1710

Storage Dam Crest length Maximum height (above OGL) Crest width The 25th year dead storage level The 50th year dead storage level Normal water level Maximum water level Maximum storage Effective/Live storage Maximum submergence

m m m m m m m 106 m3 106 m3 ha

800 73.2 10 1894.9 1901.2 1940 1943 234 216 1125

Spillway Type of spillway Uncontrolled side channel Location Left abutment Crest elevation Length

m m

1940 110

Saddle Dam Location South-west of left abutment Type Composed of outer shells, impermeable core, filter and the wet face coved by rock riprap Crest elevation Maximum height

m m

1945.5 13.6

Inlets-Outlets (Intake structures) Minimum drawdown level (MDDL) Normal water level Sill elevation of 3 lower 2.5 m x 4.0m inlet gates Sill elevation of 3 upper 2.5 m x 4.0m inlet gates Ø3.0 m steal outlet conduit for water supply (Irrigation, environmental and emergency drawdown)

m m m m m

1901.43 1940 1896 1918 1888


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2.4.3 Megech reservoir

Megech dam is located on the Megech river, on the northern side of Lake Tana sub-basin. The dam is designed to irrigate 7311 ha of land and to use as a source of future water supply for Gonder and its environs. According to the proposed method of regionalization the Megech river, which is about 70 km long, has a drainage area of about 985 km² (at the junction with Lake Tana) and an average annual discharge of 15.8 m³/s. The catchment area at the dam site is 426 km² with a mean annual flow of 6.2 m³/s. More than 80 % of the annual runoff occurs during July to September. With the constructions of the proposed dam, about 8.8 km² area is likely to be submerged permanently.

Land elevations vary from 1877 m a.s.l. at the dam site to 2957 m a.s.l. at the highest point on the watershed. Weighted average elevation of the Megech watershed is 2340 m a.s.l. The majority of the catchment is characterized by uni-modal rainfall pattern with distinct dry and wet seasons that receives its main rainfall from June to September. Gonder meteorological station lies within the Megech watershed. The annual rainfall in the watershed area ranges between 950 to 1500 mm, the average being about 1100mm.

Three major and dominant classes of land use have been identified which are cultivated land, forest/bush land and grazing land. According to data obtained from Woreda offices, about 64 percent of the watershed is under cultivation. About 50% of the watershed area is moderately steep to very steep making erosion a serious problem [40].

According to the FAO/UNESCO soil classification system, the major and dominant soils identified in the Megech watershed are Eutric Leptosols (82.6%), Eutric Vertisols (1.5%), Chromic Luvisols (3.7%) and Haplic Nitosols (12.2%). Table 2-10 presents the characteristics of Megech reservoir.


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Table 2-10 The Proposed Megech Dam Irrigation Scheme8

8 Source collected from Megech Dam Final feasibility report


Catchment area Mean annual rainfall Mean annual evaporation Mean annual inflow Mean annual sediment transport Spillway design inflow flood is 2 day ½ PMF Routed outflow flood

km2

mm mm 106 m3 103 m3

m3/s m3/s

426 1100 1800 176.3 413.4 1307 662

Storage Dam Crest length Maximum height (above OGL) Crest width Maximum storage Effective/Live storage Maximum submergence

m m m 106 m3 106 m3 ha

864 76.5 10 182 162.7 880

Spillway Type of spillway Uncontrolled side channel Location Right abutment Crest elevation Length

m m

1947.1 54

Inlets-Outlets (Intake structures) The 25th year minimum drawdown level The 50th year minimum drawdown level Normal water level Maximum water level Ø2.5 m conduit for irrigation water supply diameter Two inlet gates for irrigation water supply at an elevation Two inlet gates for irrigation water supply at an elevation One regulator out let gate for irrigation water supply at elev Ø1.0 m conduit for drinking water supply diameter One inlet gate for drinking water supply at an elevation of One inlet gate for drinking water supply at an elevation of One regulator out let gate for drinking water supply at elev One regulator gate for smaller discharges or riparian flow

m m m m m m m m m m m

1906.37 1914.38 1947.1 1950.46 1926 1905 1897 1917 1933 1900.5 1902


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2.4.4 Gumera reservoir

Gumara river is one of the main streams on the east side, flowing into Lake Tana. The river flows generally in westerly direction for a length of 132.50 km until Lake Tana. The catchment area from the head to Lake Tana is about 1893 km2. The Gumera river rises in the high mountainous area south and east of the town Debre Tabour at an approximate elevation of 3050 m a.s.l. According to the proposed method of regionalization and area-ratio method, the mean annual flow for the Gumara dam site with catchment area of 385 km2 had been estimated as 610290 ⋅ m3 and 610320 ⋅ m3 respectively. The rainfall in the project area is uni-modal type, which concentrates from the months of June to September. Using Thiessen polygon method, the annual areal precipitation on Gumera reservoir was estimated as 1500 mm.

Of the total watershed area considered for watershed management program [41], 96433.8 ha (75.14 %) is cultivated, 5262 ha (4.1 %) forest or bush land, 13616.8 ha (10.61 %) grazing, 2566.8 ha (2 %) wood land, 179.7 ha (0.14 %) as wet or swamp, 808.5 ha (0.63 %) exposed or unused area, 8252.2 ha (6.43 %) occupied by settlement or village and the rest 1219.2 ha (0.95 %) is under different uses such as cemetery, gully, roads, etc. According to FAO soil classification systems, the major and dominant soils identified in the watershed are Cambisols, Lithosols, Vertisols, Nitosols and Luvisols.

Gumara Dam ‘A’ irrigation project comprises of 33.0 m high earth fill dam with a central clay core on river Sendega Gumara for impounding inflows of the river during the monsoon period. The dam is proposed to have a gross storage of 61030.58 ⋅ m3. The live storage is 61099.23 ⋅ m3. An irrigation outlet located on the right bank of the dam for drawing the impounded water from the reservoir and releasing it back into Gumera river and to be picked up at the diversion dam, about 40 km downstream of main dam. Irrigation to the command area is proposed through canal taking off the diversion dam. Summary of the characteristics of the Gumara reservoir are presented in Table 2-11.


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Table 2-11 The Proposed Gumera Dam Irrigation Scheme9

9 Source collected from Gumera Irrigation project report


Catchment area Mean annual rainfall Mean annual evaporation Mean annual inflow Spillway design design flood

km2

mm mm 106 m3

m3/s

385 1600 1584 254.2 800

Storage Dam Normal water level Maximum water level Minimum drawdown level Crest length Maximum height above ground level Maximum storage Effective/Live storage Maximum submergence

m m m m m 106 m3 106 m3 ha

1928.25 1930 1922.1 505 33 59.69 23.99 539

Spillway Type of spillway Ungated chute spillway Location Right abutment Crest elevation Width of spillway crest Maximum surcharge

m m m

1928.25 150 1.75

Diversion weir Location 40 km below the main dam Total length

m

93.5

Saddle Dam Location Right flank Type Earth fill dam with clay core Crest elevation Length of the dam Maximum height Top width

m m m m

1933 643 8 6


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2.4.5 Tana-Beles basin transfer

Ethiopia is fortunate in having a combination of vast water resources and suitable topography that permit much of this potential to be developed at a remarkably low-cost, especially in the Blue Nile, Baro Akobo and Omo river basins of the country [42].

Currently, the Tana-Beles hydropower station, located on the South-west shores of Lake Tana some 370 km (air distance) north-west of Addis Ababa, is completed along with the inter-sub-basin transfer of water from huge natural storage capacity of Lake Tana to the Beles basin without the construction of dams or river regulating works. The aim of the inter-basin transfer is to exploit the large elevation difference between the lake and the (underground) powerhouse for the generation of hydropower, and to use the water downstream of the power plant for irrigation [43]. The main features of the project are shown in Figure 2-9, which includes (technical data of the power station is taken from Salini Construttori S.P.A, Ethiopian Electric Power Corporation (EEPCO), Beles Multipurpose Project):

• intake with an approach channel and intake structure, • headrace tunnel and surge shaft, • penstock shaft and manifold, • underground powerhouse, • open air switchyard, • tailrace tunnel and outlet structure • access roads

Water from Lake Tana, which has a storage capacity of about 91023⋅ m3 at minimum operating level (1784 m a.s.l.) and 91032 ⋅ m3 at maximum storage level (1787 m a.s.l.), will be conveyed to the power intake structure through an approach channel (see Figure 2-9). The channel is approximately 0.9 km long with a width varying from 160 m to 40 m. The channel inlet structure, which allows isolation of the approach channel from Lake Tana, is a reinforced concrete structure divided in 7 bays each with a clear opening of 5 m. The power intake structure, located at the downstream end of the approach channel, consists of trash screens (to prevent the passage of debris), two bulkhead gates and two guard gates to control flow into the headrace tunnel. The power intake structure is connected to the head of the vertical penstock shaft with approximately 12 km long and 7.2 m inner diameter headrace tunnel. Steel lined high-pressure headrace tunnel connects the 271.8 m high and 6 m inner diameter penstock shaft to the powerhouse that contains four Francis turbines with a rated power of 115 MW each for a total of 460 MW. The tunnel terminates in a four branch manifold, which deliver water to the turbines. The water, after passing through the turbines, is discharged via 100 m long draft tube to 7.1 km long tailrace tunnel. The tailrace tunnel is designed to operate with a free-flow water surface, which ultimately discharges the water to the Jehana stream (Beles sub-basin). The flow downstream of the power house is expected to irrigate 140,000 ha10.

10 http://www.ezega.com/news/NewsDetails.aspx?Page=heads&NewsID=2307


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Figure 2-9 Schematics of Tana-Beles basin transfer for hydropower generation (Adopted from EEPCO, Beles Multipurpose Project)

The 271.8 m high vertical penstock shaft is an underground pressure shaft connecting the headrace tunnel with the high pressure headrace tunnel (not shown in Figure 2-9) and conveying flows to the powerhouse. The high pressure headrace tunnel connects the penstock shaft to the power house. The main dimension of the powerhouse is presented in Table 2-12 (from Salini Construttori S.P.A, EEPCO, Beles Multipurpose Project).

Table 2-12 Main dimension of the powerhouse of Tana-Beles multipurpose hydropower station

Powerhouse height 39.5 m Machine hall floor elevation 1468 m a.s.l.

Powerhouse width 17.5 m Generator floor elevation 1464 m a.s.l.

Powerhouse length 96.5 m Turbine floor elevation 1460 m a.s.l.

Roof vault elevation 1484 m a.s.l. Valve floor elevation 1452 m a.s.l.


37

The net head is about 311 m (330 m gross head = 1780- 1450) and the rated discharge is 160 m3/s with a plant factor of 0.48. As a result, the average outflow from Lake Tana to the power house will be as high as 77 m3/s. The Lake level is controlled by the existing Chara-Chara weir, which discharges into the Abay river and used to maintain the flow required by the existing Tis-Abay I and II hydropower plants and Tis-Issat water fall. The Tana-Beles hydropower plant, the largest hydropower station in the country, was officially inaugurated on May, 201011.

11 http://www.ethiopian-news.com/ as visited in May, 2010

State of the art and proposed decision support tool

37

3 State of the art and proposed decision support tool

3.1 Proposed framework of DST Depending on the application and versatility of DSS, many researchers have given different definitions. A more comprehensive definition of DSS is given by [44] as “DSS is an interactive computer program that utilize analytical methods, such as decision analysis, optimization algorithms, program scheduling routines, for developing methods to help decision makers formulate alternatives, analyze their impacts, and interpret and select appropriate options for implementations”. DSS help managers/decision makers use and manipulate data; apply checklists and heuristics; and build and use mathematical models12. A definition applied in water resources engineering, DSS are the combination of advanced engineering models, analysis techniques, complex data, geographic information system (GIS) and graphical user interface (GUI) [45]. Based on this definition in the field of water resources, DSS can combine spatial data for elevation, land use, agricultural data, hydrograph, evaporation rates, climate data, etc, as well as multi-criteria optimization, habitat analysis, groundwater and /or surface water models into one system. In general, these watershed features, variables and techniques can be organized into three major subsystems; data base subsystem (DBS), model base subsystem (MBS) and user interface subsystem (UIS) [46].

Figure 3-1 depicts the interaction among different components of DSS in the field of water resources.

• Data Base is the collection of data (input and output data) that is organized so that its contents can easily be accessed, managed and updated. From water resources point of view it includes GIS data, time series data, summary data etc.

• Supporting Tools/ Models is required to handle the analysis of the problem. It includes hydrological models, multi-criteria decision models, river basin management, water quality and ecology, agricultural and urban planning etc.

• Interface allows decision-makers to interact with both the data base system and the models and to manipulate data between them. It should be user-friendly and usually includes graphical components in this case called a graphical user interface.

12 http://www.dssresources.com/ this site is maintained by D. J. Power as visited in September 2005

Proposed framework of DST

38

Figure 3-1 General framework of DSS for water resources

In recent years, a number of basins wide water resources management tools have been developed that included a module for reservoir operation simulation, such as IRAS (Interactive River-Aquifer Simulation), TERRA (Tennessee Valley Authority Environment and River Resource Aid), CTIWM (Cooling Technology Institute Water Management), and RiverWare as cited in [47]. Most of these are generalized packages for simulation purposes but have limited capability for development of optimal operation policies [48].

Development of DSS for sustainable water resources planning in the European Union can be cited as one of a typical example of broad spectrum DSS model [49]. It was an endeavour of collaboration of seven universities and institution across Europe. Other DSS designed for offering solutions for specific objectives and site-specific include Colorado River Basin DSS [50], Lake Victoria DSS [51], Decision Support Tools (DSTs) for Nile river Basin [52], DSS for Reservoir Water Management Conflict Resolution [53] etc.


39

In this dissertation, a methodology was proposed that can generate many alternative optimal solutions for multi-purpose multi-reservoir system operation problems in hydro-meteorological data scarce area by combining watershed models and system analysis model, which can be categorized as: simulation models, optimisation models, and combination of simulation and optimisation models.

Figure 3-2 shows the proposed general framework of a combination of four models, i.e. watershed model (rainfall-runoff), cluster analysis, reservoir simulation model, and reservoir optimisation model. The proposed methodology is very general that can be applied in any multi-purpose multi-reservoir system operations in gauged and/ or ungauged catchments. The framework explains the different steps in the flow estimation process from model selection, calibration and validation, to the formulation of regional model and choices of reservoir simulation-optimization algorithms to handle the trade-off amongst various purposes of planned and existing multi-reservoir system. With the addition of high level information, which are non technical, qualitative and experience driven, the tool enable decision makers to select optimal operating policy(ies) among different alternative policies for existing reservoirs and give them useful insights into the problem before the realization of any future water resource developments in a given watershed.

Unlike a decision support system, which normally comprises of many interconnected graphical interfaces, models and data base modules, the concept of decision support tools as used in this dissertation are designed to offer many alternative optimal solutions for planned and/or existing multi-purpose multi-reservoir systems in ungauged catchments. The designed tools are stand-alone, which can independently address specific objectives and problems in reservoir operation in gauged and ungauged catchments. Although the proposed general framework of decision support tool is developed based on the problem in the case study area, the methodology can be applied to any river basin.

Data base component

40

Figure 3-2 Conceptual framework of the proposed structure of decision support tool

The proposed decision support tool has three main components namely, data base component, model component, which further divided into regional model and hybrid reservoir simulation-optimization model, and decision making component. Descriptions of each component are presented from section 3.3.1 to section 3.4.4.

3.2 Data base component The general framework begins with the data base component of the decision support tool, which contains readily available input data for rainfall-runoff model, cluster analysis, reservoir simulation-optimization models. These include topographical data, hydro-meteorological data, land use, soil, catchment characteristics, water demand, reservoir characteristics etc. The database component can also be used to store any output data from regional model and hybrid reservoir simulation-optimization model as it was indicated in the broken line of Figure 3-2.


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3.3 Regional model component

3.3.1 General background

3.3.1.1 Regionalization

Regionalization is a technique of transferring information from donor catchments to data poor (ungauged) catchments. There are now numerous studies, which provide brief reviews of the use of regional hydrologic methods for estimating watershed model parameters at ungauged sites (including: [54], [55], [56], [57], [58], [59], [60] and [61]). In [62], four methods of regionalization are compared. Of these four methods, transferring the whole set of model parameters from donor catchment to ungauged catchment performed well as compared to other methods like arithmetic mean of all calibrated model parameters, the use of spatial proximity and regression method that relate model parameters with catchment attributes.

Previous regionalization studies have focused on a wide range of hydrologic models ranging from complex hourly and daily watershed models to the more parsimonious monthly water balance models. Although each previous study attempted to regionalize a different watershed model, nearly all studies to date follow the same general approach. As it is stated in [60], regionalization follows two steps. First, a watershed model is calibrated to whatever climate and stream flow data is available for the region of interest. This step is followed by the application of a regional hydrologic method, which attempts to relate the optimized watershed model parameters to watershed characteristics through either linear or non-linear regression form.

[60] has used slightly different approach that instead of calibrating the watershed model and then establish a relationship between model parameters and catchment characteristics; they calibrated the “abcd” monthly water balance model [63], which has four model parameters a, b, c and d, with the dual objective of reproducing the observed catchment response and, additionally, to obtain good relationships between model parameters and catchment characteristics. Their approach resulted in a nearly perfect regional relationship between model parameters and catchment properties, but did not lead to improvement in the ability of the regionalized model to model stream flow at validation catchments located within the same study area. Unfortunately, many of the catchment descriptors they used for regionalization require analysis of stream flow data and, therefore, its application to ungauged catchments is not possible.

Most of the previous methods of regionalization that attempted to relate watershed models parameters with catchment characteristics are applicable for lumped type of watershed models with limited success. Recently, however, there is an increasing demand of using distributed or semi-distributed type of hydrologic model to take care of the spatial heterogeneity of catchment characteristics. Distributed hydrologic models, with the capability to incorporate a variety of spatially-varying land characteristics and precipitation forcing data, can be computed cell by cell providing greater detail than traditional lumped methods. In recent years, advances in GIS have opened many opportunities for enhancing hydrologic modelling of watershed systems. The question is how distributed hydrologic models can be applied for ungauged catchments. It is too

Regional model component

42

difficult, if not impossible, to follow the business as usual two-step method that relates watershed model parameters with catchment characteristics for distributed type of hydrologic models.

In [64], two promising approaches for regionalization are pointed out. The first promising approach in data sparse environments is to assign values to the watershed model parameters a priori using some generalized homogeneity classification of watersheds based on land use, soil types, climate conditions, runoff ratios, etc. The idea is to cluster or group watersheds into ‘hydrologically homogeneous’ regions. Another promising approach to hydrologic regionalization involves the use of hybrid methods such as in the study by [65] where first cluster analysis and principal component analyses were employed to break the region into hydrologically homogeneous regions. Next, drainage area was used to develop a regional flow duration curve model that, in turn, was used to calibrate the watershed model at an ungauged site. Such a hybrid approach can benefit from advances relating to the definition of hydrologically homogeneous regions.

3.3.1.2 Rainfall-runoff model

Another main research challenge in the field of hydrology is the development of computational models that are capable of accurately simulating catchments’ response to rainfall. The process of transformation of rainfall into runoff over a catchment is very complex, highly nonlinear, and exhibits both temporal and spatial variability. Many rainfall-runoff models, which play an important role in water resources management, planning and design of hydraulic structures, have been developed by different researchers with various degrees of complexity to simulate this process. These models can be classified depending on the degree of representation of the underlying physical processes into three broad categories; namely, black-box or system theoretical models, conceptual models and physically-based models.

Black-box models are data-driven models that typically contain no physically-based input and output transfer functions and, therefore, are considered to be purely empirical models. These models have been very popular for a long time because on the one hand, they can be developed and implemented quickly and easily and, on the other hand, mainly avoid the problem of understanding the structure of the inherent processes that take place in the system being modelled. These models comprise a plethora of techniques (e.g. time series modelling, empirical regression, fuzzy rule-based systems and Artificial Neural Networks), mostly originating from statistics and artificial intelligence. Their low transparency, which results from the inability to interpret their internal workings in a physically meaningful way, is the main drawback of black-box models and these models generally fail to give useful insights into the system under investigation.


43

Physically based models are knowledge-driven models and they are based on detailed descriptions of the system and the processes involved in producing runoff. These models use the basic laws of physics, e.g. laws of mass balance, energy balance and momentum balance to describe the movement of water. The resulting system of partial differential equations is then solved numerically at all points (spatially distributed) in a two or a three dimensional grid representation of the catchment. Excessive data requirements, large computational demands, over-parameterisation effects, and parameter redundancy effects are the main drawbacks of physically based models.

Conceptual model approaches are a first step from physically-based model approaches in a more empirical direction. Instead of using the equations of mass, energy, and momentum to describe the process of water movement as the case in physically based models, in conceptual model a simplified but a plausible conceptual representation of the underlying physics is adopted. These representations frequently involve several inter-linked storages and simplified budgeting procedures, which ensure that at all times a complete mass balance is maintained among all the inputs, outputs, and inner storage changes.

Some examples of conceptual modelling include: the Stanford Watershed Model (SWM) [66], the Sacramento Soil Moisture Accounting (SAC-SMA) model [67], the Xinanjiang Model [68], the Soil Moisture Accounting and Routing (SMAR) Model [69], the Precipitation-Runoff Modelling System (PRMS) [70], the HBV [71], the TOPMODEL [72], SWAT-series (US department of Agriculture, Agricultural research service), WaSiM-ETH [73] and HEC-series (US Army Corps of Engineers, Hydrologic Engineering Centre). These classes of models are in general limited in assessing the effect of land use and other changes in a basin. Also their applicability is limited to areas where runoff has been measured for some years and to places where no significant changes in catchment conditions have occurred over the period of simulation since model parameters that are calibrated, not measured, are assumed to remain constant.

Selection of rainfall-runoff model is the first step in the formation of regional model. The following criteria were considered in choosing the watershed model to be used in this dissertation:

• The model should not be complex and data intensive. Its data requirement should be addressed by the available observations and measurements within the study area.

• The model structure should schematize the most important runoff generating processes in a scientifically reasonable way.

• The model should not have too many model parameters. • The model should be known to be applicable to various basins in a wide range of

environmental conditions all over the world. To verify this criterion in the case study area or to check the performance of the model in mapping a relationship between rainfall and runoff, the selected rainfall runoff model should be calibrated and validated for runoff time series of gauged catchments.


44

3.3.1.3 Cluster analysis

The second branch in the development of regional model is the identification of hydrologically homogeneous group of catchments based on selected catchment characteristics. Hydrological homogeneous group of catchments can be defined as an open system consisting of basins that have a high degree of similarity from the point of view of hydrological characteristics and/ or catchment characteristics. If it is desired to transfer or extrapolate the results to ungauged catchments then it is obviously preferable to base clustering on measurable catchment characteristics, as hydrological records would not be available. Based on this fact, physical catchment variables like land use, soil, topographic features, etc, which potentially useful in the prediction of flow could be considered to cluster those catchments showing similarity in terms of catchment characteristics.

Cluster analysis is an unsupervised learning procedure that group names and number of groups are not known in priori. Classification differs from clustering since it is a supervised learning procedure in which group names and numbers of groups are known. Since the purpose of cluster analysis is to organize observed data into meaningful structures, it combines data objects into groups (clusters) such that objects belonging to the same cluster are similar as those belonging to different clusters are dissimilar [74]. Determination of the appropriate number of clusters to retain and its membership in each cluster is considered as one of the major unresolved issues in the cluster analysis and hence, the selected cluster analysis method should address this problem.

Geographically close catchments are not necessarily homogeneous in terms of hydrological response [75]. There are methods like L- moments technique, Ward’s cluster and K-means that are recommended by different researchers for identifying homogeneous regions. More recently, modern informatics tools, such as the fuzzy C-means method and artificial neural networks (ANNs), have been applied to form groups and to allocate ungauged catchments to an appropriate sub-region using site characteristics ([76] and [77]). These techniques may identify sub-regions that are not necessarily geographically contiguous. [78] compared four methods to delineate homogenous regions based on catchment characteristics for Gan River Basin, China. They have applied geographical approach (Residual methods), Ward’s cluster method, the Fuzzy C-means method and a Kohonen neural network (KNN) to 86 sites in the Gan River Basin in China. They have found similar groupings of sites into sub-regions all but the geographical approach (Residual methods). However, of the three techniques, only the KNN method provides an objective number of sub-regions as well as defining their membership and as such is to be preferred.

Therefore, in this dissertation, a regional model was proposed by combining distributed hydrological model and cluster analysis. Referring to Figure 3-2 above, next to the database component, the proposed regional model followed two branches, namely rainfall-runoff model and cluster analysis method. Rainfall-runoff model was set up for catchments in each group that were formed by cluster analysis to generate optimized watershed model parameters for the respective group. The necessary input data and output data of the regional model can be stored in the data base component. Details and its working principle of the proposed regional model will be discussed in section 3.3.2


45

and section 3.3.3 respectively. The proposed regional model will fill some of the gaps or challenges stated in the above three sections.

3.3.2 Proposed method of regionalization to the case study area

Based on the criteria and discussion set on section 3.3.1, the water balance simulation model (WaSiM-ETH) to map a rainfall-runoff relation and artificial intelligence (self-organizing map) to cluster watersheds into hydrological homogeneous group were selected to form a regional model for the case study area. Figure 3-3 depicts structure of the proposed methodology, which is the zoom in of the proposed general framework of decision support tool depicted in Figure 3-2, with the selected watershed model and cluster analysis included.

Figure 3-3 Structure of the proposed regionalized model


46

In the proposed regional model, self-organizing map (SOM) identifies the number of hydrological homogeneous groups and its members in each group based on pre-defined catchment characteristics. Member catchments in each group were further split into two sub-groups. Let members of the first sub-group called ‘calibration catchments’ and members of the second sub-group called ‘validation catchment’ in the same group (see Figure 3-3). One or more members ‘calibration catchment’ from each group were selected arbitrarily for calibration of WaSiM-ETH and the remaining members ‘validation catchment’ were reserved for validation of the regional model. If more than one member is involved in WaSiM-ETH model calibration, the selected members are calibrated simultaneously using automatic model parameter estimation method (PEST). Hence, rather than trying to establish a relationship between model parameters and catchment characteristics, which most previous researches based on, each group has its own full set of WaSiM-ETH model parameters called optimized WaSiM-ETH model parameters (OWPs). These full set of optimized (after calibration and validation of the regional model) WaSiM-ETH model parameters are stored in the data base component of the DST (see broken line along the OWPs in Figure 3-3), which could later be retrieved for ungauged catchments in the same group.

