- differences between V2.2-beta and V3 - setup and run WRF-Var Overview - differences between V2.2-beta and V3 - setup and run - code structures Please see other related detailed tutorial presentations available at http://www.mmm.ucar.edu/wrf/users/tutorial/tutorial_presentation.htm WRF-Var Overview http://www.mmm.ucar.edu/wrf/users/tutorial/200807/VAR/WRFVAR_Tutorial_overview.pdf WRF-Var System http://www.mmm.ucar.edu/wrf/users/tutorial/200807/VAR/wrfvar_system.pdf

WRF-Var in the WRF Modeling System xlbc Background Preprocessing (WPS , real) xb Cold-Start Background Cycled Background Observation Preprocessing (OBSPROC) yo , R WRF-Var xa Update Lateral & Lower BCs (UPDATE_BC) Forecast (WRF) Radar in ASCII Radiance in BUFR Background Error (gen_be) B0 Blue --> Supported by WRF-Var Team

WRF-Var Version 3.0 (Release April 2008) Major new features: Direct assimilation of satellite radiances (AMSU, AIRS, SSMI/S, etc.). Four-Dimensional Variational Data Assimilation (4D-Var). Ensemble Transform Kalman Filter (ETKF). Hybrid variational/ensemble DA. Enhanced forecast error covariances (e.g. ensemble-based). Major software engineering reorganization. Remove obsolete features (e.g. MM5/GFS-based errors). Verification package Utilization of observations packed in NCEP PREPBUFR format Inclusion of various scripts and NCL based graphics Unified WRF/WRF-Var code repository. Unified WRF/WRF-Var namelist Extended wiki-based documentation. Not included in public release due to lack of funding. Collaborations welcome! From http://www.mmm.ucar.edu/wrf/users/tutorial/200807/VAR/WRFVAR_Tutorial_overview.pdf

Major changes in WRF-Var V3.0 One tar file includes all WRF-Var components Code structures Compilation mechanism External libraries - LAPACK, BLAS, FFTPACK, BUFR Bug fixes namelists CV options (NCAR BE model only) Single model (WRF only) Input/output files naming convention, no more fort.* output Variables (XICE-> SEAICE, dyn_opt removed) WRF-Var output precision (double -> float) Scripts (complicated DATC suite, csh->ksh) NCL scripts gen_be (rewritten stage0) obsproc

WRFDA / README.VAR V3.0.1.1 Release Notes: ----------------------- Version 3.0.1.1 has only limited bug fixes compared to version 3.0.1. - Improve compiling mechanism - Bug fix for analysis_type="VERIFY" - Bug fix for pseudo obs (spurious moisture increments) - Bug fix for incorrect sonde_sfc number in diagnostic output file jo. V3 Release Notes: ------------------ - For directions on compiling WRF-Var, see below or Users Guide Web page. http://www.mmm.ucar.edu/wrf/users/docs/user_guide_V3/users_guide_chap6.htm - For more information on WRF-Var release, visit WRF Users home page http://www.mmm.ucar.edu/wrf/users For questions, send mail to wrfhelp@ucar.edu ====================================== WRF-Var update history: - V3.0: Apr 4, 2008 - V3.0.1: Aug 6, 2008 How to compile and run? - In WRFDA directory, type 'configure wrfda - this will create a configure.wrf file that has appropriate compile options for the supported computers. Note: WRF-Var requires netCDF, BLAS, LAPACK, BUFR libraries. If your netCDF library is installed in some odd directory, set environment variable NETCDF before you type 'configure wrfda'. For example, setenv NETCDF /usr/local/netcdf-pgi setenv BLAS /usr/local/blas setenv LAPACK /usr/local/lapack setenv BUFR /usr/local/bufr WRFDA / README.VAR - Type 'compile all_wrfvar' when you are ready: - If sucessful, this will create da_wrfvar.exe and a set of utilities in directory WRFDA/var/da/. - cd to the appropriate test or run directory to run WRF-Var. See WRFDA/var/test/README for basic instructions on running da_wrfvar.exe ====================================== What is new in WRFDA V3.0? - Major software engineering reorganization. - Unified WRF/WRF-Var code repository. - Unified WRF/WRF-Var namelist - Remove obsolete features (e.g. MM5/GFS-based background errors). What is new in WRFDA V3.0 but NOT supported due to current resource limit? - Verification package - Utilization of observations packed in NCEP PREPBUFR format - Inclusion of various scripts and NCL based graphics What is NOT in WRFDA V3.0? - satellite radiance data assimilation (hopefully available in the next release) - ensemble and hybrid data assimilation - 4D-VAR

