Transcript extreme events

Federal Department of Home Affairs FDHA
Federal 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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Why can reforecasts help to improve
meteorological warnings?
Model
Obs
25. Jun. +-14d
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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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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)
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COSMO-LEPS Model Climatology
Setup
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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
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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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Calibrating an EPS
x Model Climate
Ensemble Forecast
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Extreme Forecast Index EFI (ECMWF)
p
EFI ECMW F 
2

1

0
p  F ( p)
dp
p1  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
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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???
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Extreme Forecast Index EFI (ECMWF)
EFI properties (desired?)
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Combines properties of two CDFs
in one number
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Forecast and climatology spread
influence the EFI
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Ambiguous interpretation
without further information
EFI for varying forecast mean and standard deviation
constant climatology with mean=0 and =1
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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
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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
twice per September
each Septembers
COSMO-PRP1/2
COSMO-PRP1
once in 2 Septembers
COSMO-PRP2
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once in 6 Septembers
COSMO-PRP6
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Probability of Return Period exceedance
24h total precipitation 04.09.2007 12UTC
VT: 05.09.2007 00UTC – 06.09.2007 00UTC
EFI
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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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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
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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
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Return Level [mm/24h]
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 Period [days]
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PRP with Extreme Value Analysis
COSMO-PRP2
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COSMO-PRP2 (GPD)
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PRP with Extreme Value Analysis
COSMO-PRP12 (GPD)
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COSMO-PRP60 (GPD)
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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.
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Next Steps
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Extend the model climate used for calibration
and extreme value statistics
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Probabilistic verification of the calibrated
COSMO-LEPS forecast
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Translate model output to real atmospheric values
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Conclusion
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A 30-years COSMO-LEPS climatology is about to being
completed
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New probabilistic, calibrated forecasts of extreme events are in quasi
operational use
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An objective verification is necessary
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Extreme events might only be verified with case studies
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Forecaster feedback is necessary
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