After calibration and validation of the regional model, flow from ungauged catchment can be generated by running once again the regional model for a new set of input (pre-defined catchment characteristics) data of the ungauged catchments. The trained SOM automatically assigned this ungauged catchment, depending on how the ungauged catchment’s characteristics hydrologically similar, to one of the pre-defined group. The whole set of optimized model parameters are then transferred from the group, where the ungauged catchment belongs to, to the ungauged catchment. Stream flow from the ungauged catchment, which can be used as an input flow or in between flow for the planned and/ or existing reservoir system, can then be generated using WaSiM-ETH model. Identification of ungauged catchment to one of the pre-defined groups, transferring the whole set of optimized model parameters and generation of flow from the ungauged catchments were handled in the same regional model and automatically launched sequentially once the appropriate input data of the ungauged catchment is supplied to the regional model. See section 3.3.3 for its working principle and chapter 4 for its application in the case study area. The following two sub-sections described mathematical background and adaptation of the selected model to the case study area.


47

3.3.2.1 Water balance simulation model (WaSiM-ETH)

Model concept and description of the model components Watershed models simulate hydrological processes by which precipitation is converted into stream flow. The output stream flow of a watershed model is amongst the basic input data required in many different types of water management modelling applications. For the case study area considered in this dissertation, river flow is one of the basic input data to reservoir simulation model that was used to support reservoir system operating decisions.

WaSiM-ETH [73] is a Water balance Simulation Model, which has both, physically based and conceptual model components. It is a distributed hydrological model that performs calculations per grid cell and per sub-basin. The spatial resolution of a grid cell can range from meters to kilometres with highest resolution in time for modelling hydrological processes is one minute. Because of the physical basis of many WaSiM-ETH components, the model can generally be applied to various basins in a wide range of environmental conditions all over the world [79].

WaSiM-ETH uses physically based algorithms for the majority of the process descriptions, like infiltration description, which is an integral part of the soil model, according to [80], estimation of saturation time according to [81] and solution of the 1-D Richards equation [82] for the description of the soil water fluxes in the unsaturated zone or Topmodel approach. In Topmodel approach option, the modelling of the soil water balance and of runoff generation is done using a modified variable saturated area approach after [83] extended by capillary rise and interflow. WaSiM-ETH has also interpolation facilities for the interpolation of meteorological data.

Depending on the availability of meteorological information, WaSiM-ETH uses different methods to compute potential evapotranspiration. Actual evapotranspiration is obtained by the respective reduction of potential evapotranspiration according to the actual soil moisture content. Interception is accounted for by a bucket approach. Surface runoff is calculated for each grid cell as sum of infiltration excess and snowmelt along the topographic gradient towards the next grid cell. WaSiM-ETH routs the channel flow by means of a translation module with a simple storage built in to account for diffusion. Groundwater dynamics is portrayed by a 2-D module or with an optional lumped conceptual approach. WaSiM-ETH is subdivided into several sub-models as depicted in Figure 3-4. Topmodel-approach for unsaturated flow and lumped conceptual groundwater approach for saturated flow were selected for the case study area due to lack of reliable information on soil and aquifer respectively.


48

Figure 3-4 Structure of the hydrologic model [WaSiM-ETH] (Modified from [79])

For most of the sub-models, WaSiM-ETH offers several alternative methods, which depends on the availability of input data to compute the same variable. A complete model description is given in [79]. The most important sub-models, which contains the most sensitive model parameters and relevant to this dissertation, are described below. Unless otherwise stated, the following methods and mathematical formula presented here are summarized from [79].

Potential evapotranspiration

There are three possibilities in WaSiM-ETH to compute potential evapotranspiration namely Penman-Monteith method [84] and [85], Wendling method [86] and Hamon method in [87]. In the Penman-Monteith method, many meteorological variables such as temperature, either water vapour pressure or relative humidity, global radiation, sunshine hour duration and wind speed are needed and by far this method would have been the best choice if all meteorological variables were available for the study area. For model runs using Wendling method, global radiation, which can be measured or estimated if sunshine hour duration is available, albedo and temperature are needed.


49

Hamon method requires average number of day light hours per day, which depends on latitude and solar declination and saturated vapour pressure, which intern is a function of temperature. In the case study area considered, where only temperature data are available as a long time series, the Hamon approach was chosen.

Potential evapotranspiration after Hamon in [87] can be computed as:

3.273Te7.216

12hf1651.0ETP sd

+⋅

⋅⎟⎠⎞

⎜⎝⎛⋅⋅= i (3.01)

T3.237T27.17

s e1078.6e +⋅

⋅= (3.02)

Where ETP potential evapotranspiration [mm/day] fi empirical factor, monthly value [-] (hd/12) day length [h] es saturation vapour pressure at temperature T [hPa]

T mean daily temperature [oC] The day length (hd/12) is calculated from the sunrise (or sunset) hour angle (As), which is determined by latitude (L) and solar declination (D) as follows [88]:

( )[ ][ ]

⎪⎪

⎭

⎪⎪

⎬

⎫

=

⋅−=+⋅=

90/As12h

)Dtan()Ltan(arccosAs365/dayJulian284360sin45.23D

d

(3.03)

It is always important to check all sub-models, which have empirical constants valid for areas where the sub-model was developed. The default empirical constants (see Table 3-1) in Hamon method (Equation 3.01) are valid for northern Switzerland [79]. The Hamon method was evaluated and compared with results of Penman-Monteith method using two years of daily meteorological data (see Table A-13 in appendix A). The comparison was first made using the default monthly correction factors involved in the empirical equation and then made using calibrated (modified) monthly correction factors. Monthly correction factors fi were calibrated by coupling WaSiM-ETH with PEST, which fits modelled potential evapotranspiration using Hamon method to potential evapotranspiration values in Penman-Monteith method. Table 3-1 presents the default and modified monthly correction factors of Hamon method. The modified empirical constant gave good results with a coefficient of determination R2 = 0.71 and R2= 0.93 for daily and monthly potential evapotranspiration respectively. Figure 3-5 shows results of potential evapotranspiration using default empirical constants and modified (calibrated) constants of Hamon method against the Penman-Monteith method. Table 3-2 depicts monthly potential evapotranspiration computed using Penman-Monteith method and Hamon method after modification of the correction factor.


50

Table 3-1 Default (northern Switzerland) and modified (case study area) monthly correction factors fi of Hamon method.

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Default fi 0.5 0.6 0.8 1.1 1.2 1.3 1.2 1.1 1.0 0.9 0.7 0.5 Modified fi 1.58 1.84 1.94 1.83 1.72 1.53 1.39 1.33 1.41 1.47 1.56 1.57

Figure 3-5 Comparison of daily ETP computed using Penman-Monteith and Hamon methods

Table 3-2 Two years daily mean monthly potential evapotranspiration using Penman-Monteith method and modified Hamon method

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2.97 3.21 3.43 3.59 3.31 3.00 2.48 2.66 3.07 3.20 3.05 2.90Penman 2.87 3.22 3.35 3.54 3.23 2.95 2.46 2.64 3.05 3.18 3.02 2.843.11 3.18 3.45 3.57 3.29 3.04 2.62 2.78 2.98 3.11 3.02 2.97Hamon 2.89 3.22 3.29 3.45 3.13 2.87 2.66 2.74 2.92 3.06 2.96 2.84


51

Topmodel-approach of WaSiM-ETH uses a relative reduction function of potential evaporation to compute actual evapotranspiration. Actual evapotranspiration is reduced compared to potential evapotranspiration if the content of the soil moisture storage drops below a specified level as follows. The threshold value for the soil moisture η is approximately taken as 0.6 after [89].

( )

⎪⎪⎭

⎪⎪⎬

⎫

≤≤=

<⋅⋅=

1.0SBSB0.6ETPETR

0.6SBSBSBηSBETPETR

max

maxmax

(3.04)

Where ETR actual evapotranspiration [mm] ETP potential evapotranspiration [mm] SB actual content of the soil water storage [mm] SBmax maximum capacity of the soil water storage [mm] η threshold value for the soil moisture ( η ≈ 0.6) Interception

Interception storage is defined as a storage of precipitation on vegetation and on the soil surface. A simple bucket approach is used with a capacity depending on the leaf area index, the vegetation coverage and maximum height of the water at the leafs as:

Where SImax maximum interception storage capacity [mm] υ degree of vegetation covering [m2/ m2] LAI leaf area index [m2/ m2] hSI maximum height of water at the leaf surfaces [mm]

As long as the interception reservoir contains water, actual evaporation equals potential evaporation and no evaporation will be taken from the soil. If the storage content is smaller than the potential evaporation rate, the remaining rate will be taken from the soil.

⎭⎬⎫

−=<==≥=

SIETPETR,mminETPSIforSIEI0ETR,mminETPSIforETPEI

(3.06)

Where EI interception evaporation [mm] SI content of the interception storage [mm]

( ) SISImax h1hLAISI ⋅−+⋅⋅= υυ (3.05)


52

Infiltration

WaSiM-ETH uses infiltration approach after [80] and estimation of saturation time after [81]. The time of saturation is first calculated and then the cumulated infiltration until the end of the time step. If the soil surface is saturated at the end of the time step, in the next time step only the cumulated infiltration will be calculated with out calculating the saturation time provided that the constant precipitation intensity is sufficiently high. The exceeding amount is surface runoff. Using a parameter xf (between 0 and 1) the amount of reinfiltrating water can be controlled, which may be important to consider in homogeneities of the soil properties in larger grid cells.

If PI > Ks the saturation time ts is calculated by:

( )PI

1KPIψ

PInlt s

f

ass

−=

⋅=

(3.07)

Where ts saturation time from the beginning of the time step [h] ls saturation depth [mm] na porosity ( an =Θ − Θs ) [-] ,sΘ Θ saturated and actual water content [-] fψ suction at the wetting front ( ≈ 1000 na) [mm] PI precipitation intensity [mm/h] Ks saturated hydraulic conductivity [mm/h]

The infiltrated amount of water up to this time Fs is given by:

PItnlF sass ⋅=⋅= (3.08)

The cumulated amount of infiltration F after saturation until the end of the time step is calculated after Peschke [90]by:

( ) fasss

21

2s

2

ψn2FB,ttKAwithFAB4

A2AF ⋅⋅+=−⋅=⎥

⎦

⎤⎢⎣

⎡+++= (3.09)

The exceeding amount of precipitation sFFtPI −−Δ⋅ is surface runoff QD,I.


53

Soil model (Topmodel-approach)

As it is noted in [79] the modelling of the soil water balance and of runoff generation is done using a modified variable saturated area approach after [83] extended by capillary rise and interflow. The calculation is done separately for each of the grid cells opposed to the modelling of classes of similar indices like in the original TOPMODEL. The base for the model is the spatial distribution of the topographic index sC . Using this index, the potential extent of saturation areas can be estimated depending on the mean saturation deficit within a basin:

ts

o t

aC lnT tanβ

= (3.10)

Where sC topographic index [-]

ta specific catchment area per unit length of a grid cell; this is the area draining through one meter of the edge of a grid cell [m2/m]

To saturated local hydraulic transmissivity (T0 = ∫ Ksdh) [m2/s] h depth [m] βt slope angle [m/m]

It is presumed that:

• the groundwater table is parallel to the topographic slope • the dynamics of the saturated zone can be approximated by subsequent quasi-

stationary states and • the local hydraulic transmissivity Th is an exponential function of the saturation

deficit S: mS

oh eTT−

⋅= The spatial distribution of saturated areas or more general the distribution of the saturation deficit can be found by:

ti m

o t

aS S m ln γT tanβ

⎡ ⎤= − ⋅ −⎢ ⎥

⎣ ⎦ (3.11)

Where: Sm mean saturation deficit of the basin (arithmetic average of all Si) [mm]

m recession model parameter [mm] γ mean topographic index of the (sub-) catchment

At places where Si is negative or zero any further liquid precipitation (or snowmelt) will immediately generate surface runoff. The mean saturation deficit is newly calculated in each time step as average value of all local saturation deficits from the previous time step and from the balance of all inflows into outflows a basin. After estimating all runoff components for the entire sub-basin, the new mean saturation deficit is calculated by:


54

SUZruck1-im,im, QQSS −+= (3.12)

Where: Sm,i spatially averaged saturation deficit in the actual time step i [mm]

Sm, i-1 spatially averaged saturation deficit in the previous time step i-1 [mm]

Qruck capillary rise as a mean value for the (sub-) catchment in the actual time step [mm]

QSUZ groundwater recharge from the unsaturated zone as a mean value for the (sub-) catchment [mm]

Surface runoff is created for each grid cell as the sum of infiltration excess along the topographic gradient towards the river. It is assumed that saturated hydraulic conductivity decreases dependent on soil texture with depth according to a recession constant. Surface runoff is routed to the sub-basin outlet by subdividing the basin into flow time zones. Flow time zones are zones of equal flow times for surface runoff to reach the sub-basin outlet. Retention is approached by applying a single linear storage to the surface runoff in the last flow time zone, with storage constant kD:

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅+⋅=

Δ−Δ−

−DD Kt

DK

t

1i,Di,D e1QeQQ (3.13)

Where QD,i transformed surface runoff in time step i [mm] QD,i -1 transformed surface runoff in time step i-1 [mm]

DQ∧

surface runoff in the time step I within the lowest flow time zone [mm] tΔ time step [h] KD single linear recession constant for surface runoff [h]

Interflow is calculated in defined soil layers, depending on suction, drainable water content, hydraulic conductivity and gradient for each grid cell separately and then averaged over space. The Topmodel-approach considers interflow using a conceptual approach. Like the surface runoff, the interflow storage is filled dependent on the local saturation deficit:

( ) maxin,SH SHSUZSQ −−= (3.14)

Where QSH,in interflow into the interflow storage [mm] S actual local saturation deficit [mm] SUZ content of the storage of the unsaturated zone [mm] SHmax maximum content of the interflow storage [mm] For considering retention of the interflow, a single linear storage is treated similarly as surface runoff with recession constant kH instead of kD in equation 3.13.

The vertical flow rate (percolation) can be computed as:


55

mS

skorrv

i

eKKq−

⋅⋅= (3.15)

Where qv vertical flow rate [mm] Kkorr scaling factor for considering unsaturated soils and preferred

flow paths [-] Si local saturation deficit [mm]

The base flow is calculated for each sub-basin as a whole:

m-S

γ-korr

m-S

lnTγ-B

mm

korr eeTeeQ ⋅⋅=⋅= + (3.16)

Where QB base flow [mm/time step] γ mean topographic index [-] Sm mean saturation deficit for a (sub-) basin [mm] m recession model parameter [mm] Tkorr transmissivities scaling factor [-] The summation of surface runoff for actual time step, which is the content of the lowest time zone, base flow and interflow yields the total runoff.

I. Model performance To run WaSiM-ETH, various spatially distributed data (grids), time series of meteorological and hydrological data and initial conditions are needed. Grid data includes digital elevation model, topographic index, land use map and soil map. Most of the other grid data sets can be derived from digital elevation model during pre-processing or during model initialization itself, like the data sets for aspect and slope angle using any GIS or the topographical analysis software TANALYS, which is a part of WaSiM-ETH pre and post processing software tools [79]. Digital elevation model (DEM), soil map and land use map, which were collected from Ethiopian MoWE, were used for the case study area.

Time series of meteorological data as station data are recorder in text files (see Figure A-1 in Appendix A for its format). Hydrological data are time series of observed discharges at river gauges that are required in order to calibrate the model and to evaluate the model performance. The format is identical with the format of meteorological station data, except in the second row that catchment area is used instead of altitude.

Initial conditions may be very important for the model results especially if applying the model to a short time period or to an arid or semi arid region. Therefore, there is a possibility in WaSiM-ETH to read storage or reservoir content values as initialization grids. Because these grids can also be written at the end of a model run, they can be used as initialization for following model runs. If no initialization grids are available, the internal states are initialized using constant values taken from the control file [79].


56

The control file contains the following three information. These information are usually mixed in the control file.

Three types of information in WaSiM-ETH control file are:

• parameters controlling the model run (grid write codes, statistic file write codes, output lists etc)

• file names and path names for the input and output streams • hydrologic model parameters, property tables (like for land use, soil types,

tracers), static model parameters The control file is subdivided into separate sections; each section is responsible for a sub-model, which can be activated or disabled by putting 1 or 0 respectively, or for a separate theme, like for an interpolation parameterization, or for the land use table.

WaSiM-ETH was applied at a spatial resolution of 90 by 90 m2 to check the performance of the model to generate daily stream flow for gauged rivers in the case study area. Hydro-meteorological data, land use and soil data were prepared as per the format of WaSiM-ETH through Arc-GIS and TANALYS. The snow accumulation component was disabled, as there is no snow in the study area. [79] describes the sensitivity of model parameters of each sub-models of WaSiM-ETH. Based on the sensitivity results of [79], the most sensitive model parameters are found in soil model (Topmodel-approach) and evapotranspiration component. Table 3-3 presents soil model parameters that were used during automatic calibration.

Table 3-3 WaSiM-ETH model parameters used during calibration

Parameter Description Unit m recession parameter for base flow [mm] Tkorr correction factor for the transmissivity of the soil [-] Kkorr correction factor for vertical percolation [-] kD single reservoir recession constant for surface runoff [h] SHmax maximum storage capacity of the interflow storage [mm] kH single reservoir recession constant for interflow [h] Pgren precipitation intensity threshold for generating preferential flow

into unsaturated zone [mm/h]

rk scaling of the capillary rise/refilling of soil storage from interflow [-]

With the exception of cmelt (fraction of snow melt model parameter), which is not valid for the case study area, the remaining 8 model parameters of the soil model of Topmodel-approach (see Table 3-3) were calibrated intensively by coupling WaSiM-ETH to automatic parameter estimation package PEST. PEST is a non-linear, model independent parameter estimation tool that uses two approaches. The standard method uses the Gauss-Marquardt-Levenberg algorithm. This method is fast and stable as it switches between the steepest gradient. The drawback of this method is that it might “get stuck” in local minima, depending on the surface of the error and the start values for the optimisation run. The second approach available in PEST is the global (Shuffled Complex Evolution-University of Arizona) SCE-UA search algorithm [91]. This


57

algorithm is capable of finding the global minimum of the objective function. It requires, however, substantially more effort in terms of computer processing unit time. The second approach was embedded in WaSiM-ETH for the case study area considered in this dissertation.

The universal applicability of PEST lies in its ability to perform the calibration for any model that reads its input data from one or a number of ASCII input files and writes the outcomes of its calculations to one or more ASCII output files [92]. PEST requires upper and lower bounds for adjustable model parameters; this information is vital to PEST, to inform PEST to the range of permissible values that a parameter can take.

PEST requires three types of input file [92]. These are:

• template files, one for each model input file on which parameters are identified, • instruction files, one for each model output file, on which model-generated

observation are identified, • an input control file, supplying PEST with the names of all template and

instruction files, the names of the corresponding model input and output files, the problem size, control variables, initial parameter values, measurement values and weights.

The calibration of the model was assessed by comparing measured and model output discharge at the selected gauged rivers using coefficient of determination (R2) and the Nash and Sutcliffe N-S [93] efficiency criteria, given by:

( )( )∑

∑−

−−=− 2

obsiobs,

i

2iobs,isim,

QQ

QQ1SN (3.17)

Where Qsim,i simulated discharge at time step i Qobs,i observed discharge at time step i obsQ mean observed discharge

To demonstrate the performance of WaSiM-ETH, two rivers namely Gilgel Abay and Gumera rivers in lake Tana sub-basin were selected. For these rivers, concurrent daily rainfall, temperature and discharge data from 1994 to 1997 were used for model calibration and from 1998 to 2002 were used for model validation. WaSiM-ETH’s model parameters were calibrated using PEST as described above. Discharge values for 1993 were used as a model warm up period. Table 3-4 presents optimized values of WaSiM-ETH model parameters for the two rivers.


58

Table 3-4 Optimized WaSiM-ETH soil model (Topmodel) parameters after calibration

Optimized WaSiM-ETH model parameters Rivers

m (10-2)

Tkorr (10-5)

Kkorr (102)

kD (102)

SHmax

kH (102)

Pgren

rk

Gilgel Abay 5.66 5.76 7.41 0.67 10 0.01 12 0.7

Gumera 4.28 6.5 48 4.96 5.80 0.94 1.3 1

The performance WaSiM-ETH was compared with soil water assessment tool SWAT2005 and HBV (Hydrologiska Byråns Vattenbalansavdelning) model. [94] have applied SWAT2005 hydrological model for prediction of stream flow of rivers in lake Tana sub-basin. The model was calibrated and validated using Sequential Uncertainty Fitting, Generalized Likelihood Uncertainty Estimation and Parameter Solution algorithms. [32] have used HBV model to map a relationship between rainfall and runoff and to regionalize the HBV model parameters to rivers in lake Tana sub-basin. Table 3-5 presents the performance of WaSiM-ETH, SWAT2005 and HBV model for the same case study area. Although it is difficult to say WaSiM-ETH performed better than the other two models due to the differences in calibration and validation periods, it is evident from Table 3-5, Figure 3-6, Figure 3-7 and Figure 3-8 that WaSiM-ETH performed well in both calibration and validation periods. Figure 3-6, Figure 3-7 and Figure 3-8 depict time series of observed and WaSiM-ETH model simulated daily, 10 days and monthly flow respectively at Gilgel Abay river gauging station during calibration and validation periods.

Table 3-5 Performance of the WaSiM-ETH, the HBV [32] and the SWAT2005 [94] hydrological models for two rivers in the Lake Tana sub-basin.

Gilgel Abay Gumera

N-S R2 N-S R2

Models Cal Val Cal Val Cal Val Cal Val WaSiM-ETH 0.79 0.78 0.80 0.78 0.73 0.70 0.72 0.71 HBV 0.85 0.77 - - 0.72 0.80 - - SWAT2005 using ParaSol

0.73 0.71 0.80 0.78 0.61 0.61 0.71 0.70

Cal = calibration, Val = validation


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Figure 3-6 Gilgel Abay observed and simulated daily discharge for calibration and validation period

Figure 3-7 Gilgel Abay observed and simulated 10 days discharge for calibration and validation period

Calibration Validation


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Figure 3-8 Gilgel Abay observed and simulated monthly discharge for calibration and validation period

Therefore, WaSiM-ETH was applied for the whole selected rivers in the Blue Nile river basin and the model performance criteria showed good agreement between observed and simulated daily, 10 days and monthly discharge.

3.3.2.2 Self-organizing maps or Kohonen networks

Kohonen neural network (KNN) also known as the self-organizing map (SOM) is a realistic, although very simplified, model of the human brain [95]. SOM is a non-linear mapping technique, which has the ability to learn without being shown correct outputs in sample patterns. It is unsupervised type of artificial neural network, which means that the network is presented with data but the correct output that corresponds to that data is not specified. It is more efficient with pattern association; serve as a clustering tool of high-dimensional data and for visualizing purposes.

SOM has been applied by many authors, including [96] and [97], for pattern recognition or classification. [98] used standard SOM for classifying flow conditions in the unsaturated zone. Their experiments resulted in a good correspondence between the SOM’s classifications and visual observation. The identification of catchments may be regarded as an example of the wider problem of classification of data sets. [76] indicated the feasibility of employing SOM for clustering of hydrological homogeneous regions. [78] have successfully applied SOM to delineate homogenous regions based on catchment characteristics. SOM in this dissertation is used to cluster hydrological homogeneous catchments based on catchment characteristics. As it will be explained in the application section in chapter 4, SOM is presented with 16 physical catchment characteristics in the input layer designated as xr in Figure 3-9a.


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Figure 3-9a depicts the architectural structure of SOM that consists of components called input nodes or neurons and map nodes. Associated with each input node is a weight vector of the same dimension as the input data vectors that connect to each map node and a position in the map space. None of the map nodes connects to each other. The weights of the neurons are initialized either to small random values or sampled evenly from the subspace spanned by the two largest principal component eigenvectors.

Training of SOM occurs in several steps and in many iterations. First each node’s weights are initialized, initial weight was taken as 0.35 for the case study area and then a vector is chosen at random from the set of training data and presented to the net. 16 catchment characteristics of the selected 26 catchments were used in the input layer (see Table A-1). Every node is examined to calculate which one’s weights are most like the input vector. The winning node is commonly known as the Best Matching Unit (BMU). Figure 3-9b displays the neuron with the BMU for an arbitrary input signal xr . The radius of the neighbourhood of the BMU is calculated. Any nodes found within this radius are deemed to be inside the BMU’s neighbourhood. Each neighbourhood node’s weights are then adjusted to make them more like the input vector. The closer a node is to the BMU; the more its weights get altered. This whole process is then repeated for a large number of times.

(a) (b)

c

xr

Figure 3-9: Structure and basic principle of rectangular topology of SOM

Figure 3-9a shows SOM of 3 × 3 map nodes connected to the input nodes in the input layer, which representing a two dimensional vector. Each map node has a specific topological position and contains weight vectors of the same dimension as the input vectors. A (n+m) dimensional weight vector ( )mn1nn1 m...m,m...mm ++=ϖ is assigned to each neuron, where ( )n = dim xr and m = dim(y)r denote the dimensions of the sample input and sample output, respectively. SOM does not need a target output to be specified unlike many other types of network. The following section provides theoretical description of the steps involved during SOM training. Actual values of each parameters like initial weight, initial neighbourhood size, learning rate and number of iterations that have been used for the case study area were presented in the next chapter.


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Generally, SOM is trained iteratively. Each iteration k involves an unsupervised training step using a new sample vector SOMxρ and weight vectors imϖ as follows:

Initializing the weight vectors: Prior to training, each node’s weights must be initialized. Typically these initial weight vectors imϖ will be set to small standardized random values.

Search for the Best Matching Unit At each iteration, k, one single sample vector ( )kxSOM

ρ is randomly chosen from the input data set and its distance iε to the weight vectors of SOM is calculated by:

( )( )∑+

=

−=mn

1j

2ji

jSOMi mkxε (3.18)

The neuron whose weight vector mi is closest to the input vector ( )kxSOM is the "winner", i.e. the BMU, at c, see Figure 3-9b, represented by the weight vector ( )kmc

ϖ , which is the smallest of the Euclidean distance.

Determining the BMU’s local neighbourhood After the BMU has been determined, the next step is to calculate which of the other nodes are within the BMU’s neighbourhood. All these nodes will have their weight vectors altered/ updated in the next step. A unique feature of the Kohonen learning algorithm is that the area of the neighbourhood reduces over time. Figure 3-10 shows how the neighbourhood radius reduces over time (the figure is drawn assuming the neighbourhood remains centred on the same node, in practice the BMU will move around according to the input vector being presented to the network). This can be accomplished by making the radius of the neighbourhood converge over time. The convergence depends on the function of the neighbourhood radius ( )kσ . A common choice is an exponential decay described by [99]:

The initial neighbourhood size should begin with a relatively high number sometimes even close to the number of neurons in the output layer. For the case study area considered in this dissertation, initial neighbourhood radius of 13, which is 90 % of the number of neurons in the input layer, was taken as it was suggested in the NeuroShell13 help menu.

13 http://www.wardsystems.com/

( ) ( ) maxkk

e0σkσ−

⋅= (3.19)


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Figure 3-10 The decrease in neighbourhood radius over time

Adjusting the weights: If a node is found to be within the neighbourhood then the weight vector of this node and the BMU are updated. The rule for updating the weight vector of unit i is given by:

Where k denotes the iteration step of a training procedure, ( )kαs the learning rate at step k and

( )khci the so-called neighbourhood function, which is valid for the actual BMU at c.

