deutsches zentrum für luft- und raumfahrt in der helmholtzgemeinschaft e.v. institut für physik...

Deutsches Zentrum für Luft- und Raumfahrt in der Helmholtzgemeinschaft e.V.

Institut für Physik der Atmosphäre (WuV)

Parameterisation of the Rain Drop Size Distribution

Dr. rer. nat. Martin Hagen, Patrick Tracksdorf

9th of July 2009, AQUARadar Meeting, Bonn



Table of Content

- Introductioncontinuing from last meeting

- Theoretical and Practical Framework

“On the Raindrop Size Distribution”

- Conclusions and Outlook

Radar Reflectivity Zhh (dBZ)

http://www.dlr.de/en



Examplespecial observation period3rd of August 2006




Theoretical and Practical Framework




Examplespecial observation period3rd of August 2006





Estimates obtained from the Rain Drop Size Distribution:

- Rain Rate [mm/h]

- Liquid Water Content [mm³/m³]

- Radar Reflectivity Factor [mm6/m³]

- D0 diameter of the median drop volume [mm]

max

0

33

)()(6

106.3D

dDDDvDNR

max

0

3)(6

D

dDDDNLWC

dDDDNzD

max

0

6)(

0

min

max

min

33 )()(2D

D

D

D

dDDDNdDDDN





Parameterisation of the Rain Drop Size Distribution:

- exponential Drop Size Distribution, Marshall and Palmer, 1948

- Gamma Drop Size Distribution, Ulbrich and Atlas, 1983

- modified Gamma Drop Size Distribution, Seliga and Bringi, 1974

- with:- N0 Intercept parameter [1/m³mm]- Slope parameter [1/mm]- µ Shape parameter- D0 diameter of the median drop volume [mm]- Deq equi-volumetric drop diameter [mm]

)exp()( 0 DNDN 21.01.4 R

)exp()( 0 DDNDN

)67.3exp()(0

0 D

DNDN eq ))67.3exp(()(

00 D

DµDNDN eq

eq




Theoretical and Practical FrameworkWielenbach3rd of August 2006




Theoretical and Practical FrameworkLichtenau3rd of August 2006




Lichtenau3rd of August 2006




Theoretical and Practical FrameworkLichtenau3rd of August 2006




Theoretical and Practical FrameworkLichtenau4th of August 2006Example 2




Lichtenau4th of August 2006Example 2





Parameter Variation:

ParameterJOSS-WALDVOGEL Lichtenau PARSIVEL Lichtenau

Z=a*Rb Exp. MP Exp. Gamma Z=a*Rb Exp. MP Exp. Gamma

Standard (all)

00:00 – 23:59

TV: Gunn Kinzer

a = 253.5

b = 1.42

N0 = 8000

= 3.87

N0 = 1486

= 2.75

N0 = 9835

= 2.03

µ = 4.4

a = 186

b = 1.53

N0 = 8000

= 4.14

N0 = 1816

= 2.95

N0 = 5915

= 1.62

µ = 4.0

reduced

11:00 – 12:30

a = 319

b = 1.19

N0 = 8000

= 3.54

N0 = 1523 = 2.46

N0 = 8206

= 1.85

µ = 3.9

a = 244

b = 1.24

N0 = 8000

= 3.69

N0 = 2975

= 2.86

N0 = 9300

= 1.53

µ = 3.8

reduced

07:00 – 08:00

a = 359.4

b = 1.71

N0 = 8000

= 4.14

N0 = 804

= 2.41

N0 = 2806

= 1.31

µ = 3.5

a = 293

b = 1.95

N0 = 8000

= 4.38

N0 = 1388

= 2.77

N0 = 1544

= 0.83

µ = 2.9

all 00:00 – 23:59

Terminal Velocity

Atlas (1973)

a = 266.4

b = 1.42

N0 = 8000

= 3.83

N0 = 1669

= 2.79

N0 = 8056

= 1.72

µ = 4.1

a = 196

b = 1.53

N0 = 8000

= 4.08

N0 = 2161

= 3.04

N0 = 3859

= 1.17

µ = 3.5

reduced

11:00 – 12:30

Atlas (1973)

a = 335

b = 1.19

N0 = 8000

= 3.51

N0 = 1688

= 2.48

N0 = 7424

= 1.62

µ = 3.8

a = 247

b = 1.23

N0 = 8000

= 3.63

N0 = 3654

= 2.99

N0 = 7568

= 1.21

µ = 3.6

reduced (filter off)

