EGS talk 2002 - Colorado State University
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Transcript EGS talk 2002 - Colorado State University
Critical issues of ensemble data assimilation in
application to GOES-R risk reduction program
D. Zupanski1, M. Zupanski1, M. DeMaria2, and L. Grasso1
1CIRA/Colorado State University, Fort Collins, CO
2NOAA/NESDIS Fort Collins, CO
Ninth Symposium on Integrated Observing and Assimilation Systems
for the Atmosphere, Oceans, and Land Surface
(IOAS-AOLS)
9-13 January 2005
San Diego, CA
Research partially supported by NOAA Grant NA17RJ1228
Dusanka Zupanski, CIRA/CSU
[email protected]
OUTLINE
Critical data assimilation issues related to GOES-R satellite
mission
Ensemble based data assimilation methodology: Maximum
Likelihood Ensemble Filter
Experimental results
Conclusions and future work
Dusanka Zupanski, CIRA/CSU
[email protected]
Critical data assimilation issues of GOES-R and
similar missions
Assimilate satellite observations with high special and
temporal resolution
Employ state-of-the-art non-linear atmospheric models
(without neglecting model errors)
Provide optimal estimate of the atmospheric state
Calculate uncertainty of the optimal estimate
Determine amount of new information given by the
observations
What is the value added of having new observations (e.g.,
GOES-R, CloudSat, GPM) ?
Dusanka Zupanski, CIRA/CSU
[email protected]
METHODOLOGY
Maximum Likelihood Ensemble Filter (MLEF)
(Zupanski 2005; Zupanski and Zupanski 2005)
Developed using ideas from
Variational data assimilation (3DVAR, 4DVAR)
Iterated Kalman Filters
Ensemble Transform Kalman Filter (ETKF, Bishop et al. 2001)
MLEF is designed to provide optimal estimates of
model state variables
empirical parameters
model error (bias)
MLEF also calculates uncertainties of all estimates (in terms of Pa
and Pf)
Dusanka Zupanski, CIRA/CSU
[email protected]
MLEF APPROACH
Minimize cost function J
1
1
J [ x xb ]T Pf-1[ x xb ] [ H ( x ) yobs ]T R 1[ H ( x ) yobs ] min
2
2
Analysis error covariance
Pa1 2 Pf1 2 ( I C)-1 2
C PfT 2 H T R1HPf1 2 ( R1 2 HPf1 2 )T ( R1 2 HPf1 2 )
Forecast error covariance
12
f
P
x
M
[b
f
1
f
2
b
f
Nens
... b
]
bi f M ( x bia ) M ( x)
- model state vector of dim Nstate >>Nens
- non-linear forecast model
C - information matrix of dim Nens Nens
Dusanka Zupanski, CIRA/CSU
[email protected]
EXPERIMENTAL DESIGN
Hurricane Lili case
35 1-h DA cycles: 13UTC 1 Oct 2002 – 00 UTC 3 Oct
CSU-RAMS non-hydrostatic model
30x20x21 grid points, 15 km grid distance (in the Gulf of
Mexico)
Control variable: u,v,w,theta,Exner, r_total (dim=54000)
Model simulated observations with random noise
(7200 obs per DA cycle)
Nens=50
Iterative minimization of J (1 iteration only)
Dusanka Zupanski, CIRA/CSU
[email protected]
Experimental design (continued)
21 UTC 2 Oct 2002
Cycle 33
Cycle 1 Cycle 2
13 UTC
14 UTC
00 UTC
1 Oct 2002
2 Oct 2002
3 Oct 2002
RMS analysis error
(analysis-truth)
RMS analysis error
(analysis-truth)
8.00E-01
8.00E-04
rms_u
rms_u_noobs
6.00E-01
6.00E-04
RMS
RMS (m/s)
Cycle 35
4.00E-01
2.00E-01
4.00E-04
rms_r_total
rms_r_total_noobs
2.00E-04
0.00E+00
0.00E+00
1
11
Cycle No.
