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

2. Ensemble Data Assimilation (EnsDA) Algorithm prep_ensda.sh cycle_ensda.sh WARM start: Copy files from previously completed cycle COLD start: Run randomly-perturbed ensemble forecasts to initialize fcst err cov icycle < N_cycles_max post.sh (post-processing) 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 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 - Analysis error covariance calculation - Save current cycle output files 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) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

4. Ensemble Data Assimilation (EnsDA) Algorithm Organization chart../ensda/include: Include files (control variable list, first-guess list)../ensda/makefiles: Makefile_ensda, Makefile_’MODEL’../ensda/runscripts: Run EnsDA program (runensda, envir.sh)../ensda/scripts: Scripts used to run the EnsDA program../ensda/src: Source programs../’MODEL’/src: Model source programs (general)../’MODEL’/src_ensda: Model source programs (changes due to EnsDA)../exec/ensda: Executable directory../’Obsdir’: Observations directory../ensda/work: Working (temporary) directory../hold.’print’/current:General EnsDA output../hold.’print’/cycle1, cycle2,... :Cycle specific EnsDA output Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

5. Ensemble Data Assimilation (EnsDA) Algorithm Options – envir.sh MODEL: WRF,UW-NMS,PU-NTU 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

6. Ensemble Data Assimilation (EnsDA) Algorithm Control variables !--------------------------------------- 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 ‘ !--------------------------------------- 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 !!!../include/Cntrl_vrbl_list.h../namelists/Cntrl_vrbl_’MODEL’.h Optional control variable components: - initial conditions - model bias - empirical parameters Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

7. Ensemble Data Assimilation (EnsDA) Algorithm Observations # Precip obs export iobs=02 #---------- specified by user --------- export OBSTYPE=precip export OBSFLAG=NOT let "delobs=1*60" ; export delobs #----------- end user ------------------ -------------------------- OBSTYPE – algorithm recognizable obs type delobs– time interval between two successive observation files OBSFLAG – Specifies if the OBSTYPE obs should be assimilated (YES, NOT) interface_’MODEL’_’OBSTYPE’.sh (model produced first-guess file => obs operators compatible first-guess file) runobs_’OBSTYPE’.sh (forward-only observation operator: first-guess => innovation vector R -1/2 [y-K(x)] ) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

8. Ensemble Data Assimilation (EnsDA) Algorithm Model convert_vrbls_from_1d.sh run_’MODEL’.sh convert_vrbls_to_1d.sh - Data assimilation is defined using 1-d control variable - Model is defined using its own 1-d, 2-d, or 3-d, or 4-d variable - Need ‘convert’ as an interface between the 1-d and model specific variables../’MODEL’/src: (‘MODEL’_fcst.F) read namelists: ‘MODEL_DIMENSION’,’LENGTH’,’MODEL_CNSTS’ call: ‘read/write_model_ic’,’read/write_model_bias’,’read/write_model_param’../’MODEL’/src_ensda: ‘MODEL’_get_init_fcst.F – cold start only, get model_dimension file ‘read/write_model_ic.F’,’read/write_model_bias.F’,’read/write_model_param.F’ Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

9. Ensemble Data Assimilation (EnsDA) Algorithm Including model bias DO n=1,N_time !! Main time-loop. if(num_bias.gt.0) then nerr=N_time/max(1,num_bias) nbias=0 if((n.ne.N_time).and.(mod(n,nerr).eq.0.or.n.eq.1)) then nbias=nbias+1 call read_model_bias(...,u_bias,v_bias,t_bias,...,nbias,num_bias) endif. if(num_bias.gt.0) then u_phi(:,:,:)=aa*u_phi(:,:,:)+(1.-aa)*u_bias(:,:,:) v_phi(:,:,:)=aa*v_phi(:,:,:)+(1.-aa)*v_bias(:,:,:) t_phi(:,:,:)=aa*t_phi(:,:,:)+(1.-aa)*t_bias(:,:,:). u(:,:,:)=u(:,:,:)+u_phi(:,:,:) v(:,:,:)=v(:,:,:)+v_phi(:,:,:) t(:,:,:)=t(:,:,:)+t_phi(:,:,:) endif. END DO !! End main time loop Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

10. Ensemble Data Assimilation (EnsDA) Algorithm MPI !-------------------------------------------------------------------- #ifdef MPI_USE include "mpif.h" #endif......... !==============start calculation=================== #ifdef MPI_USE CALL MPI_INIT(IERR) IF (IERR.NE. MPI_SUCCESS) STOP 'FAILED TO INIT MPI' CALL MPI_COMM_SIZE(MPI_COMM_WORLD, NPROC, IERR) CALL MPI_COMM_RANK(MPI_COMM_WORLD, MPIRANK, IERR) CALL MPI_BARRIER(MPI_COMM_WORLD,IERR) #else write(*,*) "This is a NO MPI run" MPIRANK=0 NPROC=1 #endif !================================================ !-- read ensemble size (NENS) …… !== define local dimensions and indexes allocate(jdisp(0:NPROC-1)) allocate(jlen(0:NPROC-1)) do irank=0,NPROC-1 CALL para_range(1,NENS,NPROC,irank,jsta,jend) jlen(irank)=jend-jsta+1 jdisp(irank)=jsta-1 end do CALL para_range(1,NENS,NPROC,MPIRANK,jsta,jend) #ifdef MPI_USE CALL MPI_BARRIER(MPI_COMM_WORLD,IERR) #endif N_LOC=jlen(MPIRANK) Dusanka Zupanski, CIRA/CSU Zupanski@CIRA.colostate.edu

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