1. 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 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@CIRA.colostate.edu Research partially supported by NOAA Grant NA17RJ1228

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 Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu What is the value added of having new observations (e.g., GOES-R, CloudSat, GPM) ?

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 P a and P f ) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

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

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. Experimental design (continued) 13 UTC Cycle 1 14 UTC00 UTC Cycle 2Cycle 35 1 Oct 20022 Oct 20023 Oct 2002 21 UTC 2 Oct 2002 Cycle 33 Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

8. Experimental design (continued) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu 1200 w obs 1200 Exner obs 1200 theta obs 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  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

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

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

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

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

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

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

15. CONCLUSIONS Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu  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.

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]