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Integral Radar Volume Descriptors Silke Trömel, Clemens Simmer.

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1 Integral Radar Volume Descriptors Silke Trömel, Clemens Simmer

2 Gliederung Sehr kurzer Rückblick auf die Basisgleichung von Doneaud et al. (1981) bzw. Atlas et al. (1990) und die Ergebnisse mit Pseudo-Radardaten Die tatsächliche Anwendbarkeit der IRVD-Methode - Datenbasis - Evaluierung der IRVD-Modelle abgeleitet aus Pseudo-Radardaten - IRVD-Modell aus realen Daten, Vergleich mit Marshall-Palmer-Schätzer - die Kombination: IRVD+MP-Modell Zusammenfassung

3 The theory Atlas et al. (1990) develop a unified theory for the estimation of both 1.…the total rainfall from an individual convective storm over its lifetime 2.…the areawide instantaneous rainfall from a multiplicity of such storms by use of measurements of the areal coverage of the storms with a threshold rain intensity isopleth or the equivalent threshold radar reflectivity.

4 Integral Radar Volume Descriptors (IRVD) - Orgographic rainfall amplifiers: ORO+ X ORO± X - Mean wind shear: MSHEAR X - Duration: D X - Area-time integral: ATI X - Area with reflectivities > : A( ) X - Area: Ao X - Fraction of the area: (A( )/Ao) X - Mean horizontal expected value: HMEAN X - Mean brightband fraction: MBB X - Mean effective efficiency: MEe X - Mean echo-top-height: METH X - Maximum vertical standard deviation: MVSTD X - Temporally averaged vertical mean value: VMEAN X -Trends in MBB & trend/ noise : TBB X, TNBB X, RTBB x, RTNBB x, STDBB x - Mean compactness: MCOM X - Mean horizontal standard deviation: HSTD X With X=1,..5

5 Data base Pseudo-radar data and rain rates generated by COSMO-DE (version LM3.16), a version of COSMO centered over Germany for a period of three days: - July 17, July 8, August 19, degree spatial (2.8 km) and 10 minutes temporal resolution 12 true radiosoundings Investigation of 100 rain events

6 2 models 1.) No information about orogrophy and wind shear 2.) ORO+, ORO±, MSHEAR are included Exp. variance: 98.93% Max. rel. error: 88.5% In 74 (22) out of 100 rain events the rel. error is smaller than 10% (2%). Exp. variance: 99.25% Max. rel. error: 103.2% In 79 (31) out of 100 rain events the rel. error is smaller than 10% (2%).

7 The best descriptor (fades) HMEAN already ex- plained about 95% of the variance! (Real data: 35.3%)

8 The precipitation product, the so-called PC Product by DWD, i.e. the 15-minutes composits from the 16 operational precipitation radars over Germany with 4km horizontal resolution. The radar composit data are originally given in six reflectivity classes, in units dBZ. Using Z=256R 1.42 the rain rates are computed. 7 dBZ 0.1 mm/15min. 19dBZ 0.3 mm/15min. 28dBZ 0.9 mm/15min. 37dBZ 2.5 mm/15min. 46dBZ 14 mm/15min. 55dBZ 40 mm/15min hour-accumulated measurements from about 3500 rain gauge stations, operated by the DWD, are upscaled to the COSMO model grid with a horizontal resolution of 7 km (M. Paulat, C. Frei, M. Hagen, H. Wernli)

9 The precipitation product A so-called disaggregation technique is used to combine the two data sets to produce a data set of 15minutes precipitation in Germany on a grid with a horizontal resolution of 7 km for the year 2004: (M. Paulat, C. Frei, M. Hagen, H. Wernli) R dis,15 (i,j) = R rad,15 (i,j) · R obs,d (i,j) / R rad,d (i,j) Where R rad,15 (i,j) = 15minutes radar precipitation estimate R rad,d (i,j) = daily radar precipitation estimate R obs,d (i,j) =daily value from the gridded rain gauge analysis

10 Start: 6:30 UTC 15min. –rainfall accumulation

11 Radar volume data : FBG, TUR, MUC : FBG, TUR, MUC : FRA : BLN, EIS, FRA, MUC, NHB, ROS, z.T. HAM : BLN, ROS : HAM, z.T. BLN : BLN : FRA : FRA : BLN : FRA : FRA, HAM No precipitation product 2 missing values (Thanks to Jörg Seltmann!)