11:00 – 12:30

a = 320

b = 1.20

N0 = 8000

= 3.56

N0 = 1423

= 2.43

N0 = 8287

= 1.93

µ = 3.9

a = 235

b = 1.24

N0 = 8000

= 3.69

N0 = 2975

= 2.86

N0 = 9300

= 1.53

µ = 3.8

Lichtenau 3rd of August 2006




Parameter Variation:

ParameterJOSS-WALDVOGEL Wielenbach JOSS-WALDVOGEL Lichtenau

Z=a*Rb Exp. MP Exp. Gamma Z=a*Rb Exp. MP Exp. Gamma

reduced

00:00 – 07:00

a = 217

b = 1.47

N0 = 8000

= 3.94

N0 = 2975 = 3.26

N0 = 5471

= 0.83

µ = 3.8

a = 234

b = 1.23

N0 = 8000

= 3.79

N0 = 2225

= 2.93

N0 = 12134

= 1.79

µ = 4.4

reduced

00:00 – 00:50

a = 269

b = 1.69

N0 = 8000

= 3.96

N0 = 1903 = 2.94

N0 = 564

= -0.9

µ = 1.9

a = 329

b = 1.86

N0 = 8000

= 4.37

N0 = 767

= 2.69

N0 = 800

= 0.33

µ = 2.7

reduced

01:10 – 05:00

a = 191

b = 1.53

N0 = 8000

= 3.75

N0 = 4388 = 3.35

N0 = 928

= -0.8

µ = 1.9

a = 228

b = 1.25

N0 = 8000

= 3.60

N0 = 2777

= 2.91

N0 = 14437

= 1.74

µ = 4.4

reduced

06:00 – 07:00

a = 306

b = 1.17

N0 = 8000

= 5.79

N0 = 177 = 3.05

N0 = 12.8

= -2.7

µ = 0.7

a = ---

b = ---

N0 = 8000

= 19

N0 = 302

= 2.99

N0 = 66.1

= -0.8

µ = 1.4

Lichtenau 4th of August 2006




Conclusions and Outlook

Parameterisation of the Rain Drop Size Distribution using polarimetric weather radar measurements, Disdrometer and Rain Gauge

Algorithm development for operational weather radars

Quantitative Areal Precipitation Estimation by Radar

7290 min 15 min




Thank You for Your Attention!

Questions?


Dr. rer. nat. Martin Hagen,

Patrick Tracksdorf

9th of July 2009




curriculum vitae

Name: Patrick Tracksdorf Email: [email protected]

PhD student at the German Aerospace Center DLR, Institute of Atmospheric Physics,Cloud Physics and Traffic Meteorology (21.04.2008), Project AQUARadarDLR Supervisor: Dr. rer. nat. Martin Hagen

University Supervisor: Univ.-Prof. Dr. rer. nat. Madhukar Chandra

Working Title: Time-domain and frequency-domain properties of polarimetricweather radar signals, Chemnitz University of Technology (23.02.2007)

Chemnitz University of Technology, Faculty of Electrical Engineering and Information Technology,

Professorship of Microwave Engineering and Photonics

Univ.-Prof. Dr. rer. nat. Madhukar Chandra

Student Research Assistant (01/2003 - 12/2005)Scientific Staff Member (04/2006 - 04/2008)

University Education: Chemnitz University of Technologymatriculation: 01.10.1999 - 31.03.2006course of studies: Information Technology (Dipl.-Ing.)branch of studies: Information and Communication Technology




Author Information


German Aerospace Center DLR,

Institute of Atmospheric Physics, Cloud Physics and Traffic Meteorology

Postal Address:

Deutsches Zentrum für Luft- und Raumfahrt in der Helmholtz Gemeinschaft e.V. (DLR)

Institut für Physik der AtmosphäreWolkenphysik und VerkehrsmeteorologieMünchner Straße 20D-82234, Oberpfaffenhofen-Wessling

Corresponding Author: Patrick Tracksdorf

Email: [email protected]




References

Marshall and Palmer, 1948, “The distributions of raindrops with size”, J. Meteor. 5

Ulbrich and Atlas, 1983“Natural variations in the analytical form of the raindrop size distribution”, J. Climate Appl. Meteor. 22

Seliga and Bringi, 1974Potential use of radar differential reflectivity measurements at orthogonal polarisations for measuring precipitation, J. Appl. Meteor. 15

Joss & Waldvogel, 1967, “Ein Spektrograph für Niederschlagstropfen mit automatischer Auswertung”, Pure Appl. Geophys. 68


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