The neighbourhood function is a non-increasing function of k and of the distance cid of unit i from the BMU at c. The Gaussian function is widely used to describe this relationship:

( ) ( )k2σd

ci2

2ci

ekh−

= (3.21)

Where σ is the neighbourhood radius at iteration k and icci rrd ϖϖ−= is the distance between map units c and i on the map grid.

The learning rate ( )kαs should also vary with the increasing number of training steps in the same way as indicated in equation 3.19. [100] suggested starting at an initial value

( )0αs with a value close to 1 and then to decrease gradually with an increasing number of training steps k. Initial learning rate of 0.5 was taken for the case study area. The cooperation between neighbouring neurons - a unique feature of SOM algorithm - ensures a fast convergence and a high accuracy in approximating functional relationships. Even

( ) ( ) ( ) ( ) ( )[ ]kmkxkhkαkm1)(km icisii SOM

ϖϖϖϖ −⋅⋅+=+ (3.20)

c c


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though the exponential decays described in equation 3.19 for the neighbourhood radius ( )kσ and the learning rate ( )kαs are purely heuristic solutions; they are adequate for a

robust formation of the self-organizing map [100] . Figure 3-11 shows how the shape of the pattern changes at different iterations in SOM training14.

(a) (b) (c) (d)

Figure 3-11 (a) initial iteration, (b) after 100 iteration, (c) after 200 iterations and (d) after 500 iterations

NeuroShell, which uses SOM module to process a data file through trained neural network and to produce the network’s classifications for each pattern in the file, was selected to cluster hydrologically homogeneous groups in the case study area. The SOM network used in NeuroShell is a type of unsupervised network, which has the ability to learn without being shown correct outputs in sample patterns. These networks are also able to separate data into a specified number of categories. Procedure and application of NeuroShell to the case study area can be found in section 3.3.3 and chapter 4 respectively.

3.3.3 Working principle of coupled WaSiM-ETH and NeuroShell

The selected watershed model, WaSiM-ETH, and self-organizing map, NeuroShell, were coupled to estimate flow in ungauged catchments. Figure 3-12 depicts the flow chart of the coupled model. Using NeuroShell, SOM was trained for selected physical catchment characteristics of gauged rivers in the case study area. These physical catchment characteristics of gauged rivers includes land use map, soil map and DEM and its derivatives, which are also readily available for ungauged catchments. These characteristics are presented to NeuroShell in the input layer and then propagated to the output layer. The neuron in the output layer is evaluated and then the network’s weights are adjusted during training as described in the above section. This process is repeated for all patterns for a number of epochs chosen. One output neuron is the winner. This winner neuron, in our case catchments that are hydrologically similar to each other with respect to the selected physical catchment characteristics, can have a value of one, and all others 0, or the actual values can be extracted from the output layer. Number of groups (say group 1, group 2, etc) and member of catchments in each group can be extracted from the output file. How well SOM classifies data depends on how well we set the parameters like number of epochs, neighbourhood size, initial weight and learning rate. 14 www.generation5.org/content/selforganize.asp


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The trained SOM in NeuroShell along with the number of groupings and its member catchments were saved in the data base component of the proposed DST.

Figure 3-12 Framework of the coupled WaSiM-ETH and SOM models

After the completion of training SOM, which cluster hydrological homogenous groups together, catchments in each hydrologically homogeneous group were split into ‘calibration catchment’ to calibrate WaSiM-ETH model parameters using PEST and ‘validation catchment’ to validate the regional model. That means each hydrologically homogeneous group has its own full set of optimized (calibrated) WaSiM-ETH model parameters and stored in the DST (see the next chapter for its application and results in the case study area).

For its application in ungauged catchment, the same selected physical catchment characteristics of gauged catchments were used in the input layer of trained SOM (see the red broken line in Figure 3-12 above). The trained SOM assigned the ungauged catchment into one of the hydrologically homogeneous groups formed previously, depending on how the physical characteristics of the ungauged catchment similar to one of the groups. Then the coupled model transfer the whole set of optimized WaSiM-ETH’s model parameters from the winner homogeneous group (which the ungauged


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catchment belongs to) to the ungauged river and WaSiM-ETH eventually generate daily flow for this ungauged catchment. A small program in Visual Basic (Microsoft Access) was written to facilitate the above procedure. The following steps illustrate the procedure to use the regional model to generate flow for any ungauged catchment in the case study area.

Steps: 1. Prepare WaSiM-ETH’s control file and run WaSiM-ETH for the ungauged

catchment with any dummy model parameters. 2. Physical catchment characteristics like catchment area, slope, elevation etc,

dominant land use and dominant soil type of the ungauged catchment have to be extracted from GIS layers and filled on the form as shown in the Figure 3-13 of the regional model.

3. After completing all the necessary input data in the input form and successfully run WaSiM-ETH with dummy model parameters, click on ‘Determine To Which Homogeneous Region this River Belongs to’ button. At this stage, the trained SOM will run at the background and assign this ungauged river into one of hydrologically similar groups based on how close the input characteristics of the ungauged catchment to those groups formed previously.

4. By clicking the ‘OK’ button, the coupled program will copy the whole set of optimized model parameters from the selected similar groups on step 3 to the ungauged catchment.

5. Tick the box against ‘Measured Data Available’ label which opens a dialog box to browse measured data file name if there is any. Otherwise Click on ‘Please click here to start calculation’ button.

6. Click on ‘Start running WaSiM’ button that will generate runoff for the ungauged catchment.


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Figure 3-13 Input form of the coupled program

Reservoir simulation-optimization model component

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3.4 Reservoir simulation-optimization model component

3.4.1 General

In the planning and design of water resource systems comprising a large number of reservoirs, it is necessary to optimize the operation of the entire system rather than to consider the reservoirs separately. Ideally, the reservoirs in a system should be designed and operated together to maximize net social benefits. The coordinated operation of a multiple reservoir system, to maximize the net benefit or to minimize the total deficits of the system, is a complex decision-making process.

Reservoir simulation models are effective tools to study the operation of complex physical and hydrological characteristics of a reservoir system including the experience and judgment of operators. One application of reservoir simulation modelling involves studies made specifically to re-evaluate operating policies for existing reservoir systems, which are intended to guide and manage the reservoir system so that the release made is in the best interests of the system. Reservoir simulation models are also used in allocating storage capacity and stream flow between multiple uses/users, minimizing the risks and consequences of water shortages and flooding, optimizing the beneficial use of resources (water, energy, and land), and managing environmental resources. However, since they are limited to predict the performance of a reservoir for a given operation policy (operation rule), optimisation models have an advantage in being able to search for the optimum policy from an infinite number of feasible operation policies that are defined through decision variables.

Optimization is a procedure of finding and comparing feasible solutions (operating rules) until no better solution can be found. When an optimization problem in modelling a physical system involves only one objective function, the task of finding the optimal solution is called single-objective optimization. When an optimization problem involves more than one objective function, the task of finding one or more optimum solutions is called multi-objective optimization, also know as vector optimization. A significant portion of research and application in the field of optimization considers a single objective, although most real world problems involve more than one objective. There exist single-objective optimization algorithms that work by using direct-based and gradient-based search techniques. In addition to deterministic search principles involved in an algorithm, there also exist stochastic search principles, which allow optimization algorithms to find globally optimal solutions more reliably.

Many problems in the field of water resources nowadays concern themselves with the goal of an optimal solution. Various optimization methods have, therefore, emerged, being researched and applied extensively to different optimization problems. For small-scale problems, exact solution methods such as linear programming can be used effectively. When the problems are large and complex like in multi-objective multi-reservoir systems, however, heuristic methods have to be called into play due to the exponential growth of the search space and the time required to find optimal or near optimal solution. Over the past few decades, researchers have proposed many novel nature inspired heuristic methods such as evolutionary algorithms (EAs) for optimization design based on specific domain knowledge.


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In coupled simulation-optimization model, optimization models make decisions based on the benefit achieved for system objectives over time, whereas simulation models demonstrate the outcome of the proposed rules, and allow small adjustments to target the outcome achieved by the optimization.

In this dissertation, coupled reservoir simulation-optimization approach is developed to generate different optimal solutions (reservoir operating rules) for multi-purpose multi-reservoir system. Because this research focused on multi-purpose multi-reservoir operation system, the selected optimization model should not only be able to handle the trade-off between different water users but also be multi-dimensional.

The proposed coupled reservoir simulation-optimization model begun with the necessary input data for the reservoir simulation model like inflow to each reservoirs, inflows between cascaded reservoirs called in-between flows, open water evaporations, areal precipitations, water demands, reservoir characteristics etc, which were stored in the database component of the proposed DST. Different modules of the selected simulation model should be checked with random initial operation rules to test its capability to handle problems of multi-purpose multi-reservoir system.

The actual cycle of the coupled reservoir simulation-optimization model starts when the results of randomly generated initial operating rules are not met the objective functions. In this case, the optimization model generates new set of operation rules and supply to the simulation model. Again, the results of these new generations of operating rules are evaluated against the objective functions. That means, the selected optimization model suggests operating rules and the simulation model tests these rules against the pre-defined objective functions. This process may involve several cycles of optimization and simulation runs until one of the termination criteria is satisfied.

3.4.2 Definition and formulation of Multi-objective optimization problems

Multi-objective Optimization Problem (MOP) (also called multi-criteria optimization, multi-performance or vector optimization problem) can be defined (in words) as the problem of finding a vector of decision variables, which satisfies constraints and optimizes a vector function whose elements represent the objective functions [101]. These functions form a mathematical description of performance criteria that are usually in conflict with each other. Hence, the terms “optimize” means finding such a solution, which would give the values of all the objective functions acceptable to the decision maker.

The general MOP can be formally defined as: find the vector ηz...,,z,zZ 21= , which will satisfy J inequality constraints, K equality constraints and will optimize the vector function ( ) ( ) ( ) ( )( )Zf,...Zf,ZfZf M21= .


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A multi-objective optimization problem has a number of objective functions (M). The problem usually has a number of constraints, which any feasible solution must satisfy.

The following is general form of multi-objective optimization problem.

( )( )( )

( ) ( )

m

j

k

L ui i i

Minimize/ Maximize f , m =1,2,....,M;

Subject to g 0, j = 1,2,...., J;

h = 0, k = 1,2,....,K;

, i = 1,2,......, .

Z

Z

Z

z z z η

⎫⎪

≥ ⎪⎬⎪⎪≤ ≤ ⎭

(3.22)

For the case study considered in this dissertation, a solution vector Z refers to decision variable that contains monthly optimum reservoir target level (storage). Two objective functions (M= 2) i.e. minimizing irrigation water supply deficit and maximizing hydropower production were considered (see Equation 3.39 and Equation 3.40). A minimization problem can easily be converted to a maximization problem by multiplying the objective function by -1 [102]. Associated with the problem, there are J inequalities, e.g. reservoir target level should always be greater than dead storage level of the reservoir and K equality constraints, e.g. the released public water supply, which considered as the highest priority demand in the case study area is always equal to the demand. The terms ( ) ( )j kg Z and h Z are called constraint functions. The last sets of constraints are called variable bounds. Five constraints mainly related to reservoir release capacity (q) of each reservoir, which is a function of reservoir level and variable bounds, restricting each decision variable zi to take a value within a lower

( ) ( )L ui iz and an upper z bound (see Equation 3.38). These variable bounds constitute a

decision variable space, or simply the decision space. A solution Z that does not satisfy all the constraints and all variable bounds stated above is called an infeasible solution. On the other hand, if any solution Z satisfies all constraints and variable bounds is known as feasible solution. Therefore, in the presence of constraints, the entire decision variable space need not be feasible.

The presence of multiple conflicting objectives (such as simultaneously minimizing the flood damage or minimizing irrigation deficit and maximizing hydropower (energy) output) is natural in many water resources problems and makes the optimization problem interesting to solve. Since no solution can be termed as an optimal solution to multiple conflicting objectives, the resulting multi-objective optimization problem resorts to a number of trade-off optimal solutions from which the decision maker will select one with the addition of high level qualitative information.

Z is called pareto optimal, if no feasible vector of decision variables exists, which would decrease some criterion without causing a simultaneous increase in at least one other criterion. Unfortunately, this concept usually gives not a single solution, but rather a set of solutions called the pareto optimal set. The vectors Z corresponding to solutions included in the pareto optimal set are called non-dominated solutions, which describes the optimal trade-off solutions between the objectives. Plot of objective functions whose non-dominated vectors are in the pareto optimal set is called the pareto front. Figure 3-14 illustrates the situation in objective space for a minimization problem of objective


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function F1 and F2. The blue points correspond to non-dominated solutions and make up the so-called pareto front. The red point corresponds to a solution that is dominated by at least one of the solutions corresponding to the pareto-front. The ultimate objective of multi-objective optimization problem is to produce such pareto front, which contains non-dominated solution so that decision makers or users can make better decision for different combinations of objective functions (see Figure 5-6 to Figure 5-9 for the case study).

Figure 3-14 Typical pareto front for two objective functions

3.4.3 Solution methods for multi-objective reservoir operation problems

3.4.3.1 Conventional method

Numerous traditional/conventional and Evolutionary algorithms exist for solving multi-objective problems. Amongst others, here are some of classical or conventional methods: utility functions, indifference functions, the lexicographic approach, weighted approach, ε-constraint approach, goal programming approach, goal attainment method, adaptive search method, interactive approaches, ELECTRE method, the surrogate worth trade-off method etc. [103] have used weighted and constraint approaches for multi-objective analysis and reported that the weighting method fails, when the non-inferior set is not convex, but the constraint method is able to generate the entire non-inferior set. [104] have applied multi-objective dynamic programming model for analyzing a reservoir operation problem, involving three conflicting objectives. [105] and [106] analyzed the tradeoffs for multiple objectives planning through linear programming. [107] used ELECTRE method for ranking of river basin planning alternatives in a multi criterion environment. Various solution techniques to handle multiple objectives have been reviewed by [108]. A comprehensive comparison of single and multi-objective problems, classical optimization algorithms and evolutionary algorithms are reviewed in a book by [109].


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Almost all classical direct and gradient-based optimization methods suggest converting multi-objective optimization problem to a single-objective optimization problem by emphasizing one particular pareto-optimal solution at a time. When such a method is to be used for finding multiple solutions, it has to be applied many times, finding a different hopefully better solution at each simulation run. For instance, the weighted sum approach suggests minimizing a weighted sum of multiple objectives, the є-constraint method suggests optimizing one objective function and use all other objectives as constraints, the value function method suggests maximizing an overall value function (or utility function) relating all objectives, and goal programming methods suggest minimizing a weighted sum of deviations of objectives from user-specified targets.

These conversion methods result in a single-objective optimization algorithm. In most cases, the optimal solution to the single-objective optimization problem is expected to be a Pareto-optimal solution. These proofs make classical multi-objective optimization algorithms interesting [109]. On the other hand, in their practical use each of these algorithms may have to be used many times, hopefully each time finding a different Pareto-optimal solution. Moreover, each of these classical methods requires some knowledge about the problem and involves a number of user-defined parameters, which are difficult to set in an arbitrary problem. Such a solution is also specific to the parameters used in the conversion method. In order to find a different Pareto-optimal solution, the parameters must be changed and the resulting new single-objective optimization problem has to be solved again. Thus, in order to find N different Pareto-optimal solutions, at least N different single-objective optimization problems need to be formed and solved. Even after forming N single-objective optimization problems and solving them, some algorithms do not guarantee finding solutions in the entire Pareto-optimal region.

Classical/ conventional optimization methods are inconvenient to solve multi-objective optimization problems. Evolutionary algorithms (EAs), on the other hand, can find multiple optimal solutions in one single simulation run due to their population-approach. Thus, EAs are ideal candidates for solving multi-objective optimization problems [109]. Evolutionary algorithms are relatively new, but very powerful techniques used to find solutions for many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run.

Over the past decade, a number of multi-objective evolutionary algorithms (MOEAs) have been suggested. Since evolutionary algorithms (EAs) work with a population of solutions, a simple EA can be extended to maintain a diverse set of solutions. With an emphasis for moving toward the true Pareto-optimal region, an EA can be used to find multiple Pareto-optimal solutions in one single simulation run.


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In this dissertation, HEC-5 reservoir simulation model and evolutionary algorithm were integrated to generate many optimal solutions (pareto-front) for multi-objective multi-reservoir system operations of the case study area.

3.4.3.2 Evolutionary algorithms (EAs) method

As it was discussed above, the classical way to solve multi-objective optimization problems is to follow preference-based approach, where a relative preference vector is used to scalarize multiple objectives. However, over the last few years there have been a number of non-classical, stochastic search and optimization algorithms. Of these, the evolutionary algorithms, which are stochastic search methods, mimic nature’s evolutionary principles to derive their search towards an optimal solution. Since a population of solutions is processed in each iteration, the outcome of an EA is also a population of solutions. If an optimization problem has a single optimum, all EA population members can be expected to converge to that optimum solution. However, if an optimization problem has multiple optimal solutions, an EA can be used to capture multiple optimal solutions in its final population. This ability of an EA to find multiple optimal solutions in one single simulation run makes EAs unique in solving multi-objective optimization problems.

Unlike classical optimization methods, EAs operate on population of potential solutions applying the principle of survival of the fittest to produce better and better approximations to a solution. The artificial creatures in EAs, known as individuals, are typically represented by fixed length strings or vectors. Each individual encodes a single possible solution to the problem under consideration. For a typical reservoir operation problem, in order to use EA to search optimum operating rules, each of reservoir releases (genes) can be encoded as binary string or real value. Concatenated these values gives a string/ chromosomes.

Figure 3-15 depicts simple structure of evolution algorithm. EA is started with an initial population comprising individuals that are initialized randomly (that is, each value in every string is set using a random number generator). The objective function is then evaluated for these individuals. Every individual is then assigned a fitness value. Population members with high fitness scores, therefore, represent better solutions to the problem than individuals with lower fitness scores. Following this initial phase, the main iterative cycle of the algorithm begins. Individuals are selected according to their fitness for the production of offspring. Parents are recombined to produce offspring. All offspring will be mutated with a certain probability to keep the diversity of the population. The fitness of the offspring is then computed. The offsprings are inserted into the population replacing the parents, thus, producing a new generation. This cycle is performed until the optimization criteria are reached.


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Figure 3-15 Simple structure of evolutionary algorithm

There have been three main independent implementation instances of EAs: (1) genetic algorithms (GAs), developed by [110] and thoroughly reviewed by [111]; (2) evolution strategies (ESs), developed in Germany by [112] and [113]; and (3) evolutionary programming (EP), originally developed by [114] and subsequently refined by [115]. Each of these three algorithms has been proved capable of yielding approximately optimal solutions given complex, multimodal, non-differential, and discontinuous search spaces.

These algorithms are broadly similar, yet there are significant differences. All operate on fixed length strings, which contain real values in ESs and EP and binary numbers in the canonical GA. All algorithms incorporate a mutation operator: for ESs and EP mutation is the driving force. GAs and ESs also use a recombination operator, which is the primary operator for the GA. All three use a selection operator which applies evolutionary pressure, either extinctive (in ESs and EP, the operator determines which individuals will be excluded from the new population) or preservative (in the GA the operator selects individuals for breeding). In GAs and EP selection is probabilistic, while ESs uses a deterministic selection. ESs and meta-EP allow self-adaptation, where parameters controlling mutation are allowed to evolve along with object variables. More formal descriptions are given by [116], [117], and [115].

Good surveys of evolutionary algorithm methods for multi-objective functions include in [119], [119] and [120]. Comparisons of several evolutionary approaches are given in [121], [122] and [123].

In application to water resource problems, infeasible chromosomes may be generated that fail to satisfy the system constraints, such as continuity and component capacities. Each generated chromosome must, therefore, be checked against the system constraints.


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Chromosomes failing to meet the constraints could be excluded from subsequent participation in the evolutionary process, but this may lead to useful genetic material being lost. Alternatives to exclusion are successive regeneration of chromosomes until they meet constraints, or application of a penalty function to reduce the fitness of chromosomes failing to meet constraints. Many argue that the former approach, adopted by [125], disrupts the GA process and in effect requires many additional generations [125]. Constrained multi-objective optimization is important from the point of view of practical problem solving, but not much attention has been given so far in this regard among the EA researchers.

State of the art of multi-reservoir operation models Few works has been found in the application of GA for multi-reservoir operating problems. The research by [125] applied a GA to four– reservoir problem. The objective was to maximize the benefits from power generation and irrigation water supply, subject to constraints on storages and releases from the reservoirs. [127] applied GA to the reservoir system operation and compared the performance of the GA approach with that of DP. It was concluded that GA performs better than the DP model. [127] used a GA model to evaluate operating rules for multi reservoir systems, demonstrating that GA can be used to identify effective operating policies. [128] expressed that the GA approach is robust and can be easily applied to a reservoir system operation problem. They evaluated GAs for optimal reservoir system operation using the four-reservoir problem, deterministic, finite-horizon problem with a view to presenting fundamental guidelines for implementation of the approach to practical problems. [129] applied genetic algorithm for the optimization of multi-reservoir system in Indonesia (Brantas Basin), by considering the existing development situation in the basin and two future water resource development scenarios over a 36 ten-day periods and proved that the GA was able to produce solutions very close to those produced by DP.

[89] applied successfully special variant of Evolutionary strategies, the Covariance Matrix Adaptation (CMA) to the design of 3D turbine blade optimization. [130] proposed a new approach using genetic algorithm (GA) and linear programming (LP) to determine operational decisions for reservoirs of a hydro system throughout a planning period. [131] applied the same algorithm on part of the Roadford Water Supply System, UK, and the performance of the approach were well comparable with RELAX algorithm. [132] applied NSGA-II to multi-reservoir system optimization. They set two objective functions and three cases having different constraint conditions to achieve non-dominated solutions. [133] proposed and applied a real coded hypercubic distributed genetic algorithm for optimizing operation system. The proposed algorithm were tested to the four-reservoir operation system and applied successfully in the planning of multi-reservoir system in northern Taiwan. [134] developed a hybrid evolutionary search algorithm, which combines GAs and the simulated annealing (SA) to optimize the classical single-criterion operation of multi-reservoir systems. They have concluded that the proposed hybrid algorithm has the ability of addressing large and complex problems and is a new promising search algorithm for multi-reservoir optimization problems. [135] compared the performance of multi-objective CMA-ES (MO-CMA-ES) with three other major simulation optimization algorithms for solving high dimensional multi-objective optimization problems in water resources. Results showed MO-CMA-ES performed well.


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3.4.4 Proposed coupled reservoir simulation-optimization model to the case study area

Figure 3-16 presents general framework of the proposed combined reservoir simulation and optimization models for the case study area, which is part of the proposed DST depicted in Figure 3-2.

Figure 3-16 Structure of the proposed reservoir simulation and optimization models for multi-purpose multi-reservoir system operation

Taking in to considerations of the high performance of single objective CMA-ES (SO-CMA-ES) and MO-CMA-ES for the benchmark function tests and its application in real world optimization problems, both algorithms were chosen as state of the art algorithm in this dissertation. Therefore, HEC-5 as a reservoir simulation model and SO-CMA-ES and MO-CMA-ES as optimization models were selected for the case study. HEC-5, developed by the Hydrologic Engineering Centre of the U.S. Army Corps of Engineers [136], is one of the most widely used public-domain reservoir simulation model for a


77

complicated multi-reservoir system. HEC-5A is flexible to be embedded into an optimization models and provide a detailed and realistic representation of a water resource system [127] but require pre-determined rule curves. CMA-ES is an evolutionary algorithm that can deal with many complexities such as multi-objective, non-linearity, discontinuity and discreteness, which limit the application of traditional optimization methods. The combination of HEC-5 and CMA-ES can overcome the difficulty of pre-defined operating rules for complex multi-reservoir systems.

3.4.4.1 HEC-5 reservoir simulation model

HEC-5A Simulation of Flood Control and Conservation Systems computer program was developed by [136] to simulate the operation of multi-purpose, multi-reservoir systems for flood control, water supply, hydropower and in-stream flow maintenance for water quality control. The model can perform investigations of storage allocations and other operational modifications at existing reservoirs as well as feasibility studies for proposed new projects. Multi-reservoir operating policies are based on the rule curves of each reservoir and the principles of index balance and equivalent reservoirs.

HEC-5 reservoir simulation model is designed to perform sequential reservoir operation based on specified project demands and constraints. Reservoir model data are defined starting at the upstream boundaries of the system and data for each location are entered sequentially downstream. Non-reservoir locations are called control points (CP), where flow constraints and demands can be specified. Demands, which include minimum channel flows, diversion requirements and energy requirements, can be specified at the reservoir and at downstream locations. The program can handle two types of constraints; physical reservoir constraints, which include available storage for flood control and conservation purposes and maximum outlet capacity; and operational constraints that include maximum non-damaging flows and reservoir release rate of change. The entire reservoir system, based on reservoir and control point data, is defined in an ASCII (text) data file (see sample HEC-5 control file in Appendix B). Detail input data description is provided in the HEC-5 user’s manual.

HEC-5 simulates multiple-purpose multiple-reservoir systems on essentially any stream tributary configuration using a variable computational time interval. The model makes release decisions to empty flood control pools and to meet user-specified diversion, in-stream flow, and hydroelectric energy targets, based on computed reservoir storage levels and flows at downstream locations. Multiple-reservoir release decisions are based on balancing the percent depletion in user-specified storage zones. Several alternative hydrologic flood routing methods are available.

Typical multipurpose reservoirs consist of three pools: a flood control pool, a conservation pool, and an inactive pool as is shown in Figure 3-17. The flood control pool is normally kept empty to permit storage of runoff during times of high inflow. However, the releases should not exceed the downstream channels capacity. The conservation pool is storage for one or more of the following purposes: hydropower generation, navigation, water supply, irrigation etc. The inactive pool is generally not available to meet downstream water needs. This storage is normally set aside for hydropower head, recreation, assure minimum level for pump diversion and/or to store the sediment expected to accumulate over the life of the project.


78

The conservation pool can further be divided into two or more pools called buffer pools (zones) depending on the priority demand. Buffer storage may be required for one of the two reasons. First, it may be used in multi-purpose projects to continue releases for a high priority demand when normal conservation storage has been exhausted by supplying water for both high and low priority demands. Second, it may be used in a single purpose project to continue releases at a reduced rate after normal conservation storage has been exhausted by supplying water at a higher rate. In either case, the boundary between the normal conservation and buffer storage is used to change the operation criteria. The proper location of this boundary and its seasonal variation are important.

Figure 3-17 Different storage zone used in HEC-5 reservoir simulation model

The number of storage zones are defined on the first Job Record (J1 see sample HEC-5 control file in Appendix B) for all reservoirs in the model. Actual storage allocated to each level is defined with the reservoir data, on the RL Record. RL Records at conservation zone and buffer zone can be specified as constant or may vary seasonally. During the optimization process, the RL Records are changed many times until the objective is met.

