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Ensemble assimilation & prediction at Météo-France

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 .

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Ensemble assimilation & prediction at Météo-France

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  1. Ensemble assimilation & predictionat Météo-France Loïk Berre & Laurent Descamps

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

  3. 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

  4. Reference (unperturbed) assimilation cycleand the cycling of its errors eb = Mea+ 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)

  5. 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)

  6. 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.

  7. 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 « sb’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).

  8. 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).

  9. INCREASE OF SAMPLE SIZE BY LOCAL SPATIAL AVERAGING: CONCEPT Idea: MULTIPLY(!) the ensemble size Ne by a number Ng of gridpoint samples. latitude 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 longitude

  10. 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* ~ rsb with r=signal / (signal+noise) • r is a low-pass filter (as K in data assim°). ( see Laure Raynaud’s talk also ! )

  11. RESULTS OF THE FILTERING sb ENS 1 « FILTERED » sb ENS 1 « RAW » sb ENS 2 « FILTERED » sb ENS 2 « RAW »

  12. 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

  13. 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

  14. 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.

  15. REDUCTION OF NORTHERN AMERICA AVERAGE GEOPOTENTIAL RMSE WHEN USING SIGMAB’s OF THE DAY NOV 2006 - JAN 2007 (3 months) FEB - MARCH 2008 (1 month) SEPT - OCT 2007 (1 month) Forecast range (hours) Height (hPa) _____ =

  16. +24h 500 hPa WIND RMSE over EUROPE ( sb’s of the day versus climatological sb’s )  Reduction of RMSE peaks (intense weather systems)

  17. Wavelet filtering ofcorrelations « of the day » Raw length-scales (6 members) Wavelet length-scales (6 members) ( see Olivier Pannekoucke’s talk also ! ) (Pannekoucke, Berre and Desroziers, 2007 ; Deckmyn and Berre 2005)

  18. LAM ensemble (Arome) : seasonal dependence of correlations _____ anticyclonic winter - - - - - convective summer (Desroziers et al, 2007)

  19. Conclusions of Part 1 • A 6-member ensemble assimilation in real time (double suite).  flow-dependent « sigmab’s of the day ».  operational within 2008. • Spatial filtering of sigmab’s 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.

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