a new 4-dimensional variational data assimilation system for wrf
DESCRIPTION
A new 4-dimensional variational data assimilation system for WRF. Juan Zhao , Bin Wang LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing. 2008-07-01. University Allied Workshop. Outline. Introduction to a new DA approach (HSP-4DVAR) - PowerPoint PPT PresentationTRANSCRIPT
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A new 4-dimensional variational data assimilation system for WRF
Juan Zhao , Bin Wang
LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing
2008-07-01University Allied Workshop
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Outline
Introduction to a new DA approach
(HSP-4DVAR)
Observing system simulation experiment (OSSE)
Summary
University Allied Workshop
![Page 3: A new 4-dimensional variational data assimilation system for WRF](https://reader033.vdocuments.mx/reader033/viewer/2022061614/568145ab550346895db2a509/html5/thumbnails/3.jpg)
Outline
Introduction to a new DA approach
(HSP-4DVAR)
Observing system simulation experiment (OSSE)
Summary
University Allied Workshop
![Page 4: A new 4-dimensional variational data assimilation system for WRF](https://reader033.vdocuments.mx/reader033/viewer/2022061614/568145ab550346895db2a509/html5/thumbnails/4.jpg)
4DVARCost function of 4DVAR (incremental form):
1 11 1( ) ( ) ( ( ) ) ( ( ) )
2 2T T
obs obsJ x x B x y x y O y x y
Introduction to HSP-4DVAR
University Allied Workshop
a bx x x
0 0( ) ( ( , )) ( ( , ))
i it t b t t by x H M x x H M x
0( ( , ))
iobs obs t t by y H M x
1 T T 1( ) M H (HM )obsJ x B x O x y
Calculate by making the nonlinear optimal iteration:
adjoint
(ECMWF,2002)
1 2[ , , , ]TNx x x x N-dimensionalmodel space(N: 106~108)
N*N
An effective and efficient 4DVAR
The huge computing cost of the iterative procedure based on the adjoint technique greatly limits the wide applications of traditional 4DVAR !
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1 2( , , , )y mP y y y
1 2( , , )x mP x x x
Historical Sample Projection (HSP)-4DVAR (Bin Wang et al, 2008)
HSP-4DVAR
11 1( ) ( ) ( )
2 2T T
y obs y obsJ B P y P y
1 1( )T Ta b x y y y obsx x P B P P P y
1obs obsy o y
Introduction to HSP-4DVAR
University Allied Workshop
new cost function:
calculate explicitly:
1 2[ , , , ]Tm
m~102
?
TO oom-dimensionalsample spaceAbandon adjoint model
Avoid making nonlinear optimal iteration
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Estimation of B matrixIntroduction to HSP-4DVAR
University Allied Workshop
1 2
1 2
1( , , , )
11
( )
T
m
m
B b b
bm
m
Utilize historical forecast samples to estimate B
1 2
1 2
1( , , , )
11
( )
T
m
m
B bb
b x x x x x xm
x x x xm
In model space
In sample space
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Estimation of B matrixIntroduction to HSP-4DVAR
University Allied Workshop
1 2
1 1 1
0 0 0
0 0 0, , ,
0 0 0
0 0 0
m
1 1 11
1 1 1 1 1
1
1 1 1 1
m m m
b m m mm
m m m
not full rank(rank = m - 1)
underestimation of B
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Take Xb as one of the samples !
Introduction to HSP-4DVAR
University Allied Workshop
Estimation of B matrix
1 1 11
1 1 11 1 1
1 11 1 1
1 1 1 1
1 1 1
m m m
b m m mm
m m m
full rank(rank = m)
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localizationIntroduction to HSP-4DVAR
University Allied Workshop
Use the analysis as the only sample
Much more timesaving than EnKF localization
( : Schur filtering operator)
1 1( )T Ta b x y y y obsx x P B P P P y
( )Ta x y obsx P P y 1 1( )T T Ty y y yP B P P P
( )Ta x y obsx P P y
Purpose: to filter the false covariance between one point and another far point in B
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Analysis——in the middle of window
Introduction to HSP-4DVAR
University Allied Workshop
Xa
00 0603
Xa
traditional 4DVARnew 4DVAR
3DVAR
00 0603
Xa
mean value theorem (Math)
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Outline
Introduction to a new DA approach(HSP-4DVAR)
Observing system simulation experiment (OSSE)
Summary
University Allied Workshop
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Experiment design
University Allied Workshop
• Domain configuration: 189×89×29, 30km
• TRUE—— forecasts from ECMWF global analysis (2.50×2.50) in the beginning of the assimilation window
• CTL—— forecasts from background field; background field is produced from a 48h forecast with NCEP/NCAR reanalysis (10×10) at 48h prior to the beginning of the assimilation window
• ASS—— forecasts from analysis field
• Simulated obs: temperature (T) on model level 1, 10, 19, 28, interpolated from ‘TRUE’
OSSE—— experiment design
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University Allied Workshop
Experiment results
OSSE—— experiment results
00 03-03
assimilation window
06 12 2418
CTL
ASS_middle(ASS)
00mX
00bX
ASS_start 03sX
03bX
00sX
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1
5
9
13
17
21
25
29
0.0 0.8 1.6 2.4 3.2 4.0 4.8
CTL ASS
perturbation potential temperature (K)
mod
el le
vel
1
5
9
13
17
21
25
29
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
water vapor mixing ratio (k/kg)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
1.6 2.4 3.2 4.0 4.8 5.6 6.4
zonal wind (m/s)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0
meridional wind (m/s)
mod
el le
vel