Operational control points are specified on the RO Records. Each reservoir operates for its own requirements and for only those downstream control points specified on the RO Record. Other reservoir model data include; reservoir outlet capacities, reservoir areas, elevations and diversions as a function of reservoir storages (RS Records) can be specified in RQ, RA, RE and RD Records respectively. A net evaporation depth, which is the difference between reservoir’s open water evaporation and areal precipitation on the reservoir, are specified in RE Records. When precipitation exceeds the evaporation there is a net gain to the reservoir (which in this case the net evaporation will be negative in RE Records). Reservoir model data at each hydropower reservoir includes installed capacity, an overload ratio, a tail water elevation, efficiency, plant factor and monthly energy requirements (defined in the P1, P2 and PR Records).


79

3.4.4.2 Optimization of reservoir operation

I. Single objective CMA-ES The CMA-ES (Covariance Matrix Adaptation Evolution Strategy), a special variant of Evolution Strategies, is an evolutionary algorithm for real parameter optimization of difficult non-linear, non-convex optimization problems in continuous domain. The CMA-ES is one of the most powerful evolutionary algorithms for real-valued single objective optimization [137] with many successful applications (for an overview see [138]).

The main advantages of the CMA-ES lie in its invariance properties, which are achieved by carefully designed variation and selection operators, and in its efficient (self-) adaptation of the mutation distribution. The CMA-ES is invariant against order preserving (i.e. strictly monotonic) transformations of the fitness function value and in particular against rotation and translation of the search space-apart from the initialization. If either the strategy parameters are initialized accordingly or the time needed to adapt the strategy parameters is neglected, any affine transformation of the search space does not affect the performance of the CMA-ES. Rotation of the search space to test invariance and to generate non-separable functions was proposed by [139], and the importance of such invariance properties for evolutionary algorithms is discussed in depth by [139] and [141]. Note that an algorithm not being invariant against a certain group of transformations means that it is biased towards a certain class of problems defined with respect to those transformations, for example to tasks with separable fitness functions. Such a bias is only desirable if the applications for which the algorithm is designed fall into that special class [137].

The CMA-ES does not require a tedious parameter tuning for its application. In fact, the choice of strategy internal parameters is not left to the user (arguably with the exception of population size λ)15. For the case study considered in this dissertation, only the population size was changed from its default value. Finding good (default) strategy parameters is considered as part of the algorithm design, and not part of its application—the aim is to have a well-performing algorithm as is. The default population size λ is comparatively small to allow for fast convergence.

Basic mathematical equations of CMA-ES Many continuous domain EAs use a normal distribution ( Ν (m, C)), which is uniquely determined by its mean m and its symmetric and positive definite matrix C, to sample new search points [142]. In the CMA-ES, the search distribution is a multivariate normal distribution. The normal distribution, given all variances and covariance, has the largest entropy of all distributions. Furthermore, the isotropic distribution does not favour any direction. Both make the normal distribution a particularly attractive candidate for randomized search. Randomized search algorithms are regarded to be robust in a rugged (non-smooth) search landscape, which can compromise discontinuities (sharp) ridges, or local optima. This makes the method feasible on non-smooth and even non-continuous problems, as well as on multimodal and/or noisy 15 http://www.lri.fr/~hansen/index.html


80

problems. The aim of covariance matrix adaptation in roughly speaking is to fit the search distribution to the objective function to be minimized. Unless otherwise stated the following mathematical descriptions of CMA-ES were summarized from [142].

A population of new search points, in the CMA-ES, is generated by sampling a multi-variate normal distribution. The basic equation to sample the search points for generation number g = 0, 1, 2 is written as:

Where ≈ the same distribution on the left and right side ( )1gkX + k-th offspring (search point) from generation 1g + ( )gm mean value of the search distribution at generation g

( )gσ overall standard deviation, step size, at generation g ( )gC covariance matrix at generation g

2λ ≥ population size, sample size, number of offspring To continue and complete the iteration step, the new mean ( )1gm + , updates of the covariance matrix ( )1gC + and finally the step size ( )1gσ + at the next generation 1g + are computed as follows:

1. Choosing mean at the next generation (selection and recombination genetic operator)

The new mean ( )1gm + of the search distribution at generation 1g + is a weighted average of μ selected points from the sample ( ) ( )1g

λ1g

1 X,...,X ++

( ) ( )

μ1,2,...,ifor 0w,1w

Xwm

μ

1iii

1gλ:i

μ

1ii

1g

=

⎪⎪⎭

⎪⎪⎬

⎫

>=

⋅=

∑

∑

=

+

=

+

(3.24)

Where λ μ ≤ parent population size i.e. the number of selected point 1,2,...μiw = positive weight coefficients for recombination, 0w...ww μ21 >≥≥

( )1gλ:iX + the i-th best individual out of ( ) ( )1g

λ1g

1 X,...,X ++ from equation 3.23 λ:i denotes the index of the i-th ranked individual Setting μ1wi = , in

equation 3.24 calculates the mean value of μ selected points. Equation 3.24 implements recombination by taking a weighted sum of μ individuals, and selection by choosing λ μ ≤ and/ or assigning different weights iw .Usually,

4 μ eff λ≤ indicates a reasonable setting of iw .

( ) ( ) ( )( ) ( )( )g2gg1gk C,σ,mNX ≈+ for k= 1,2,…, λ (3.23)


81

2. Update of the Covariance Matrix at the next generation

In CMA-ES, update of the covariance matrix combines the Rank-one-Update and Rank-μ -Update as follows: First, the covariance matrix from a single population of one generation, which is unreliable for small population, is estimated. Here it is assumed that the population contains enough information to reliably estimate the covariance matrix from the population. For the sake of convenience it is further assumed that ( )gσ = 1. The matrix

( )1gC +λ , which is the unbiased maximum likelihood estimator of ( )gC , estimates variances

of sampled steps, ( ) ( )g1gi mX −+ . To re-estimate the original covariance matrix, the matrix

( )1gC +λ is modified and the same weighted selection mechanism as in equation 3.24 is

used.

( ) ( ) ( )( ) ( ) ( )( )∑=

+++ −−⋅=μ

1i

Tg1g:i

g1g:ii

1gμ mXmXwC λλ (3.25)

Where the matrix ( )1gμC + is an estimator for the distribution of selected steps; just as

( )1gC +λ is an estimator of the original distribution of steps before selection. Sampling

from ( )1gμC + tends to reproduce selected, i.e. successful steps, giving a justification for

what a better covariance matrix means. The variance effective selection mass effμ must be large enough to ensure the matrix

( )1gμC + is a reliable estimator implementing in equation 3.23, equation 3.24 and equation

3.25. It is evident that the population size λ must be small to achieve fast search. That means, it is not possible to get reliable estimator for a good covariance matrix from equation 3.25 alone as 4 μ eff λ≈ will be small for small population sizeλ . Additional information from previous generation, g, is incorporated as a remedy. After sufficient number of generations, the mean of the estimated covariance matrices, from all generations, equation 3.26, becomes a reliable estimator for the selected steps.

( )( )

( )1iμ

g

0ii

1g Cσ

11g

1C 2+

=

+ ∑+= (3.26)

To assign recent generations a higher weight, since equation 3.26 have the same weight for all generation steps, an exponential smoothing is introduced. Letting ( ) IC 0 = to be the unit matrix and a learning rate ( )1g

cov Cthen ,1c 0 +≤< can be computed as:

( ) ( ) ( )( )

( )

( ) ( )( ) ( )

( ) ⎪⎪⎭

⎪⎪⎬

⎫

−+−=

+−=

+

=

++

∑ g

g1g:i

μ

1iicov

gcov

1gμ2gcov

gcov

1g

σmX

OPwcCc1

Cσ

1cCc1C

λ

(3.27)

Where 1ccov ≤ learning rate for updating the covariance matrix. OP denotes the outer product of a vector with itself.


82

For 1ccov = , no prior information is retained and ( )( )

( )1gμ2g

1g Cσ

1C ++ = .

For 0ccov = , no learning takes place and ( ) ( )01g CC =+ .This covariance matrix update is called update-μ-rank . It is noted in [142] that the choice of covc is crucial. Small values lead to slow learning, too large values lead to a failure, because the covariance matrix degenerates.

The selected steps, ( ) ( )( ) ( )gg1g:i σmX −+λ , was used to update the covariance matrix in

equation 3.27. The sequence of successful steps, which the strategy takes over a number of generations, is knows as an evolution path. An evolution path can be expressed by a sum of consecutive steps that referred to as cumulation. An exponential smoothing as in equation 3.27 was used to construct the evolution path, ( ) 0P 0

c = .

( ) ( ) ( ) ( )( ) ( )

( )g

g1g

effccg

cc1g

c σmm

μc2cPc1P−

⋅−+⋅−=+

+ (3.28)

Where ( )gcP evolution path at generation g.

1cc ≤ , learning rate for cumulation The rank-one update of the covariance matrix ( )gC via the evolution path ( )1g

cP + computed as:

( ) ( ) ( ) ( ) ( ) T1g

c1g

ccovg

cov1g PPcCc1C +++ +⋅−= (3.29)

An empirically valid choice for the learning rate in equation 3-29 is 2cov n2c ≈ . Where

n is search space dimension.

Therefore, in CMA-ES, update of the covariance matrix combines the update-μ-rank (Equation 3.27) and rank-one-update (Equation 3.29), where covμ determines their relative weighting.

( ) ( ) ( ) ( ) ( )

( ) ( )

( )

( ) ( )

( )

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛−++⋅−=

+

=

+

+++

∑4444444 34444444 21

44 344 21

update-μ-rank

T

g

g1g:i

μ

1ig

g1g:i

i

covcov

update-one-rank

T1g

c1g

ccov

covgcov

1g

σmX

σmX

w

μ11cPP

μcCc1C

λλ (3.30)

Where 1μ cov ≥ . Choosing effcov μμ = is recommended as most appropriate [142].


83

( ) 22effcovcov nn,μ,μminc ≈ (3.31)

Equation 3.30 combines the advantages of update-μ-rank and rank-one update. On the one hand, the information within the population of one generation is used efficiently by the update-μ-rank . On the other hand, information of correlations between generations is exploited by using the evolution path for the rank-one update. The former is important in large populations, the latter is particularly important in small populations [142].

3. Step size control

The last step to complete the cycle is the introduction of step size control, which is needed because in one hand, if effμ is larger than one, the optimal overall step length can not be well approximated by the adaptation rule in equation 3.30. On the other hand, the largest reliable learning rate for the covariance matrix update in equation 3.30 is too slow to achieve competitive change rates for the overall step length. In CMA-ES, an evolution path, i.e. a sum of successive steps was adopted to control the step size ( )gσ . The step size at the next generation, 1g + , can be computed as:

( ) ( )( )

( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

Ν=

++ 1

I,0EP

dcexpσσ

1gc

σ

σg1g (3.32)

Where σc learning rate for the cumulation for the step size control σd damping parameter for step size update

E expectation value ( )I,0Ν multi-variate normal distribution with zero mean and unity covariance

matrix

II. Multi-Objective CMA-ES Multi Objective Covariance Matrix-Adaptation Evolution Strategy (MO-CMA-ES), which is based on the non-dominated sorting approach, is an elicit variant of single objective CMA-ES for real-valued multi-objective optimization (MOO) [137]. As it is cited on [137], a large population is needed to evolve a diverse set of solutions, each ideally representing a (Pareto-) optimal compromise between the objectives for multi-objective optimization. The optimal strategy parameters for the members of this population may differ considerably and should therefore be adapted individually. This suggests that it is reasonable to apply a MOO selection mechanism to a population of individuals each of which uses the strategy adaptation of the CMA-ES. To achieve this [137] develop a single-objective, elitist CMA-ES with (1+λ)-selection, where λ can be chosen as small as one. The standard single-objective CMA-ES relies on non-elitist (µ, λ)-selection, that is, the best µ of λ offspring form the next parent population and all former parents are discarded.


84

In the elitist (1+λ)-CMA-ES the parent population consists of a single individual generating λ offspring and the best individual out of parent and offspring becomes the parent of the next generation. [137] developed MO-CMA-ES by integrating the (1+λ)-CMA-ES, which inherits all invariance properties from the original CMA-ES, with the MOO framework by considering, roughly speaking, a population of (1+λ) evolution strategies, which are subject to multi-objective selection. The selection is based on non-dominated sorting using either the crowding-distance or the contributing hypervolume, which rank individuals on the same level, as second sorting criterion.

3.4.5 Formulation of coupled simulation-optimization model

3.4.5.1 Coupled single objective CMA-ES (SO-CMA-ES) algorithm and HEC-5 Formulation of optimization problem Total water demand shortage (deficit) for domestic water supply, irrigation, hydropower generation and environmental flows are considered to define the objective function in the case study area. Therefore, the objective is to minimize deficit for domestic water supply, environmental flow and irrigation and to maximize hydropower generation. For all reservoirs considered in this dissertation, the storage in buffer zone is reserved for highest priority demand like domestic water supply and environmental flow. Therefore, the upper levels of the buffer zone (target levels) ( )jbuffer,

iZ for each reservoir j and for each month i of the year are optimized independently irrespective of the other demands like irrigation. Accordingly, the proposed combined HEC-5 and SO-CMA-ES algorithm is formulated for each reservoir (individual reservoir operation) and for multi-objective multi-reservoir systems as follows:

Single-reservoir operation

( ) ( ) ( ) ( ) ( )

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−= ∑∑

== 444 3444 21444 3444 21deficit Irrigation

n

1i

jirr,i

jirr,i

flow talEnvironmen and supply waterPublic

n

1i

jPub,i

jpub,i )SS()SS(minF1min (3.33)

Where ( )jpub,iS release for public water supply and environmental flow for month i

and reservoir j [106 m³] ( )jpub,

iS demand for for public water supply and environment for month i and reservoir j [106 m³] ( )jirr,

iS release for irrigation for month i and reservoir j [106 m³] ( )jirr,

iS demand for irrigation for month i and reservoir j [106 m³] In this case, target levels of the buffer zone ( )jbuffer,

iZ and conservation zone ( )jcons,iZ for

each reservoir j and for each month i of the year are optimized for their own demand irrespective of the operation of other tandem and parallel reservoirs.


85

Multi-reservoir operations In multi-reservoir operations, target levels of the conservation zone ( )jcons,

iZ of all reservoirs are optimized simultaneously. The ultimate goal of the coupled model is to minimize total deficit in total water supply (for environmental flow, domestic water supply and irrigation) and to maximize hydropower production. The inner summation in equation 3.34 is used for each month i and the outer summation is used for each number of reservoirs j (5 in our case). The (–1) sign in equation 3.34 is used to change maximization of hydrpower production into minimization of hydropower deficit.

( ) ( ) ( ) ( )

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅= ∑∑∑∑

= == = 4 34 2144444 344444 21(F2)Hydropower

m

1j

n

1i

ji2

(F1)supply water Total

m

1j

n

1i

jTWS,i

jTWS,i1 p)1()SS(minFmin ωω (3.34)

Where 1ω weight for irrigation shortage term in the objective function ][−Κ 2ω weight for energy production term in the objective function ][−Κ ( )j

ip hydropower production for month i and reservoir j [ MWh ] ( )jTWS,

iS total demand for public water supply, environment and irrigation for month i and reservoir j [106 m³]

( )jTWS,iS release for total demand for month i and reservoir j [106 m³]

Two weighting factors 1ω and 2ω in equation 3.34 are used to convert multi-objective optimization problems into single objective optimization problem so that SO-CMA-ES can also be applied to solve multi-objective problems. This technique shares the draw back of converting multi-objective optimization problems into single-objective optimization problem that was outlined in section 3.4.3. For practical use, the conversion technique may have to be used many times for different combinations of user-defined weighting factors, hopefully each time finding a different pareto-optimal solution. As it will be confirmed in chapter 5 (comparison of SO-CMA-ES and MO-CMA-ES for multi-objective optimization problems), the conversion technique do not guarantee finding solutions in the entire pareto-optimal region.

The coupled SO-CMA-ES and HEC-5 model always compares the numerical values of shortages between total water supply and hydropower production regardless of their unit of measurments. The weighting factors in equation 3.34 are introduced to induce shortage artificially to either total water supply ( 1ω ) or to hydropower production ( 2ω ) respectively. It does not, however, necessarly mean that equal priority is given to total water supply and hydropower production if 21 ωω = . But whenever the total water supply deficit term is multiplied by 11 >ω or the hydropower production term is divided by 12 >ω , then more artificial deficits are introduced to total water supply and vice versa. For example, in a single model run for 21 ωω = if the total water supply shortage is less than hydropower production, the coupled model spends more time in the next few model runs to bring the shortage of hydropower production to the same level


86

as the shortage of total water supply. Therefore, multiplying the actual hydropower deficit or dividing the actual total water supply deficit by a weighting factor greater than one increases the deficit of hydropower production artificially so that the coupled model gives more priority to hydropower generation. The same holds true for total water supply. Mathematically, say for 21 ωω = → DeficitHDPDeficitTWS HECHEC = then

DeficitHDPDeficitTWS121 HECHEC1and1If >⋅=> ωωω (3.35)

DeficitTWSDeficitHDP212 HECHEC1and1If >⋅=> ωωω (3.36)

Where DeficitTWSHEC actual total water supply deficit DeficitHDPHEC actual hydropower production deficit DeficitTWS1 HEC⋅ω artificially induced total water supply deficit DeficitHDP2 HEC⋅ω artificially induced hydropower production deficit In equation 3.35, where artificially induced total water supply deficit is higher than actual total water supply deficit, the coupled model gives more priority to total water supply to bring the induced total water supply deficit to almost the same level as that of hydropower deficit. The same holds true for artificially induced hydropower deficit in equation 3.36. In the coupled model, users or decision makers (see Figure 3-18) should provide these weighting factors depending on the desired priority level between hydropower production and irrigation. In order to construct possible pareto-curve, users has to run the model for many times with different combinations of weighting factors, which is one of the drawbacks of SO-CMA-ES algorithm (see its application for multi-objective problems in section 5.2.1.3 in chapter 5 and how this weighting factor was introduced in the coupled model in Figure B-5 appendix B). Decision variables In both single and mulit-reservoir operations, monthly target levels (values of rule curves) for each reservoirs are defined as decision variables.

( ) ( )( ) )argmin(FZ,Z **

m...,1,jjcons,jbuffer, =

= (3.37)

Where ( )jbuffer,iZ target level of the buffer zone for month i and reservoir j [m]

( )jcons,iZ target level of the conservation zone for month i and reservoir j [m]


87

Subject to

( ) ( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( ) ( )

m1,...,j1,...,12,ifor

qQq

SS

zZ

zZ

ZZZ

jmax

ji

jmin

jPub,i

jpub,i

jmin

jbuffer,i

jmax

jflood,i

jflood,i

jcons,i

jbuffer,i

==

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

<≤

=

≥

<

≤≤

(3.38)

Where ( )jflood,iZ top of flood control zone for reservoir j [m]

( )jmaxz top of the reseroir for reservoir j [m]

( )jminz buttom of buffer zone for reservoir j [m]

)( jminq minimum downstream release for reservoir j [ sm /3 ]

( )jmaxq maximum downstream release from reservoir j [m3/s]

( )jiQ downstream release of reservoir j [m3/s]

( )jminq minimum downstream required flow from reservoir j [m3/s]

Small program using Perl (see the programme in appendix B), which prepare template file from HEC-5 control file and Matlab programming languages were written to couple simulation model (HEC-5A in our case) with single objective optimization algorithm (CMA-ES). Template file is a copy of HEC-5 control file with decision variables, which receives values of decision variables at each iteration from optimization model and used as an input file for HEC-5. For the application of CMA-ES, initial solution, initial standard deviation (step-size variables should be defined such that the same standard deviations can be reasonably applied to all variables) and eventually the termination criteria (e.g. a function tolerance) need to be set by the user.


88

Figure 3-18 Framework of combined single objective CMA-ES and HEC-5

Figure 3-18 illustrates the procedures of the combined HEC-5 reservoir simulation model and CMA-ES optimization algorithm. The framework has two key features. First, searching for optimal target levels (rule curves ( )jbuffer,

iZ and ( )jcons,iZ for buffer zone and

conservation zone respectively) are accomplished by the CMA-ES algorithm and supplied to the template file of HEC-5. Second, the HEC-5 (uses template file as an input file) calculates the reservoir releases of the system associated with the rule curve derived from CMA-ES algorithm. The cycle continue until the objective function is satisfied i.e. minimizing hydropower and total water supply deficits.

The coupled model is multi-dimensional in the decision space and set to handle up to 65 (5 reservoirs * 13 target reservoir levels) dimensions for all reservoirs in the case study area. It can also be extended for handling multi-criteria optimization problems among different water users like irrigation water supply versus energy production and navigation versus hydropower energy production by introducing different weights set by users.


89

3.4.5.2 Coupled multi-objective CMA-ES algorithm and HEC-5

Multi-objective formulation of the objective function

( ) ( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛−= ∑∑

= =

m

1j

n

1i

jTWS,i

jTWS,i )SS(minF1min (3.39)

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛= ∑∑

= =

m

1j

n

1i

jipmaxF2max (3.40)

Where min(F1) minimizing total water supply (for public water supply, environment and irrigation) deficit [106 m3] max(F2) maximizing hydropower production [MWh] Decision variables

( ) ( )( ) )argmin(FZ,Z **

m...,1,jjcons,jbuffer, =

= (3.41)

subject to

( ) ( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( ) ( )

m1,...,j1,...,12,ifor

qQq

SS

zZ

zZ

ZZZ

jmax

ji

jmin

jPub,i

jpub,i

jmin

jbuffer,i

jmax

jflood,i

jflood,i

jcons,i

jbuffer,i

==

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

<≤

=

≥

<

≤≤

(3.42)

In this section Multi Objective Covariance Matrix-Adaptation Evolution Strategy (MO-CMA-ES), which is one of the C++ library available in MOO-EALib supported by SHARK, were coupled with HEC-5 reservoir simulation model to generate pareto-front for multi-objective problems.

MOO-EALib is a library, which is developed by SHARK16, providing basic components to easily build evolutionary algorithms for multi objective optimization. SHARK is a modular C++ library for the design and optimization of adaptive systems. Multiple multi-objective evolutionary algorithms have been implemented in SHARK, which most of them relying on the concept of indicator-based selection operators. First of all, they provide users and developers with a simple and quick entry to MOO. Secondly, they serve as an example on how to assemble quite complex optimization procedures from the basic building blocks provided by the MOO-EALib and SHARK in general.

16 http://shark-project.sourceforge.net/

Decision making component

90

MO-CMA-ES, which is written by [137], was adopted to suit for the case study area. It was modified to read the control file of HEC-5, which contains monthly values of rule curves, number of objective functions and number of dimensionality of the problem. We wrote small program using Perl to couple the modified MO-CMA-ES with HEC-5. In the coupled program (see Figure 3-19), values of the rule curve, which is generated by MO-CMA-ES, were supplied to HEC-5 and HEC-5 was used to compute shortages in total water supply (for irrigation, public water supply and environmetal flow) and hydropower generation. The computed shortages were evaluated against the predefined objective functions, which is minimization of total water supply and hydropower deficits. Another better values of rule curves were generated in MO-CMA-ES and supplied to HEC-5. Such cycles were continued to generate all possible optimum solutions for multi-objective problems. Physical constraints of the reservoirs as expressed in equation 3.42 were also handled in the same coupled program.

Figure 3-19 Framework of the combined multi-objective CMA-ES and HEC-5

3.5 Decision making component This component is the last and more subjective component of the proposed decision support tool. Depending on the type of optimization algorithm used, the coupled reservoir simulation-optimization model generate many individual optimal solutions or a pareto-front, which contains all possible optimal solution for the given problem. It is difficult to say one optimal solution is better than the other optimal solutions especially for those problems that have conflicting interest. In this case, decision makers are making their final decision based on non-technical, qualitative and experience driven knowledge.

Application of the methodology to the case study area

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4 Application of the methodology to the case study area

4.1 Regional model The proposed regional model to estimate flow in ungauged catchments were tested on tributaries of the Blue Nile river basin, Ethiopia. Despite the fact that there are more than 100 gauging station as it was described in chapter 3, runoff data series from 40 gauging stations were obtained from MoWE. Due to differences in surface water hydrology compared to the rest of the sub-basin in the Blue Nile river, 9 gauging stations in Dabus sub-basin were excluded from the formation of regional model. After checking homogeneity and consistency of the runoff data series, only runoff time series from 26 gauging stations having relatively good quality of runoff data were selected for regionalization.

4.1.1 Identification of hydrological homogeneous groups

Physical catchment characteristics, which are also available for ungauged catchments, like catchment area [km2], dominant land use [%], dominant soil type [%], slope [%], longest distance from the most upstream to the out let of a river [km], weighted average topographic index [-], weighted average elevation [m] and shape of the catchment [-] were selected as a base to identify hydrological homogeneous groups. These information were extracted from 90 m by 90 m grid DEM using ARC-GIS. Main catchment characteristics of the selected 26 rivers are found in Table A-1 appendix A.

SOM in NeuroShell was used to identify or cluster hydrological homogeneous groups. Physical characteristics of the selected catchments were imported to NeuroShell. 16 neurons in the input layer of SOM were used. These include catchment area in km 2, slope in percent, longest distance from the most upstream point to outlet of the catchment in km, dimensionless weighted average topographic index, average elevation in m, dimensionless shape of the catchment, five dominant soil types in percent and five dominant land uses in percent. Initial number of neurons (number of similar groups or clusters) in the rectangular topology of the output layer was taken as 14. Parameters (see Figure 4-1) such as learning rate, initial weights, neighbourhood size, and number of epochs were set. ‘The learning rate and neighbourhood size are automatically reduced in NeuroShell as training progresses, honing on the answer. The neighbourhood size, should begin with a relatively high number (sometimes even close to the number of neurons in the output layer), such as 90 percent of the number of neurons in the input layer. The learning rate should begin with a relatively high number such as .5’ (extracted from NeuroShell 2 Release 4.0 help menu).

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92

Figure 4-1 Architecture of the unsupervised SOM network in NeuroShell2

In our case, the initial neighbourhood size and initial weight were taken as 13 and 0.35 respectively. The numbers of epochs were increased from 1,000 to 10,000 to train SOM. The neighbourhood size was decreasing with learning until during the last training events i.e. when the neighbourhood size became zero. At this time, only the winning neuron's weights are changed and the learning rate will be very small, which consequently the clusters have been defined. Following the above procedure and initial parameters, the selected 26 sub-catchments were grouped in to five hydrological homogeneous groups (see Figure 4-2). Accordingly, four rivers namely, Main Beles, Uke, Great Anger and Dedessa near Dembi were clustered into group 1. Donder, Ardy, Andassa, Buno Bedele, Belo and Guder rivers were grouped under group 2. Most rivers in South Gojam sub-basin of the Blue Nile River namely, Birr, Temcha, Dura, Lower Fetta, Fetta rivers and Neshi River (in Fincha sub-basin) were pooled together in group 3. Most rivers in Lake Tana sub-basin namely, Gilgel Abay, Koga, Gumera, Gilgel Beles river (in Beles sub-basin), Chemoga river (in South Gojam sub-basin) were clustered in group 4. Group 5 comprised of rivers in the Muger sub-basin (Muger, Alelitu, Sibilu rivers) and rivers in Jemma sub-basin (Robi Jida and Robi Gumero rivers).


