EGS talk 2002

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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
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
Research partially supported by NOAA Grant
NA17RJ1228
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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 Zupanski_at_CIRA.colostat
e.edu
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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 Zupanski_at_CIRA.colostat
e.edu
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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 Zupanski_at_CIRA.colostat
e.edu
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MLEF APPROACH
Minimize cost function J
Analysis error covariance
Forecast error covariance
- model state vector of dim Nstate gtgtNens
- non-linear forecast model
- information matrix of dim Nens ? Nens
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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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
  (dim54000)
• Model simulated observations with random noise
• (7200 obs per DA cycle)
• Nens50
• Iterative minimization of J (1 iteration only)

Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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Experimental design (continued)
13 UTC
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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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
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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RESULTS
Sub-cycles 1-4 u- obs groups
System is learning about the truth via updating
analysis error covariance.
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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RESULTS
Sub-cycles 5-8 v- obs groups
Most information in sub-cycles 5 and 6.
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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RESULTS
Sub-cycles 9-12 w- obs groups
Most information in sub-cycle 10.
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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RESULTS
Sub-cycles 13-16 Exner- obs groups
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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RESULTS
Sub-cycles 17-20 theta- obs groups
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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RESULTS
Sub-cycles 21-24 r_total- obs groups
Sub-cycles with little information can be
excluded ? data selection.
Dusanka Zupanski, CIRA/CSU Zupanski_at_CIRA.colostat
e.edu
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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 Zupanski_at_CIRA.colostat
e.edu