How much is it going to rain? What is the probability of such an event to happen?

Federal Department of Home Affairs FDHAFederal Office of Meteorology and Climatology MeteoSwiss

Improving COSMO-LEPS forecasts of extreme events with reforecasts

F. Fundel, A. Walser, M. Liniger, C. Appenzeller

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How much is it going to rain?

What is the probability of such an event to happen?

Are there systematic model errors?

Do model errors vary in space, time?

Did the model ever forecast a such an event?

Should a warning be given?

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ModelObs

25. Jun. +-14d

Why can reforecasts help to improve meteorological warnings?

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Spatial variation of model bias

Difference of CDF of observations and COSMO-LEPS 24h total precipitation

10/2003-12/2006

Model too wet, worse in southern Switzerland

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“However, the improved skill from calibration using large datasets is equivalent to the skill increases afforded by perhaps 5–10 yr of numerical modeling system development and model resolution increases.” (Wilks and Hamill, Mon. Wea. Rev. 2007)

“Use of reforecasts improved probabilistic precipitation forecasts dramatically, aided the diagnosis of model biases, and provided enough forecast samples to answer some interesting questions about predictability in the forecast model.” (Hamill et. al, BAMS 2006)

“…reforecast data sets may be particularly helpful in the improvement of

probabilistic forecasts of the variables that are most directly relevant to many forecast users…” (Hamill and Whitaker, subm. to Mon. Wea. Rev 2006)

Proven use of reforecasts

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COSMO-LEPS Model Climatology

Setup• Reforecasts over a period of 30 years (1971-2000)• Deterministic run of COSMO-LEPS (1 member)

(convective scheme = tiedtke)• ERA40 Reanalysis as Initial/Boundary• 42h lead time, 12:00 Initial time• Calculated on hpce at ECMWF• Archived on Mars at ECMWF (surf (30 parameters),

4 plev (8 parameters); 3h step)• Post processing at CSCS

Limitations• Reforecasts with lead time of 42h are used to calibrate

forecasts of up to 132h• Only one convection scheme (COSMO-LEPS uses 2)• New climatology needed with each model version change• Building a climatology is slow and costly• Currently only a monthly subset of the climatology is used for

calibration (warning indices need to be interpreted with respect to the actual month)

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x Model Climate Ensemble Forecast

Calibrating an EPS

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Extreme Forecast Index EFI (ECMWF)

( )∫ −−

=1

0 1

)(2dp

pp

pFpEFI ECMWF

π

-1 < EFI > 1EFI = -1 : All Forecast are below the climatology

EFI = 1 : All Forecast are above the climatology

F(p)

p

F(p) = proportion of EPS members below the p percentile

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Extreme Forecast Index EFI (ECMWF)

EFI for 24h total precipitation05.09.2007 00 UTC – 06.09.2007 00 UTC 05.09.2007 06 UTC – 06.09.2007 06 UTC

COSMO-LEPS ECMWF

0.8???

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Extreme Forecast Index EFI (ECMWF)

EFI properties (desired?)

• Combines properties of two CDFs in one number

• Forecast and climatology spread influence the EFI

• Ambiguous interpretation

without further information

EFI for varying forecast mean and standard deviationconstant climatology with mean=0 and =1

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Approach:• fit a distribution function to the model climate

(e.g. Gamma for precipitation)• find the return levels according to a given

return period• find the number of forecasts exceeding the

return level of a given return period

Advantages:• calibrated forecast• probabilistic forecast• straight forward to interpret• return periods are a often related to warning levels (favorably for forecasters)

Limitation:• Not applicable on extreme (rare) events

Return Periods

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New index

Probability of Return Period exceedance PRP

• Dependent on the climatology used to calculate

return levels/periods• Here, a monthly subset of the climatology is used

(e.g. only data from September 1971-2000)

• PRP1 = Event that happens once per September

• PRP100 = Event that happens in one out of 100 Septembers

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Probability of Return Period exceedance

once in 6 Septembers once in 2 Septembers

each Septembers twice per September

COSMO-PRP1/2 COSMO-PRP1

COSMO-PRP2 COSMO-PRP6

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24h total precipitation 04.09.2007 12UTCVT: 05.09.2007 00UTC – 06.09.2007 00UTC

Probability of Return Period exceedance

EFI COSMO-PRP2

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PRP based Warngramms

twice per September (15.8 mm/24h) once per September (21 mm/24h) once in 3 Septembers (26.3 mm/24h) once in 6 Septembers (34.8 mm/24h)

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PRP with Extreme Value Analysis Extremal types Theorem:

Maxima of a large number of independent random data of the same distribution function follow the Generalized Extreme Value distribution (GEV)

→ 0 : Gumbel > 0 : Frechet < 0 : Weibull

=position; =scale; =shape

C. Frei, Introduction to EVA

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The underlying distribution function of extreme values y=x-u above a threshold u is the Generalized Pareto Distribution (GPD) (a special case of the GEV)

=scale; =shape

C. Frei, Introduction to EVA

PRP with Extreme Value Analysis

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Steps towards a GPD based probabilistic forecast of extreme events

• Find an eligible threshold for the detection of extreme events

(97.5% percentile of the climatology)

• Fit the GPD to the found extreme values

• Calculate return levels for chosen return periods

• Find the proportion of forecast members exceeding a return level

PRP with Extreme Value Analysis

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Return Period [days]

Ret

urn

Lev

el [

mm

/24h

]

GPD fit to extreme values (>97.5 %-ile i.e. top 25) of COSMO-LEPS 24h precipitation (1 grid point only)and 5%,95% confidence intervals

PRP with Extreme Value Analysis

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COSMO-PRP2 COSMO-PRP2 (GPD)

PRP with Extreme Value Analysis

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COSMO-PRP60 (GPD)COSMO-PRP12 (GPD)

PRP with Extreme Value Analysis

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Difficulties of GPD based warning products

• In case of precipitation very dry regions sometimes do not have enough

days of precipitation (solution: extend reforecasts/mask regions)

• A low number of extreme events increases the uncertainty of the GPD fit

(solution: extend reforecasts)

• Verification of extreme events is difficult due to the low number of

events available.

PRP with Extreme Value Analysis

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Next Steps

• Extend the model climate used for calibrationand extreme value statistics

• Probabilistic verification of the calibratedCOSMO-LEPS forecast

• Translate model output to real atmospheric values

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Conclusion

• A 30-years COSMO-LEPS climatology is about to being

completed

• New probabilistic, calibrated forecasts of extreme events are in quasi operational use

• An objective verification is necessary

• Extreme events might only be verified with case studies

• Forecaster feedback is necessary