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Figure 4-2 Five hydrologically homogeneous groups in the case study area

Box plots were used for visual comparisons of results. Each box plot in Figure 4.3 contains the normalized catchment characteristics values for all groups. The box plot is a quick way of examining one or more sets of data graphically. It is particularly useful for comparing distributions between several groups or sets of data. It includes the presence of possible outliers. It shows a measure of dispersion such as the upper quartile, lower quartile, consists of most extreme values (maximum and minimum values) of the data set as well as the median as a measure of central location, which is useful for comparing sets of data. It also gives an indication of the symmetry or skewness of the distribution. Open circles (if present) indicate outliers.

Referring to the first box plot in Figure 4.3, catchments in group 1 (G1) cover wide range of catchment area as compared to other catchments in other groups. Small topographic index value is a unique characteristic of the catchments in group 1. Table 4-1 and Figure 4-3 illustrates unique catchment characteristics in each group.

Anger, Dedessa sub-basins

Lake Tana sub-basin

Jemma, Muger sub-basins

South Gojam sub-basin

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Figure 4-3 Box plots showing the distribution of 16 catchment characteristics in each group

Table 4-1 Unique catchment characteristics in each group

Group Unique characteristics

G1

• cover wide range of catchment area • have less topographic index value • wider range of landuse19 • wider range of topographic elevation

G2 • small landuse19 coverage • relatively flat slope

G3 • have the largest topographic index value G4 • Dominated by soil54

G5 • dominated by landuse211 • contains the largest river length


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4.1.2 WaSiM-ETH model setup

After the identification of hydrologically homogeneous groups, from each group one or more rivers were selected as ‘calibration catchment’ and calibrated for the whole runoff data series using coupled WaSiM-ETH and PEST model. For all ‘calibration catchment’ and ‘validation catchment’, land use and soil map of the Abay river basin depicted on chapter 2 were converted in to WaSiM-ETH’s 90 m by 90 m grid format. The program "TANALYS'' (Topographical Analysis), which is a basic tool for working with WaSiM-ETH, was used to automatically derive and deliver the relevant input raster data, structures and relationships for WaSiM-ETH. Model setup and calibration of WaSiM-ETH model parameters using coupled WaSiM-ETH and PEST can be found in chapter 3 of this dissertation., Flow time series of ‘validation catchments’ has never been involved during calibration. These catchments are reserved to validate the regional model.

Uke river, from group 1, was selected as ‘calibration catchment’ and the remaining three rivers namely, Main Beles, Great Anger and Dedessa near Dembi were selected as ‘validation catchment’. Following the same procedure outlined in chapter 3, WaSiM-ETH’s model parameters were calibrated for Uke river. The optimized (after calibration) WaSiM-ETH model parameters were used for ‘validation catchment’, in this case Main Beles, Great Anger and Dedessa near Dembi rivers to validate the regional model for group 1.

Donder and Buno Bedele rivers were taken as ‘calibration catchment’ from group 2. These rivers were calibrated simultaneously using the coupled WaSiM-ETH and PEST model. The optimized model parameters were used to validate the regional model for group 2. Dura and Fetta rivers from group 3, Gilgel Abay and Gumera rivers from group 4 and Robi Gumero and Sibilu rivers from group 5 were chosen as ‘calibration catchment’. With the exception of rivers in group 5, where WaSiM-ETH was calibrated and validated for flow data series from 1995 to 1999, other rivers in other groups concurrent daily rainfall, temperature and runoff from 1986 to 1999 were used for WaSiM-ETH model calibration and validation. For rivers in group 4, in Lake Tana sub-basin, the model was calibrated and validated from 1986 to 2005. The optimized WaSiM-ETH model parameters for each group were stored in the DST database of this dissertation and presented in chapter 5.

Optimization of multi-reservoir using single objective CMA-ES

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4.2 Optimization of multi-reservoir using single objective CMA-ES

4.2.1 Reservoir model setup

The proposed coupled SO-CMA-ES algorithm and HEC-5 reservoir simulation model was used to setup optimal control variables (i.e. rule curves) of natural and artificial reservoirs in Lake Tana sub-basin. These include Koga reservoir, Ribb reservoir, Megech reservoir, Gumera reservoir, Tana-Beles basin transfer for hydropower production (completed in 2010) and Tis-Abay I and II (existing hydropower stations).

Physical reservoir characteristics (reservoir area, elevation, and volume relations, which were collected from the respective reservoirs design report) of each reservoir, physical constraints (reservoirs’ outlet capacity) and operational constraints, net evaporation, inflow to each reservoir and local inflows at each control points of the five reservoirs (including the lake Tana) were set up in the control file of HEC-5 reservoir simulation model.

All reservoirs in the case study area were divided into four storage zones namely; inactive storage zone, buffer storage zone, conservation storage zone and flood storage zone. The buffer storage zone was reserved for public water supply and minimum down stream environmental flow, which in this dissertation categorized as the highest priority demand. In the course of optimization, the seasonal boundary between conservation storage zone and buffer storage zone were changed until an optimum operation rule curves are achieved.

4.2.1.1 Input Data to HEC-5

I. Hydro-meteorological data Inflow to Lake Tana including flow from ungauged catchments, inflow to four upstream artificial reservoirs and in between flow (flows between Lake Tana and four upstream artificial reservoirs), were generated using the proposed regional model. The mean monthly and annual values of the runoff time series for the period 1986-1999 into Lake Tana and four proposed reservoirs are presented in appendix A.1.

Areal precipitation over Lake Tana and four upstream reservoirs were estimated using Thiessen polygon method from point rainfall (1985 to 2005) measured at 21 meteorological stations, which was collected from NMSA, in and around Lake Tana sub-basin. As it was mentioned previously, only temperature data was available to compute evapotranspiration. Hence, potential evapotranspiration was computed using modified Hamon method, which uses only temperature data (see chapter 3 for calibration of default values in Hamon method). Open water evaporation was estimated by multiplying potential evapotranspiration with dryness factor (1.2 for Ethiopia). Figure A-1 to Figure A-5 in appendix A.2.1 present areal precipitation and open water evaporation over Lake Tana, Megech, Ribb and Koga reservoirs. Due to its closeness and the prevailing climatic characteristics, open water evaporation and areal


97

precipitation of Gumera reservoir are about the same as the respective values of Ribb reservoir. The hydro-meteorological information was saved in HEC-DSS file.

II. Water demands There are different water use sectors in Lake Tana sub-basin. However, five main sectors, which include irrigation, hydropower, public water supply, minimum downstream environmental flow and flow needed for aesthetic value of Tis-Issat waterfall were considered in the coupled HEC-5 reservoir simulation model and SO-CMA_ES and Mo-CMA-ES optimization algorithms.

Irrigation water requirements Irrigation water requirements were estimated using window based CROPWAT computer programme from FAO (CROPWAT 4 Windows 4.3). [23] proposed two cropping patterns for irrigation projects in Lake Tana sub-basin. Crops for the proposed cropping patter 1 (CP1) comprises of maize, wheat, barley, sunflower, potatoes, sugarcane, fruits, red pepper and onion with 80% and 100% cropping intensities for dry (November/ December - April) and wet season (May/ June – September/ October) respectively. The main constitutes for cropping patter 6 (CP6) is rice, which covers 60% and 80% of the cropped area for dry (January – May) and wet season (July - November) respectively. In this research the revised cropping pattern adopted in Koga Irrigation project [143] was used for non-rice crops in Koga and Megech reservoirs. Crop coefficient (Kc) value for development stage of the crops, first planting and last harvesting date for each crop were taken from reports of Koga Irrigation project [143] . For Ribb reservoir, the cropping pattern CP6 of [23] was used. For Gumera reservoir, cropping pattern adopted in feasibility study of Gumara Irrigation Project by [21] with cropping intensities of 90% and 24% for wet and dry season respectively were used. The reduction in cropping intensity of Gumera for dry season is due to the reduction in dam height. Figure 4-4 presents cropping pattern CP1 used in CROPWAT 4. Table 4-2 presents a summary of gross irrigation water requirement (GIWR) with 50% irrigation efficiency and 80% dependable rainfall for Megech reservoir. Gross Irrigation water requirement, effective precipitation and evapotranspiration for other reservoirs can be found on appendix B.2.


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Figure 4-4 Cropping pattern for non-rice crops (CP1)

Table 4-2 Monthly total gross irrigation water requirement in mm for Megech (Source: This study and [23])

ETP Reff GIWR

Ma RS Ma RS Ma RS Jan 104 151 2 0 143 152 Feb 119 128 9 5 164 202 Mar 134 132 2 13 170 178 Apr 140 129 20 11 66 68 May 134 123 63 42 0 6 Jun 119 115 146 96 0 0 Jul 100 108 157 151 0 0 Aug 100 104 154 133 0 0 Sep 113 102 103 86 0 22 Oct 113 102 34 33 0 88 Nov 104 103 10 9 91 58 Dec 94 85 1 0 157 42 Total 1373 1382 701 579 791 812

Key ETP Potential evapotranspiration Reff Effective rainfall GIWR Gross irrigation water requirement Ma Abay master plan RS Research output


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Public water supply, minimum downstream environmental flow and hydropower demand In addition to supplying the agricultural demand, Megech reservoir is also serving for Gonder domestic water supply. Domestic demand for Gonder town was taken as

6105.31 ⋅ m3 annually [40] for the reservoir’s lifetime of 50 year. This value was disaggregated in monthly time step for this study. However, detail domestic water demand assessment for Gonder town is required in order to come up with best reservoir operation policy for Megech reservoir.

For all reservoirs in the case study area except Lake Tana reservoir, monthly riparian flow was estimated based on the historical series mean monthly flows multiplied by the Koga [38] ratios between release and long-term flow. Minimum flow requirement for visual amenity of the Tis-Issat waterfall, located downstream of Lake Tana, were estimated during the feasibility study of Tis-Abay II hydropower plant by [144]. [145] estimated the minimum environmental flow requirement to the fall with no allowance for the aesthetic quality of the fall using the South African desktop reserve model. Table 4-3 presents monthly minimum flow requirement for aesthetic value of the fall and minimum environmental flow downstream of the fall without considering the aesthetic value of the fall. For this case study, combined flow, which is the monthly maximum value for each month proposed by either studies, were taken to consider minimum environmental flow and flow that are needed for aesthetic value of the fall (tourist need). However, at least minimum environmental flow proposed by [145] should be reserved in buffer zone under highest priority demand.

Table 4-3 Minimum environmental flow downstream of Lake Tana reservoir (Source: [144] and [145])

TS EF C 106 m3 M3/s 106 m3 m3/s 106 m3 m3/s

Jan 161 60 68 25 161 60 Feb 146 60 56 23 146 60 Mar 27 10 42 16 42 16 Apr 26 10 28 11 28 11 May 27 10 23 9 27 10 Jun 26 10 21 8 26 10 Jul 54 20 39 16 54 20 Aug 54 20 83 31 83 31 Sep 104 40 192 74 192 74 Oct 107 40 117 44 117 44 Nov 104 40 109 42 109 42 Dec 161 60 86 32 161 60 Annual 995 864 1146


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The other water demand sector is hydropower generation from Tis-Abay I, Tis-Abay II and Tana-Beles hydropower plants (see Table 4-4 for their characteristics).

The theoretically power available from falling water can be expressed as

Where P power [W] ρ density [Kg/m3] g acceleration due to gravity [m/s2] q discharge [m3/s] h gross head [m] The practical available power will always be less than the theoretically power due to energy losses, which are caused by flow disturbances at the intake to the pipeline, at valves and bends, friction in the pipeline, friction and design ineffincies in the turbine and generator. The energy losses in the pipeline and at valves and bends, are called head losses: they represent the difference between the gross head and the net head that is available at the turbine. Practically available power can be expressed as

Where μ efficiency [-]: it considers head loss in pipelines and efficiencies of turbines and generators and expressed by a decimal. As it is shown in equation 4.1 and equation 4.2, the amount of electricity that can be generated at a hydropower plant is determined by two factors: head and flow. Head is how far the water drops. It is the distance from the highest level of the dammed water to the tail water. Flow is volume of water per unit time passing through the system that is used to turn the turbine. Generally, a high head plant needs less water flow than a low-head plant to produce the same amount of electricity. In the proposed optimization models, the product of head and flow were maximized to yield maximum hydropower production.

The other key input in the design process is plant factor that can be defined as the ratio of the average power load (over a number of years of operation) of an electric power plant to its rated capacity. It expresses the average percentage of full capacity used over a given period of time. It is very important to ensure the capacity of the penstocks, turbines, generators etc of a hydropower station to be capable of using a higher flow than the annual mean flow if the scheme is to be cost effective. This should be taken into account during the planning stage. Historically, hydropower station components have usually been sized to give an overall plant factor of about 50 to 55%. Some

hqgρP ⋅⋅⋅= (4.1)

hqgρμP ⋅⋅⋅⋅= (4.2)

TS= Environmental flow by [144]focused on Aesthetic value EF= Environmental flow by [145] focused on Ecosystem C = Combined flow focused Aesthetic value and Ecosystem


101

schemes, especially those where there is an out-of-river canal, may have a greater plant factor than 50 %17.

Tis-Abay I power plant is designed for a total maximum discharge of three turbines ( )103 ⋅ at 30 m3/sec, rated net head of 46 m, power factor of 0.8, and installed capacity of 11.4 MW. Tis-Abay II power station is designed for total maximum discharge of two turbines ( )752 ⋅ at 150 m3/sec, rated head of 53.2 m, power factor of 0.90, and with 73 MW installed capacity. Input data to HEC-5 reservoir simulation model like available head, capacity of each penstock, installed capacity and plant factor were taken from the EEPCO and [24]. The plant factor of Tis-Abay I and Tis-Abay II are the average over a number of years of operation where as the plant factor of Tana-Beles is fixed during the planning and design stage to 0.48.

Table 4-4 Characteristics of Tis-Abay I, II and Tana-Beles hydropower plants Hydropower

plant No of

turbines Maximum

discharge (m3/s) Net head

(m) Installed

capacity (MW) Plant factor

Tis-Abay I 3 30 46 11.4 0.80 Tis-Abay II 2 150 53.2 73 0.90 Tana-Beles 4 160 311 460 0.48

4.2.1.2 Schematization of HEC-5 and CMA-ES model

I. Individual reservoir Figure 4-5 shows sample schematization of model set up for Megech reservoir. This reservoir operates for demands at two control points (CP1.0 and CP11). The first control point (CP1.0) is for public water supply and minimum downstream flow for environment. The public water supply part of the released flow at this control point is completely diverted from the system. Where as the environmental flow part is diverted from this point but later on added as an additional flow for the downstream reservoir (Lake Tana). However, the environmental flow will not be taken as an additional flow for the downstream control point (CP11) [i.e. not available for irrigation]. The second control point (CP11) is allocated for irrigation demand. In HEC-5, based on reservoir storage level, two levels of flow target (Desired and Required flow) can be defined. Desired flows are met when there is sufficient water supply above the buffer level. Required flows are met when the water level drops into the buffer level. In this dissertation, public water supply and environmental flow are required flow and other demands are desired flow.

17 http://www.med.govt.nz/


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According to [20] for the planned irrigation projects on average approximately 20% of the irrigation water supplied to irrigation will eventually be returned as drainage water. Other studies like the feasibility studies for Koga and Gumara irrigation projects have estimated the return flow to the system as 10-15% and 10% respectively. For all reservoirs in the case study, the average value (i.e. 15%) of the flow at irrigation control points will eventually return to the system as a return flow.

Figure 4-5 Schematics of Megech reservoirs used in HEC-5 simulation model

In the coupled simulation-optimization model, the objective function is set to minimize sum of irrigation, municipal water supply, and environmental flow deficits. First 24 initial monthly target storage levels also known as rule curve (RL in HEC-5, see Figure B-1) (12 for buffer storage zone and 12 for normal conservation storage zone) were randomly generated. There are two ways of initializing the optimization process; the first method is to use one constant value for buffer zone and another constant value for the conservation zone. The selected constant values should be within the upper and lower boundary of the respective storage zone. The coupled model generate randomly with these initial constant values and the given standard deviation. For instance, constant value of 6 3109.9 10 m⋅ for conservation zone and 6 336.0 10 m⋅ for buffer zone with a standard deviation of 1000 for Megech reservoir were taken as follows:

Where ( )inactive topmegechZ storage level of top of inactive zone for Megech reservoir

( )consmegechZ initial storage level of conservation zone for Megech reservoir ( )cons topmegechZ storage level of top of conservation zone for Megech reservoir

It is recommended to select initial storage level for conservation zone closer to the storage level at the top of conservation zone.

( ) ( ) ( )

666

cons topmegech

consmegech

inactive topmegech

108.181109.109101.35

ZZZ

⋅≤⋅≤⋅

≤≤ (4.3)


103

Similarly, initial storage level for buffer zone can be selected but this time the selected initial storage level should be closer to storage level at the top of inactive zone. Total demand of public water supply and environmental flow could give us good initial storage level for buffer zone.

Where ( )buffermegechZ initial storage level of buffer zone for Megech reservoir

Small computer code (see appendix B) was written and used to generate initial random storage level based on the given initial constant storage levels.

The second method is to use historical seasonal values (monthly target storage levels) as initial target levels for existing reservoir. The first method is preferable if the coupled model is running for the first time. However, if there exist historical rule curve or rule curve generated from previous model run, then the second method is much faster to converge.

Small programme (see appendix B) was written in matlab environment to handle the physical constraints. Table 4-5 presents the lower and upper boundary of each reservoirs. Accordingly, storage levels of sample population are bounded between top of conservation zone 6 3181.8 10 m⋅ and top of inactive zone 6 335.1 10 m⋅ . Samples outside these bounds are considered as not a number (NaN). In addition, the values of the upper rule curve are always greater than or equal to the values of the lower rule curve. At each trails, new values of target storage levels were generated by the optimization model and the simulation model was used to evaluate the performance of the system with respect to the set up objectives. Likewise, the values of rule curves were continously modified towards optimality until the objective met. Finally, optimum values of both rule curves, which resulted in minimum deficits, were extracted and supplied to the simulation model to generate detail and supplementary information (like monthly distribution of deficit if there is any, optimum monthly target reservoir elevation, monthly flows downstream of the reservoir etc).

Table 4-5 Lower boundary (top of inactive zone) and upper boundary (bottom of flood level) for each reservoirs

Buffer zone Conservation Reservoir Lower boundary (m a.s.l.) Upper boundary (m a.s.l.)

Megech 1916 1947.1 Ribb 1901 1940 Gumera 1922.11 1928 Koga 2005 2015 Tana 1784 1787

( ) ( ) ( )

666

cons topmegech

buffermegech

inactive topmegech

109.109100.36101.35

ZZZ

⋅≤⋅≤⋅

<< (4.4)


104

II. System of reservoirs

Figure 4-6 shows schematization of model set up for Lake Tana reservoir and four upstream reservoirs. It also depicts different planned and existing water resources development, including inter basin transfer between Lake Tana sub-basin and Beles sub-basin. Control points for each reservoirs were set up in the same way as described above. Except for Megech and Lake Tana, control points for other reservoirs were solely serving demands for irrigation and environmental flow. Lake Tana’s control points were used for irrigation (using pumping stations), environmetal and flows that are needed for aesthetic value of the waterfall, hydropower production and irrigation downstream of Tana-Beles hydropower station.

Figure 4-6 Schematic of Lake Tana and four upstream reservoirs used in HEC 5

simulation model


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4.2.2 Existing condition and scenarios

4.2.2.1 Existing condition: sectoral approach I. Tis-Abay I and II hydropower production

Tis-Abay I and Tis-Abay II hydroelectric power plants are located on the Abay river, some 35 km downstream of Lake Tana. Some part of the flow after leaving the Chara Chara weir is diverted to these plants and the remaining part will flow to the Tis-Issat waterfall. There is a river called Andassa river, which its average flow is below the required minimum flow for the waterfall, between the Chara Chara weir and the power stations. The flow from this river was considered as an incremental local flow for the waterfall in HEC-5 model set up. Dead storage and flood level was set at 1784 m a.s.l. and 1787 m a.s.l. respectively. The conservation level and buffer level were optimized to maximize the hydropower production with two environmental flow conditions (flow required for ecosystem and aesthetic value of the waterfall).

II. Tana-Beles hydropower production at different navigation level

The coupled model was used to maximize hydropower generation from Tana-Beles hydropower station with two environmental flow conditions of the waterfall. Water from this reservoir is directly diverted through 0.9 km long inlet approach channel and 12 km headrace tunnel to Beles sub-basin for Tana-Beles hydropower stations. This station has an installed capacity of 460 MW and plant factor of 0.48. In this scenario, the trade-off between hydropower and navigation was also considered at different navigation levels.

4.2.2.2 Scenario 1: reservoirs optimized individually (sectoral approach)

Four future reservoirs (Koga is completed and the others are under construction) and Lake Tana were optimized for their own demands. This is sectoral approach by which each sectors are trying to maximize their own benefit irrespective of downstream demands. Megech reservoir, which is located north of Lake Tana, is designed to irrigate 7311 ha and to supply drinking water for Gonder city. The model for this reservoir is set up in such away that the storage in the buffer zone, which varied monthly, was reserved for domestic water supply and environmental flow. Domestic water supply and environmental flow were given the highest priority as compared to irrigation. The other three reservoirs Ribb, Gumera and Koga which are located east, southeast and south of the lake are designed solely to irrigate 19925 ha, 16771 ha and 7000 ha respectively. For these three reservoirs the storage in the buffer zone, which varied monthly, were reserved only for environmental flow.

4.2.2.3 Scenario 2: SO-CMA-ES for full water resources development of Lake Tana sub-basin (integrated approach)

In this dissertation, full water resources development of Lake Tana sub-basin refers to demands on existing and under construction reservoirs in the sub-basin i.e. Ribb, Gumera, Megech, Koga, Lake Tana reservoirs and three pumping stations on Lake Tana reservoir. Gilgel Abay reservoir and Jema reservoir are excluded from this scenario. In

Optimization of multi-reservoir using MO-CMA-ES

106

this and in the next two scenarios, integrated approach was followd where by all sectors were involved to maximize the overall benefit of all stakeholders.

Scenario 2 illustrates the use of SO-CMA-ES with different combinations of weights as outlined in section 3.4.5 for multi-objective problems. Objective functions were set to minimize irrigation, public water supply, environmental flow deficits and to maximize hydropower production subject to a given constraints. Different weight factors (see section 5.2.1.3) were given to hydropower production to investigate the trade-off between hydropower production and total water supply deficits.

4.3 Optimization of multi-reservoir using MO-CMA-ES

4.3.1 Multi-reservoir model setup

Section 4.2 illustrates the use of SO-CMA-ES optimization algorithm for single and system of reservoirs for both single and multi objective problems. Its application for multi-objective system of reservoirs is nothing more than a number of successive model runs for different weights. The generated possible pareto-curve may miss some of the possible candidate optimal points depending on the choice of the weights. In this section the coupled model, MO-CMA-ES and HEC-5, was used to generate pareto-front for two scenarios. The same model set up for system of reservoirs (see section 4.2), which includes Lake Tana and four upstream reservoirs, was used. Physical constraint of each reservoir were handled in the same coupled model in such a way that the minimum monthly values of the upper rule curve is greater than any values in the lower rule curve at all times and the maximum value of the upper rule curve should not exceed the flood level of each reservoir.

4.3.1.1 Scenario 3: MO-CMA-ES for partial water resources development of Lake Tana sub-basin

Demands for this scenario is the same as those demands mentioned on section 4.2. The scenario enables us to compare results of MO-CMA-ES and SO-CMA-ES for multi-objective multi-reservoir problems.

4.3.1.2 Scenario 4: MO-CMA-ES for full water resources development of Lake Tana sub-basin

In this dissertation, full water resources development of Lake Tana sub-basin refers to demands mentioned on section 4.2 and additional planned irrigation demands from Lake Tana pumping stations like South-West Tana pumping, North-West Tana pumping and North-East Tana pumping. Irrigation demand from two more artificial reservoirs i.e. Gilgel Abay and Jema reservoir and irrigation demand downstream of Tana-Beles hydropower station are not considered. This scenario further investigate the trade-off between irrigation, hydropower and navigation.

Results and Discussions

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5 Results and Discussions 5.1 Estimations of flow in ungauged catchment

5.1.1 Ungauged tributaries of the Blue Nile river basin

SOM was used to identify hydrologically homogeneous groups in the case study area as outlined in the previous chapter. The selected 26 sub-catchments were grouped in to five hydrologically homogeneous groups as shown in Figure 4-2 of chapter 4. Except for sub-catchments in group 5, sub-catchments that are geographically close to each other do not necessarily belong to the same hydrologically homogeneous group.

The regional model was validated with ‘validation catchments’ in each group having flow data that have never been involved during calibration of the model. Model performance is evaluated by considering one or more model performance criteria of the residuals between model simulated outputs and observed catchment outputs. In this study the coefficient of determination (R2 value) and the Nash and Sutcliff (N-S) value between observed and simulated flows and the goodness of volume fit based on the deviation between observed and simulated average annual flow volume were used to evaluate the performance of the regional model. With respect to the flows to reservoirs and Lake Tana, the proper simulation of annual runoff volumes were considered important.

Table 5-1 to Table 5-5 show the results of the proposed methodology. Validation periods are different for different validation catchments depending on the availability of runoff data. In the same tables daily runoff time series were aggregated into 10 days and monthly time steps and evaluated with all model performance criteria. An improvement of model performance were observed from daily to 10 days and then to monthly time steps. This is mainly due to the fact that the sums of positive and negative errors in the daily time steps were significantly reduced in the aggregation process. For visual inspection, Figure A-2 to Figure A-11 in appendix A1.1 shows measured and WaSiM-ETH model out put for selected rivers in each group.

In group 1 (see Table 5-1), daily runoff records (1985-1999) for Uke river was involved during calibration process and the remaining rivers, Dedessa near Dembi, Great Anger and Main Beles were used as validation catchments for this group. Their R2 value ranges from 0.51 to 0.83, from 0.74 to 0.87 and from 0.80 to 0.89 for daily, 10 days and monthly time steps respectively.

Estimations of flow in ungauged catchment

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Table 5-1: Model performance for sub-catchments in group 1

In group 2, daily runoff records (1993-1999) of Buno Bedele and Donder rivers, which are geographically not close to each other, were calibrated simultaneously and four other rivers in the same group were used as validation catchments. The R2 values of the validation catchment ranges from 0.50 to 0.73, from 0.70 to 0.80 and from 0.82 to 0.85 for daily, 10 days and monthly time steps respectively. Table 5-2 depicts optimized regional model parameters for group 2 and the performance of the regionalized model for sub-catchments in group 2.


