Ensemble data assimilation and model Ensemble data assimilation and model error estimation algorithmerror estimation algorithm

Developed byDeveloped by

Milija Zupanski and Dusanka ZupanskiMilija Zupanski and Dusanka ZupanskiCIRA/CSUCIRA/CSU

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

GEOS column model component of the algorithm developed in collaboration with:

Arthur Hou and Sara Zhang NASA/GMAOChristian Kummerow CSU/ATM Science Department

Ensemble Data Assimilation (EnsDA) Algorithmprep_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.shGiven ‘OBSTYPE’ and ‘delobs’, select and copy available obs files

assimilation.shIterative minimization of cost function, save current cycle output

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

Ensemble Data Assimilation (EnsDA) Algorithmassimilation.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/CSUZupanski@CIRA.colostate.edu

Ensemble Data Assimilation (EnsDA) AlgorithmOrganization 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/CSUZupanski@CIRA.colostate.edu

Ensemble Data Assimilation (EnsDA) AlgorithmOptions – 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/CSUZupanski@CIRA.colostate.edu

Ensemble Data Assimilation (EnsDA) AlgorithmControl 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 1q T F T 3u T F F 0v T F F 0param1 F T F 0param2 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/CSUZupanski@CIRA.colostate.edu

Ensemble Data Assimilation (EnsDA) AlgorithmObservations

# 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 filesOBSFLAG – 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/CSUZupanski@CIRA.colostate.edu

Ensemble Data Assimilation (EnsDA) AlgorithmModel

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/CSUZupanski@CIRA.colostate.edu

Ensemble Data Assimilation (EnsDA) AlgorithmIncluding 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 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/CSUZupanski@CIRA.colostate.edu

Ensemble Data Assimilation (EnsDA) AlgorithmMPI

!-------------------------------------------------------------------- #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/CSUZupanski@CIRA.colostate.edu

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