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?
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Improving COSMO-LEPS forecasts of extreme events with reforecastsF. 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?
Did the model ever forecast a such an event?
Should a warning be given?
25. Jun. +-14d
Difference of CDF of observations and COSMO-LEPS 24h total precipitation
Model too wet, worse in southern Switzerland
“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)
(convective scheme = tiedtke)
4 plev (8 parameters); 3h step)
x Model Climate
F(p) = proportion of EPS members below
the p percentile
-1 < EFI > 1
EFI = -1 : All Forecast are below the climatology
EFI = 1 : All Forecast are above the climatology
EFI for 24h total precipitation
05.09.2007 00 UTC – 06.09.2007 00 UTC05.09.2007 06 UTC – 06.09.2007 06 UTC
EFI properties (desired?)
Combines properties of two CDFs in one number
Forecast and climatology spread influence the EFI
without further information
EFI for varying forecast mean and standard deviation
constant climatology with mean=0 and =1
(e.g. Gamma for precipitation)
return level of a given return period
Probability of Return Period exceedance PRP
(e.g. only data from September 1971-2000)
twice per September
once in 2 Septembers
once in 6 Septembers
24h total precipitation 04.09.2007 12UTC
VT: 05.09.2007 00UTC – 06.09.2007 00UTC
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)
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
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)
C. Frei, Introduction to EVA
Steps towards a GPD based probabilistic forecast of extreme events
(97.5% percentile of the climatology)
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]
Difficulties of GPD based warning products
days of precipitation (solution: extend reforecasts/mask regions)
(solution: extend reforecasts)