Critical issues of ensemble data assimilation in application

Critical issues of ensemble data assimilation in application to GOES-R risk reduction program D. Zupanski 1, M. De. Maria 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 Research partially supported by NOAA Grant NA 17 RJ 1228 Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

OUTLINE ØCritical data assimilation issues related to GOES-R satellite mission ØEnsemble based data assimilation methodology: Maximum Likelihood Ensemble Filter ØExperimental results ØConclusions and future work Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

Critical data assimilation issues of GOES-R and similar missions ØAssimilate satellite observations with high special and temporal resolution ØEmploy state-of-the-art non-linear atmospheric models (without neglecting model errors) ØProvide optimal estimate of the atmospheric state ØCalculate uncertainty of the optimal estimate ØDetermine amount of new information given by the observations What is the value added of having new observations (e. g. , GOES-R, Cloud. Sat, GPM) ? Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

METHODOLOGY Maximum Likelihood Ensemble Filter (MLEF) (Zupanski 2005; Zupanski and Zupanski 2005) Developed using ideas from ØVariational data assimilation (3 DVAR, 4 DVAR) ØIterated Kalman Filters ØEnsemble Transform Kalman Filter (ETKF, Bishop et al. 2001) MLEF is designed to provide optimal estimates of Ømodel state variables Øempirical parameters Ømodel error (bias) MLEF also calculates uncertainties of all estimates (in terms of Pa and Pf) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

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 Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

EXPERIMENTAL DESIGN ØHurricane Lili case Ø 35 1 -h DA cycles: 13 UTC 1 Oct 2002 – 00 UTC 3 Oct ØCSU-RAMS non-hydrostatic model Ø 30 x 21 grid points, 15 km grid distance (in the Gulf of Mexico) ØControl variable: u, v, w, theta, Exner, r_total (dim=54000) ØModel simulated observations with random noise (7200 obs per DA cycle) ØNens=50 ØIterative minimization of J (1 iteration only) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu

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

Experimental design (continued) ØSplit cycle 33 into 24 sub-cycles ØCalculate eigenvalues of (I-C) -1/2 in each sub-cycle (information content) Information content of each group of observations 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 Zupanski@CIRA. colostate. edu

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

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

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

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

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

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

CONCLUSIONS ØEnsemble based data assimilation methods, such as the MLEF, can be effectively used to quantify impact of each observation type. ØThe procedure is applicable to a forecast model of any complexity. Only eigenvalues of a small size matrix (Nens x Nens) need to be evaluated. ØData assimilation system has a capability to learn form observations. Value added of having new observations (e. g. , GOES-R, Cloud. Sat, GPM) can be quantified applying a similar procedure. Dusanka Zupanski, CIRA/CSU Zupanski@CIRA. colostate. edu