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Integral Radar Volume Descriptors

Integral Radar Volume Descriptors. Silke Trömel, Clemens Simmer. 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.

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Integral Radar Volume Descriptors

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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 • …the total rainfall from an individual convective storm over its • lifetime • …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. - Mean effective efficiency: MEeX - Mean echo-top-height: METHX - Mean brightband fraction: MBBX Integral Radar Volume Descriptors (IRVD) - Area-time integral: ATIX • Trends in MBB & trend/ noise : TBBX, TNBBX, • RTBBx, RTNBBx, STDBBx - Fraction of the area: (A(t)/Ao)X - Mean compactness: MCOMX - Area with reflectivities > t: A(t)X - Mean horizontal expected value: HMEANX - Area: AoX - Mean horizontal standard deviation: HSTDX - Duration: DX - Temporally averaged vertical mean value: VMEANX - Maximum vertical standard deviation: MVSTDX - Mean wind shear: MSHEARX - Orgographic rainfall amplifiers: ORO+XORO±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, 2004 - July 8, 2005 - August 19, 2005 • 0.025 degree spatial (2.8 km) and 10 minutes temporal resolution • 12 true radiosoundings • Investigation of 100 rain events

  6. 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%). 2 models

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

  8. 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. The precipitation product, 2004 (M. Paulat, C. Frei, M. Hagen, H. Wernli) - 24 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 -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=256R1.42 the rain rates are computed.

  9. The precipitation product (M. Paulat, C. Frei, M. Hagen, H. Wernli) 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: Rdis,15(i,j) = Rrad,15(i,j) · R obs,d(i,j) / R rad,d(i,j) Where Rrad,15(i,j) = 15minutes radar precipitation estimate Rrad,d(i,j) = daily radar precipitation estimate Robs,d(i,j) =daily value from the gridded rain gauge analysis

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

  11. Radar volume data (Thanks to Jörg Seltmann!) No precipitation product No precipitation product 2 missing values 28.04.2004: FBG, TUR, MUC 21.06.2004: FBG, TUR, MUC 18.07.2004: FRA 19.07.2004: BLN, EIS, FRA, MUC, NHB, ROS, z.T. HAM 23.07.2004: BLN, ROS 22.09.2004: HAM, z.T. BLN 09.06.2004: BLN 07.07.2004: FRA 17.07.2004: FRA 18.07.2004: BLN 20.07.2004: FRA 12.08.2004: FRA, HAM

  12. 12 radiosoundings 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. At best radiosoundings at 0,6,12,18 UTC are available.

  13. I used the coarser 7km·7km resolution of the precipitation product and upscaled the radar data to this coarse resolution (nearest neighbour). 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

  14. Downscaling the precipitation data instead of upscaling the radar data. 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 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) Zd = (d/D)–hZD The scale transformation function of the instantaneous PPI polar reflectivity obtained from the 1° radar beamwidth can be written as Ztransformed [dBZ] = (20/D)–0.10ZD [dBZ] • ZD [dBZ]= measured reflectivity at the observation range interval D • Zd [dBZ]= transformed reflectivity of the measured reflectivity (ZD) 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 ZD • d/D = scale factor • = scaling exponent

  16. 65 rain eventsDie Gaussian kernel for smoothing has s=6

  17. Marshall-Palmer Estimator MP1:Z=296 R 1.47 (Marshall, J.S., Palmer, W. McK., 1948: The distribution of raindrops with size. J. Meteor., 5, 165-166. MP2: Z=200 R 1.6 (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 R1.47 MP2: Z=200 R1.6

  19. Results for different models and different distance functions

  20. 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%). 2 models

  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. - Mean effective efficiency: MEeX - Mean echo-top-height: METHX - Mean brightband fraction: MBBX Integral Radar Volume Descriptors (IRVD) - Area-time integral: ATIX • Trends in MBB & trend/ noise : TBBX, TNBBX, • RTBBx, RTNBBx, STDBBx - Fraction of the area: (A(t)/Ao)X - Mean compactness: MCOMX - Area with reflectivities > t: A(t)X - Mean horizontal expected value: HMEANX - Area: AoX - Mean horizontal standard deviation: HSTDX - Duration: DX - Temporally averaged vertical mean value: VMEANX - Maximum vertical standard deviation: MVSTDX - Mean wind shear: MSHEARX - Orgographic rainfall amplifiers: ORO+XORO±X -Max., mean and min. distance to the radar: DIMAx, DIMEx, DIMIx - Emp. mean + standard dev.: EMEANx, ESTDx -Expected value + standard dev. >t of the Weibull distributed variable: MEANtx, HSTDtx With X=1,..5

  24. Significant detected IRVDs for V/ATIusing 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 Including MP1 and MP2 as descriptors No MP- descriptors 77.47% expl. Var. in V/ATI using 5 91.45% expl. Var. in V using 5 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: 9075.4mm Mean: 1371.5mm

  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 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: 17.07.2004, Frankfurt Accumulated rainfall: 7004.95mm=l/m2, 1.34215·1011m3 Relative error (MP): -26.5% Relative error (MP+IRVD): -1.83% Absolute error (MP): -1859mm Absolute error (MP+IRVD): -128mm real_53.gs

  37. Example: 23.07.2004, Berlin Accumulated rainfall: 1702.59mm=l/m2, 4.842·109m3 Relative error (MP): 10.1% Relative error (MP+IRVD) : 8.08% Absolute error (MP): 171mm Absolute error (MP+IRVD): 138mm real_34.gs

  38. Zusammenfassung • 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 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. • 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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