2005/11/19 THORPEX

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1 005/11/19 HORPEX

2 EnKF

3 time

5 Gaussian ~O10 6 =t0 =t1 P

6 nalysis Ens. mean Obs. FCS Ens. mean =t0 =t1 =t P

7 , etc. P =t0 P =t1 =t0 =t1

8 =t0 =t1

9 nalysis Ens. mean Obs. FCS Ens. mean =t0 =t1 P

11 [C] p est estimation σ σ σ σ σ σ σ σ + + = + + = ep p σ ep p σ + + = & ep ep p p p σ σ σ σ σ σ

12 ] ep[ 1 1 f f f p ] ep[ 1 1 o o o H H p y R y } { ep[ & o o f f o f o f H H p p p y R y + = PDF PDF

13 College Park, MD College Park College Park

15 nkf EnKF

16 nkf R a Errors of the day y o f

17 nkf m m-1 reeding SV m m/ + -

18 nkf EnKF Liu et al. 005 EnKF Vaisala Vaisala

19 ~O100 ~O10 6 ~O10 1, Patil et al. 000

20 Lorenc 003

EnKF EnKF Perturbed observation PO method Square root filtering SRF method We do not investigate this Serial EnSRF Whitaker and Hamill 00 EKF ishop et al.

21 EnKF EnKF Perturbed observation PO method Square root filtering SRF method We do not investigate this Serial EnSRF Whitaker and Hamill 00 EKF ishop et al. 001 EKF nderson 001 Effective in serial treatment of observations LEKF Ott et al. 00; 004 Simultaneous treatment of observations We implement and compare Serial EnSRF and LEKF erial EnSRF localizes covariance P around bservation locations. EKF treats local patches independently. N local patches cover the entire globe. Local patch Weighting function

22 orenz 40 Lorenz-96 model Lorenz 1996; Lorenz and Emanuel RMSE: 1.15 LEKF with obs. localization Serial EnSRF Covariance inflation factor Localization length scale Localization length scale

23 30L7 Perfect model scenario he SPEEDY model Molteni 003 Primitive-Equation dynamical core Simplified physics Variables u [m/s] v [m/s] [K] q [kg/kg] Ps [Pa] Obs. Err. Stdev

24 00Z RMSE 30 ensemble members 3DVR 31m LEKF 8m Serial EnSRF 5m

25 nsrf analysis increment is better capturing error structures. attice-like pattern in the 3DVR background error field. 3DVR EnKF Shades: background error, Contour: analysis increment

26 3DVR SPRED RMSE

27 EnKF Dee and da Silva 1998

28 Houtekamer et al. 005, Whitaker et al D-Var 4D-Var EnKF Dee and da Silva 1998, Danforth et al. 005

29 EnKF

31 alman filtering KF Kalman filtering KF is an optimal weighted mean between forecast and observation. a f f = + K y H i i i o i Here, the optimal weight Kalman gain is given as f f 1 K i = Pi H [ HPi H + R] Error covariance is estimated by the forecast: f P i = MP a i M + Q i KF estimation of P is optimal when the model is linear and perfect. Error covariance forecast is usually underestimated partly because of model nonlinearity. hus, covariance inflation is required. f P i = 1 + δmp a i M Inflation parameter

32 nsemble Kalman filtering EnKF Ensemble formulation m ~ 100 N ~ 10,000,000 N E E N P ssumption: Limited number of ensembles can estimate P o avoid sampling errors, we localize covariance. y the ensemble formulation, we can forecast error covariance from ensemble forecasting: P i f = 1 + δmp i a M E i f = 1+ δme i a

33 he SPEEDY model Molteni 003 rognostic variables u, v,, q, Ps esolution 30L rimitive-equation dynamic core implified physics Convection a simplified mass-flu scheme Large-scale condensation, Clouds Level 0.00 Short-wave radiation two spectral bands Long wave radiation four spectral bands Surface flues of momentum and energy bulk aerodynamic formula Vertical diffusion o diurnal forcing omputational time seconds for 6-hour forecast on a.7ghz Celeron PC Sigma p/ps Pressure hpa

実験 M10240L2000 については, 計算機資源節約のため, 実験 M10240L の 1 月 24 日 00 時の第一推定値を初期値とする 1 週間の実験を行った 4. 結果実験 M10240 L は,10240 メンバーによりサンプリング誤差を小さく抑えることに成功し, 局所化なしにもかか

実験 M10240L2000 については, 計算機資源節約のため, 実験 M10240L の 1 月 24 日 00 時の第一推定値を初期値とする 1 週間の実験を行った 4. 結果実験 M10240 L は,10240 メンバーによりサンプリング誤差を小さく抑えることに成功し, 局所化なしにもかか 10240 メンバーを用いたアンサンブルデータ同化実験近藤圭一, 三好建正 ( 理研, 計算科学,JST CREST) 1. はじめにデータ同化は, 数値モデルと観測を高度に融合させることで, より精緻な初期値解析値を得る手法であり, 数値予報モデルの予報精度に大きく影響を与える大気の流れを考慮した高度なデータ同化手法にアンサンブルカルマンフィルタ (EnKF; Evensen 1994) があり,