WRFDA / var / test / README Setup and run WRFDA / var / test / README 1) To run WRF-Var, first create a working directory, for example, WRFDA/var/test, then follow the steps below: cd WRFDA/var/test (go to the working directory) ln -sf WRFDA/run/LANDUSE.TBL ./LANDUSE.TBL ln -sf $DAT_DIR/rc/2007010200/wrfinput_d01 ./fg (link first guess file as fg) ln -sf WRFDA/var/obsproc/obs_gts_2007-01-02_00:00:00.3DVAR ./ob.ascii (link OBSPROC processed observation file as ob.ascii) ln -sf $DAT_DIR/be/be.dat ./be.dat (link background error statistics as be.dat) ln -sf WRFDA/var/da/da_wrfvar.exe ./da_wrfvar.exe (link executable) mkdir trace (if &wrfvar9 trace_use=true) vi namelist.input (a very basic namelist.input for running the tutorial test case is shown below. Only time and domain settings need to be specified for a certain case if using default settings provided in WRFDA/Registry/Registry.wrfvar. However, it is VERY IMPORTANT to make sure the settings in &physics record are consistent with those in your WRF settings.) da_wrfvar.exe >&! wrfda.log

namelist.input &wrfvar1 / &wrfvar2 / &wrfvar3 / &wrfvar4 / &wrfvar5 / trace_use=false, (Note: if not specified, default trace_use=true is applied. A subdirectory trace has to be created in your working directory before running da_wrfvar.exe) / &wrfvar10 / &wrfvar11 / &wrfvar12 / &wrfvar13 / &wrfvar14 / &wrfvar15 / &wrfvar16 / &wrfvar17 / &wrfvar18 analysis_date="2007-01-02_00:00:00.0000", &wrfvar19 / &wrfvar20 / &wrfvar21 time_window_min="2007-01-01_21:00:00.0000", (this variable is actually not used in WRF-Var for conventional data assimilation. The actual obs time window is deciced in obsproc. Set it to be the same as time_window_min in obsproc namelist.3dvar_obs for your own reference.) &wrfvar22 time_window_max="2007-01-02_03:00:00.0000", to be the same as time_window_max in obsproc &wrfvar23 / namelist.input &time_control start_year=2007, start_month=01, start_day=02, start_hour=00, end_year=2007, end_month=01, end_day=02, end_hour=00, / &dfi_control &domains e_we=45, e_sn=45, e_vert=28, dx=200000, dy=200000, &physics (VERY IMPORTANT: it is essential to make sure the settings here are consistent with those in your WRF settings) mp_physics=3, sf_sfclay_physics=1, sf_surface_physics=1, num_soil_layers=5 &fdda &dynamics &bdy_control &grib2 &namelist_quilt

WRFDA / var / test / README Setup and run WRFDA / var / test / README 2) To run da_update_bc.exe, follow the steps below: cd WRFDA/var/test (the directory where you ran WRF-Var) cp -p $DAT_DIR/rc/2007010200/wrfbdy_d01 ./wrfbdy_d01 (IMPORTANT: make a copy of wrfbdy_d01 as the wrf_bdy_file will be overwritten by da_update_bc.exe) vi param.in &control_param wrfvar_output_file = './wrfvar_output' wrf_bdy_file = './wrfbdy_d01' wrf_input = '$DAT_DIR/rc/2007010200/wrfinput_d01' cycling = .false. (set to .true. if WRF-Var first guess comes from a previous WRF forecast.) debug = .true. low_bdy_only = .false. (set to .true. if inner domain) update_lsm = .false. / ln -sf WRFDA/var/da/da_update_bc.exe ./da_update_bc.exe ./da_updatebc.exe

