use ensemble error covariance information in grapes 3dvar jiandong gong, ruichun wang nwp center of...
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Use ensemble error covariance information in GRAPES 3DVAR
Jiandong GONG, Ruichun WANG
NWP center of CMAOct 27, 2015
wx U
)UUHMU()UUHMU(2
1
2
1hvp
1hvp dwOdwwwJ TT
GRAPES 3/4DVar Cost function
)HM()HM(2
1
2
1 11 dxOdxxBxJ TT
Here
BT UU hvp UUUU
Incremental formulation (Courtier et al. 1994)
oyMxHd )
Add alpha control variable in GRAPES 3DVAR
Define “alpha” control variable with localization filter:
(3dimension) or (2D)
for horizontal localization, for vertical localization.
In detail, horizontal spectral filter and vertical EOF mode used:
(2D)
(3D)
use single to decrease size
Alpha control variable in GRAPES 3DVar
Cost-function with climate and alpha control variable
N for number of ensemble members
;
3D control variable
2D alpha variable
or 3D lower dimension alpha variable
Climate dimension vs Flow-dependent dimension
𝑑 𝑋 1=𝑈𝑃𝑈 𝐾 ( 1√𝑁−1
∑𝑖=1
𝑁
(𝑇 𝐾𝑇 𝑃 𝛿 𝑋 𝑖𝑓 )∘𝑈 h
𝛼𝑈𝑣𝛼𝑣 𝑖
𝛼)Psi unbalanced & Chi localization
Localization on horizontal (20member)No localizationLocal Scale=1500KM
Local Scale=150KM Local Scale=1000KM
GRAPES Hybrid 3DVar: 2D alpha-control variable
Clim 1.0Ens 0.0
Clim 0.9ENS 0.1
Clim 0.5Ens 0.5
Clim 0.1Ens 0.9
Localize in u&v space or psi&chi space
u&v space psi&chi space
Horizontal localization impact on balance
U & V localization Psi & 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.
1 0.608p
g
C q z
Hydrostatic balance
Vertical localization impact on balance
ρ𝑙 ,𝑘=1
1.0+𝐾 𝑧 ( 𝑧𝑙−𝑧𝑘 )2
Background Error vertical correlation function:
20member 60member hybrid (All observation, 0.5/1.0L60 analysis + 1.0/1.0L60 ensemble)
Items 3DVARControl
Hybrid 3DVar (3D Loc, 20m)
Hybrid 3DVar (3D Loc, 40m)
Hybrid 3DVar (3D Loc, 60m)
Hybrid 3DVar (2D Loc, 60m)
Control variable
,,,q,,,q
+ 3D
,,,q
+ 3D
,,,q
+ 3D
,,,q
+ 2D
CV number4x58xgauss grid (ggrid)
(4x58+20x8)x ggrid
(4x58+40x8)x ggrid
(4x58+60x8)x ggrid
(4x58+60)x ggrid
Ratio to CV 1 1.68 2.38 3.07 1.26
Iterate step 65 71 69 66 66
CPU cores 8x32 8x32 8x32 8x32 8x32
Minim time 64s 131s 195s 250s 75s
CPU Time(inner loop) 152s 220s 279s 335s 180s
Cld wall Time(inner loop) 194s 272s 343s 412s 230s
CV Ratio to Cld wall time 1 1.4 1.76 2.12 1.18
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 3rd order vertical smoother for noise Generate 20 to 60 ensemble members
Ensemble RMSE average and Climate RMSE
EnsembleRMSE average (12days),
inflate1.5 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 runControl 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 EOFWeighting coefficient for climate and ensemble
Case study 1: (2013050812)
Contour: 3DVAR analysis 300hpa heightShared: 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
TR EA
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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