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

- Evaluierung der IRVD-Modelle abgeleitet aus Pseudo-Radardaten

- IRVD-Modell aus realen Daten, Vergleich mit Marshall-Palmer-Schätzer

- die Kombination: IRVD+MP-Modell

• Zusammenfassung

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 itslifetime

2. …the areawide instantaneous rainfall from a multiplicity of suchstorms

by use of measurements of the areal coverage of the storms with a threshold rain intensity isopleth or the equivalent threshold radarreflectivity.

Integral Radar Volume Descriptors (IRVD)

- Orgographic rainfall amplifiers: ORO+X ORO±X

- Mean wind shear: MSHEARX

- Duration: DX

- Area-time integral: ATIX

- Area with reflectivities > : A()X

- Area: AoX

- Fraction of the area: (A()/Ao)X

- Mean horizontal expected value: HMEANX

- Mean brightband fraction: MBBX

- Mean effective efficiency: MEeX

- Mean echo-top-height: METHX- Maximum vertical standard deviation: MVSTDX

- Temporally averaged vertical mean value: VMEANX

-Trends in MBB & trend/ noise : TBBX, TNBBX, RTBBx, RTNBBx, STDBBx

- Mean compactness: MCOMX

- Mean horizontal standard deviation: HSTDX

With X=1,..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

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 therel. error is smaller than 10% (2%).

Exp. variance: 99.25%Max. rel. error: 103.2%In 79 (31) out of 100 rain events therel. error is smaller than 10% (2%).

The best descriptor (fades)

HMEAN already ex-plained about 95%of the variance!

(Real data: 35.3%)

The precipitation product, 2004

-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.

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.

- 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

(M. Paulat, C. Frei, M. Hagen, H. Wernli)

The precipitation product

A so-called disaggregation technique is used to combine the two data sets to producea data set of 15minutes precipitation in Germany on a grid with a horizontal resolutionof 7 km for the year 2004:

(M. Paulat, C. Frei, M. Hagen, H. Wernli)

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 estimateRrad,d(i,j) = daily radar precipitation estimateRobs,d(i,j) =daily value from the gridded rain gauge analysis

Start: 6:30 UTC

15min. –rainfall accumulation

Be rl in

Eis berg

F eldb erg

F ran kf ur t

H a m b urg

F ürholz en

N euh ei le nba ch

R os to ck

T ürk heim

Radar volume data

28.04.2004: FBG, TUR, MUC 21.06.2004: FBG, TUR, MUC18.07.2004: FRA19.07.2004: BLN, EIS, FRA, MUC, NHB, ROS, z.T. HAM23.07.2004: BLN, ROS22.09.2004: HAM, z.T. BLN

09.06.2004: BLN07.07.2004: FRA17.07.2004: FRA18.07.2004: BLN20.07.2004: FRA12.08.2004: FRA, HAM

No precipitation productNo precipitation product

2 missing values

(Thanks to Jörg Seltmann!)

12 radiosoundings

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

Information about temperature, pressure or wind in different heights are neededfor the calculation of some descriptors.These variables are estimated from the nearest radiosounding in time and space.

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 theradar 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

Downscaling the precipitation data instead of upscaling the radar data.

- I used ordinary kriging to interpolate the precipitation product on a2km x 2km grid.

-Averaging instead of nearest neighbour interpolation to produce a reflectivitydata 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 thescaling of radar reflectivity (Chumchean et al., 2004) is not longer necessary.

Scaling of radar reflectivity for correcting range-dependent bias (Chumchean et al., 2004)

Zd = (d/D)–ZD

Ztransformed [dBZ] = (20/D)–0.10ZD [dBZ]

The scale transformation function of the instantaneous PPI polar reflectivity obtained from the 1° radar beamwidth can be written as

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 dd [km] = reference observation intervalD [km] = observation range of the measured reflectivity ZD

d/D = scale factor = scaling exponent

65 rain eventsDie Gaussian kernel for smoothing has=6

Cite Date Names of rain eventsHamburg (11) 22.9.04 real_01,..,real_11.dat

Frankfurt (4) 07.07.04 real_20,…real_23.dat

Berlin (4) 23.07.04 real_30, …real_34.dat

Frankfurt (10) 20.07.04 real_35.dat, …real_38.dat, real_40.dat, ..real_43.dat, real_85.dat, real_86.dat

Hamburg (5) 12.08.04 real_44.dat, real45.dat, real_48.dat, real_49.dat, real_87.dat

Frankfurt (4) 17.07.04 real_50.dat, …, real_53.dat

Frankfurt (4) 18.07.04 real_55.dat,…, real_58.dat

Frankfurt (7) 12.08.04 real_67.dat, …, real_71.dat, real_73.dat, real_74.dat

Berlin (3) 18.07.04 real_75.dat, …, real_77.dat

Frankfurt (4) 19.07.04 real_81.dat, …, real_84.dat

Berlin (9) 09.06.04 real_90.dat, real_91.dat, real_93.dat, …, real_99.dat

Marshall-Palmer Estimator

MP1: Z=296 R 1.47

MP2: Z=200 R 1.6

(Marshall, J.S., Palmer, W. McK., 1948: The distributionof raindrops with size. J. Meteor., 5, 165-166.

(Sauvageot, H., 1992: Radar meteorology. Artech House,Boston.Battan, L.J., 1973: Radar observation of the atmosphere.University of Chicago Press, Chicago.)

Marshall-Palmer-Estimator

MP1: Z=296 R1.47 MP2: Z=200 R1.6

Results for different models and different distance functions

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 therel. error is smaller than 10% (2%).