Optimized regional model parameters m (10-2)

Tkorr (10-5)

Kkorr (103)

kD (102)

SHmax

kH (101)

Pgren

rk

Group 1 5.78 0.149 1.46 2.02 3.6 1.09 10 0.01

Regionalized model performance

R2 (N-S) Volume fit

Daily 10 days Monthly Uke 0.82 (0.60) 0.85 (0.62) 0.88 (0.62) 0.70

D.Nr.Demb 0.69 (0.55) 0.79 (0.70) 0.83 (0.71) 1.12

Great Anger 0.83 (0.72) 0.87 (0.75) 0.89 (0.75) 1.40

Main Beles 0.57 (0.59) 0.74 (0.74) 0.80 (0.79) 1.53


Tkorr (10-5)

Kkorr (103)

kD (102)

SHmax

kH (102)

Pgren

rk

Group 2 8.93 0.92 0.09 3.73 58 3.68 10 1


R2 (N-S) Volume fit

Daily 10 days Monthly Donder 0.74 (0.65) 0.83 (0.85) 0.93 (0.89) 0.87

Ardy 0.63 (0.50) 0.89 (0.73) 0.92 (0.79) 0.83

Andassa 0.50 (0.46) 0.80 (0.64) 0.85 (0.70) 0.68

Buno Bedele 0.77 (0.75) 0.79 (0.75) 0.82 (0.78) 0.82

Bello 0.68 (0.60) 0.76 (0.70) 0.82 (0.77) 0.65

Guder 0.73 (0.67) 0.80 (0.70) 0.85 (0.71) 0.60


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In group 3 (see Table 5-3), daily records (1993-1999) of Fetta and Dura rivers, which are located south of Lake Tana sub-basin, were calibrated simultaneously and the other four rivers in the same group were reserved for validation of the model. Validation rivers in this group are geographically close to each other and their R2 values ranges from 0.53 to 0.73 for daily, from 0.62 to 85 for 10-day and from 0.65 to 0.89 for monthly time steps.



Tkorr (10-5)

Kkorr (103)

kD (102)

SHmax

kH (102)

Pgren

rk

Group 3 6.57 7.21 0.25 1.06 20 2.75 10 0.5


R2 (N-S) Volume fit

Daily 10 days Monthly Birr Nr.Jiga 0.53 (0.51) 0.71 (0.66) 0.83 (0.78) 0.82

Temcha 0.59 (0.56) 0.81 (0.78) 0.88 (0.82) 1.06

Dura 0.75 (0.61) 0.82 (0.77) 0.85 (0.80) 0.79

L. Fetta 0.73 (0.70) 0.85 (0.82) 0.89 (0.87) 0.90

Neshi 0.59 (0.52) 0.62 (0.55) 0.68 (0.55) 0.67

Fetta 0.76 (0.70) 0.89 (0.77) 0.95 (0.81) 0.86

In group 4, daily records (1993-2005) of Gilgel Abay and Gumera rivers, which are located in Lake Tana sub-basin, were calibrated simultaneously. Gilgel Abay has relatively long, good quality of data in the Blue Nile river basin and presented best value of R2 and volume fit. Coefficients of determination of the validation rivers in this group range from 0.59 to 0.70, from 0.72 to 0.88 and from 0.78 to 0.91 for daily, 10 days and monthly time steps respectively. Table 5-4 depicts model performance for sub-catchments in group 4.


110



Tkorr (10-5)

Kkorr (103)

kD (102)

SHmax

kH (102)

Pgren

rk

Group 4 4.28 6.49 4.81 4.96 5.8 0.94 1.26 1


R2 (N-S) Volume fit

Daily 10 days Monthly Chemoga 0.63 (0.44) 0.80 (0.48) 0.89 (0.52) 0.65

G. Beles 0.70 (0.60) 0.88 (0.80) 0.91 (0.80) 0.76

G. Abay 0.81 (0.80) 0.90 (0.86) 0.93 (0.91) 0.91

Koga 0.59 (0.56) 0.72 (0.70) 0.78 (0.80) 0.65

Gumera 0.72 (0.67) 0.82 (0.76) 0.86 (0.90) 0.86

In group 5, daily records (1994-1999) of Robi Gumero and Sibilu near Chancho rivers, which are located in eastern part of the Blue Nile river basin, were calibrated simultaneously. The remaining three catchments were used as validation catchments and their R2 values ranges from 0.58 to 0.62, from 0.74 to 0.89 and from 0.83 to 0.92 for daily, 10 days and monthly respectively. Due to shortage in hydro-meteorological data, the regional model were validated only from 1994 to 1999. Table 5-5 presents model performance for sub-catchments in group 5.


Optimized regionalized WaSiM-ETH model parameters m (10-2)

Tkorr (10-5)

Kkorr (103)

kD (102)

SHmax

kH (102)

Pgren

rk

Group 5 3.81 0.45 2.36 0.70 1.22 11.4 10 1


R2 (N-S) Volume fit

Daily 10 days Monthly Robi Jida 0.61 (0.52) 0.85 (0.55) 0.92 (0.60) 0.40

Robi Gumero 0.69 (0.44) 0.89 (0.50) 0.95 (0.77) 0.57

Muger near Chancho

0.58 (0.45) 0.74 (0.49) 0.83 (0.65) 0.64

Aleltu near Chancho

0.62 (0.52) 0.81 (0.57) 0.88 (0.59) 0.47

Sibilu near Chancho

0.74 (0.59) 0.81 (0.75) 0.85 (0.50) 0.72


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In all criteria, the results for rivers in group 1 to 4 are better than those of rivers in group 5. This is mainly due to the existence of large number of meteorological stations (temperature and rainfall) for rivers in group 1, group 2, group 3 and group 4.

5.1.2 Ungauged catchments in Lake Tana sub-basin

Recent assessments of the hydrological system of Lake Tana sub-basin show uncertainties with respect to major lake water balance terms. Previous researches on the sub-basin pointed out that the main source of uncertainty is the inflows from ungauged catchment. Among others [31], [146], [147] and [32] estimated total flow from gauged and ungauged to Lake Tana that gave significantly different inflow values.

According to [146], the total gauged area in the Lake Tana sub-basin is presently about 42 % and the area in the Tana sub-basin, which is gauged by primary stations (Gilgel Abay, Koga, Gumera, Ribb and Megech) over a long period, is 36 %. For this research daily runoff times series from 10 gauging stations were collected from Ethiopian MoWE. The locations of most gauging stations have been selected following the main road in view of their easy accessibility. However, from a hydrometric point of view the chosen locations are not always optimal. Field survey by experts in [20] and [146] concluded that the discharge value for some of the gauging stations are not reliable due to mainly siltation, bank overflow, unstable cross sections and can not be used for any precise discharge assessments. It was mentioned in [146], [20] and confirmed in this study as well, that the runoff data for the Megech appeared less accurate (many outliers, especially in the month of August). The Ribb river is known to over flow at the gauging site upstream of the bridge during high river stages. The overflow is mainly caused by the reduced carrying capacity of the river due to sedimentation and the obstruction of the bridge.

The performance of WaSiM-ETH model and HBV-IHMS [32] rainfall runoff model for runoff time series of relatively small catchments (Gumero (165 km2), Garno (98 km2) and Gelda (27 km2)) were not satisfactory. We assumed that the runoff time series of these rivers could not be considered trustworthy. Therefore, we considered these rivers as ungauged river and inflow from these rivers were estimated using the procedure outlined in chapter 3.1.

In this research, inflow to Lake Tana and inflow to each artificial reservoir were estimated using the proposed regional model and following the steps outlined in section 3.1. Physical catchment characteristics like catchment area, shape, slope, average elevation etc of a river at each control points (junctions to Lake Tana and reservoirs inflow) were generated using ARC-GIS from 90 m by 90 m DEM. These physical catchment characteristics were used as an input to SOM. Rerunning the trained SOM assigned the new catchments at each control points to one of the homogeneous group that was formed previously. Results of the SOM showed control points at junction Megech, at junction Gemero and control point to Megech reservoir belong to group three and other control points to Lake Tana and artificial reservoirs belong to group four.


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The regional model was used onec again to transfer the whole set of WaSiM-ETH from the respective groups and to generate flow at each control points of artificial reservoirs and junctions to Lake Tana. Table 5-6 and Table 5-7 below depict the regional model out put at each control points of the four proposed reservoirs and Lake Tana junctions. The whole data set is presented in Appendix A2 of this dissertation.

Table 5-6 Mean monthly (1986-2005) inflow to each artificial reservoirs in Lake Tana sub-basin

Mean monthly inflow to each artificial reservoirs (106 m3) Megech Ribb Gumera Koga

this study

other study18

this study

other study17

this study

other study17

this study

other study17

Jan 5.3 1.2 5.3 1.8 2.9 2.0 2.1 2.1 Feb 4.2 0.9 4.0 1.3 2.2 1.2 1.5 1.6 Mar 3.5 1.0 3.4 1.3 1.9 1.0 1.5 1.5 Apr 3.1 1.2 3.0 2.0 1.6 0.9 1.5 1.3 May 3.3 1.8 4.5 2.1 2.5 1.2 2.3 1.4 Jun 5.8 7.8 8.2 7.7 4.5 4.8 5.5 5.2 Jul 25.3 30.8 93.6 54.0 51.8 49.4 21.6 24.8

Aug 65.2 88.2 170.2 92.0 92.5 101.7 40.3 38.2 Sep 42.1 31.9 85.4 35.2 47.1 52.9 25.5 22.6 Oct 21.6 6.6 34.3 0.4 19.3 18.8 13.6 10.2 Nov 11.5 2.9 14.4 5.4 7.8 6.8 5.8 4.3 Dec 7.3 1.9 8.0 2.6 4.4 3.5 3.2 2.9

198.3 176.3 434.3 215.7 238.3 244.2 124.3 161.1 Annual Estimated by [21] 445.0

As can be seen from Table 5-6 above, the results of the regional model are quite comparable with previous studies except for Ribb reservoir. However, our result for inflow to Ribb reservoir ( )36 m10434 ⋅ is close to the estimate ( )36 m10445 ⋅ by [20]. For the same reason we have mentioned earlier, the runoff data series from Ribb river cannot be trusted and any hydrological analysis based on the measured data could lead to under estimation of flow on the same river.

18 Data collected from [22], [25] and [39]


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Table 5-7 Mean monthly (1986-2005) inflow to Lake Tana at selected junctions in Lake Tana sub-basin

Mean annual total inflow (from gauged and ungauged catchments) to Lake Tana presented in Table 5-7 above were compared with other studies by [146], [147] and [32]. [146] and [147] have estimated inflow from ungauged catchment as the rest term of the water balance; where as this research and [32] have used regionalization approach. [32] regionalized HBV-IHMS rainfall runoff model parameters with catchment characteristics by using single and multiple regressions for tributary rivers in the Lake Tana sub-basin. [32] have calibrated the rainfall runoff model from 1993 to 2000 runoff data series and validated from 2001 to 2003 for Ribb, Gumera, Gilgel Abay, Megech and Kiliti rivers. They have also validated the regional model for the same period from 2001 to 2003, which may not guaranty the performance of the regional model since the runoff data series for model validation were also involved during calibration of the regional model. The mean annual total inflow to Lake Tana by [146], [147], [32] and results of this research are 6105028 ⋅ m3, 6105487 ⋅ m3,

6106699 ⋅ m3 and 6102.6523 ⋅ m3 respectively.

Mean monthly inflow to Lake Tana at each junctions (106 m3) Month

Megech Jun. (1018 km2)

Gemero Jun. (368 km2)

Garno Jun. (169 km2)

Ribb Jun. (1772 km2)

Gumera Jun. (1396 km2)

Gelda Jun. (257 km2)

Gilgel A.Jun. (4036 km2)

Total inflow to Lake Tana

Jan 8.0 2.7 2.0 15.9 14.3 2.1 36.3 81.5Feb 5.5 1.8 1.4 10.1 8.6 1.4 23.3 51.9Mar 5.0 1.6 1.2 10.4 9.3 1.2 25.3 53.8Apr 4.9 1.5 1.0 9.5 8.8 1.0 35.8 61.9May 10.7 2.8 1.3 17.6 21.6 2.8 87.8 138.2Jun 32.3 8.4 2.5 47.9 48.2 8.5 249.4 377.0Jul 112.9 39.7 23.5 264.9 224.1 36.5 706.3 1379.2Aug 156.8 60.2 50.6 426.8 362.3 57.7 877.9 1987.8Sep 86.2 32.9 27.7 245.9 221.9 38.5 600.7 1270.2Oct 54.5 20.4 12.2 114.8 111.7 19.8 361.7 682.2Nov 24.8 9.1 5.6 52.5 50.7 7.6 138.7 286.1Dec 12.6 4.3 3.0 30.2 30.9 3.8 69.0 153.4Annual 514.1 185.4 132.0 1246.3 1112.3 181.0 3212.2 6523.2% total inflow

7.8

2.8

2.0 18.9 16.9 2.7 48.8

100

Derived optimum rule curve

114

5.2 Derived optimum rule curve

5.2.1 Results of coupled SO-CMA-ES algorithm and HEC-5

5.2.1.1 Existing condition: sectoral approach

I. Optimized hydropower productions of Tis-Abay hydropower plant

Water for Tis-Abay hydropower station I and Tis-Abay hydropower station II are released from Lake Tana reservoir. As it was described in chapter 3, environmental flows downstream of Chara Chara weir were taken from two previous studies. In this section, Tis-Abay I and II hydropower productions were examined under different environmental flows scenarios. In the first scenario, only mean monthly estimated flow by [145] that are needed for ecosystem was considered. Where as in the second scenario mean monthly estimated flow by [144] that are needed for aesthetic value of the waterfall (for local community and tourist attraction) was considered in addition to flows allocated for the ecosystem. Table 5-8 presents a summary of optimized monthly and annual hydropower productions for the two environmental flow conditions. Annually there are about 20 GWh difference in hydropower production between the two scenarios, though the difference in mean maximum and minimum monthly productions are marginal. Although it is difficult to quantify the aesthetic value of the Tis-Issat waterfall for the local community, annual income from tourist and sale of electricity could give a hint on the best choice between the two scenarios if we consider this as the only water resource development of the sub-basin.

Table 5-8 Optimized power production for Tis-Abay hydropower station

II. Optimized hydropower production of Tana-Beles hydropower plant

In this section, Tis-Abay hydropower stations have been considered as a stand-by station when the Tana-Beles station is operational. Therefore, Tana-Beles hydropower production and minimum release for the Tis-Issat waterfall were taken as the only water resources development in the sub-basin. Table 5-9 presents mean monthly required and produced hydropower and percentage of demand met for optimal reservoir operation. Two different environmental flow scenarios as discussed in the above section were considered in this section as well. Taking in to consideration of the high available head

Mean monthly

Stat

ion

Condition considered

Maximum production

(MWh)

minimum production

(MWh)

Mean monthly

production (MWh)

Mean annual

production (MWh)

Only environmental flow 40,280 12,626 31,773 381,277 Tis-

Abay Environmental flow and aesthetic

40,587

10,900

30,093

361,121


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(311 m) of Tana-Beles as compared to Tis-Abay hydropower plant, model results showed no significant difference in hydropower production between the two environmental flow scenarios.

Table 5-9: Optimized hydropower production for Tana-Beles hydropower station

III. Tana-Beles hydropower production at different navigation level

Navigation on Lake Tana plays an important role in the transport of people and goods, especially to and from the more isolated western part of the lake. As it has been noted on [24], there is serious concern at the Transport and Navigation Enterprise in Bahr Dar that the levels of Lake Tana in future will drop to unacceptable low levels because of all planned developments. According to the Enterprise, the minimum level of Lake Tana should be 1785.0 m a.s.l. If water levels drop below this level, navigation is restricted because of the many shallows in the lake [24]. In this section, the effect of navigation on hydropower production or vice versa was examined by varying the levels of the lake, which are kept for navigation purpose from 1784.0 m a.s.l. with an increment of 10 cm until 1785.5 m a.s.l.

In this case, Tana-Beles hydropower production and the release of minimum flow (for both ecosystem and aesthetic value) to the Tis-Issat waterfall were considered as the only water resources development of the sub-basin. Table 5-10 presents twenty years mean monthly minimum, mean monthly maximum, mean monthly and mean annual hydropower production at different navigation levels.

Only environmental flow Environmental and aesthetic

Mean monthly hydropower

M

onth

required (GWh)

produced (GWh)

% demand met

produced (GWh)

% demand met

Jan 164 152 92.3 152 92.3 Feb 150 138 91.9 137 91.8 Mar 164 151 91.8 151 91.7 Apr 159 146 91.7 146 91.7 May 164 151 91.7 151 91.6 Jun 159 146 91.7 146 91.6 Jul 164 152 92.6 151 92.1 Aug 164 160 97.2 154 93.9 Sep 159 155 97.2 153 96.4 Oct 164 160 97.6 159 96.8 Nov 159 156 98.3 154 96.8 Dec 164 161 98.2 159 97.0 Annual 1936 1826 94.4 1812 93.6


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Table 5-10 Tana-Beles hydropower production at different navigation levels

Figure 5-1 shows mean annual hydropower production of Tana-Beles hydropower station under different navigation level. It can be concluded from Figure 5-1 that the product of the available head and flow plays an important role to the change in hydropower production for navigation level from 1784.0 m a.s.l. to 1785.0 m a.s.l. This is mainly due to the fact that hydropower production is a function of both flow and head (see the non-linear characteristics of Figure 5-1). Continuous decrease in hydropower production for an increase in available head for navigation level greater than 1785.0 m a.s.l. is an indication that the available flow is the dominant factor. It was found that the change in Tana-Beles hydropower production is not significant to the change in navigation levels from 1784.0 m a.s.l. to 1784.9 m a.s.l. because of the high head (311 m) and low plant factor (0.48) of the Tana-Beles hydropower station. For navigation level greater than 1784.9 m a.s.l., however, the reduction is significant and there are even some zero monthly hydropower productions under extreme dry season.

Mean monthly Lake Tana navigation level (m a.s.l.)

minimum production (GWh)

maximum production (GWh)

Mean monthly production (GWh)

Mean annual production (GWh)

1784.0 137.46 159.02 151.02 1812.28 1784.1 137.48 158.38 151.09 1813.12 1784.2 137.46 159.02 151.24 1814.91 1784.3 137.46 159.02 151.24 1814.91 1784.4 137.46 159.02 150.59 1807.08 1784.5 137.46 159.02 150.59 1807.08 1784.6 138.15 159.05 151.53 1818.36 1784.7 138.15 159.07 151.59 1819.02 1784.8 138.19 159.08 151.44 1817.31 1784.9 138.19 159.08 151.12 1813.45 1785.0 138.19 159.43 150.80 1809.64 1785.1 138.17 159.43 149.77 1797.25 1785.2 131.80 158.57 148.02 1776.18 1785.3 120.83 158.60 145.18 1742.22 1785.4 120.58 159.22 143.89 1726.70 1785.5 86.33 159.66 140.16 1681.89


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Figure 5-1 Tana-Beles mean annual hydropower production at different navigation levels (Tana-Beles as the only water resources development of the lake). From Figure 5-1 and Table 5-10, for the current demand (if Tana-Beles hydropower production and Tis-Issat waterfall are the only water resource development) maximum mean annual hydropower production can be achieved at navigation level of 1784.7 m a.s.l. Annually about 9 GWh reduction from its maximum hydropower production at 1784.7 m a.s.l. were found if the navigation level is raised to 1785.0 m a.s.l. as demanded by Lake Tana Transport and Navigation Enterprise. The trade-off between navigation and hydropower production is expected to increase with the realization of future water resources development scenarios in Lake Tana sub-basin that will be discussed in section 5.2.2.

5.2.1.2 Scenario 1: reservoirs optimized individually (sectoral approach)

The four upstream artificial reservoirs and Lake Tana were optimized for their own demand that includes minimum downstream requirement for environment, domestic water supply for Gonder city (only for Megech reservoir), irrigation requirements and flows needed for aesthetic value of the Tis-Issat waterfall. In this sectoral approach, every sector tries to maximize their own benefit irrespective of downstream demands by other sectors. First, four upstream artificial reservoirs were optimized separately for their own demand and then Tana-Beles hydropower station at navigation level fixed at 1784.0 m a.s.l. as follows.


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I. Megech, Ribb, Gumera and Koga reservoirs for irrigation

In the process of optimization, for all artificial reservoirs considered in this section, 12 monthly upper target storages were set for conservation level (normal operation for irrigation demands) and 12 monthly lower target storage were set for buffer level (for domestic water supply and environmental flow). Except for Megech reservoir where the buffer zone was used for both domestic water supply and environmental flow, the buffer zone for other reservoirs was used solely for environmental flow.

Rule curves are sets of target storages or target reservoir levels. In general, all demands are satisfied as long as the current water levels in the reservoir are on or above the upper rule curve. If the current water levels are between the upper and lower rule curves, first priority demand and a fraction of less priority demand are satisfied. Only a fraction of highest priority demand is satisfied when the water level is between the lower rule curve and top of inactive zone. The ultimate objective of the reservoir operator is to bring the current reservoir level to the values of the upper rule curves by releasing water if the reservoir level is above the upper rule curve or by storing water when the reservoir level is below the upper rule curve. It is highly recommended to keep the water level above the buffer zone at any circumstances.

Figure 5-2 shows sample optimized upper and lower rule curves and actual reservoir level at the end of the operation period of Ribb irrigation reservoir for the year 1993 and 1994. Accordingly, all highest priority demands (only environmental flow in this case) were satisfied as the actual water levels of the reservoir for all months were above the values of the lower rule curve. It was also observed from the same figure that the values of the upper rule curve and the actual water levels of the reservoir were identical for all months except for June, July and August. Irrigation demands for these three months (rainy season) are zero and, therefore, reservoirs in these three months can be used to store the incoming flow. On August 1994, the actual water level of the reservoir was above the upper rule curve but below the flood level (in this case crest level of the dam). In this case, depending on the hydrometeorological condition of the catchment, some amount of water should be released to bring the reservoir level to the value of the upper rule curve otherwise flood may occur.


119

Figure 5-2 Sample simulated water level for 1993 and 1994, upper and lower rule curve for Ribb irrigation reservoir.

Figure 5-3 shows the performance of the coupled SO-CMA-EA model in the course of optimization for Megech reservoir. Figure 5-3a refers to the evaluation of the model objective functions (F1 = 0 if there is no deficit), which is the sum of water supply for irrigation, domestic water supply and environmental flow deficits. Figure 5-3b shows how the 24 values of the rule curves are changing during optimization. It can be seen from both figures that the 24 values of the rule curves were very unstable (zigzag lines) for the first 1000 model runs and then it reached its optimal value (straight line) after an about 2000 model runs and continued until the stopping criteria set by users met.

(a) (b)

Figure 5-3 Evaluation of model performance during optimization


120

Sometimes it may be needed to reduce the number of dimensions (N=24 in this case) to save some computational time as it is known the total required computational time increases as the number of dimensions increases. This is especially important for multi-purpose multi-reservoir systems, which normally deals with higher number of dimensions. The impact of changing the number of dimensions on model results was investigated by reducing the number of dimensions to 13. This was done by keeping the lower rule curve constant through out the year while the upper rule curve was set to vary monthly. Figure 5-4 presents optimized rule curves of Megech reservoir for both conditions (N=24 and N=13). For N=13 (12 values of upper rule curve and one value of lower rule curve), 61041.207 ⋅ m3 of water should be stored in the buffer zone from month to month while for N=24 the amount varied from a minimum of 61034.293 ⋅ m3 to a maximum of 61049.141 ⋅ m3. On average 61002.0 ⋅ m3 per year of water, which ultimately be used for irrigation demand, can be saved by varying the lower rule curve. The significance of varying the lower rule curve would have come into a bigger picture when there were big seasonal variations in the highest priority demand. The estimated domestic water supply demand of Megech reservoir is not significantly (as compared to the irrigation demand) varying from month to month. The same analysis has been done for Ribb, Gumera and Koga reservoirs that have environmental flow as the only highest priority demand, and results showed that there existed marginal advantages of varying the lower rule curve. Table 5-11 shows average monthly irrigation water demand and shortage in 106 m3 for Megech reservoir for N= 24 and N= 13. As per the table except for December, the monthly irrigation water deficits are almost the same for constant and variable lower rule curves. For this reservoir the public water supply for Gonder city and minimum environmental flows were satisfied in both conditions. There were no irrigation water and minimum environmental flows deficits for Ribb, Gumera and Koga reservoirs. Therefore, constant lower rule curve for each reservoir can be used if needed for multi-objective multi-reservoir system.

Figure 5-4 Upper and lower rule curves for Megech reservoir


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Table 5-11 Monthly irrigation water demand and irrigation deficit in 106 m3 for both lower rule curves

Short1:- Shortage in 106 m3 when seasonal lower rule curve was used Short2:- Shortage in 106 m3 when constant lower rule curve was used As it was described in chapter 2, areas upstream of the shores of Lake Tana in general, Fogera flood plain in particular are frequently inunduated by overflow of rivers and back flow of Lake Tana. In this research, maximum regulated and natural flow downstream of the proposed reservoirs were examined. Results at the end of reservoir operation period indicated that maximum flow downstream of Ribb reservoir was reduced from 144 m3/s to 88 m3/s. The change in maximum flow downstream of Gumera reservoir was found to be insignificant due to its small storage capacity. Maximum flow downstream of Megech and Koga reservoirs were decreased by 25 m3/s and 10 m3/s respectively. Although it showed general decrease in maximum flows at junctions with Lake Tana, relatively high flows were still observed owing to large amount of unregulated flow between the proposed reservoirs and Lake Tana.

II. Lake Tana reservoir for hydropower production

In the second case of sectoral approach, Tana-Beles hydropower station was optimized for its own demand for navigation level fixed at 1784.0 m a.s.l. Total flow to Lake Tana was taken as the sum of environmental flow from upstream reservoirs, 15% return flow from upstream irrigation and in between flow from gauged and ungauged catchments. This was accomplished by freezing the optimized rule curves of upstream artificial reservoirs while operation rule curve of Lake Tana was allowed to vary monthly. Two demands, i.e. hydropower production and flows that are needed for aesthetic value of the waterfall were considered. Table 5-12 presents model output for different number of population size. As it was described in chapter 3, CMA-ES does not require a tedious parameter tuning for its application with the exception of population size. The number of population was increased from its default value (11) to population size of 52. Maximum hydropower production (1806.89 GWh) was obtained at population size of 22. After population size of 22, hydropower production oscillated between 1804.28 GWh and 1802.39 GWh without further improvement despite the increase in population size. The same analysis was done for other reservoirs as well. In general, the number of iterations increased for an increase in the number of population size that demanded more computational time. In all cases, the performance of CMA-ES was improved for a population size different from the default value. Therefore, for all reservoirs considered in this research, population size was changed from its default value.