V3 wrfinput float CLAT(Time, south_north, west_east) ; float CLONG(Time, south_north, west_east) ; float LANDUSEF(Time, land_cat_stag, south_north, west_east) ; float MAPFAC_MX(Time, south_north, west_east) ; float MAPFAC_MY(Time, south_north, west_east) ; float MAPFAC_UX(Time, south_north, west_east_stag) ; float MAPFAC_UY(Time, south_north, west_east_stag) ; float MAPFAC_VX(Time, south_north_stag, west_east) ; float MAPFAC_VY(Time, south_north_stag, west_east) ; float MF_VX_INV(Time, south_north_stag, west_east) ; float PSHLTR(Time, south_north, west_east) ; float Q10(Time, south_north, west_east) ; float QSHLTR(Time, south_north, west_east) ; float SEAICE(Time, south_north, west_east) ; float SOILCBOT(Time, soil_cat_stag, south_north, west_east) ; float SOILCTOP(Time, soil_cat_stag, south_north, west_east) ; float TSHLTR(Time, south_north, west_east) ; V2.2 wrfinput float LAT_LL_D(Time) ; float LAT_LL_T(Time) ; float LAT_LL_U(Time) ; float LAT_LL_V(Time) ; float LAT_LR_D(Time) ; float LAT_LR_T(Time) ; float LAT_LR_U(Time) ; float LAT_LR_V(Time) ; float LAT_UL_D(Time) ; float LAT_UL_T(Time) ; float LAT_UL_U(Time) ; float LAT_UL_V(Time) ; float LAT_UR_D(Time) ; float LAT_UR_T(Time) ; float LAT_UR_U(Time) ; float LAT_UR_V(Time) ; float LON_LL_D(Time) ; float LON_LL_T(Time) ; float LON_LL_U(Time) ; float LON_LL_V(Time) ; float LON_LR_D(Time) ; float LON_LR_T(Time) ; float LON_LR_U(Time) ; float LON_LR_V(Time) ; float LON_UL_D(Time) ; float LON_UL_T(Time) ; float LON_UL_U(Time) ; float LON_UL_V(Time) ; float LON_UR_D(Time) ; float LON_UR_T(Time) ; float LON_UR_U(Time) ; float LON_UR_V(Time) ; float TRATX(Time, south_north, west_east) ; float URATX(Time, south_north, west_east) ; float VRATX(Time, south_north, west_east) ; float XICE(Time, south_north, west_east) ; In case you have any applications using the variables that are available in V2.2 but not V3

V3 wrfout V2.2 wrfout float LAT_LL_D(Time) ; float ALBBCK(Time, south_north, west_east) ; float LAT_LL_T(Time) ; float EDT_OUT(Time, south_north, west_east) ; float LAT_LL_U(Time) ; float EMISS(Time, south_north, west_east) ; float LAT_LL_V(Time) ; float HGT_SHAD(Time, south_north, west_east) ; float LAT_LR_D(Time) ; float MAPFAC_MX(Time, south_north, west_east) ; float LAT_LR_T(Time) ; float MAPFAC_MY(Time, south_north, west_east) ; float LAT_LR_U(Time) ; float MAPFAC_UX(Time, south_north, west_east_stag) ; float LAT_LR_V(Time) ; float MAPFAC_UY(Time, south_north, west_east_stag) ; float LAT_UL_D(Time) ; float MAPFAC_VX(Time, south_north_stag, west_east) ; float LAT_UL_T(Time) ; float MAPFAC_VY(Time, south_north_stag, west_east) ; float LAT_UL_U(Time) ; float MAX_MSTFX(Time) ; float LAT_UL_V(Time) ; float MAX_MSTFY(Time) ; float LAT_UR_D(Time) ; float MF_VX_INV(Time, south_north_stag, west_east) ; float LAT_UR_T(Time) ; float PRATEC(Time, south_north, west_east) ; float LAT_UR_U(Time) ; float QNDROPSOURCE(Time, bottom_top, south_north, west_east) ; float LAT_UR_V(Time) ; float SEAICE(Time, south_north, west_east) ; float LON_LL_D(Time) ; float XICEM(Time, south_north, west_east) ; float LON_LL_T(Time) ; float LON_LL_U(Time) ; float LON_LL_V(Time) ; float LON_LR_D(Time) ; float LON_LR_T(Time) ; float LON_LR_U(Time) ; float LON_LR_V(Time) ; In case you have any applications using the variables that are available in V2.2 but not V3 float LON_UL_D(Time) ; float LON_UL_T(Time) ; float LON_UL_U(Time) ; float LON_UL_V(Time) ; float LON_UR_D(Time) ; float LON_UR_T(Time) ; float LON_UR_U(Time) ; float LON_UR_V(Time) ; float XICE(Time, south_north, west_east) ; dyn_opt

gen_be Major difference is in stage0 Previous stage0 versions: gen_be_stage0-4 contained in the released WRFVAR 2.2 beta stand-alone gen_be_Stage0 code provided to CWB. This version of gen_be_Stage0 produces the same results as the gen_be_stage0 in the released WRFVAR 2.2 beta. The difference and advantage is that the stand-alone gen_be_Stage0 is simplified and a lot faster to compile. The current V3 code will produce a little bit different results than the previous codes because of the following major changes: in stage0, (1) vor, div, psi, chi are calculated on WRF's native C-grid (not interpolated A-grid) (2) compute full psi, chi before differencing (not after differencing) (3) stage0 output with names e.g. pert.2006090100.e001 where the date is perturbation valid time

