1. 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

2. 2 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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? Background term Observation term

3. 3 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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)

4. 4 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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

5. 5 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Evaluation Method PDF (qualitative) Normal Probability Plot (more quantitative)

6. 6 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Example I: Temperature T2m from SYNOPT@500hPa from aircraft obs

7. 7 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Example II: Rainfall pp from SYNOP log(pp) from SYNOP pp from radar log(pp) from radar

8. 8 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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

9. 9 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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

10. 10 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Ensemble Anomalies ECMWF GME NCEP UM model physics perturbations Temperature at ~10m, +3h (03UTC) rlam_heat=0.1

11. 11 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Ensemble Anomalies ECMWF GME NCEP UM model physics perturbations Temperature at ~10m, +9h (09UTC)

12. 12 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Ensemble Anomalies Temperature at ~10m +3h +9h 26.7% 81.7% Temperature at ~5400m +3h +9h 68.2% 89.7%

13. 13 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Timeseries of Normrange Temperature +3h, 10m +9h, 10m +3h, 5400m +9h, 5400m

14. 14 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Timeseries of Normrange U component of wind +3h, 10m +9h, 10m +3h, 5400m +9h, 5400m

15. 15 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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

16. 16 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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

17. 17 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch 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

18. 18 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Thank you for your attention

19. 19 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Example II: Humidity from Radiosondes qv@850hPaRH@850hP log(qv)@850hPanormRH@850hPa

20. 20 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Ensemble Anomalies Hourly Precipitation +3h +9h

21. 21 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Ensemble Anomalies ECMWF GME NCEP UM model physics perturbations Temperature at ~5400m, +3h (03UTC)

22. 22 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Ensemble Anomalies ECMWF GME NCEP UM model physics perturbations Hourly Precipitation, +3h (03UTC)

23. 23 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Ensemble Anomalies ECMWF GME NCEP UM model physics perturbations Hourly Precipitation, +9h (09UTC)

24. 24 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Timeseries of Normrange Specific humidity +3h, 10m +9h, 10m +3h, 5400m +9h, 5400m

25. 25 COSMO Ensemble Statisticsdaniel.leuenberger@meteoswiss.ch COSMO GM 2009, Offenbach Methods to deal with Nonnormality „No cost smoother“ (Kalnay et al., 2007) Apply weights from time t+1 at time t „Running in place“ Use observations more than once by iterating several times over same assimilation window using the no cost smoother until convergence „Outer loop“ in LETKF Bring analysis mean closer to observations by iteration of update step (inner loop) Advance to next assimilation time by using nonlinear model (outer loop) using better guess of mean analysis from inner loop Have proven to improve LETKF in presence of nonlinearity / non-Gaussianity in Lorenz model (Yang and Kalnay, 2008)