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

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.

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

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  1. 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. Observation term Background term 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?

  3. Background pdf large obs error medium obs error small obs error Observation pdf Non-Normality in EnKF Pdf after update with stochastic EnKF Pdf after update with deterministic EnKF Lawson and Hansen, MWR (2004)

  4. 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. Evaluation Method • PDF(qualitative) • Normal Probability Plot(more quantitative)

  6. T2m from SYNOP T@500hPa from aircraft obs Example I: Temperature

  7. pp from SYNOP pp from radar log(pp) from SYNOP log(pp) from radar Example II: Rainfall

  8. 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. 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. Ensemble Anomalies Temperature at ~10m, +3h (03UTC) model physics perturbations rlam_heat=0.1 ECMWF GME NCEP UM

  11. Ensemble Anomalies Temperature at ~10m, +9h (09UTC) model physics perturbations ECMWF GME NCEP UM

  12. Temperature at ~10m Temperature at ~5400m +3h+9h +3h+9h 26.7%81.7% 68.2%89.7% Ensemble Anomalies

  13. +3h, 10m +9h, 10m +3h, 5400m +9h, 5400m Timeseries of Normrange Temperature

  14. +3h, 10m +9h, 10m +3h, 5400m +9h, 5400m Timeseries of Normrange U component of wind

  15. 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. 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. 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. Thank you for your attention

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