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

Improving COSMO-LEPS forecasts of extreme events with reforecasts F. Fundel, A. Walser, M. Liniger, C. Appenzeller. 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?

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

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  1. Improving COSMO-LEPS forecasts of extreme events with reforecastsF. Fundel, A. Walser, M. Liniger, C. Appenzeller

  2. 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?

  3. Why can reforecasts help to improve meteorological warnings? Model Obs 25. Jun. +-14d

  4. 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

  5. Proven use of reforecasts “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)

  6. 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)

  7. Calibrating an EPS x Model Climate Ensemble Forecast

  8. Extreme Forecast Index EFI (ECMWF) p F(p) = proportion of EPS members below the p percentile F(p) -1 < EFI > 1 EFI = -1 : All Forecast are below the climatology EFI = 1 : All Forecast are above the climatology

  9. Extreme Forecast Index EFI (ECMWF) EFI for 24h total precipitation 05.09.2007 00 UTC – 06.09.2007 00 UTC 05.09.2007 06 UTC – 06.09.2007 06 UTC ECMWF COSMO-LEPS 0.8???

  10. EFI properties (desired?) Combines properties of two CDFs in one number Forecast and climatology spread influence the EFI Ambiguous interpretation without further information Extreme Forecast Index EFI (ECMWF) EFI for varying forecast mean and standard deviation constant climatology with mean=0 and =1

  11. Return Periods 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

  12. 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

  13. twice per September each Septembers once in 2 Septembers once in 6 Septembers Probability of Return Period exceedance COSMO-PRP1/2 COSMO-PRP1 COSMO-PRP2 COSMO-PRP6

  14. Probability of Return Period exceedance 24h total precipitation 04.09.2007 12UTC VT: 05.09.2007 00UTC – 06.09.2007 00UTC EFI COSMO-PRP2

  15. 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)

  16. 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

  17. PRP with Extreme Value Analysis 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

  18. PRP with Extreme Value Analysis 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

  19. PRP with Extreme Value Analysis 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 Return Level [mm/24h] Return Period [days]

  20. PRP with Extreme Value Analysis COSMO-PRP2 COSMO-PRP2 (GPD)

  21. PRP with Extreme Value Analysis COSMO-PRP12 (GPD) COSMO-PRP60 (GPD)

  22. PRP with Extreme Value Analysis 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.

  23. Next Steps • Extend the model climate used for calibration • and extreme value statistics • Probabilistic verification of the calibrated • COSMO-LEPS forecast • Translate model output to real atmospheric values

  24. 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

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