21
31
1
11
Cycle No.
21
31
Dusanka Zupanski, CIRA/CSU
[email protected]
Experimental design (continued)
Split cycle 33 into 24 sub-cycles
Calculate eigenvalues of (I-C) -1/2 in each sub-cycle
(information content)
Information content of each group of observations
Sub-cycles Sub-cycles Sub-cycles Sub-cycles
1-4
5-8
9-12
13-16
1200
u obs
1200
v obs
1200
w obs
1200
Exner obs
Sub-cycles
17-20
Sub-cycles
21-24
1200
theta obs
1200
r_total obs
Dusanka Zupanski, CIRA/CSU
[email protected]
RESULTS
Sub-cycles 1-4
u- obs groups
Eigenvalues (I-C)-1/2
1.00E+00
8.00E-01
sub-cycle 1
6.00E-01
sub-cycle 2
4.00E-01
sub-cycle 3
sub-cycle 4
2.00E-01
0.00E+00
1
11
21
31
41
Eigenvalue rank
System is “learning” about the truth via updating
analysis error covariance.
Dusanka Zupanski, CIRA/CSU
[email protected]
RESULTS
Sub-cycles 5-8
v- obs groups
Eigenvalues (I-C)-1/2
1.00E+00
8.00E-01
sub-cycle 5
6.00E-01
sub-cycle 6
4.00E-01
sub-cycle 7
sub-cycle 8
2.00E-01
0.00E+00
1
11
21
31
41
Eigenvalue rank
Most information in sub-cycles 5 and 6.
Dusanka Zupanski, CIRA/CSU
[email protected]
RESULTS
Sub-cycles 9-12
w- obs groups
Eigenvalues (I-C)-1/2
1.00E+00
8.00E-01
sub-cycle 9
6.00E-01
sub-cycle 10
sub-cycle 11
4.00E-01
sub-cycle 12
2.00E-01
0.00E+00
1
11
21
31
41
Eigenvalue rank
Most information in sub-cycle 10.
Dusanka Zupanski, CIRA/CSU
[email protected]
RESULTS
Sub-cycles 13-16
Exner- obs groups
Eigenvalues (I-C)-1/2
1.0000E+00
9.9995E-01
9.9990E-01
9.9985E-01
9.9980E-01
9.9975E-01
9.9970E-01
sub-cycle 13
sub-cycle 14
sub-cycle 15
sub-cycle 16
1
11
21
31
41
Eigenvalue rank
Dusanka Zupanski, CIRA/CSU
[email protected]
RESULTS
Sub-cycles 17-20
theta- obs groups
Eigenvalues (I-C)-1/2
1.00E+00
9.95E-01
sub-cycle 17
9.90E-01
sub-cycle 18
9.85E-01
sub-cycle 19
9.80E-01
sub-cycle 20
9.75E-01
9.70E-01
1
11
21
31
41
Eigenvalue rank
Dusanka Zupanski, CIRA/CSU
[email protected]
RESULTS
Sub-cycles 21-24
r_total- obs groups
Eigenvalues (I-C)-1/2
1.00E+00
8.00E-01
sub-cycle 21
6.00E-01
sub-cycle 22
sub-cycle 23
4.00E-01
sub-cycle 24
2.00E-01
0.00E+00
1
11
21
31
41
Eigenvalue rank
Sub-cycles with little information can be
excluded data selection.
Dusanka Zupanski, CIRA/CSU
[email protected]
CONCLUSIONS
Ensemble based data assimilation methods, such as the
MLEF, can be effectively used to quantify impact of each
observation type.
The procedure is applicable to a forecast model of any
complexity. Only eigenvalues of a small size matrix (Nens x
Nens) need to be evaluated.
Data assimilation system has a capability to learn form
observations.
Value added of having new observations (e.g., GOES-R,
CloudSat, GPM) can be quantified applying a similar procedure.
Dusanka Zupanski, CIRA/CSU
[email protected]