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. Observation term. Background term. Introduction I.

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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


Introduction i

Observation term Ensemble Forecasts in view of Data Assimilation

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 Ensemble Forecasts in view of Data Assimilation

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)


Data Ensemble Forecasts in view of Data Assimilation

  • 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 Ensemble Forecasts in view of Data Assimilation

  • PDF(qualitative)

  • Normal Probability Plot(more quantitative)


Example i temperature

T2m from SYNOP Ensemble Forecasts in view of Data Assimilation

[email protected] from aircraft obs

Example I: Temperature


Example ii rainfall

pp from SYNOP Ensemble Forecasts in view of Data Assimilation

pp from radar

log(pp) from SYNOP

log(pp) from radar

Example II: Rainfall


General findings for observation term
General Findings for Observation Term Ensemble Forecasts in view of Data Assimilation

  • 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 Ensemble Forecasts in view of Data Assimilation

  • 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 Ensemble Forecasts in view of Data Assimilation

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

model physics perturbations

rlam_heat=0.1

ECMWF

GME

NCEP

UM


Ensemble anomalies2
Ensemble Anomalies Ensemble Forecasts in view of Data Assimilation

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

model physics perturbations

ECMWF

GME

NCEP

UM


Ensemble anomalies3

Temperature at ~10m Ensemble Forecasts in view of Data Assimilation

Temperature at ~5400m

+3h+9h

+3h+9h

26.7%81.7%

68.2%89.7%

Ensemble Anomalies


Timeseries of normrange

+3h, 10m Ensemble Forecasts in view of Data Assimilation

+9h, 10m

+3h, 5400m

+9h, 5400m

Timeseries of Normrange

Temperature


Timeseries of normrange1

+3h, 10m Ensemble Forecasts in view of Data Assimilation

+9h, 10m

+3h, 5400m

+9h, 5400m

Timeseries of Normrange

U component of wind


General findings for background term
General Findings for Background Term Ensemble Forecasts in view of Data Assimilation

  • 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 Ensemble Forecasts in view of Data Assimilation

  • 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 Ensemble Forecasts in view of Data Assimilation

  • 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


Thank you for your attention
Thank you for your attention Ensemble Forecasts in view of Data Assimilation


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