Use ensemble error covariance information in GRAPES 3DVAR Jiandong GONG, Ruichun WANG NWP center of CMA Oct 27, 2015

GRAPES 3/4DVar Cost function Here Incremental formulation (Courtier et al. 1994)

Add alpha control variable in GRAPES 3DVAR

Alpha control variable in GRAPES 3DVar 3D control variable 2D alpha variable or 3D lower dimension alpha variable Climate dimension vs Flow-dependent dimension Psi unbalanced & Chi localization

Localization on horizontal (20member) No localization Local Scale=1500KM Local Scale=150KM Local Scale=1000KM

GRAPES Hybrid 3DVar: 2D alpha-control variable Clim 1.0 Ens 0.0 Clim 0.9 ENS 0.1 Clim 0.5 Ens 0.5 Clim 0.1 Ens 0.9

Localize in u&v space or psi&chi space u&v space psi&chi space

Horizontal localization impact on balance U & V localizationPsi & Chi localization

Localization on vertical (First 8 EOF’s eigenvector, difference vertical correlation scale) 2D horizontal localization 3D localization, narrow local corr. 3D localization, middle local corr. 3D localization, broad local corr.

Localization on vertical 2D horizontal localization 3D localization, narrow local corr. 3D localization, middle local corr. 3D localization, broad local corr. Hydrostatic balance

Vertical localization impact on balance Background Error vertical correlation function:

20member  60member hybrid ( All observation, 0.5/1.0L60 analysis + 1.0/1.0L60 ensemble ) Items 3DVAR Control Hybrid 3DVar (3D Loc, 20m) Hybrid 3DVar (3D Loc, 40m) Hybrid 3DVar (3D Loc, 60m) Hybrid 3DVar (2D Loc, 60m) Control variable , , , q +  3D , , , q +  3D , , , q +  3D , , , q +  2D CV number 4x58xgauss grid (ggrid) (4x58+20x8)x ggrid (4x58+40x8)x ggrid (4x58+60x8)x ggrid (4x58+60)x ggrid Ratio to CV Iterate step CPU cores 8x32 Minim time 64s131s195s250s75s CPU Time (inner loop) 152s220s279s335s180s Cld wall Time (inner loop) 194s272s343s412s230s CV Ratio to Cld wall time

Real observation data cycling run Ensemble member generation (EDA)  Perturb all observations in 3DVAR Perturb with Gaussian(0,1) PDF distribution RH perturbation within [0%~100%] No surface perturbation (SST,etc) No Physics perturbation  Spin-up running for 4 days  Increment Digital Filter Initialization (IDFI) for each member  Spectral horizontal filter for sampling noise, wave cut at T106 (Massimo,2011)  5 grid 3 rd order vertical smoother for noise  Generate 20 to 60 ensemble members

Ensemble RMSE average and Climate RMSE Ensemble RMSE average (12days), inflate 1.5 times Climate background error

Ensemble RMSE for U & V wind En3DVAR will have more impact on tropic region, and on upper troposphere

Real observation data cycling run Control run ( May 4 to 16, 2013)  All observation, climate Background error  0.5/1.0 L60 resolution Hybrid experiment  Extend alpha control variable, 3D localization (1700km,Lkz=0.5)  First 6 vertical EOF’s eigenvector for vertical localization  20 ensemble members (computer resource)  Ensemble error inflation 1.5, for small number of ensemble member  Climate/Ensemble: 0.8/0.5, top to level 48 (tropopause), smooth damping to zero, Moisture analysis use climate B  Localization on Psi/chi variable for better mass-wind balance

Hybrid parameter Vertical correlation matrix for EOF Weighting coefficient for climate and ensemble

Case study 1: ( ) Contour: 3DVAR analysis 300hpa height Shared: Hybrid -3DVAR height difference

Case Study 2: (Tropical Storm Mahasen) May 6, Tropical perturbation May 9, Tropical low pressure area May 10, Tropical cyclone May 11, Tropical strom May 16 Low pressure and low pressure area

Weaken Tropical storm Larger ensemble divergence for Tropical Strom location and intensity

NH TREA GRAPES Height analysis RMSE (Unit:m) SH

NH TR GRAPES U-wind analysis RMSE (Unit:m/s) SH TR

Future plan Hybrid GDAS System develop and tuning  Horizontal de-correlation length increase with model level in 3DVAR, so for horizontal localization  Direct estimate vertical error covariance, not use pre-defined structure again, with short vertical correlation.  Increase ensemble members (20m to 60m)  Balance issue (eg. 4D-IAU)  Combine with 4DVAR, to develop GRAPES EN4DVAR New Global Ensemble member perturbation method (LETKF)  Computer cost expensive for perturb obs in VAR system Perturb land surface moisture and SST, to enlarge ensemble spread in low troposphere

Acknowledgement:  Yan LIU, Yongzhu LIU, Lin Zhang, Huijuan LU, Jincheng WANG  Fengfeng Chen, Jian Sun, Yong Su, …

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