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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.

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slide1

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

introduction i

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?
non normality in enkf

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)

slide4
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
evaluation method
Evaluation Method
  • PDF(qualitative)
  • Normal Probability Plot(more quantitative)
example ii rainfall

pp from SYNOP

pp from radar

log(pp) from SYNOP

log(pp) from radar

Example II: Rainfall
general findings for observation term
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
ensemble anomalies
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
ensemble anomalies1
Ensemble Anomalies

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

model physics perturbations

rlam_heat=0.1

ECMWF

GME

NCEP

UM

ensemble anomalies2
Ensemble Anomalies

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

model physics perturbations

ECMWF

GME

NCEP

UM

ensemble anomalies3

Temperature at ~10m

Temperature at ~5400m

+3h+9h

+3h+9h

26.7%81.7%

68.2%89.7%

Ensemble Anomalies
timeseries of normrange

+3h, 10m

+9h, 10m

+3h, 5400m

+9h, 5400m

Timeseries of Normrange

Temperature

timeseries of normrange1

+3h, 10m

+9h, 10m

+3h, 5400m

+9h, 5400m

Timeseries of Normrange

U component of wind

general findings for background term
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
discussion
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
conclusions
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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