Ensemble assimilation

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Ensemble assimilation predictionat Météo-France
Loïk Berre Laurent Descamps
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Outline

• 1. Ensemble assimilation (L. Berre)
• ? to provide flow-dependent B.
• 2. Ensemble prediction (L. Descamps)
• ? for probabilistic forecasting.

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Part 1Ensemble assimilation
Loïk Berre, Gérald Desroziers, Laure Raynaud,
Olivier Pannekoucke, Bernard Chapnik, Simona
Stefanescu, Benedikt Strajnar, Rachida El
Ouaraini, Pierre Brousseau, Rémi Montroty
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Reference (unperturbed) assimilation cycleand
the cycling of its errors

eb M ea em
ea (I-KH) eb K eo

K reference gain matrix (possibly hybrid)
Idea simulate the error cycling of this
reference system with an ensemble of perturbed
assimilations ?
(e.g. Ehrendorfer 2006 Berre et al 2006)
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An ensemble of perturbed assimilations to
simulate the error evolution(of a reference
(unperturbed) assimilation cycle)
Flow-dependent B
Observation perturbations are explicit, while
background perturbations are implicit (but
effective). (Houtekamer et al 1996 Fisher 2003
Ehrendorfer 2006 Berre et al 2006)
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Strategies to model/filter ensemble Band link
with ensemble size

• Two usual extreme approaches for modelling B in
  Var/EnKF
• Var correlations are often globally averaged
  (spatially).
• ? robust with a very small ensemble,
• but lacks heterogeneity completely.
• EnKF correlations and variances are often purely
  local.
• ? a lot of geographical variations potentially,
• but requires a rather large ensemble, it
  ignores
• the spatial coherence (structure) of local
  covariances.
• An attractive compromise is to calculate local
  spatial averages
• of covariances, to obtain a robust
  flow-dependence with a small ensemble,
• and to account for the spatial coherence of local
  covariances.

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A real time assimilation ensemble

• 6 global members T359 L60 with 3D-Fgat (Arpège).
• Spatial filtering of error variances,
• to further increase the sample size and
  robustness (90).
• A double suite uses these  sbs of the day  in
  4D-Var.
• ? operational within 2008.
• Coupling with six LAM members during two seasons
  of
• two weeks, with both Aladin (10 km) and Arome
  (2.5 km).

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ONE EXAMPLE OF RAW sb MAPS (Vor, 500 hPa) FROM
TWO INDEPENDENT 3-MEMBER ENSEMBLES
 RAW  sb ENS 1
 RAW  sb ENS 2
Large scale structures look similar well
connected to the flow ! ? Optimize further the
estimation, by accounting for spatial structures
(of signal noise).
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INCREASE OF SAMPLE SIZE BY LOCAL SPATIAL
AVERAGING CONCEPT
Idea MULTIPLY(!) the ensemble size Ne by a
number Ng of gridpoint samples.
latitude

• If Ne6, then
• the total sample size is
• Ne x Ng 54.
• The 6-member filtered estimate is as accurate
• as a 54-member raw estimate,
• under a local homogeneity asumption.

Ng9
longitude
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INCREASE OF SAMPLE SIZE BY LOCAL SPATIAL
AVERAGING OPTIMAL ESTIMATE FORMALISM
IMPLEMENTATION
Apply the classical BLUE optimal equation (as in
data assim), with a filter r accounting for
spatial structures of signal and noise
r
sb r sb with r signal / (signalnoise)

• r is a low-pass filter
• (as K in data assim).

( see Laure Raynauds talk also ! )
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RESULTS OF THE FILTERING
sb ENS 1  FILTERED 
sb ENS 1  RAW 
sb ENS 2  FILTERED 
sb ENS 2  RAW 
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Connection between large sigmab and intense
weather ( 08/12/2006 , 03-06UTC )
Mean sea level pressure storm over France
Ensemble dispersion large sigmab over France
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Connection between large sigmab and intense
weather ( 15/02/2008 , 12UTC )
Colours sigmab field
Purple isolines mean sea level pressure
Large sigmab near the tropical cyclone
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Validation of ensemble sigmabs  of the day 
HIRS 7 (28/08/2006 00h)
Ensemble sigmabs
 Observed  sigmabs cov( H dx , dy ) H B
HT (Desroziers et al 2005) gt model error
estimation.
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REDUCTION OF NORTHERN AMERICA AVERAGE
GEOPOTENTIAL RMSE WHEN USING SIGMABs OF THE DAY
NOV 2006 - JAN 2007 (3 months)
FEB - MARCH 2008 (1 month)
SEPT - OCT 2007 (1 month)
Forecast range (hours)
Height (hPa)
_____

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24h 500 hPa WIND RMSE over EUROPE ( sbs of the
day versus climatological sbs )
? Reduction of RMSE peaks (intense weather
systems)
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Wavelet filtering ofcorrelations of the day
Raw length-scales (6 members)
Wavelet length-scales (6 members)
( see Olivier Pannekouckes talk also ! )
(Pannekoucke, Berre and Desroziers, 2007
Deckmyn and Berre 2005)
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LAM ensemble (Arome) seasonal dependence of
correlations
_____ anticyclonic winter - - - - - convective
summer
(Desroziers et al, 2007)
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Conclusions of Part 1

• A 6-member ensemble assimilation in real time
  (double suite).
• ? flow-dependent  sigmabs of the day .
• ? operational within 2008.
• Spatial filtering of sigmabs strengthens their
  robustness.
• ? later extension to  correlations of the day 
  (spectral/wavelet),
• and to high-resolution LAMs.
• Comparisons with innovation diagnostics and
  impact experiments
• are encouraging. Use innovations to estimate
  model errors.
• Applications for ensemble prediction too
• see PART 2 by Laurent Descamps.