Statistical Characteristics of High-Resolution COSMO Ensemble Forecasts in view of Data Assimilation

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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

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Introduction I

• General assumption in Ensemble Kalman Filter
  MethodsErrors 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?

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Non-Normality in EnKF
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
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Example II Rainfall
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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

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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

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Ensemble Anomalies
Temperature at 10m, 3h (03UTC)
model physics perturbations
rlam_heat0.1
ECMWF
GME
NCEP
UM
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Ensemble Anomalies
Temperature at 10m, 9h (09UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
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Ensemble Anomalies
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Timeseries of Normrange
Temperature
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Timeseries of Normrange
U component of wind
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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
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Example II Humidity from Radiosondes
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Ensemble Anomalies
Hourly Precipitation
3h 9h
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Ensemble Anomalies
Temperature at 5400m, 3h (03UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
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Ensemble Anomalies
Hourly Precipitation, 3h (03UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
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Ensemble Anomalies
Hourly Precipitation, 9h (09UTC)
model physics perturbations
ECMWF
GME
NCEP
UM
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Timeseries of Normrange
Specific humidity
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Methods to deal with Nonnormality

• No cost smoother (Kalnay et al., 2007)
• Apply weights from time t1 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)