Transcript Document 7612038

Comparison of ensemble-based and variational-based
data assimilation schemes in a Quasi-Geostrophic model.
Shu-Chih Yang et al.
3D-Var
Hybrid (3DVar+20 BVs)
12-hour 4D-Var
LETKF (40 ensemble)
24-hour 4D-Var
4D-Var
3D-Var
HYBD
RMS error (10-2)
1.44
Time (minutes)
0.15
LETKF
12hr
24 hr
l=3
l=5
l=7
l=9
0.70
0.56
0.35
0.67
0.48
0.44
0.44
1.5
1.8
2.5
0.3
1.0
1.9
2.4
Analysis increment (color shaded)
vs. dynamically fast growing errors (contours)
12Z Day 24
Initial increment (smoother) vs. BV
00Z Day 25
analysis increment vs. BV
LETKF
Initial increment vs. Initial SV
12-hour 4DVAR
analysis increment vs. Final SV
3D-LETKF
time
to
t1
4D-LETKF
No-cost LETKF smoother (cross): apply at t0 the same
weights found optimal at t1, works for 3D- or 4D-LETKF
No-cost LETKF smoother
LETKF analysis
at time i
Smoother analysis
at time i-1
xai  xif  Eif Wi
x
i 1
a
x
i 1
a
i 1
a
E W
LETKF Analysis
i
“Smoother” reanalysis
LETKF minimizes the errors of the day and thus
provides an excellent first guess to the 3D-Var analysis
3DVar
3DVar with the
background of the first 50
days provided from LETKF
3DVar with the
background provided from
LETKF (forecast mean)
LETKF
We conclude from this experiment that the errors of the day (and
not just ensemble averaging) are important in LETKF and 3D-Var.
ENSEMBLE KALMAN FILTER IN THE PRESENCE OF
MODEL ERRORS
Hong Li, Eugenia Kalnay
SPEEDY MODEL (Molteni 2003)
•
T30L7 global spectral model
•
total 96x48 grid points on each level
•
State variables u,v,T,Ps,q
Dense
Observations
Data Assimilation: LETKF
Methods to handle model errors
1) Multiplicative inflation
2) Dee & da Silva (1998)
3) Low-order (Danforth et al, MWR, 2007)
Control run
200% inflation
Dee & da Silva
Low-order
Simultaneous estimation of
inflation and observation
errors
Hong Li
Eugenia Kalnay
Diagnosis of observation error statistics
(Navascues et al, 2006, Desroziers et al, 2006)
 d oa dTob  R
 d ab d obT  (1  )HBHT
Desroziers et al 2006 and Navascues et al 2006 have only used these
relations in a diagnostic mode, from past 3D-Var/4D-Var stats!! Here
we estimate both  and R online.
R
method
Tests within LETKF with L40 model
method
t=1.0
R(1b)
(1a)
(2)
Rinit
0.1
10.0
10.0
Estimated
R
Estimated

rms
0.999
0.098
0.263
0.999
0.100
0.265
1.001
0.097
0.266
0.999
0.100
0.265
Starting with very wrong R the right R and optimal inflation are
recovered.
online estimated observational
errors
The original wrong specified R converges to the
right R quickly (about 5-days)
Back up slides
Adaptive sampling with the LETKFbased ensemble spread
Junjie Liu
•
Purpose
–
–
–
•
Sample 10% adaptive DWL wind observations to get 90%
improvement of full coverage
Compare ensemble spread method with other sampling
strategies
How the results are sensitive to the data assimilation schemes
(3D-Var and LETKF)
Note
–
same adaptive observations from ensemble spread method are
assimilated by both 3D-Var and LETKF
500hPa zonal wind RMS error
Rawinsonde; climatology; uniform; random; ensemble spread; “ideal”; 100%
3D-Var
RMSE
4.04
2.36
0.92
0.74
0.43
LETKF
0.36
0.30
1.18
0.38
0.36
0.33
0.32
0.29
0.23
With 10% adaptive observations, the analysis accuracy is significantly
improved for both 3D-Var and LETKF.
 3D-Var is more sensitive to adaptive strategies than LETKF. Ensemble
spread strategy gets best result among operational possible strategies
500hPa zonal wind RMS error (2% adaptive obs)
Rawinsonde; climatology; uniform; random; ensemble spread; “ideal”; 100%
3D-Var
LETKF
With fewer (2%) adaptive observations, ensemble spread sampling
strategy outperforms the other methods in LETKF
For 3D-Var 2% adaptive observations are clearly not enough
Analysis sensitivity study within LETKF
Hxa
S
 R 1HPa HT
y
The self sensitivity is the trace of the matrix S.
It can show the analysis sensitivity with respect to:
a) different types of observations (e.g., rawinsonde,
satellite, adaptive observation and routine
observations)
b) the observations in different area (e.g., SH, NH)
Analysis sensitivity of adaptive observation (one obs. selected from
ensemble spread method over ocean) and routine observations (every grid
point over land) in Lorenz-40 variable model
10-day forecast RMS error
Analysis sensitivity
• About 17% information of the analysis comes from observations over land.
• About 85% information comes from observation for the adaptive
observation (a single observation over ocean).
• The single adaptive observation is more important than single observation
over land.