Jan Feb Mar Apr May Jun-Aug

Sep Oct Nov Dec Sum

Demand 6.40 11.08 10.77 2.28 0.16 0.00 1.35 5.14 2.31 2.20 41.68 Short1 0.01 0.03 0.00 0.01 0.00 0.00 0.20 0.27 0.08 0.02 0.63 Short2 0.01 0.03 0.01 0.01 0.00 0.00 0.21 0.27 0.07 0.04 0.65


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Table 5-12 Tana-Beles hydropower production at different CMA-ES population size

CMA-ES population size

No. of iterations

Mean annual hydropower production (GWh)

Water supply deficit (106 m3)

11 (default) 5458 1801.84 17.8 17 9165 1803.87 17.8 22 9022 1806.89 17.8 32 11106 1803.71 17.8 42 12938 1804.28 17.8 52 17006 1802.39 17.8

5.2.1.3 Scenario 2: full water resources development of Lake Tana sub-basin using SO-CMA-ES (integrated approach)

In this scenario, all requirements for all reservoirs were optimized simultaneously. As it was discussed in section 5.2.1.2 above and since, there were marginal advantages of varying the lower rule curves, constant lower rule curve for each reservoirs were used in all multi-objective optimization problems. Therefore, the number of dimensions N=120 (5 reservoirs, 24 values of upper and lower rule curves for each reservoir) were reduced to N=65 (5 reservoirs, 12 values of upper rule curve and 1 value of lower rule curve for each reservoirs). This section demonstrated the use of SO-CMA-EA for multi-objective optimization problems. Table 5-13 and Figure 5-5 present total water supply and hydropower production deficits for different combinations of weighting factors. Model results for 121 ==ωω showed that the numerical value of hydropower production deficit was greater than the numerical value of actual water supply deficit. This means that for this demand scenario, the optimization algorithm was in favour of hydropower production as it has spent more time to reduce the hydropower deficit to the same level as deficit in total water supply. In order to give more priority to total water supply, users have to induce deficits artificially. This can be done either by multiplying the total water supply term in equation 3.34 by a weighting factor greater than one or the hydropower production term in the equation by a weighting factor less than one. Here, the

hydropower production term was divided by a ratio of weighting factors 12

1 >ωω (see

Table 5-13) to give more priority to total water supply. Accordingly, minimum deficit in hydropower production (operation in favour of hydropower) and minimum deficit in total water supply (operation in favour of total water supply) were obtained at weighting factor ratios of 1 and 2000 respectively. Optimum reservoir operation was found at a weighting factor ratio of 1000, where the sum of total water supply and hydropower deficit was minimum. Figure 5-5 depicts possible pareto-front using SO-CMA-ES. See section 5.2.2.2 for comparison of pareto-fronts using SO-CMA-ES and MO-CMA-ES for the same multi-objective problems.


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Table 5-13 Deficits in total water supply and hydropower production at different priority level

Ratio w1: w2 Shortage in 1 50 100 500 1000 1500 2000 Total water supply 289 288.6 229.2 199 34.4 33.7 32.2 Hydropower 141 141.6 149.1 167 172.6 185.9 186.7Sum 430 430.2 382.3 366 207 219.6 218.9

Figure 5-5 Approximate pareto-curve using coupled SO-CMA-ES and HEC-5

5.2.2 Results of coupled MO-CMA-ES algorithm and HEC-5 (integrated approach)

5.2.2.1 Scenario 3: partial water resources development of Lake Tana sub-basin using MO-CMA-ES

In this scenario, all requirements for four artificial reservoirs and Lake Tana were optimized simultaneously using coupled MO-CMA-ES and HEC-5 for navigation level of 1784.0 m a.s.l. Unlike SO-CMA-ES where the coupled model has been running many times with different combinations of weighting factors, pareto-curve was generated in a single coupled MO-CMA-ES and HEC-5 model run. Figure 5-6 depicts the coupled MO-CMA-ES and HEC-5 model out puts at different number of iterations. For the first 1000 model run, hydropower deficit was reduced from about 800 GWh to


124

135 GWh, while total water supply deficit was decreased from about 610004 ⋅ to 610165 ⋅ m3. As the number of iteration increases beyond 1000, deficit in total water

supply decreased significantly as compared to deficit in hydropower production. It was found that the change in pareto-front was not significant after 50000 iterations. In the same figure, two points were marked as solutions in favour of hydropower production and total water supply. Solutions in favour of hydropower production and total water supply are points where hydropower production and total water supply deficits respectively are minimum. These points were generated after the model results were exported to Matlap environment.

Figure 5-6 An approximate pareto-front for partial WRD scenario using MO-CMA-ES

Table 5-14 Comparision of deficits in total water supply and hydropower production for two partial WRD scenarios

Partial water resources development (WRD)

with out aesthetic value with aesthetic value of the waterfall Mean annual deficit in

Mean annual deficit in

Res

ervo

ir op

erat

ion

in

favo

ur o

f

HDP demand (GWh)

TWS demand (106 m3) TWS HDP

HDP demand (GWh)

TWS demand (106 m3) TWS HDP

TWS 67 112 63 131

HDP 1936 1013

215 83 1936 1280

199 116


125

From Table 5-14 for an increase in water demand by 26%, the model result showed an increase in hydropower production deficit by 17% and 40% for reservoir operation in favour of total water supply and hydropower production respectively. Comparing with results in Table 5-9 where Tana-Beles hydropower production is the only water resources development, the realization of four planned irrigation projects further reduce hydropower production by 7 GWh for reservoir operation in favour of total water supply.

5.2.2.2 Scenario 4: full water resources development of Lake Tana sub-basin using MO-CMA-ES

As it was mentioned in chapter 4, only in this dissertation, full water resources development of Lake Tana sub-basin referred to demands mentioned on section 4.2 and additional planned irrigation demands from Lake Tana pumping stations like South-West Tana pumping, North-West Tana pumping and North-East Tana pumping. Also in this scenario, environmental flow includes not only flows that are needed for ecosystem but also flows for aesthetic value of the Tis-Issat waterfall. Referring to the Ethiopian river basin master plan, there are additional planned water resources development in the Lake Tana sub-basin, which were not considered here. Figure 5-7 depicts the coupled MO-CMA-ES and HEC-5 model output at different number of iterations. For the first 1000 model run, hydropower deficit was reduced from about 800 GWh to 150 GWh, while total water supply deficit was decreased from about 610004 ⋅ to 610175 ⋅ m3. As the number of iteration increases beyond 1000, deficit in total water supply decreased significantly as compared to deficit in hydropower production.

Figure 5-7 An approximate pareto-front for full WRD scenario using MO-CMA-ES


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I. Comparison of SO-CMA-ES and MO-CMA-ES for multi-objective problems

Comparison has been done between SO-CMA-ES and MO-CMA-ES algorithms for the same multi-objective optimization scenario. From Figure 5-8, four out of seven non-dominated solutions of SO-CMA-ES were found with in dominated solutions of MO-CMA-ES and interestingly, the remaining three points were found outside the domaine of MO-CMA-ES. It does not, however, necessarily mean that the non-dominated solutions of SO-CMA-ES are always found within the donminated solutions of MO-CMA-ES. One needs to have experience and priori knowledge on different combinations of weights. As can be seen from Table 5-15, for changes in total water supply of about 61020 ⋅ m3, SO-CMA-ES resulted an increase in hydropower deficit of about 47 GWh. In other words, for reservoir operation in favour of total water supply, SO-CMA-ES yielded the lowest total water supply deficit of 6102.32 ⋅ m3 at the expense of lossing 46.7 GWh hydropower production. For reservoir operation in favour of hydropower production, MO-CMA-ES performed better in reducing both deficits in total water supply and hydropower production. For both algorithms, the change in deficits were not significant for reservoir operation in favour of total water supply and optimum reservoir operation. From sectoral approach point of view and if highest priority is given to total water supply (mainly for irrigation and Tis-Issat waterfall), results of SO-CMA-ES is encouraging. However, there is no guarantee to say it always provide the best result in reducing total water supply deficit for different demand scenario as weights are subjective. In addition, for hydropower production sector MO-CMA-ES performed well as compared to SO-CMA-ES. From integrated approach point of view that allow compromises among different sectors, MO-CMA-ES provided different alternative solutions for decision makers. See Figure 5-8 for the relative position of points in favour of total water supply, hydropower production and optimum reservoir operations.

Figure 5-8 Approximate pareto-front for full WRD generated using SO-CMA-ES and MO-CMA-ES


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Table 5-15 Comparison of SO-CMA-ES and MO-CMA-ES for multi-objective problems

II. Comparison of different water resources development using MO-CMA-ES

A comparison has also been done among different water resources development of Lake Tana sub-basin that includes full water resources development, partial water resources development with and with out aesthetic value of the waterfall (referred in Figure 5-9 as Tis-Issat) and full water resources development at different navigation levels. Figure 5-9 and Table 5-16 present results of the coupled MO-CMA-ES model for three demand scenarios. Taking partial water resources development with out aesthetic value of the waterfall as a reference, there was in general an increase in total water supply and hydropower production deficits as the demands increases. For an increase in water demand by 26% from the reference demand ( )m 101013 36⋅ , the model result showed an increase in hydropower production deficit by 17%, 40% and 21% for reservoir operation in favour of total water supply, hydropower production and optimum reservoir operation respectively. Increase in hydropower production deficit of 25%, 52% and 21% were obtained for 42% increase in water demand for reservoir operation in favour of total water supply, hydropower production and optimum reservoir operation respectively. Taking Tana-Beles hydropower station as the only water resources development as a reference, the realisation of four planned reservoirs and pumping stations for irrigation purpose further reduce Tana-Beles hydropower production by 16 GWh and 6 GWh for reservoir operation in favour of total water supply and optimum operation respectively. In general the increase in water demand up stream of Lake Tana and Lake Tana itself for irrigation purpose further decrease the Tana-Beles hydropower production.

Mean annual total water supply (106 m3)

Mean annual hydropower production (GWh)

SO-CMA-ES MO-CMA-ES SO-CMA-ES MO-CMA-ES

Ope

ratio

n in

fa

vour

of

deficit

demand met (%)

deficit

demand met (%)

deficit

demand met (%)

deficit

demand met (%)

TWS 32.2 97.8 53 96.3 186.7 90.4 140 92.8 HDP 288.6 79.9 219 84.8 141.6 92.7 126 93.5 Opt 34.4 97.6 60 95.8 172.6 91.1 130 93.3


128

Table 5-16 Comparison of different water resources development of Lake Tana sub-basin

Figure 5-9 An approximate pareto-front for different water resources development scenarios

Water resources development (WRD) partial WRD with out aesthetic value of the waterfall

partial WRD with aesthetic value of the waterfall

Full WRD




Res

ervo

ir op

erat

ion

in fa

vour

of TWS

demand (106 m3)

TWS HDP

TWS demand (106 m3)

TWS HDP

TWS demand (106 m3)

TWS HDP

TWS 67 112 63 131 54 140

HDP 215 83 199 116 224 126

Opt

1013

68 107

1280

63 129

1438

61 130


129

III. Comparison of full water resources development at different navigation level using MO-CMA-ES

As it was mentioned in chapter 4, navigation on Lake Tana plays crucial role in the transport of people and goods. For full water resources development scenario, different navigation levels of Lake Tana were included to see its effect on total water supply and hydropower production deficits or vice versa. Figure 5-10 depicts the relationship amongst the different navigation levels of Lake Tana (every 20 cm interval), total water supply and hydropower production deficits. A quick look at of Figure 5-10 indicated that reservoir operation in favour of total water supply was more sensitive for change in navigation level than operation in favour of hydropower production.

Figure 5-10 An approximate pareto curve at different navigation levels using MO-CMA-ES


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Table 5-17 Percentage demand met of mean annual total water supply and hydropower production at different navigation levels of Lake Tana using MO-CMA-ES

Reservoir operation in favour of

Total water supply Optimum Hydropower % demand met

% demand met

% demand met

Lake

Tan

a na

viga

tion

leve

l (m

a.s.

l.)

TWS HDP TWS HDP TWS HDP

1784.0 96.34 92.78 95.86 93.30 84.74 93.51 1784.2 96.15 92.73 96.10 92.82 85.08 93.37 1784.4 94.69 92.68 94.68 92.72 84.36 93.15 1784.6 93.46 92.21 93.34 92.40 87.07 92.98 1784.8 96.13 91.37 96.09 91.44 84.16 92.60 1785.0 93.27 90.32 93.20 90.41 84.64 91.69 A closer look at in Table 5-17 and taking the demand of Tana Transport Enterprise in to consideration, optimum value can be found at navigation level of 1784.8 m a.s.l. This level is less than the level demanded by the enterprise (1785.0 m a.s.l.). However, navigation level fixed at 1785.0 m a.s.l. resulted in zero monthly hydropower production for some extreme dry season. Table 5-17 presents aggregate percentage demand met for all reservoirs, which does not indicate how these deficits are distributed for each reservoir. Figure 5-11 depicts percentage demand met for each reservoir at selected navigation levels. The numbers on each block of artificial reservoirs and Lake Tana represent percentage demand met of total water supply and hydropower production respectively. From Figure 5-11, it can be concluded that reservoir operation in favour of hydropower production of Tana-Beles was not the best choice for Ribb, Megech and Koga reservoirs as the percentage demand met values were significantly low (< 50%). In addition to zero hydropower production for some months, navigation level fixed at 1785.0 m a.s.l. resulted percentage demand met less than 50 for Koga reservoir under reservoir operation in favour of total water supply and optimum operation. Comparing the distribution of deficits for navigation level fixed at 1784.4, 1784.6 and 1784.8 m a.s.l. and taking the demand by Tana Transport Enterprise in to account, 1784.8 m a.s.l. is the best choice. Keeping the lake level higher will benefit not only the enterprise but also other stakeholders among others are Fishers Cooperative and Tour boat operators.


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Figure 5-11 Percentage demand met for each reservoir at selected navigation levels Figure 5-12 shows actual and simulated Lake Tana water level at the end of reservoir operation in favour of total water supply for navigation level set at 1784.8 m a.s.l. The simulated water levels are bounded between 1784.8 and 1787.0 m a.s.l. The lowest simulated water level is found at 1996 following two previous drought years.


132

Figure 5-12 Observed and simulated Lake Tana water levels for navigation level fixed

at 1784.8 m a.s.l. for reservoir operation in favour of TWS Pareto-front generated using coupled HEC-5 and MO-CMA-ES algorithm contains many non-dominated solutions, which may not be used asis for decision makers. In general those successive points close to operation in favour of total water supply have flat slope as compared to points close to operation in favour of hydropower production. This means for small change in total water supply result in large change in hydropower production. Points close to operation in favour of hydropower production have relatively higher slope that yield big difference in total water supply for small change in hydropower production. Therefore, it is necessary to zoom in and examine the trade-off between successive non-dominated points. Figure 5-13 depicts extracted non-dominated points where there exist clear change in slope for two navigation levels and Table 5-18 presents percentage demand met for different selected non-dominated points for all reservoirs. Such reconstructed pareto-front and tables that contains detail deficits for all reservoirs provide useful information for decision makers and planners. Table 5-19 and Table 5-20 present monthly deficit in total water supply and hydropower production and monthly upper target levels for all reservoirs at navigation level of 1784.8 m a.s.l.


133

Figure 5-13 Extracted non-dominated points for navigation level fixed at 1784.8 and

1785.0 m a.s.l. Table 5-18 Percentage demand met at selected points of pareto-front for navigation

level of 1784.8 m a.s.l.

% demand met in total water supply % demand met in HDP

Sele

cted

op

erat

ion

poin

ts

Megech Koga Ribb Gumera Tana Total Tana-Beles

TWS 91.30 78.76 90.92 78.13 99.65 96.08 91.37 1 91.14 78.79 90.92 75.31 99.63 95.90 91.46 2 91.10 79.01 90.42 72.77 99.65 95.70 91.53 3 91.03 79.05 89.62 70.16 99.65 95.44 91.69 4 88.79 78.16 88.89 69.68 99.65 95.16 91.72 5 89.99 78.96 88.98 66.01 99.65 95.06 91.77 6 90.02 73.84 87.42 64.75 99.65 94.61 91.80 7 81.51 68.72 89.20 58.17 99.65 93.77 91.96 8 67.06 34.72 83.76 72.56 99.65 91.89 91.98 9 59.52 44.02 84.07 71.35 99.65 91.72 92.04 10 59.04 41.58 80.74 70.39 99.65 91.13 92.08 11 56.64 39.15 73.10 70.19 99.65 89.93 92.08 12 56.97 33.94 69.22 70.07 99.65 89.28 92.14 13 57.30 32.34 66.53 69.97 99.65 88.90 92.14 HDP 49.69 19.46 35.62 65.99 99.88 84.06 92.60


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Table 5-19 Monthly deficit in total water supply and hydropower production for all reservoirs at navigation level of 1784.8 m a.s.l.

Table 5-20 Monthly upper target reservoir level for all reservoirs for navigation level of 1784.8 m a.s.l.

Res. Megech Koga Ribb Gumera Tana Upper target level for reservoir operation in favour of

Month TWS HDP Opt TWS HDP Opt TWS HDP Opt TWS HDP Opt TWS HDP Opt Jan 1933.81 1937.24 1933.87 2011.58 2013.56 2011.61 1923.34 1935.24 1923.4 1927.03 1923.87 1927.02 1786.74 1786.75 1786.74 Feb 1930.08 1929.64 1930.16 2010.06 2012.78 2010.03 1916.33 1928.22 1916.26 1925.85 1922.91 1925.84 1786.54 1786.71 1786.53 Mar 1926.9 1946.07 1927.11 2012.95 2012.54 2012.97 1908.06 1934.85 1907.75 1923.42 1924.49 1923.52 1786.24 1786.26 1786.24 Apr 1925.77 1917.34 1925.98 2009.61 2013.30 2009.62 1928.71 1911.05 1928.89 1926.34 1923.68 1926.34 1785.97 1786.02 1785.98 May 1924.51 1931.20 1924.63 2009.57 2013.15 2009.56 1906.41 1913.90 1906.26 1926.52 1923.19 1926.53 1785.95 1786.09 1785.96 Jun 1940.75 1944.80 1940.7 2014.49 2010.52 2014.51 1928.96 1915.56 1928.95 1925.33 1924.02 1925.35 1785.85 1786.42 1785.86 Jul 1926.18 1926.01 1926.05 2013.82 2014.69 2013.81 1919.24 1915.77 1918.81 1926.67 1925.45 1926.65 1786.30 1786.21 1786.31 Aug 1935.42 1944.18 1935.41 2011.91 2014.57 2011.89 1915.73 1928.54 1915.59 1927.92 1925.97 1927.92 1786.80 1786.74 1786.80 Sep 1944.08 1934.68 1944.03 2013.09 2013.96 2013.08 1934.77 1925.66 1934.86 1927.21 1926.36 1927.21 1786.94 1786.97 1786.94 Oct 1935.18 1931.83 1935.21 2012.97 2008.87 2012.97 1934.94 1933.91 1935.03 1924.74 1925.27 1924.71 1787.00 1787.00 1787.00 Nov 1935.25 1929.58 1935.24 2012.66 2010.55 2012.66 1935.09 1933.43 1934.94 1926.11 1923.23 1926.08 1786.88 1786.83 1786.87 Dec 1935.14 1945.08 1935.17 2012.42 2009.17 2012.41 1928.82 1928.22 1928.9 1926.99 1927.21 1926.93 1786.62 1786.60 1786.62

Res. Megech Koga Ribb Gumera Tana Tana-Beles Mean monthly TWS shortage (106 m3) for reservoir operation in favour of HDP shortage (GWh)

Month TWS HDP Opt TWS HDP Opt TWS HDP Opt TWS HDP Opt TWS HDP Opt TWS HDP Opt Jan 0.00 9.52 0.00 0.00 7.89 0.00 0.01 34.99 0.00 2.51 0.88 2.65 0.00 0.00 0.00 12.58 12.54 12.58 Feb 0.00 1.59 0.00 0.00 13.03 0.00 0.24 25.64 0.11 10.14 11.62 10.14 0.00 0.00 0.00 12.18 12.14 12.18 Mar 0.00 14.65 0.07 10.20 10.09 10.20 0.00 33.05 0.00 4.03 14.68 4.44 0.00 0.00 0.00 13.50 13.46 13.50 Apr 0.00 0.00 0.00 0.00 2.33 0.02 12.83 0.00 12.83 0.48 0.27 0.48 2.40 0.00 2.40 19.81 12.50 19.81 May 0.00 4.69 0.00 0.02 0.80 0.01 0.00 9.07 0.03 0.13 0.00 0.13 1.28 1.28 1.28 22.28 21.18 21.24 Jun 3.71 3.71 3.71 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.08 0.09 0.00 0.00 0.00 20.53 13.25 20.34 Jul 0.00 1.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 12.94 12.23 12.94 Aug 0.76 2.29 0.78 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 10.02 8.67 10.02 Sep 2.72 0.55 2.72 0.00 0.00 0.00 0.25 0.00 0.31 0.00 0.00 0.00 0.00 0.00 0.00 9.51 8.22 9.51 Oct 0.29 0.08 0.32 0.28 0.00 0.28 1.78 9.15 1.78 0.00 0.00 0.00 0.00 0.00 0.00 10.41 9.73 10.41 Nov 0.01 0.00 0.00 0.08 4.31 0.09 0.65 2.58 0.65 0.10 0.00 0.10 0.00 0.00 0.00 11.36 9.44 11.36 Dec 0.00 5.62 0.02 0.04 0.24 0.03 0.50 1.34 0.55 0.06 0.25 0.05 0.00 0.00 0.00 11.82 9.83 11.82 Annual 7.49 44.18 7.62 10.63 38.70 10.63 16.26 115.82 16.25 17.58 27.78 18.08 3.67 1.28 3.67 166.95 143.22 165.71 Met (%) 91.36 49.03 91.20 78.34 21.13 78.34 91.01 35.94 91.01 79.01 66.82 78.41 99.65 99.88 99.65 91.37 92.60 91.44

Conclusions and Recommendations

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6 Conclusions and Recommendations

The goal of the present dissertation was to develop decision support tools for existing and planned reservoirs for basins having no or limited runoff data, and to apply the tool to real-world multi-purpose multi-reservoir problems. The tool has three components: data-base, a platform to estimate flow to each reservoirs (from gauged or ungauged rivers), and a platform to generate optimal pareto-front for single and multi-purpose multi-reservoir systems. Note that the proposed tool can be used for any river basin. The main results of the tool in the case study area are summarized as follows:

The data-base component comprises of time series of model inputs and model output in tabular and graphic forms. The second component of the tool is used to generate flow in daily, 10 days and monthly time steps. In the second component of the tool, SOM and WaSiM-ETH were coupled. By using SOM with pre-defined physical catchment characteristics of 26 selected sub-catchments of the Blue-Nile river basin, five hydrological homogeneous groups were formed. A set of optimized WaSiM-ETH model parameters for each group were obtained by calibrating one or more sub-catchments from each group. For sub-catchments in group 2, group 3, group 4 and group 5, the selected sub-catchments were calibrated simultaneously. Then the whole set of WaSiM-ETH model parameters were transferred to ungauged catchments based on their similarity of hydrological homogeneity groups to generate stream flow.

The coupled regional model needed only temperature, rainfall, land use map, soil map and DEM, which can be available for ungauged catchments. The regional model generally overestimated the low flow part of the hydrograph. For most selected sub-catchments of the Blue-Nile river basin, the model performed well on 10 days and monthly time step than daily time step due to reduction of the sum of plus and minus errors through aggregation of the daily flow in to 10 days and monthly flow time step.

The value of datum of zero flow (Ho) corresponds to zero discharge in the stream, which is a hypothetical parameter to fit a rating curve (observed discharge versus observed gauge height) and cannot be measured in the field. The estimated value of Ho of most rating curves and less number of meteorological stations in some parts of the study area could be the reasons for model’s overestimation of the lower part of the hydrograph. It is observed in some gauging stations in Dedessa sub-catchments where the datum correction Ho value is above 0.5, the rating curve gave zero flow for some months whereas in reality there are substantial amount of flow during those months.

Results could be improved with long and good quality of hydro-meteorological data from large number of meteorological stations in the study area. The proposed methodology could be used for any rivers in the Blue Nile river basin following the steps described in the dissertation. In general, the results for sub-catchments that their data has never been involved during calibration showed the proposed regionalization method is quite satisfactory in transferring information from data rich catchments to data poor catchments or ungauged catchments which is vital for any water resources development activities in the basin.


136

The third component of the tool comprises of reservoir simulation and optimization models to derive optimal rule curves. Twenty years inflow data series to each artificial reservoirs and Lake Tana reservoir that were generated using the proposed regional model were used to generate optimal rule curves. This is to demonstrate the applicability of the proposed coupled simulation-optimization model. For practical case, longer time series are needed. The control strategies (rule curves) were set up in the HEC-5 reservoir simulation model to guide the releases of the reservoir system; and single and multi-objective Covariance Matrix Adaptation Evolution Strategy (SO-CMA-ES and MO-CMA-ES) optimization algorithms were adopted to optimise reservoir operation rule curves for different water resources development in Lake Tana sub-basin. Both, SO-CMA-ES and MO-CMA-ES algorithms were adopted for searching set of non-dominated or pareto optimal solutions according to the trade-offs between objectives. A trade-off amongst different water users like hydropower production, navigation, irrigation water supply and flow that are needed for the aesthetic value of the Tis-Issat waterfall were considered. For all scenarios, domestic water supply and environmental flows were given the highest priority.

Graphical comparison between the two optimization models for multi-objective optimization problems showed some of the non-dominated solutions of SO-CMA-ES were found with in dominated solutions of MO-CMA-ES. This indicated the conversion of multi-objective problems into single objective problem might not guarantee in finding all possible non-dominated solutions. MO-CMA-ES was also found to be superior in generating pareto-front than SO-CMA-ES for multi-objective multi-reservoir systems. Moreover, the pareto-front of MO-CMA-ES is more flexible and convenient for decision makers as it provides many non-dominated solutions in a single model run.

Different future water resources development scenarios of Lake Tana sub-basin on existing Tana-Beles hydropower station, irrigation projects, Lake Tana navigation and aesthetic value of the Tis-Issat waterfall were investigated. Two approaches i.e. sectoral and integrated approaches were compared. In sectoral approach each sector tries to maximum its own benefit regardless of downstream activities where as integrated approach tries to maximize the overall benefit of all stakeholders. Integrated approach is suppose to resolve conflict between different stakeholders. Different stakeholders involved in Lake Tana sub-basin among others include Ethiopian Electric Power Cooperation, Tana Transport Enterprise and tour boat operators, farmers upstream and downstream of Lake Tana, Fishers and Fishers cooperative, culture and tourisim Bureau, regional Bureau of water and energy and regional environmental protection authority. These stakeholders in one or other ways will be affected positively or negatively by different water resources development of the sub-basin. It is our recommendation to consult these stakeholders and adapt the most appropriate joint reservoir operation. This research has highlighted the value of integrated approaches to assessing the impacts of planned water resources development.


