Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach
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Transcript of Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach
Eidgenössisches Departement des Innern EDIBundesamt für Meteorologie und Klimatologie MeteoSchweiz
Statistical Characteristics of High-
Resolution COSMO Ensemble
Forecasts in view of Data Assimilation
Priority Project KENDA
Daniel LeuenbergerMeteoSwiss, Zurich, Switzerland
COSMO GM 2009, Offenbach
2 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach
Introduction I
• General assumption in Ensemble Kalman Filter Methods:„Errors are of Gaussian nature and bias-free“
• Prerequisite for
• „optimal“ combination of model fc and observations or
• easily finding a minimum of the cost function
• How normal are these terms in the COSMO model?
)()(2
1
2
1)( 11 xyRxyxxPxxx HHJ T
bbT
b
Background term Observation term
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Non-Normality in EnKF
Background pdf
small obs error medium obs error large obs error
Observation pdf
Pdf after update with stochastic EnKF
Pdf after update with deterministic EnKF
Lawson and Hansen, MWR (2004)
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Data
• Forecast departures (observation term)
• Different variables, observation systems, heights, lead times and seasons
• Based on a 3 month summer (2008) and winter (2007/2008) period of operational COSMO-DE forecasts
• Ensemble anomalies (background term)
• Different variables, levels, lead times and days
• Based on 9 days (Aug. 2007) of the experimental COSMO-DE EPS
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Evaluation Method
• PDF(qualitative)
• Normal Probability Plot(more quantitative)
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Example I: Temperature
T2m from SYNOP T@500hPa from aircraft obs
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Example II: Rainfall
pp from SYNOP
log(pp) from SYNOP
pp from radar
log(pp) from radar
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General Findings for Observation Term
• Small deviations from normality around mean in COSMO-DE for forecast departures of temperature, wind and surface pressure out to 12h lead time (normranges 80-95%).
• „Fat tails“, i.e. more large departures than expected in a Gaussian distribution
• Better fit in free atmosphere than near surface
• Deviation from normality in humidity and precipitation
• Transformed variables (log(pp) and NRH) have better properties concerning normality and bias
• Negligible differences COSMO-DE vs. COSMO-EU
• Slightly larger deviation from normality in a sample of rainy days
9 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach
Ensemble Anomalies
• Background error calculated from ensemble spread (anomalies around mean)
• Look at distribution of ensemble anomalies of COSMO-DE EPS forecasts • at +3h and +9h• near surface and at ~5400m above surface
• Example of 15.8.2007
• Time series of normranges over 9 days
bkb xx
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Ensemble Anomalies
ECMWF
GME
NCEP
UM
model physics perturbations
Temperature at ~10m, +3h (03UTC)
rlam_heat=0.1
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Ensemble Anomalies
ECMWF
GME
NCEP
UM
model physics perturbations
Temperature at ~10m, +9h (09UTC)
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Ensemble Anomalies
Temperature at ~10m
+3h +9h
26.7% 81.7%
Temperature at ~5400m
+3h +9h
68.2% 89.7%
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Timeseries of Normrange
20
30
40
50
60
70
80
90
100
8 9 10 11 12 13 14 15 16
day
no
rmra
ng
e (%
)
Temperature
+3h, 10m+9h, 10m+3h, 5400m+9h, 5400m
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20
30
40
50
60
70
80
90
100
8 9 10 11 12 13 14 15 16
day
no
rmra
ng
e (%
)
Timeseries of NormrangeU component of wind
+3h, 10m+9h, 10m+3h, 5400m+9h, 5400m
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General Findings for Background Term
• Larger deviations from normality than in observation term (but smaller statistics, based just on 9 summer days)
• Smallest deviations in wind (normrange generally 70-90%)
• Larger deviations in
• temperature (20-90%)
• specific humidity (60-80%)
• precipitation (exponential distribution)
• Consistently better fit at +9h than at +3h
• Tendency for better fit in free atmosphere than near surface
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Discussion
• Looked only at global distributions. Locally, non-Gaussianity is expected to be more significant (needs yet to be checked)
• LETKF ensemble will differ from the current setup of COSMO-DE EPS
• Gaussian spread in initial conditions
• Non-gaussianity will grow during non-linear model integration
• For data assimilation more gaussian perturbations will be needed
• A final conclusion about non-Gaussianity of a COSMO ensemble in view of the LETKF not possible with current setup of COSMO-DE EPS
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Conclusions
• Observation term seems to be reasonably normally distributed avaraged over many cases, except for humidity and precipitation
• Transformation of variables can improve normality
• High-resolution COSMO EPS might produce non-normal anomalies in some cases
• Will repeat such analyses with LETKF ensemble
• Ways to improve the LETKF in highly nonlinear / non-normal conditions are currently being investigated
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Thank you for your attention