CTL ASS
00h
University Allied Workshop
OSSE—— experiment results
RMSE
ASS : ASS_middle
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1
5
9
13
17
21
25
29
0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4
CTL ASS
perturbation potential temperature (K)
mod
el le
vel
1
5
9
13
17
21
25
29
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
water vapor mixing ratio (g/kg)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
2.4 3.2 4.0 4.8 5.6 6.4
zonal wind (m/s)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0
meridional wind (m/s)
mod
el le
vel
CTL ASS
03h
University Allied Workshop
OSSE—— experiment results
RMSE
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1
5
9
13
17
21
25
29
0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4
CTL ASS
perturbation potential temperature (K)
mod
el le
vel
1
5
9
13
17
21
25
29
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
water vapor mixing ratio (g/kg)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
1.6 2.4 3.2 4.0 4.8 5.6 6.4
Y Axis Title
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2
meridional wind (m/s)
mod
el le
vel
CTL ASS
06h
University Allied Workshop
OSSE—— experiment results
RMSE
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1
5
9
13
17
21
25
29
0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.6
perturbation potential temperature (K)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
water vapor mixing ratio (g/kg)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
1.6 2.4 3.2 4.0 4.8 5.6 6.4
zonal wind (m/s)
mod
el le
vel
CTL ASS
1
5
9
13
17
21
25
29
1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2
meridional wind (m/s)
mod
el le
vel
CTL ASS
12h
University Allied Workshop
OSSE—— experiment results
RMSE
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00h
OSSE—— experiment results
RMSE
1
5
9
13
17
21
25
29
-1.6 -1.2 -0.8 -0.4 0.0 0.4
zonal wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8
meridional wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8
perturbation potential temperature (K)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-0.4 -0.3 -0.2 -0.1 0.0 0.1
water vapor mixing ratio (g/kg)
mod
el le
vel
ASS_start ASS_middle
ASS_start = ASS_start — CTLASS_middle = ASS_middle — CTL
< 0 better > 0 worse
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03h
University Allied Workshop
OSSE—— experiment results
RMSE
1
5
9
13
17
21
25
29
-1.2 -0.8 -0.4 0.0 0.4 0.8
zonal wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-2.2 -1.8 -1.4 -1.0 -0.6 -0.2 0.2 0.6 1.0
meridional wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-1.2 -0.9 -0.6 -0.3 0.0 0.3 0.6
perturbation potential temperature (K)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-0.4 -0.3 -0.2 -0.1 0.0 0.1
water vapor mixing ratio (g/kg)
mod
el le
vel
ASS_start ASS_middle
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06h
University Allied Workshop
OSSE—— experiment results
RMSE
1
5
9
13
17
21
25
29
-1.0 -0.6 -0.2 0.2 0.6 1.0
zonal wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
meridional wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
perturbation potential temperature (K)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-0.3 -0.2 -0.1 0.0 0.1
water vapor mixing ratio (g/kg)
mod
el le
vel
ASS_start ASS_middle
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12h
University Allied Workshop
OSSE—— experiment results
RMSE
1
5
9
13
17
21
25
29
-0.6 -0.2 0.2 0.6 1.0
zonal wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
meridional wind (m/s)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
perturbation potential temperature (K)
mod
el le
vel
ASS_start ASS_middle
1
5
9
13
17
21
25
29
-0.3 -0.2 -0.1 0.0 0.1 0.2
water vapor mixing ratio (g/kg)
mod
el le
vel
ASS_start ASS_middle
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06h
University Allied Workshop
OSSE—— experiment results
precipitation
CTL
ASS
TRUE
ASS : ASS_middle
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12h
University Allied Workshop
OSSE—— experiment results
CTL
ASS
TRUE
precipitation
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18h
University Allied Workshop
OSSE—— experiment results
CTL
ASS
TRUE
precipitation
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24h
University Allied Workshop
OSSE—— experiment results
CTL
ASS
TRUE
precipitation
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Outline
Introduction to a new DA approach(HSP-4DVAR)
Observing system simulation experiment (OSSE)
Summary
University Allied Workshop
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Summary (1)
The new WRF HSP-4DVAR system performs well
• abandon the adjoint technique• avoid making the nonlinear optimal iteration very time-saving
• B is flow-dependent implicitly in the assimilation window explicitly from window to window
A promising approach to be applied in operational NWPs
University Allied Workshop
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Summary (2)
University Allied Workshop
Plans:
• More experiments to test the new DA system (conventional and unconventional obs data)
• Further improvement of B (analog prediction sample, EOF technique……)
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Thank you!Comments and questions are
welcome!
University Allied Workshop