137

Taking Tana-Beles hydropower station as the only water resources development as a reference, the realisation of four planned reservoirs and pumping stations for irrigation purpose further reduce Tana-Beles hydropower production by 16 GWh and 6 GWh for reservoir operation in favour of total water supply and optimum operation respectively. In general the increase in water demand upstream of Lake Tana and Lake Tana itself for irrigation purpose further decrease the Tana-Beles hydropower production. Analysis on the relative percentage demand met for each reservoir at selected navigation levels revealed that optimum navigation level can be achieved at 1784.8 m a.s.l. It is, however, necessary to extend the deck on the ports where the lake water level is close to the ground. Keeping the lake level higher will benefit not only the enterprise but also other stakeholders among others are Fishers, Fishers Cooperative and Tour boat operators. Thanks to the high net head and low plant factor of Tana-Beles hydropower station (the station operates 48% of its capacity) that relieved some stresses on the sub-basin. Increasing the hydropower production to its full capacity and construction of additional reservoirs in the sub-basin, will exert more pressure to the lake and has to be analysed before the realization of any future water resources development in the sub-basin. Under such circumstances proper adaptation mechanisms to increase irrigation efficiency (50% current irrigation efficiency) and optimal irrigation scheduling are vital. The pareto-curve generated using MO-CMA-ES can be used by decision makers and planners to select the best reservoir operation of each reservoir. The choice of rule curves along the pareto-curve depends, however, not only on the cost-benefit analysis of water use but also priorities set by decision makers and additional qualitative information on those demands that are difficult to quantify in monetary terms. In general, the proposed decision support tool provide an important insight to decision makers and planners before the realization of any future water resources development in the Lake Tana sub-basin. Additional reservoirs from gauged and/or ungauged catchments can easily be hooked to the proposed tools. The capability of the tool for two additional artificial reservoirs (Gilgel Abay and Jema reservoirs) and one additional irrigation control point downstream of Tana-Beles hydropower station were tested for dummy values. It is important to note that, the rule curves generated in this study are dynamic in nature and, therefore, it is necessary to generate new joint rule curve for any change in the demand sector.


138

The stand-alone developed tool, i.e. regional and integrated reservoir simulation-optimization models, can be used by decision makers and planners in other watersheds where there exist scarce hydro-meteorological data and multi-objective problems in multi-reservoir system. However, it further needs graphical user interface to link all the inputs-outputs of the regional and reservoir simulation-optimization models to the database and vice versa. Every model lives with uncertainties and these uncertainities are not covered in this study. It is, however, important to quantify such uncertainities in model inputs, model parameters and in model structure. Neverthless, the results highlighted a paramount importance of the proposed regional model and integrated reservoir simulation-optimization model to support decision makers and planners. The tools enable decision makers and planners to choose an optimal policy amongst competing water uses in existing and planned multi-objective multi-reservoir system in hydro-meteorological data scarce area.

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[133] Taesoon K., Jun-Haeng H. and Chang-Sam J. (2006) ‘Multi-reservoir system optimization in the Han River basin using multi-objective genetic algorithms’, Hydrological processes, 20, pp. 2057–2075.

[134] Chen, L. and Chang, F. J. (2007) ‘Applying a real-coded multi-population genetic algorithm to multi-reservoir operation’, Hydrological processes, 21, pp. 688-698.

[135] Xun-Gui Li and Xia Wei (2007) ‘An Improved Genetic Algorithm-Simulated Annealing Hybrid Algorithm for the Optimization of Multiple Reservoirs’, Water Resour Manage 22, pp.1031–1049.

[136] Schütze, N. Wöhling, T., de Paly, M. (2010) ‘A comparative study of three simulation optimization algorithms for solving high dimensional multi-objective optimization problems in water resources EGU General Assembly, 2-7 May 2010, Vienna.

[137] U.S. Army Corps of Engineers Hydrologic Engineer Center (1998) ‘HEC-5 simulation of flood control and conservation systems’, user’s manual version 8.0, Davis, California.

[138] Igel C., Hansen N. and Roth S. (2007) ’Covariance Matrix Adaptation for Multi-objective Optimization’, Evolutionary Computation 15(1), pp. 1-28.

[139] Hansen, N. (2009) ‘References to CMA-ES applications’ http://www.lri.fr/~hansen/cmaapplications.pdf

[140] Hansen, N., Ostermeier, A. and Gawelczyk, A. (1995) ‘On the adaptation of arbitrary normal mutation distributions in evolution strategies: The generating set adaptation’, In Eshelman L. (éd.), Proceedings of the 6th International Conference on Genetic Algorithms, Pittsburgh, Morgan Kaufmann, pp. 57–64.

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References

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[141] Salomon, R. (1996) ‘Reevaluating genetic algorithm performance under coordinate rotation of benchmark functions’, BioSystems 39(3), pp. 263–278.

[142] Hansen, N. (2000) ‘Invariance, self-adaptation and correlated mutations in evolution strategies’, In Proceedings of the 6th International Conference on Parallel Problem Solving from Nature (PPSN VI), vol. 1917 of LNCS, Springer-Verlag. pp. 355–364.

[143] Hansen, N. (2006) ‘An Analysis of Mutative σ-Self-Adaptation on Linear Fitness Functions’, Evolutionary Computation, 14(3), pp. 255-275.

[144] Mott MacDonald and associate (2005) ‘Crop Water Requirements’, Koga Dam and Irrigation Project report, Ministry of Water Resource, Addis Ababa, Ethiopia.

[145] Humphreys, H., Bellier, C., Kennedy, R. and Donkin, (1997) ‘Tis-Abay II Hydroelectric Project: Environmental Impact Assessment’, Final Report.

[146] McCartney, M.P., Abeyu, S. and Yilma, S. (2008) ‘Estimating Environmental Flow Requirements Downstream of the Chara Chara Weir on the Blue Nile River’, paper presented at Hydrology and Ecology of the Nile River Basin under Extreme conditions, June 16-19, Addis Ababa, Ethiopia.

[147] SMEC. (2007) ‘Hydrological Study of The Tana-Beles Sub-Basins (part 1)’, Snowy Mountains Engineering Corporation: Australia; 77.

[148] Gieske, A, Wale, AW., Getachew, HA., Alemseged, TH. and Rientjes, T. (2008) ‘Non-linear parameterization of Lake Tana’s flow system’, Proceedings of the Workshop on Hydrology and Ecology of the Nile River Basin under Extreme Conditions, Abtew, W. and Melesse AM. (eds), , Addis Ababa, Ethiopia, pp. 128–145.

Appendix A. Hydro-meteorology

148

Appendix A. Hydro-meteorology A.1 Hydrology 1 Formats of WaSiM-ETH for hydrometeorological data Figure A-1 shows formats and description of each input rows and columns. The first 5 rows contain describing data like station coordinates and altitudes and station names. The first 4 data columns contain the date and time of the data. Row 1: comment Row 2: after column 4: altitudes for each meteo-station (int. or float). Basin area for hydrologic data Row 3: after column 4: x-coordinates of the stations (int. or floating point values) Row 4: after column 4: y-coordinates of the stations (int. or floating point values) Row 5: after column 4: short identifier for each station e.g. 6-chars Row 6 and onward rows: after column 4: actual hydro-meteo data

Figure A- 1 Formats of Hydro-meteorological time series data for WaSiM-ETH


149

Table A- 1 Catchment characteristics used in SOM

Catch. code

Area (km2)

Slope (%)

Length (km)

Shape (-)

soil40 (%)

soil44 (%)

soil46 (%)

soil48 (%)

soil54 (%)

use19 (%)

use211 (%)

use231 (%)

use243 (%)

use313 (%)

Topoindex (-)

Elev (m)

19 202.00 1.90 40.20 2.01 0.00 0.00 0.00 2.00 94.00 0.00 8.00 0.00 91.00 0.00 12.41 1739.00 27 1681.00 1.21 86.60 2.23 5.00 0.00 0.00 0.00 88.00 16.00 0.00 0.00 0.00 42.00 12.37 2199.00 35 1656.00 0.90 83.70 1.93 2.00 56.00 0.00 0.00 41.00 3.00 97.00 0.00 0.00 0.00 12.76 2284.00 39 1279.00 0.88 82.90 2.06 3.00 87.00 0.00 9.00 0.00 0.00 96.00 4.00 0.00 0.00 12.36 2270.00 64 612.00 1.90 60.00 1.49 3.00 56.00 0.00 0.00 37.00 20.00 58.00 6.00 15.00 0.00 12.45 2447.00

104 470.00 0.64 47.20 1.69 38.00 20.00 34.00 8.00 0.00 0.00 59.00 34.00 0.00 7.00 13.01 2657.00 116 310.00 0.78 39.20 1.95 40.00 19.00 29.00 12.00 0.00 0.00 53.00 37.00 0.00 11.00 12.98 2728.00 131 930.00 0.39 77.10 2.04 96.00 0.00 4.00 0.00 0.00 0.00 98.00 0.00 2.00 0.00 13.57 2722.00

82 546.00 1.38 67.10 2.33 4.00 13.00 0.00 17.00 65.00 0.00 93.00 0.00 5.00 2.00 12.80 2116.00 87 174.00 2.13 33.20 1.32 17.00 0.00 0.00 63.00 20.00 11.00 57.00 0.00 0.00 32.00 12.15 1954.00 67 362.00 2.23 50.50 1.95 12.00 31.00 4.00 13.00 40.00 1.00 77.00 22.00 0.00 0.00 12.54 2727.00 72 973.00 0.98 63.80 2.07 0.00 28.00 0.00 6.00 62.00 0.00 100.00 0.00 0.00 0.00 12.12 2292.00 95 711.00 0.74 84.70 2.80 11.00 1.00 0.00 0.00 86.00 0.00 100.00 0.00 0.00 0.00 13.33 2206.00 59 3116.00 0.58 124.30 2.23 6.00 63.00 14.00 8.00 0.00 21.00 29.00 3.00 47.00 0.00 12.72 1470.00 78 195.00 0.46 31.93 2.20 0.00 2.40 0.00 0.00 97.00 0.00 100.00 0.00 0.00 0.00 13.19 2475.00

106 605.00 1.27 68.30 2.02 7.00 11.00 0.00 23.00 48.00 20.00 78.00 2.00 0.00 0.00 12.91 2091.00 58 742.00 1.51 78.25 2.15 25.00 22.00 0.00 9.70 40.00 0.00 75.30 24.50 0.20 0.00 12.85 1785.00 60 278.00 0.66 43.11 1.76 1.00 59.00 0.00 0.50 35.00 32.00 50.80 0.00 16.00 0.00 12.69 2467.00 26 480.00 0.84 51.50 2.18 12.00 0.00 0.00 0.00 88.00 2.00 66.00 0.00 10.00 22.00 12.34 2100.00

130 736.00 0.42 78.50 2.50 97.00 0.00 3.00 0.00 0.00 14.00 86.00 0.00 0.00 0.00 13.26 2808.00 36 300.00 0.67 49.10 2.41 15.00 48.00 0.00 4.00 26.00 0.00 93.00 7.00 0.00 0.00 13.36 2083.00 88 219.00 1.42 43.60 2.16 0.00 0.00 0.00 30.00 70.00 2.00 81.00 0.00 0.00 17.00 12.70 2000.00 73 425.00 2.46 52.80 1.97 1.00 8.00 0.00 41.00 51.00 0.00 97.00 3.00 0.00 0.00 12.16 2509.00

114 447.00 0.53 72.00 2.82 78.40 19.60 4.00 0.00 0.00 36.10 63.90 0.00 0.00 0.00 12.91 2794.74 15 4674.00 0.79 130.00 1.76 9.57 0.00 0.00 20.09 45.46 13.98 12.35 2.93 48.38 22.37 17.13 1961.74 85 322.00 0.54 54.00 2.25 8.07 7.92 0.00 0.94 42.50 0.00 97.73 2.22 0.05 0.00 12.21 2631.00


150

2 Graphical representation of regional/ WaSiM-ETH model calibration and

validation from each group.

Figure A- 2 Measured and WaSiM-ETH model out put of Uke river after calibration in group 1

Figure A- 3 Measure and regional model out put of Dembi river (validation of group 1)


151

Figure A- 4 Measured and WaSiM-ETH model out put of Buno Bedelle river after calibration in

group 2

Figure A- 5 Measure and regional model out put of Ardy river (validation of group 2)


152

Figure A- 6 Measured and WaSiM-ETH model out put of Dura river after calibration in group 3

Figure A- 7 Measure and regional model out put of Lower Fetta river (validation of group 3)


153

Figure A- 8 Measured and WaSiM-ETH model out put of Gilgel Abay river after calibration in

group 4

Figure A- 9 Measure and regionalized model out put of Gilgel Beles river (validation of group 4)


154

Figure A- 10 Measured and WaSiM-ETH model out put of Sibilu river after calibration in group 5

Figure A- 11 Measure and regionalized model out put of Robi Jiga river (validation of group 5)


155

3 Estimated monthly inflow to each proposed dam and at each junction to Lake Tana reservoir

Table A- 2 Estimated monthly inflow to Lake Tana at junction Gilgel Abay (106 m3)

Table A- 3 Estimated monthly inflow to Lake Tana at junction Ribb (106 m3)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total 1986 29.2 18.9 19.4 58.3 25.9 90.0 577.0 588.0 484.5 363.6 111.5 52.7 2419.0 1987 29.4 18.6 22.6 19.5 87.7 376.7 631.9 793.5 529.6 330.4 119.0 55.5 3014.4 1988 33.9 24.7 21.4 22.8 94.3 285.6 895.4 893.1 634.4 376.5 138.3 58.3 3478.7 1989 33.3 22.7 32.5 50.4 79.0 224.7 604.6 894.4 493.8 214.7 97.4 54.6 2802.1 1990 34.3 22.1 21.9 17.3 50.1 100.5 625.3 1116.7 724.7 354.8 99.5 46.6 3213.8 1991 30.6 19.5 17.6 33.7 55.8 358.3 1293.8 1218.3 880.7 408.0 135.1 68.8 4520.2 1992 38.1 24.0 20.3 35.6 90.1 172.4 593.6 907.3 590.4 428.0 181.9 79.2 3160.9 1993 44.4 27.4 28.8 31.1 62.9 218.7 583.8 733.1 606.2 400.7 160.9 65.8 2963.8 1994 35.4 21.8 21.2 17.9 76.7 191.5 545.6 860.5 647.1 256.9 93.6 49.2 2817.4 1995 29.5 19.3 19.4 21.5 66.0 214.5 642.3 764.6 526.5 197.8 78.2 52.3 2631.9 1996 35.1 22.8 41.8 88.0 268.1 495.5 767.6 1030.7 658.8 302.6 117.2 69.0 3897.2 1997 41.4 31.2 36.6 66.0 136.1 359.9 682.3 712.8 414.0 332.8 243.2 124. 3180.3 1998 55.8 29.9 31.8 21.7 89.6 178.9 548.5 805.5 636.0 510.7 164.0 66.0 3138.4 1999 37.6 22.9 18.8 16.7 46.6 224.6 896.6 972.3 582.5 586.8 202.6 124. 3732.0 Mean 36.3 23.3 25.3 35.8 87.8 249.4 706.3 877.9 600.7 361.7 138.7 69.0 3212.2

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total 1986 10.4 7.3 7.9 7.6 5.6 37.2 274.9 457.9 294.6 107.8 34.9 20.1 1266.2 1987 12.8 8.5 9.7 6.9 13.8 38.7 169.4 371.4 140.2 49.0 22.7 14.9 858.0 1988 10.4 9.1 9.2 6.9 7.7 37.6 398.1 567.7 321.2 128.4 52.3 24.1 1572.6 1989 14.6 9.4 15.8 13.8 16.4 41.8 212.2 410.5 174.8 118.0 74.7 34.7 1136.7 1990 18.9 11.6 9.4 7.7 6.1 7.4 297.2 569.3 381.0 261.0 58.9 25.5 1653.8 1991 14.5 9.2 7.9 6.9 6.5 8.1 352.1 513.1 295.1 126.9 69.1 34.9 1444.3 1992 18.5 11.6 10.0 12.7 30.6 29.6 182.6 435.9 210.5 110.3 84.7 36.8 1173.8 1993 19.8 12.2 15.8 18.5 37.0 74.5 259.9 364.5 285.8 114.2 49.2 24.5 1275.8 1994 14.7 9.5 8.0 6.4 10.4 55.9 328.8 578.0 357.6 94.8 34.8 20.6 1519.3 1995 12.8 8.6 8.0 6.3 10.0 20.9 131.4 302.2 140.8 44.2 20.2 13.2 718.4 1996 9.6 7.0 7.1 8.4 21.2 186.5 275.9 369.1 197.0 66.6 31.6 23.3 1203.3 1997 14.4 9.4 14.5 14.0 27.9 78.7 332.4 279.2 117.2 125.2 97.2 66.1 1176.2 1998 33.9 16.2 12.4 9.9 45.9 39.0 230.0 352.9 207.0 76.3 31.6 18.0 1073.1 1999 17.1 11.4 9.2 7.2 7.0 14.4 263.8 404.2 319.4 183.8 73.4 66.1 1376.8 Mean 15.9 10.1 10.4 9.5 17.6 47.9 264.9 426.8 245.9 114.8 52.5 30.2 1246.3


156

Table A- 4 Estimated monthly inflow to Lake Tana at junction Megech (106 m3)

Table A- 5 Estimated monthly inflow to Lake Tana at junction Gumera (106 m3)




157

Table A- 6 Estimated monthly inflow to Lake Tana at junction Gelda (106 m3)

Table A- 7 Estimated monthly inflow to Lake Tana at junction Gemero (106 m3)




158

Table A- 8 Estimated monthly inflow to Lake Tana at junction Garno (106 m3)

Table A- 9 Estimated monthly inflow to Koga reservoir (106 m3)




159

Table A- 10 Estimated monthly inflow to Gumera reservoir (106 m3)

Table A- 11 Estimated monthly inflow to Ribb reservoir (106 m3)




160

Table A- 12 Estimated monthly inflow to Megech reservoir (106 m3)



161

A.2 Meteorology Computed arieal precipitation and arieal open water evaporation of the four proposed reservoirs and the Lake Tana

Figure A- 12 Mean monthly aerial precipitation and mean daily open water evaporation of Lake

Tana


162

Figure A- 13 Mean monthly aerial precipitation and mean daily open water evaporation of Megech reservoir

Figure A- 14 Mean monthly aerial precipitation and mean daily open water evaporation of Ribb reservoir


163

Figure A- 15 Mean monthly aerial precipitation and mean daily open water evaporation of

Gumera reservoir

Figure A- 16 Mean monthly aerial precipitation and daily open water evaporation of Koga

reservoir


164

Table A- 13 Meteorological data used for evapotranspiration computation

Temperature (0C)

Relative humidity

Actual sunshine (hr)

Wind speed (m/sec) e

ET (mm/d)

Jan 10 20.55 0.7 8.14 0.48 2.98 Jan 20 20.52 0.69 7.72 0.53 2.9 Jan 30 20.35 0.68 8.74 0.44 3.04 Feb 9 20.41 0.68 7.09 0.46 3.05 Feb 19 20.17 0.76 7.92 0.54 3.25 Mar 1 21.81 0.75 7.37 0.56 3.29 Mar 11 21.32 0.75 6.9 0.5 3.4 Mar 21 21.67 0.69 7.44 0.62 3.49 Mar 31 20.83 0.7 7.38 0.57 3.42 Apr 10 21.61 0.69 7.46 0.44 3.59 Apr 20 21.94 0.74 7.66 0.62 3.68 Apr 30 20.51 0.75 7.47 0.55 3.51 May 10 20.26 0.71 7.54 0.48 3.41 May 20 20.15 0.67 6.91 0.41 3.24 May 30 19.45 0.68 7.18 0.51 3.27 Jun 9 19.64 0.68 6.46 0.46 3.07 Jun 19 19.57 0.72 6.67 0.55 3.12 Jun 29 19.09 0.74 5.32 0.42 2.84 Jul 9 18.03 0.73 4.52 0.52 2.64 Jul 19 17.46 0.73 3.27 0.45 2.4 Jul 29 17.41 0.7 3.45 0.4 2.42 Aug 8 17.9 0.7 4.17 0.53 2.6 Aug 18 18.13 0.76 4.14 0.45 2.64 Aug 28 18.18 0.78 4.61 0.53 2.73 Sep 7 18 0.75 5.5 0.56 2.88 Sep 17 18.46 0.7 6.9 0.55 3.16 Sep 27 18.72 0.7 6.23 0.51 3.03 Oct 7 19.03 0.75 7.5 0.51 3.21 Oct 17 19.43 0.73 7.77 0.4 3.26 Oct 27 18.16 0.74 8.16 0.51 3.21 Nov 6 18.37 0.72 8.57 0.41 3.12 Nov 16 18.63 0.75 8.31 0.44 2.99 Nov 26 19.24 0.66 8.31 0.37 3 Dec 6 19.55 0.73 8.62 0.35 3.02 Dec 16 19.8 0.73 8.92 0.36 2.99 Dec 26 19.39 0.76 8.29 0.37 2.87


165

Temperature (0C)

Relative humidity

Actual sunshine (hr)

Wind speed (m/sec)

ET (mm/d)

Jan 10 19.02 0.75 8.14 0.39 2.89 Jan 20 19 0.66 7.72 0.47 2.77 Jan 30 19.58 0.65 8.74 0.51 2.96 Feb 9 20.48 0.71 7.09 0.44 3.1 Feb 19 21.13 0.71 7.92 0.48 3.3 Mar 1 21.35 0.73 7.37 0.64 3.19 Mar 11 21.39 0.73 6.9 0.64 3.34 Mar 21 21.45 0.71 7.44 0.63 3.48 Mar 31 18.71 0.72 7.38 0.64 3.26 Apr 10 21.21 0.71 7.46 0.57 3.54 Apr 20 21.03 0.74 7.66 0.57 3.61 Apr 30 20.02 0.73 7.47 0.67 3.46 May 10 19.45 0.69 7.54 0.55 3.35 May 20 18.37 0.71 6.91 0.48 3.15 May 30 19.34 0.6 7.18 0.5 3.2 Jun 9 18.5 0.7 6.46 0.44 3.03 Jun 19 18.12 0.71 6.67 0.42 3.02 Jun 29 18.54 0.73 5.32 0.47 2.81 Jul 9 18.73 0.72 4.52 0.55 2.67 Jul 19 17.73 0.71 3.27 0.7 2.4 Jul 29 17.45 0.69 3.45 0.62 2.4 Aug 8 17.89 0.7 4.17 0.73 2.59 Aug 18 17.59 0.76 4.14 0.61 2.59 Aug 28 17.94 0.74 4.61 0.67 2.68 Sep 7 18.36 0.74 5.5 0.45 2.91 Sep 17 17.6 0.73 6.9 0.55 3.09 Sep 27 18.43 0.69 6.23 0.56 3 Oct 7 18.36 0.71 7.5 0.66 3.13 Oct 17 18.14 0.75 7.77 0.46 3.13 Oct 27 18.76 0.78 8.16 0.46 3.29 Nov 6 18.79 0.71 8.57 0.42 3.18 Nov 16 17.98 0.69 8.31 0.44 2.91 Nov 26 18.77 0.72 8.31 0.38 2.99 Dec 6 18.59 0.71 8.62 0.36 2.95 Dec 16 18.47 0.71 8.92 0.39 2.87 Dec 26 18.78 0.71 8.29 0.33 2.8

Appendix B. Reservoirs

166

Appendix B. Reservoirs 1 Sample HEC-5 control file

Figure B- 1 Sample HEC-5 reservoir simulation model’s control file


167

2 Reservoir characteristics Table B- 1 Elevation-Area-Volume relations of Koga reservoir

Elevation (m a.s.l.)

Area (km2)

Volume (106 m3)

Elevation Area (km2)

Volume (106 m3)

Elevation Area (km2)

Volume (106 m3)

2004 0.19 0.2 2010 7.14 14.2 2016 19.99 97.62005 0.31 0.4 2011 9.95 22.9 2017 21.88 118.62006 0.98 1 2012 11.84 33.8 2018 23.78 141.52007 1.9 2.4 2013 13.88 46.4 2019 25.54 166.22008 2.92 4.8 2014 15.83 61.5 2020 27.4 192.72009 4.52 8.4 2015 18.08 78.5

Table B- 2 Elevation-Area-Volume relations of Gumera reservoir

Elevation (m a.s.l.) 1922.1 1925 1930 1935 1940 1945 1950 1953 1955 1960

Area (km2) 2.36 2.83 3.88 5 6.07 7.05 8 8.59 8.99 10

Volume (106 m3) 34 43.88 66.06 93.91 126.15 164.43 206.76 235.31 254.34 306.71

Table B- 3 Elevation-Area-Volume relations of Megech reservoir

Elevation (m a.s.l.) 1876 1880 1885 1890 1895 1900 1905 1910

Volume (106 m3) 0 0.05 0.53 1.99 4.65 8.60 13.82 20.85 Area (km2) 0 0.04 0.17 0.41 0.65 0.90 1.21 1.62 Elevation (m a.s.l.) 1915 1920 1925 1930 1935 1940 1945 1950

Volume (106 m3) 30.22 42.46 58.12 77.71 101.79 130.88 165.52 206.24 Area (km2) 2.14 2.77 3.51 4.35 5.30 6.36 7.52 8.79


168

Table B- 4 Elevation-Area-Volume relations of Ribb reservoir


Volume (106 m3)

Area (km2)


Volume (106 m3)

Area (km2)

1888 4.22 0.94 1902 28.98 2.60 1890 6.34 1.18 1904 34.39 2.81 1892 8.95 1.43 1906 40.21 3.01 1894 12.02 1.64 1908 46.43 3.21 1896 15.53 1.88 1910 53.06 3.42 1898 19.53 2.12 1912 60.12 3.64 1900 24.01 2.36 1914 67.64 3.88


Volume (106 m3)

Area (km2)


Volume (106 m3)

Area (km2)

1916 75.66 4.14 1930 150.70 6.82 1918 84.22 4.44 1932 164.81 7.30 1920 93.39 4.74 1934 179.99 7.91 1922 103.22 5.10 1936 196.43 8.64 1924 113.81 5.49 1938 214.47 9.30 1926 125.23 5.93 1940 233.70 9.97 1928 137.51 6.36 1930 150.70 6.82


169

Irrigation water requirement Table B- 5 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement for Koga reservoir


170

Table B- 6 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement for Megech reservoir


171

Table B- 7 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement for Gumara reservoir


172

Table B- 8 Monthly potential evapotranspiration, effective rainfall and gross irrigation water requirement for Ribb reservoir


173

Figure B- 2 Matlab programme used to handle physical reservoir constraints

[xmin fmin]= cmaes ('fit_hec5', [109952*ones(12,1); 36000*ones(12,1)], ones(24,1)*1000)

Figure B- 3 Matlab programme used to handle physical reservoir constraints


174

Figure B- 4 Perl computer programme used to couple single CMA-ES with HEC-5 for sigle reservoir


175

Figure B- 5 Perl computer programme used to couple SO-CMA-ES with HEC-5 for multi-reservoir multi-objective problems

decision support tool to optimize the operation of … · and lake tana, which is the largest fresh...

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