Statistical Postprocessing of LM Weather Parameters Ulrich Damrath Volker Renner Susanne Theis Andreas Hense

Statistical PostprocessingStatistical Postprocessingof LMof LM

Weather ParametersWeather Parameters

Ulrich DamrathVolker Renner

Susanne TheisAndreas Hense

25.09.2003COSMO - 5. Annual Meeting

Overview

- Introduction

- Short Description of Neighbourhood Method

- Verification Results

- Calibration

- Concluding Remarks


LM Total Precipitation [mm/h] 08.Sept.2001, 00 UTC, vv=14-15 h


Assumption: LM-forecasts within a spatio-temporal neighbourhood are assumed to constitute a sample of the forecast at the central grid point

Neighbourhood Method


xx

Definition of Neighbourhood I

y t


Definition of Neighbourhood II

Size of Area

Formof Area

LinearRegressions

hs


Products

Probabilistic Information• Quantiles• (Exceedance probabilities for certain threshold values)

„Statistically smoothed” fields• Quantiles for p = 0.5• Expectation Values



Original Forecast Expectation Values



Original Forecast Quantiles for p=0.9


LM T2m [oC] 08.Sept.2001, 00 UTC, vv=15 h

Original Forecast Quantiles for p=0.5


Direct model output of the LM for precipitationat a given grid point


...supplemented by more quantiles(forecast of uncertainty)


...supplemented by the 90 %-quantile(forecast of risk)


VerificationDataLM forecasts; 1.-15.09.2001; 00 UTC starting time1 h values; 6-30 h forecast timeall SYNOPs available from German stationscomparison with nearest land grid point

NM-Versionssmall: 3 time levels (3 h); radius: 3s ( 20 km)medium: 3 time levels (3 h); radius: 5s ( 35 km)large: 7/3 time levels (7/3 h); radius: 7s ( 50 km)

Averagingsquare areas of different sizestemperatures adjusted with -0.65 K/(100 m)


RMSE(T) for VariousArea Averages

1.1

1.2

1.3

1.4

original 3x3 5x5 7x7 9x9 11x11

[K]

RMSE(T) for 3 NM-Versions(0.5-Quantiles)

1.1

1.2

1.3

1.4

small medium large

[K]


Reliability Diagram T

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90

10 20 30 40 50 60 70 80 90

small


Richardson, D.S., 2001: Measures of skill and value of ensemble prediction systems, their interrelationshipand the effect of ensemble size. Q.J.R.Meteorol.Soc., Vol.127, pp. 2473-2489)


Reliability Diagram T

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90

10 20 30 40 50 60 70 80 90

small

large


FBI for Various Area Averages

0.0

0.5

1.0

1.5

2.0

0.1 0.2 0.5 1 2 5

Precipitation Threshold in mm/h

original

3x3

5x5

7x7

9x9

11x11


TSS for Various Area Averages

05

10152025303540

0.1 0.2 0.5 1 2 5


original

3x3

5x5

7x7

9x9

11x11


HSS for Various Area Averages

0

5

10

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30

35

0.1 0.2 0.5 1 2 5


original

3x3

5x5

7x7

9x9

11x11


ETS for Various Area Averages

0

5

10

15

20

0.1 0.2 0.5 1 2 5


original

3x3

5x5

7x7

9x9

11x11


LOR for Various Area Averages

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.1 0.2 0.5 1 2 5


original

3x3

5x5

7x7

9x9

11x11


FBI for 3 NM-Versions (Exp. Values)

0.0

0.5

1.0

1.5

2.0

2.5

0.1 0.2 0.5 1 2 5


original

small

medium

large

11x11


ETS for 3 NM-Versions (Exp. Values)

0

5

10

15

20

0.1 0.2 0.5 1 2 5


original

small

medium

large

11x11


FBI for 3 NM-Versions (0.5-Quantiles)

0.0

0.5

1.0

1.5

2.0

0.1 0.2 0.5 1 2 5


original

small

medium

large

11x11


ETS for 3 NM-Versions (0.5-Quantiles)

0

5

10

15

20

25

0.1 0.2 0.5 1 2 5


original

small

medium

large

11x11


Reliability Diagram RR(0.1-Quantile >= 0.1 mm/h)

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90

10 20 30 40 50 60 70 80 90

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medium

large


Reliability Diagram for 0.9-Quantiles of RR

02468

1012141618

0.1 0.2 0.5 1 2 5

Minimum Value in mm/h

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medium

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Reliability Diagram for 0.9-Quantiles of RR

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0.1 0.2 0.5 1 2 5

Minimum Value in mm/h

small

medium

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chance


Based on Richardson (2001) we derive a relation:

p' = p' (p,M,,)

M: effective sample size,related to the parameters of the beta distribution (r,s)

Calibration (addressing the effect of limited sample size only)


Preliminary Result of Calibration

Eliminationof and

Artificial choice:M=10

Reliability diagram of 1 h accumulated precipitation in the period 10.-24. July 2002(LM forecasts starting at 00 UTC; small version of neighbourhood method)


[mm/h]

Relative value of precipitation forecasts (original forecast and 90 % quantiles)for users, whose cost/lost ratio is equal to 10 % for the threshold valuesgiven by the abscissa

original forecast

smallmediumlarge


Concluding Remarks

“Statistically Smoothed” Fields

For temperature no mean advantage is to be seen in comparison with simple averaging

The results for precipitation are difficult to judge upon; proper choice amongst the various possibilities is still an open question

Reliability Diagrams

Possible improvement by calibration remains to be explored

The results for the lower quantiles of precipitation indicate the need for improving the model (reduce the overforecasting of slight precipitation amounts)

Higher quantiles of precipitation seem to be valuable already without calibration


Concluding Remarks (ctd.)

• Results of the neighbourhood method will be compared to those of more extensive experimental ensemble integrations

• Calibration of quantiles will hopefully be further developed

• The method will be tested on the 2.8 km LM version and compared to other/simpler methods. Application in combination with a small ensemble (LAF) will be investigated

• The program has been implemented at MeteoSwiss and may be made available to other COSMO members

Outlook

Documents

Statistical Postprocessing of LM Weather Parameters Ulrich Damrath Volker Renner Susanne Theis Andreas Hense