Ensemble assimilation & prediction

at Météo-FranceLoïk Berre & Laurent Descamps

Outline

1. Ensemble assimilation (L. Berre) to provide flow-dependent B.

2. Ensemble prediction (L. Descamps) for probabilistic forecasting.

Part 1:Ensemble assimilation

Loïk Berre, Gérald Desroziers, Laure Raynaud, Olivier Pannekoucke, Bernard

Chapnik, Simona Stefanescu, Benedikt Strajnar,

Rachida El Ouaraini, Pierre Brousseau, Rémi Montroty

Reference (unperturbed) assimilation cycleand the cycling of its errors

(e.g. Ehrendorfer 2006 ; Berre et al 2006)

ea = (I-KH) eb + K eo

eb = M ea + em

Idea: simulate the error cycling of this reference systemwith an ensemble of perturbed assimilations ?

K = reference gain matrix(possibly hybrid)

Observation perturbations are explicit, while background perturbations are implicit (but effective).

(Houtekamer et al 1996; Fisher 2003 ;Ehrendorfer 2006 ; Berre et al 2006)

An ensemble of perturbed assimilations : to simulate the error evolution

(of a reference (unperturbed) assimilation cycle)

Flow-dependent B

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 ignoresthe spatial coherence (structure) of local covariances.

An attractive compromise is to calculate local spatial averagesof covariances, to obtain a robust flow-dependence with a small ensemble,and to account for the spatial coherence of local covariances.

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 « b’s 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).

« RAW »b

ENS #1

Large scale structures look similar & well connected to the flow !

Optimize further the estimation, by accounting for spatial structures (of signal & noise).

ONE EXAMPLE OF “RAW” ONE EXAMPLE OF “RAW” bb MAPS (Vor, 500 hPa) MAPS (Vor, 500 hPa)

FROM TWO INDEPENDENT FROM TWO INDEPENDENT 33-MEMBER ENSEMBLES-MEMBER ENSEMBLES

« RAW »b

ENS #2

INCREASE OF SAMPLE SIZEINCREASE OF SAMPLE SIZE

BY LOCAL SPATIAL AVERAGING: BY LOCAL SPATIAL AVERAGING:

CONCEPTCONCEPT

Idea: MULTIPLY(!) the ensemble size Ne

by a number Ng of gridpoint samples.

If Ne=6, 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.

Ng=9

latitude

longitude

INCREASE OF SAMPLE SIZEINCREASE OF SAMPLE SIZE

BY LOCAL SPATIAL AVERAGING: BY LOCAL SPATIAL AVERAGING:

OPTIMAL ESTIMATE FORMALISM & IMPLEMENTATIONOPTIMAL ESTIMATE FORMALISM & IMPLEMENTATION

b* ~ b

with

= signal / (signal+noise)

Apply the classical BLUE optimal equation (as in data assim°),

with a filter accounting for spatial structures of signal and noise:

is a low-pass filter

(as K in data assim°).

( see Laure Raynaud’s talk also ! )

RESULTS OF THE FILTERINGRESULTS OF THE FILTERING

b ENS 2 « RAW » b ENS 2 « FILTERED »

b ENS 1 « FILTERED »b ENS 1 « RAW »

Ensemble dispersion:

large sigmab over France

Mean sea level pressure :

storm over France

Connection between large sigmab and intense weather ( 08/12/2006 , 03-06UTC )

Colours:

sigmab field

Purple isolines :

mean sea level pressure

Connection between large sigmab and intense weather ( 15/02/2008 , 12UTC )

Large sigmab near the tropical cyclone

Validation of ensemble sigmab’s « of the day » HIRS 7 (28/08/2006 00h)

Ensemble sigmab’s

« Observed » sigmab’s

cov( H dx , dy ) ~ H B HT

(Desroziers et al 2005)

=> model error estimation.

REDUCTION OF NORTHERN AMERICA

AVERAGE GEOPOTENTIAL RMSE

WHEN USING SIGMAB’s OF THE DAY

Height (hPa)

Forecast range (hours)

_____ =

NOV 2006 - JAN 2007 (3 months) FEB - MARCH 2008 (1 month)

SEPT - OCT 2007 (1 month)

+24h 500 hPa WIND RMSE over EUROPE

( b’s of the day versus climatological b’s )

Reduction of RMSE peaks (intense weather systems)

Wavelet filtering ofcorrelations « of the day »

Raw length-scales(6 members)

(Pannekoucke, Berre and Desroziers, 2007 ; Deckmyn and Berre 2005)

Wavelet length-scales(6 members)

( see Olivier Pannekoucke’s talk also ! )

LAM ensemble (Arome) : seasonal dependence of correlations

_____ anticyclonic winter

- - - - - convective summer(Desroziers et al, 2007)

Conclusions of Part 1

A 6-member ensemble assimilation in real time (double suite).A 6-member ensemble assimilation in real time (double suite). flow-dependent « sigmab’s of the day ».flow-dependent « sigmab’s of the day ». operational within 2008.operational within 2008.

Spatial filtering of sigmab’s strengthens their robustness.Spatial filtering of sigmab’s strengthens their robustness. later extension to « correlations of the day » (spectral/wavelet),later extension to « correlations of the day » (spectral/wavelet),and to high-resolution LAMs.and to high-resolution LAMs.

Comparisons with innovation diagnostics and impact experiments Comparisons with innovation diagnostics and impact experiments are encouraging. Use innovations to estimate model errors.are encouraging. Use innovations to estimate model errors.

Applications for ensemble prediction too: Applications for ensemble prediction too: see PART 2 by Laurent Descamps.see PART 2 by Laurent Descamps.