12 12 radiosoundings At best radiosoundings at 0,6,12,18 UTC are available. Information about temperature, pressure or wind in different heights are needed for the calculation of some descriptors. These variables are estimated from the nearest radiosounding in time and space.

13 Data base - Radar and precipitation data with 15min. temporal resolution - Precipitation data with 7km·7km spatial resolution - Radar data with range-dependent spatial resolution, 128 range bins in 1°x 1km resolution, 18 elevations I used the coarser 7km·7km resolution of the precipitation product and upscaled the radar data to this coarse resolution (nearest neighbour).

14 Data base - Radar and precipitation data with 15min. temporal resolution - Precipitation data with 7km·7km spatial resolution - Radar data with range-dependent spatial resolution, 128 range bins in 1°x 1km resolution, 18 elevations Downscaling the precipitation data instead of upscaling the radar data. - I used ordinary kriging to interpolate the precipitation product on a 2km x 2km grid. -Averaging instead of nearest neighbour interpolation to produce a reflectivity data set on a 2km x 2km grid, i.e. close to the coarsest radar resolution. In this way a reduction of the range dependent bias is achieved and the scaling of radar reflectivity (Chumchean et al., 2004) is not longer necessary.

15 Scaling of radar reflectivity for correcting range- dependent bias (Chumchean et al., 2004) Z d = (d/D) – Z D Z transformed [dBZ] = (20/D) –0.10 Z D [dBZ] The scale transformation function of the instantaneous PPI polar reflectivity obtained from the 1° radar beamwidth can be written as Z D [dBZ]= measured reflectivity at the observation range interval D Z d [dBZ]= transformed reflectivity of the measured reflectivity (Z D ) to be equivalent to reflectivity at the reference observation range interval d d [km] = reference observation interval D [km] = observation range of the measured reflectivity Z D d/D = scale factor = scaling exponent

16 65 rain events Die Gaussian kernel for smoothing has =6 CiteDateNames of rain events Hamburg (11) real_01,..,real_11.dat Frankfurt (4) real_20,…real_23.dat Berlin (4) real_30, …real_34.dat Frankfurt (10) real_35.dat, …real_38.dat, real_40.dat,..real_43.dat, real_85.dat, real_86.dat Hamburg (5) real_44.dat, real45.dat, real_48.dat, real_49.dat, real_87.dat Frankfurt (4) real_50.dat, …, real_53.dat Frankfurt (4) real_55.dat,…, real_58.dat Frankfurt (7) real_67.dat, …, real_71.dat, real_73.dat, real_74.dat Berlin (3) real_75.dat, …, real_77.dat Frankfurt (4) real_81.dat, …, real_84.dat Berlin (9) real_90.dat, real_91.dat, real_93.dat, …, real_99.dat

17 Marshall-Palmer Estimator MP1: Z=296 R 1.47 MP2: Z=200 R 1.6 (Marshall, J.S., Palmer, W. McK., 1948: The distribution of raindrops with size. J. Meteor., 5, (Sauvageot, H., 1992: Radar meteorology. Artech House, Boston. Battan, L.J., 1973: Radar observation of the atmosphere. University of Chicago Press, Chicago.)

18 Marshall-Palmer-Estimator MP1: Z=296 R 1.47 MP2: Z=200 R 1.6

19 Results for different models and different distance functions

20 2 models 1.) No information about orogrophy and wind shear 2.) ORO+, ORO±, MSHEAR are included Exp. variance: 98.93% Max. rel. error: 88.5% In 74 (22) out of 100 rain events the rel. error is smaller than 10% (2%). Exp. variance: 99.25% Max. rel. error: 103.2% In 79 (31) out of 100 rain events the rel. error is smaller than 10% (2%).

21 Evaluation of the models obtained with pseudo-radar data Method: Least-squares

22 Evaluation of the models obtained with pseudo-radar data Method: Least-errors

23 Integral Radar Volume Descriptors (IRVD) - Orgographic rainfall amplifiers: ORO+ X ORO± X - Mean wind shear: MSHEAR X - Duration: D X - Area-time integral: ATI X - Area with reflectivities > : A( ) X - Area: Ao X - Fraction of the area: (A( )/Ao) X - Mean horizontal expected value: HMEAN X - Mean brightband fraction: MBB X - Mean effective efficiency: MEe X - Mean echo-top-height: METH X - Maximum vertical standard deviation: MVSTD X - Temporally averaged vertical mean value: VMEAN X -Trends in MBB & trend/ noise : TBB X, TNBB X, RTBB x, RTNBB x, STDBB x - Mean compactness: MCOM X - Mean horizontal standard deviation: HSTD X With X=1,..5 -Max., mean and min. distance to the radar: DIMA x, DIME x, DIMI x -Expected value + standard dev. > of the Weibull distributed variable: MEAN x, HSTD x - Emp. mean + standard dev.: EMEAN x, ESTD x

