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

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

special observation period 3rd of August 2006 Example

special observation period 3rd of August 2006 Example

special observation period 3rd of August 2006 Example

Theoretical and Practical Framework

Theoretical and Practical Framework

Theoretical and Practical Framework

special observation period 3rd of August 2006 Example

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]

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]

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

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

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

Lichtenau 3rd of August 2006

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

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

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

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

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

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

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 = 1523 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

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 = 2975 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 = 1903 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 = 4388 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

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

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

curriculum vitae Name: Patrick Tracksdorf Email: patrick.tracksdorf@DLR.de PhD student at the German Aerospace Center DLR, Institute of Atmospheric Physics, Cloud Physics and Traffic Meteorology (21.04.2008), 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 (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 Technology matriculation: 01.10.1999 - 31.03.2006 course of studies: Information Technology (Dipl.-Ing.) branch of studies: Information and Communication Technology

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 Email: patrick.tracksdorf@DLR.de

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

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

special observation period 3rd of August 2006 Example

Theoretical Framework

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]

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