Exp. variance: 99.25%Max. rel. error: 103.2%In 79 (31) out of 100 rain events therel. error is smaller than 10% (2%).

Evaluation of the models obtained with pseudo-radar data

Rain events (ordered)

0 10 20 30 40 50 60

|Re

lativ

e e

rror

|

0

1

2

3

4

0

1

2

3

4

MP 1st input set2nd input set

Method: Least-squares

Evaluation of the models obtained with pseudo-radar data

Rain events (orderd)

0 10 20 30 40 50 60

|Rel

ativ

e er

ror|

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

MP 2nd input set2nd input set, 5 regressors

Method: Least-errors

Integral Radar Volume Descriptors (IRVD)

- Orgographic rainfall amplifiers: ORO+X ORO±X

- Mean wind shear: MSHEARX

- Duration: DX

- Area-time integral: ATIX

- Area with reflectivities > : A()X

- Area: AoX

- Fraction of the area: (A()/Ao)X

- Mean horizontal expected value: HMEANX

- Mean brightband fraction: MBBX

- Mean effective efficiency: MEeX

- Mean echo-top-height: METHX- Maximum vertical standard deviation: MVSTDX

- Temporally averaged vertical mean value: VMEANX

-Trends in MBB & trend/ noise : TBBX, TNBBX, RTBBx, RTNBBx, STDBBx

- Mean compactness: MCOMX

- Mean horizontal standard deviation: HSTDX

With X=1,..5

-Max., mean and min. distance to the radar: DIMAx, DIMEx, DIMIx

-Expected value + standard dev. > of the Weibull distributed variable: MEANx, HSTDx

- Emp. mean + standard dev.: EMEANx, ESTDx

Significant detected IRVDs for V/ATIusing real-radar data

77.47% expl. Var.

Marshall-Palmer and the IRVD estimators

Rain events (ordered)

0 10 20 30 40 50 60

Rel

ativ

e er

ror

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

IRVD MP1 MP2

Method: Least-squares

Marshall-Palmer and the IRVD estimators

Rain events (ordered)0 10 20 30 40 50 60

|Rel

ativ

e er

ror|

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

MPIRVD: LSIRVD: rel. error=min.

Method: Least-errors vs. least-errors

Marshall-Palmer and the IRVD estimators

Rain events (ordered)0 10 20 30 40 50 60

|Rel

ativ

e er

ror|

0.001

0.01

0.1

1

10

0.001

0.01

0.1

1

10

MPIRVD: LSIRVD: rel. error=min.

Method: Least-squares vs. least-errors

Results for different models and different distance functions

Significant IRVDs considering 65 rain events

Descriptor Frequency

TNBB5, fkt(35) 63/65

RTNBB2, fkt(65) 63/65

ESTD, fkt(121) 62/65

STDW2,fkt(132) 62/65

DIMA5, fkt(150) 14/65

STDW3, fkt(133) 3/65

METH4, fkt(44) 2/65

77.47% expl. Var. in V/ATI using 5

Descriptor Frequency

MP1, fkt(151) 65/65

ESTD5, fkt(125) 42/65

METH2, fkt(42) 42/65

MEFF5,fkt(50) 31/65

METH5, fkt(45) 27/65

MAXS4, fkt(54) 22/65

MEAN, fkt(130) 19/65

STDW, fkt(132) 19/65

91.45% expl. Var. in V using 5

Including MP1 and MP2 as descriptorsNo MP- descriptors

85.4% expl. Var. in V using MP1 alone

Best results for the IRVD+MP model fitted with LE

Empirical distribution of tracked rain events

Min: 37.5mmMax: 9075.4mmMean: 1371.5mm

Accumulated rainfall [mm]

0 1000 2000 3000 4000 5000 6000 7000 8000 900010000

Num

ber

of e

vent

s

0

5

10

15

20

25

30

35

40

45

0

5

10

15

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35

40

45

Results for different models and different distance functions

Absolute errors

Rain events

0 10 20 30 40 50 60

Ab

solu

te e

rro

r in

acc

um

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ted

mill

imie

ter

rain

fall

-6000

-4000

-2000

0

2000

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10000

Acc

um

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ted

ra

infa

ll [m

m]

-6000

-4000

-2000

0

2000

4000

6000

8000

10000Absolute error of MP1Accumulated rainfall LS: IRVD+MP

Method: Least-squares

IRVD+MP model fitted with LE vs MP

Significant IRVDs considering 65 rain events

Descriptor Frequency

MP1, fkt(151) 65/65

ESTD5, fkt(125) 42/65

METH2, fkt(42) 42/65

MEFF5,fkt(50) 31/65

METH5, fkt(45) 27/65

MAXS4, 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)

Example: 17.07.2004, Frankfurt

real_53.gs

Relative error (MP): -26.5%Accumulated rainfall: 7004.95mm=l/m2, 1.34215·1011m3

Absolute error (MP): -1859mmRelative error (MP+IRVD): -1.83%Absolute error (MP+IRVD): -128mm

Example: 23.07.2004, Berlin

real_34.gs

Relative error (MP): 10.1%Accumulated rainfall: 1702.59mm=l/m2, 4.842·109m3

Absolute error (MP): 171mmRelative error (MP+IRVD) : 8.08%Absolute error (MP+IRVD): 138mm

Zusammenfassung

• Die Pseudo-Modelle konnten mit realen Daten evaluiert werden, d.h. die jeweiligenSets von IRVDs enthalten Informationen über den Niederschlagsprozess.

• Die Pseudo-Modelle stellen jedoch im Mittel keine Verbesserung gegenüber demMarshall-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 vonder 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.