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Critical issues of ensemble data assimilation in application to GOES-R risk reduction program

Critical issues of ensemble data assimilation in application to GOES-R risk reduction program D. Zupanski 1 , M. Zupanski 1 , M. DeMaria 2 , and L. Grasso 1 1 CIRA/Colorado State University, Fort Collins, CO 2 NOAA/NESDIS Fort Collins, CO

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Critical issues of ensemble data assimilation in application to GOES-R risk reduction program

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  1. 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 Zupanski@CIRA.colostate.edu

  2. 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@CIRA.colostate.edu

  3. 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@CIRA.colostate.edu

  4. 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@CIRA.colostate.edu

  5. MLEF APPROACH Minimize cost function J Analysis error covariance Forecast error covariance - model state vector of dim Nstate >>Nens - non-linear forecast model - information matrix of dim Nens  Nens Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  6. 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 Zupanski@CIRA.colostate.edu

  7. 21 UTC 2 Oct 2002 Cycle 33 Cycle 1 Cycle 2 Cycle 35 14 UTC 00 UTC 1 Oct 2002 2 Oct 2002 3 Oct 2002 Experimental design (continued) 13 UTC Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  8. Sub-cycles 1-4 Sub-cycles 5-8 Sub-cycles 9-12 Sub-cycles 13-16 Sub-cycles 17-20 Sub-cycles 21-24 1200 u obs 1200 v obs 1200 r_total obs 1200 w obs 1200 Exner obs 1200 theta obs 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@CIRA.colostate.edu

  9. RESULTS Sub-cycles 1-4 u- obs groups System is “learning” about the truth via updating analysis error covariance. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  10. RESULTS Sub-cycles 5-8 v- obs groups Most information in sub-cycles 5 and 6. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  11. RESULTS Sub-cycles 9-12 w- obs groups Most information in sub-cycle 10. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  12. RESULTS Sub-cycles 13-16 Exner- obs groups Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  13. RESULTS Sub-cycles 17-20 theta- obs groups Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  14. RESULTS Sub-cycles 21-24 theta- obs groups Sub-cycles with little information can be excluded  data selection. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

  15. 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@CIRA.colostate.edu

  16. References Zupanski, M., 2005: The Maximum Likelihood Ensemble Filter. Theoretical aspects. Accepted in Mon. Wea. Rev. [Available at ftp://ftp.cira.colostate.edu/milija/papers/MLEF_MWR.pdf] Zupanski, D., and M. Zupanski, 2005: Model error estimation employing ensemble data assimilation approach. Submitted to Mon. Wea. Rev. [Available at ftp://ftp.cira.colostate.edu/Zupanski/manuscripts/MLEF_model_err.revised2.pdf]

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