Parameterisation of the Rain Drop Size Distribution Dr. rer. nat

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1 Parameterisation of the Rain Drop Size Distribution Dr. rer. nat
Parameterisation of the Rain Drop Size Distribution Dr. rer. nat. Martin Hagen, Patrick Tracksdorf 9th of July 2009, AQUARadar Meeting, Bonn

2 Table of Content Introduction continuing from last meeting
Theoretical and Practical Framework “On the Raindrop Size Distribution” Conclusions and Outlook Radar Reflectivity Zhh (dBZ)

3 special observation period 3rd of August 2006
Example

4 special observation period 3rd of August 2006
Example

5 special observation period 3rd of August 2006
Example

6 Theoretical and Practical Framework

7

8 Theoretical and Practical Framework

9 Theoretical and Practical Framework

10

11 special observation period 3rd of August 2006
Example

12 Theoretical and Practical Framework
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]

13 Theoretical and Practical Framework
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] - L Slope parameter [1/mm] - µ Shape parameter - D0 diameter of the median drop volume [mm] - Deq equi-volumetric drop diameter [mm]

14 Theoretical and Practical Framework
Wielenbach 3rd of August 2006 Theoretical and Practical Framework

15 Theoretical and Practical Framework
Wielenbach 3rd of August 2006 Theoretical and Practical Framework

16 Theoretical and Practical Framework
Lichtenau 3rd of August 2006 Theoretical and Practical Framework

17 Lichtenau 3rd of August 2006

18 Theoretical and Practical Framework
Lichtenau 3rd of August 2006 Theoretical and Practical Framework

19 Theoretical and Practical Framework
Lichtenau 3rd of August 2006 Theoretical and Practical Framework

20 Theoretical and Practical Framework
Lichtenau 4th of August 2006 Example 2 Theoretical and Practical Framework

21 Theoretical and Practical Framework
Lichtenau 4th of August 2006 Example 2 Theoretical and Practical Framework

22 Theoretical and Practical Framework
Lichtenau 4th of August 2006 Example 2 Theoretical and Practical Framework

23 Theoretical and Practical Framework
Lichtenau 4th of August 2006 Example 2 Theoretical and Practical Framework

24 JOSS-WALDVOGEL Lichtenau
Parameter Variation: Lichtenau 3rd of August 2006 Parameter JOSS-WALDVOGEL Lichtenau PARSIVEL Lichtenau Z=a*Rb Exp. MP Exp. Gamma Standard (all) 00:00 – 23:59 TV: Gunn Kinzer a = 253.5 b = 1.42 N0 = 8000 L = 3.87 N0 = 1486 L = 2.75 N0 = 9835 L = 2.03 µ = 4.4 a = 186 b = 1.53 L = 4.14 N0 = 1816 L = 2.95 N0 = 5915 L = 1.62 µ = 4.0 reduced 11:00 – 12:30 a = 319 b = 1.19 L = 3.54 N0 = L = 2.46 N0 = 8206 L = 1.85 µ = 3.9 a = 244 b = 1.24 L = 3.69 N0 = 2975 L = 2.86 N0 = 9300 L = 1.53 µ = 3.8 07:00 – 08:00 a = 359.4 b = 1.71 N0 = 804 L = 2.41 N0 = 2806 L = 1.31 µ = 3.5 a = 293 b = 1.95 L = 4.38 N0 = 1388 L = 2.77 N0 = 1544 L = 0.83 µ = 2.9 all 00:00 – 23:59 Terminal Velocity Atlas (1973) a = 266.4 L = 3.83 N0 = 1669 L = 2.79 N0 = 8056 L = 1.72 µ = 4.1 a = 196 L = 4.08 N0 = 2161 L = 3.04 N0 = 3859 L = 1.17 a = 335 L = 3.51 N0 = 1688 L = 2.48 N0 = 7424 a = 247 b = 1.23 L = 3.63 N0 = 3654 L = 2.99 N0 = 7568 L = 1.21 µ = 3.6 reduced (filter off) a = 320 b = 1.20 L = 3.56 N0 = 1423 L = 2.43 N0 = 8287 L = 1.93 a = 235