24 Significant detected IRVDs for V/ATI using real-radar data 77.47% expl. Var.

25 Marshall-Palmer and the IRVD estimators Method: Least-squares

26 Marshall-Palmer and the IRVD estimators Method: Least-errors vs. least-errors

27 Marshall-Palmer and the IRVD estimators Method: Least-squares vs. least-errors

28 Results for different models and different distance functions

29 Significant IRVDs considering 65 rain events DescriptorFrequency TNBB 5, fkt(35)63/65 RTNBB 2, fkt(65)63/65 ESTD, fkt(121)62/65 STDW 2,fkt(132) 62/65 DIMA 5, fkt(150)14/65 STDW 3, fkt(133) 3/65 METH 4, fkt(44)2/ % expl. Var. in V/ATI using 5 DescriptorFrequency MP1, fkt(151)65/65 ESTD 5, fkt(125)42/65 METH 2, fkt(42)42/65 MEFF 5,fkt(50)31/65 METH 5, fkt(45)27/65 MAXS 4, fkt(54)22/65 MEAN, fkt(130) 19/65 STDW, fkt(132) 19/ % expl. Var. in V using 5 Including MP1 and MP2 as descriptors No MP- descriptors 85.4% expl. Var. in V using MP1 alone

30 Best results for the IRVD+MP model fitted with LE

31 Empirical distribution of tracked rain events Min: 37.5mm Max: mm Mean: mm

32 Results for different models and different distance functions

33 Absolute errors Method: Least-squares

34 IRVD+MP model fitted with LE vs MP

35 Significant IRVDs considering 65 rain events DescriptorFrequency MP1, fkt(151)65/65 ESTD 5, fkt(125)42/65 METH 2, fkt(42)42/65 MEFF 5,fkt(50)31/65 METH 5, fkt(45)27/65 MAXS 4, fkt(54)22/65 MEAN, fkt(130) 19/65 STDW, fkt(132) 19/65 Including MP1 and MP2 as descriptors Adler and Mack (1984) Rosenfeld and Gagin (1989) Rosenfeld et al. (1990) Rosenfeld et al. (1995) Ludlam (1980)

36 Example: , Frankfurt real_53.gs Relative error (MP): -26.5% Accumulated rainfall: mm=l/m 2, ·10 11 m 3 Absolute error (MP): -1859mm Relative error (MP+IRVD): -1.83% Absolute error (MP+IRVD): -128mm

37 Example: , Berlin real_34.gs Relative error (MP): 10.1% Accumulated rainfall: mm=l/m 2, 4.842·10 9 m 3 Absolute error (MP): 171mm Relative error (MP+IRVD) : 8.08% Absolute error (MP+IRVD): 138mm

38 Zusammenfassung Die Pseudo-Modelle konnten mit realen Daten evaluiert werden, d.h. die jeweiligen Sets von IRVDs enthalten Informationen über den Niederschlagsprozess. Die Pseudo-Modelle stellen jedoch im Mittel keine Verbesserung gegenüber dem Marshall-Palmer Schätzer dar. Der hohe erklärte Varianzanteil durch HMEAN ist evtl. durch das einfache single moment bulk scheme generiert worden. Auch ein IRVD-Modell, dass direkt auf Basis realer Radardaten erstellt wurde, ver- bessert nicht die Genauigkeit des traditionellen Schätzers. Um ein Modell abzuleiten, welches über einen weiten Bereich glaubwürdige Nieder- schlagsschätzer liefern soll, empfiehlt sich bei beschränkter Datengrundlage von der Minimierung der quadrierten absoluten Fehler zur Minimierung der relativen Fehler überzugehen Die Kombination des Marshall-Palmer Schätzers mit nur wenigen, integralen Radarvolumendeskriptoren liefert eine deutliche Verbesserung in der Schätzung. - Der Informationsgehalt der verwendeten Deskriptoren echo top height und effective efficiency im IRVD+MP-Modell wurde bereits für instantane Nieder- schlagsschätzung mehrfach bestätigt und publiziert.


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