Ensemble assimilation & prediction at Météo-France Loïk 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 cycle and 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 system with 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 B and 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.

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  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”  b MAPS (Vor, 500 hPa) FROM TWO INDEPENDENT 3-MEMBER ENSEMBLES « RAW »  b ENS #2

INCREASE OF SAMPLE SIZE BY LOCAL SPATIAL AVERAGING: CONCEPT 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 SIZE BY LOCAL SPATIAL AVERAGING: OPTIMAL 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 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/ h) Ensemble sigmab’s « Observed » sigmab’s cov( H dx, dy ) ~ H B H T (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 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 of correlations « 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). flow-dependent « sigmab’s of the day ».  flow-dependent « sigmab’s of the day ». operational within  operational within  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.  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.