Model Error in the Forecast Ensemble System at Météo-France (PEARP)

Transcription

1 1. Model Error in the Forecast Ensemble System at Météo-France (PEARP) M. Boisserie L. Descamps P. Arbogast CNRM, Météo-France, Toulouse.

2 2 Introduction For a long time, it was assumed that model error should be relatively small, at least for short forecast times (Buizza et al., 2). So that forecast error would be dominated by the initial condition rather than the model (Toth et al., 1996). Until recently, the operational forecast ensembles consist of parallel forecasts using the same numerical model but different initial conditions. However, by doing that, the spread of the forecast is typically too small. In practice, forecast uncertainty also arises due to the fact that models are not perfect

3 3 Prevision Ensemble ARPege (PEARP) Ensemble Initialization Technique (Applied since Dec 29) Pertubed analysis : Use l Assimilation d Ensemble ARPEGE (AEARP) which consists of perturbing the observations (G. Desroziers, L. Berre) 6 perturbed analysis Linear combinaison with 56 singular vectors. Model error : Use 8 different physics Ensemble size : 34 perturbed + 1 control membre = 35 membres

4 4 Ensemble Forecasting System of Météo-France (PEARP)

5 5 Motivation Major sources of model uncertainties Parameterization of sub-grid scales Numerics (spatial and time resolution) Physics (radiation, turbulence, moist processes) Representation of model uncertainties Multi-physics (done) White random noise based on model error covariance matrix (Q)

6 How to compute model error? (Daley 1992) P f t+1 = Pp t+1 + Q t Pf = Forecast error covariance matrix Pp = Predictability error covariance matrix Q = Model error covariance matrix 6 This approach assumes that the spread of the ensemble data assimilation represents the analysis uncertainties

7 7 Verification of the analysis error estimation 1 Analysis ensemble : 6 perturbed analyses (AEARP) + 1 control 7 analyses Study period : between 18 Jan et 14 Fev 21 days 2 Verification of the reliability of the analysis ensemble Scores : Rank diagrams (or Talagrand diagrams) Account for observational uncertainties in the scores.

8 8 Results : analysis error Z5 running at UTC GLOBAL T85 running at UTC GLOBAL Tropics Tropics

9 9 Results : model error (Z5) T + H Forecast error Pf Predictability error Pp T + 6H Q (= Pf - Pp) Forecast error Pf Predictability error Pp Q (= Pf - Pp) Q (= Pf - Pp) Forecast error Pf T + H Predictability error Pp T + 9H Forecast error Pf Q (= Pf - Pp) Predictability error Pp

10 Z5 running at UTC T + H Results : model error T85 running at UTC T + H 1 T85, running at UTC, nb = 1441 T + 36H T85, running at UTC, nb = 1644 T + 72H T85, running at UTC, nb = 1465 T + 96H T85, running at UTC, nb = T85, running at UTC, nb = 1441 T + 36H T85, running at UTC, nb = 1644 T + 72H T85, running at UTC, nb = 1465 T + 96H T85, running at UTC, nb =

11 1 Summary The dispersion of our analysis ensemble is relatively correct. Therefore, the analysis ensemble spread is a good estimate of the initial error Using Daley s approach, we expect to obtain a reliable estimate of the model error covariance P f t+1 = Pp t+1 + Q t Other statistical tools to analyse model error : Mean and variance of the standardized variables Rank diagram at different time steps

12 12 EXTRA SLIDES

13 13 Expression de l erreur modèle (Daley 1992) Prévision du modèle : xt+1 f = M(x t a ) (1),où xt a = xt tr + ɛ a t Expression d un état parfait : = M(x tr t ) + ɛ q t (2) x tr t+1 Si on fait (1) - (2), on obtient : xt+1 f x t+1 tr = M(x t a ) M(xt tr ) ɛ q t ou x tr t+1 = x f t+1 ɛf t,et ɛ f t+1 = ɛp t+1 ɛq t x f t+1 (x f t+1 ɛf t+1 ) = M(x a t ) M(x a t ɛ a t ) (ɛ p t+1 ɛf t+1 ) ɛ p t+1 = M(x a t ) M(x a t ɛ a t+1 ) ɛp t+1 = M(x a t ) Expression de la matrice de l erreur modèle Q t : P f t+1 = Pp t+1 + Q t x a t ɛ a t+1

14 4 ARPEGE model characteristics Resolution : T358, 65 levels Stretching coefficient = 2.4 Up to 5 km altitude

15 Characteristics of the multi-physics KFB : shallow convection scheme CAPE : convection closure scheme : convergence humide remplacée par une fermeture en énergie CAPE TKE : Turbulent Kinetic Energy (TKE) SM : micro-physics by Smith ; Bg : micro-physics by Bougeault