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Eidgenössisches Departement des Innern EDI Bundesamt für Meteorologie und Klimatologie MeteoSchweiz Statistical Characteristics of High-Resolution COSMO Ensemble Forecasts in view of Data Assimilation Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

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Statistical Characteristics of High-Resolution COSMO Ensemble Forecasts in view of Data Assimilation. Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach. Observation term. Background term. Introduction I. - PowerPoint PPT Presentation

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Page 1: 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

Page 2: Priority Project KENDA Daniel Leuenberger MeteoSwiss, 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

Page 3: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

3 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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)

Page 4: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

4 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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

Page 5: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

5 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

Evaluation Method

• PDF(qualitative)

• Normal Probability Plot(more quantitative)

Page 6: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

6 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

Example I: Temperature

T2m from SYNOP T@500hPa from aircraft obs

Page 7: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

7 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

Example II: Rainfall

pp from SYNOP

log(pp) from SYNOP

pp from radar

log(pp) from radar

Page 8: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

8 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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

Page 9: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

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

Page 10: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

10 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

Ensemble Anomalies

ECMWF

GME

NCEP

UM

model physics perturbations

Temperature at ~10m, +3h (03UTC)

rlam_heat=0.1

Page 11: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

11 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

Ensemble Anomalies

ECMWF

GME

NCEP

UM

model physics perturbations

Temperature at ~10m, +9h (09UTC)

Page 12: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

12 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

Ensemble Anomalies

Temperature at ~10m

+3h +9h

26.7% 81.7%

Temperature at ~5400m

+3h +9h

68.2% 89.7%

Page 13: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

13 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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

Page 14: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

14 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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

Page 15: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

15 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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

Page 16: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

16 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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

Page 17: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

17 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

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

Page 18: Priority Project KENDA Daniel Leuenberger MeteoSwiss, Zurich, Switzerland COSMO GM 2009, Offenbach

18 COSMO Ensemble Statistics [email protected] COSMO GM 2009, Offenbach

Thank you for your attention