Ensemble data assimilation and model error estimation algorithm Developed by

1. Ensemble data assimilation and model error estimation algorithm Developed by Milija Zupanski and Dusanka Zupanski CIRA/CSU GEOS column model component of the algorithm developed in collaboration with: Arthur Hou and Sara Zhang NASA/GMAO Christian Kummerow CSU/ATM Science Department Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

2. Ensemble Data Assimilation (EnsDA) Algorithm prep_ensda.sh WARM start: Copy files from previously completed cycle COLD start: Run randomly-perturbed ensemble forecasts to initialize fcst err cov cycle_ensda.sh icycle < N_cycles_max fcsterr_cov.sh - Prepare first-guess (background) vector - Prepare forecast error covariance (from ensembles) prep_obs.sh Given ‘OBSTYPE’ and ‘delobs’, select and copy available obs files assimilation.sh Iterative minimization of cost function, save current cycle output post.sh (post-processing) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

3. Ensemble Data Assimilation (EnsDA) Algorithm assimilation.sh script assimilation.sh iter < ioutmax forward.sh: Transformation from model space to observation space Hessian preconditioning (only for iter=1) Gradient calculation (ensembles) Cost function calculation (diagnostic) Minimization (ensemble subspace) Step-length (line-search) Control variable update (transformation from ensemble subspace to model (physical) space) - Analysis error covariance calculation - Save current cycle output files Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

4. Ensemble Data Assimilation (EnsDA) Algorithm Options – envir.sh MODEL: KdVB, GEOS, WRF, … OBS: OBSTYPE, delobs,OBSFLAG STAT: Mode (max likelihood), Mean (ensemble mean) DA_TYPE: Filter, Smoother COVAR: Localized, Non-localized forecast error covariance N_CYCLES: Number of data assimilation cycles CYCLE_INTERVAL: Time interval between cycles ENS_SIZE: Number of ensemble members START: Cold (from scratch), Warm (from previous cycle) IOUTMAX: Number of minimization iterations MINIM_ALG: Minimization algorithm (C-G, L-BFGS) MPI_RUN: Parallel run (YES, NO) nCPU_ensfcst: No. of CPUs for ensemble fcst nCPU_da: No. of CPUs for data assimilation Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

5. Ensemble Data Assimilation (EnsDA) Algorithm Control variables Optional control variable components: - initial conditions - model bias - empirical parameters ../include/Cntrl_vrbl_list.h !--------------------------------------- max_num_of_cntrl_vrbls = 5 if(.not.allocated (cvar_list)) then allocate (cvar_list(1:max_num_of_cntrl_vrbls)) end if !--------------------------------------- ncv= 1 cvar_list(ncv)%ndim = 3 cvar_list(ncv)%start_index(1) = 1 cvar_list(ncv)%start_index(2) = 1 cvar_list(ncv)%start_index(3) = 1 cvar_list(ncv)%start_index(4) = 1 cvar_list(ncv)%end_index(1) = NNXP(1) cvar_list(ncv)%end_index(2) = NNYP(1) cvar_list(ncv)%end_index(3) = NNZP(1) cvar_list(ncv)%end_index(4) = 1 cvar_list(ncv)%name = 'T ' cvar_list(ncv)%stddev = 1.5 cvar_list(ncv)%description = 'Temperature ‘ !--------------------------------------- ../namelists/Cntrl_vrbl_’MODEL’.h 6 p T F F 0 t T F T 1 q T F T 3 u T F F 0 v T F F 0 param1 F T F 0 param2 F T F 0 !-- first line number is the number of control variables defined --! !-- vrbl name, ic flag, param flag, bias flag, number of biases ----! !--- recall that vrbl name has 9 characters !!!!! !--- All inputs have to be separated by at least one blank space !!! Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

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