25 Parameter Variation: Lichtenau 4th of August 2006 Parameter
JOSS-WALDVOGEL Wielenbach JOSS-WALDVOGEL Lichtenau Z=a*Rb Exp. MP Exp. Gamma reduced 00:00 – 07:00 a = 217 b = 1.47 N0 = 8000 L = 3.94 N0 = L = 3.26 N0 = 5471 L = 0.83 µ = 3.8 a = 234 b = 1.23 L = 3.79 N0 = 2225 L = 2.93 N0 = 12134 L = 1.79 µ = 4.4 00:00 – 00:50 a = 269 b = 1.69 L = 3.96 N0 = L = 2.94 N0 = 564 L = -0.9 µ = 1.9 a = 329 b = 1.86 L = 4.37 N0 = 767 L = 2.69 N0 = 800 L = 0.33 µ = 2.7 01:10 – 05:00 a = 191 b = 1.53 L = 3.75 N0 = L = 3.35 N0 = 928 L = -0.8 a = 228 b = 1.25 L = 3.60 N0 = 2777 L = 2.91 N0 = 14437 L = 1.74 06:00 – 07:00 a = 306 b = 1.17 L = 5.79 N0 = 177 L = 3.05 N0 = 12.8 L = -2.7 µ = 0.7 a = --- b = --- L = 19 N0 = 302 L = 2.99 N0 = 66.1 µ = 1.4

26 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

27 Thank You for Your Attention!
Questions? Parameterisation of the Rain Drop Size Distribution Dr. rer. nat. Martin Hagen, Patrick Tracksdorf 9th of July 2009

28 Parameterisation of the Rain Drop Size Distribution Dr. rer. nat
Parameterisation of the Rain Drop Size Distribution Dr. rer. nat. Martin Hagen, Patrick Tracksdorf 9th of July 2009, AQUARadar Meeting, Bonn

29 curriculum vitae Name: Patrick Tracksdorf PhD student at the German Aerospace Center DLR, Institute of Atmospheric Physics, Cloud Physics and Traffic Meteorology ( ), Project AQUARadar DLR Supervisor: Dr. rer. nat. Martin Hagen University Supervisor: Univ.-Prof. Dr. rer. nat. Madhukar Chandra Working Title: Time-domain and frequency-domain properties of polarimetric weather radar signals, Chemnitz University of Technology ( ) 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/ /2005) Scientific Staff Member (04/ /2008) University Education: Chemnitz University of Technology matriculation: course of studies: Information Technology (Dipl.-Ing.) branch of studies: Information and Communication Technology

30 Author Information Dr. rer. nat. Martin Hagen, Patrick Tracksdorf
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 Atmosphäre Wolkenphysik und Verkehrsmeteorologie Münchner Straße 20 D-82234, Oberpfaffenhofen-Wessling Corresponding Author: Patrick Tracksdorf

31 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, 1974 Potential 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

32 Parameterisation of the Rain Drop Size Distribution Dr. rer. nat
Parameterisation of the Rain Drop Size Distribution Dr. rer. nat. Martin Hagen, Patrick Tracksdorf 9th of July 2009, AQUARadar Meeting, Bonn

33 special observation period 3rd of August 2006
Example

34 Theoretical Framework

35 Theoretical Framework
Estimation of the parameters of the Rain Drop Size Distribution: “Method of Moments”, Waldvogel, 1974 “Method of Moments”, Tokay and Short, 1996 Gamma Rain Drop Size Distribution, Parameters, N0, D0, L, µ used: x=[3,4,6]

36 Parameterisation of the Rain Drop Size Distribution Dr. rer. nat
Parameterisation of the Rain Drop Size Distribution Dr. rer. nat. Martin Hagen, Patrick Tracksdorf 9th of July 2009, AQUARadar Meeting, Bonn