gen_be For example, if you want to do 24h-12h forecast differences with forecasts initialized every 12 hour, you will have T_FORECAST1=12, T_FORECAST2=24, FILE_INTERVAL=12, and with the following forecasts available and organized as: 2008030700/wrfout_d01_2008-03-07_12:00:00 2008030700/wrfout_d01_2008-03-08_00:00:00 2008030712/wrfout_d01_2008-03-08_00:00:00 2008030712/wrfout_d01_2008-03-08_12:00:00 2008030800/wrfout_d01_2008-03-08_12:00:00 2008030800/wrfout_d01_2008-03-09_00:00:00 2008030812/wrfout_d01_2008-03-09_00:00:00 2008030812/wrfout_d01_2008-03-09_12:00:00 diff.2008030700 has forecast difference from (2008030700/wrfout_d01_2008-03-08_00:00:00 - 2008030712/wrfout_d01_2008-03-08_00:00:00) diff.2008030712 has forecast difference from (2008030712/wrfout_d01_2008-03-08_12:00:00 - 2008030800/wrfout_d01_2008-03-08_12:00:00) diff.2008030800 has forecast difference from (2008030800/wrfout_d01_2008-03-09_00:00:00 - 2008030812/wrfout_d01_2008-03-09_00:00:00) diff.2008030812 has forecast difference from (2008030812/wrfout_d01_2008-03-09_12:00:00 - 2008030900/wrfout_d01_2008-03-09_12:00:00) and so on... V2 pert.2008030800.e001 has forecast difference from (2008030700/wrfout_d01_2008-03-08_00:00:00 - 2008030712/wrfout_d01_2008-03-08_00:00:00) pert.2008030812.e001 has forecast difference from (2008030712/wrfout_d01_2008-03-08_12:00:00 - 2008030800/wrfout_d01_2008-03-08_12:00:00) pert.2008030900.e001 has forecast difference from (2008030800/wrfout_d01_2008-03-09_00:00:00 - 2008030812/wrfout_d01_2008-03-09_00:00:00) pert.2008030912.e001 has forecast difference from (2008030812/wrfout_d01_2008-03-09_12:00:00 - 2008030900/wrfout_d01_2008-03-09_12:00:00) and so on... V3

gen_be - scripts and namelists WRFDA/var/scripts/gen_be/gen_be_wrapper.ksh #! /bin/ksh #----------------------------------------------------------------------- # Script gen_be_wrapper.ksh # # Purpose: Calculates background error statistics for WRF-Var. #[1] Define job by overriding default environment variables: export RUN_GEN_BE_STAGE0=true export RUN_GEN_BE_STAGE1=true export RUN_GEN_BE_STAGE2=true export RUN_GEN_BE_STAGE2A=true export RUN_GEN_BE_STAGE3=true export RUN_GEN_BE_STAGE4=true export RUN_GEN_BE_DIAGS=true export RUN_GEN_BE_DIAGS_READ=true export RUN_GEN_BE_MULTICOV=true export WRFVAR_DIR=/karri/users/xinzhang/support/WRFDA export FC_DIR= export STRIDE= #t46 45km: export START_DATE=2007010200 export END_DATE=2007013100 export NUM_LEVELS=28 export REGION=con200 export EXPT=expt export BIN_TYPE=5 export EXP_DIR=/karri/users/xinzhang/support/$REGION/$EXPT #Example of changes required for "be_method=ENS": #export BE_METHOD=ENS #export NE=56 #export FCST_RANGE=12 #[2] Run gen_be: ${WRFVAR_DIR}/var/scripts/gen_be/gen_be.ksh WRFDA/var/scripts/gen_be>ls -l gen_be.ksh gen_be_cov2d.ksh gen_be_cov3d.ksh gen_be_ensrf.csh gen_be_ep1.csh gen_be_ep2.csh gen_be_plot_wrapper.ksh gen_be_set_defaults.ksh gen_be_stage0_wrf.ksh gen_be_stage4_global.ksh gen_be_stage4_regional.ksh gen_be_wrapper.ksh namelists Unused variables removed

WRFDA/var/da/inc/ *.inc Registry Mechanics %compile all_wrfvar WRFDA/Registry/Registry.wrfvar registry program: tools/registry Registry/Registry WRFDA/var/da/inc/ *.inc CPP ____________ Fortran90 WRF-VAR source WRFDA/var/da/da_*/ *.f90 da_wrfvar.exe

Before compilation WRFDA/var/da>ls -l total 56 -rw-r--r-- 1 1319 Aug 22 17:07 convertor.make -rw-r--r-- 1 11547 Aug 22 18:06 da.make drwxr-xr-x 13 442 Aug 22 17:13 da_airep drwxr-xr-x 14 476 Aug 22 17:13 da_airsr drwxr-xr-x 13 442 Aug 22 17:13 da_bogus drwxr-xr-x 13 442 Aug 22 17:13 da_buoy drwxr-xr-x 3 102 Aug 22 17:13 da_control drwxr-xr-x 15 510 Aug 22 17:13 da_define_structures drwxr-xr-x 21 714 Aug 22 17:13 da_dynamics drwxr-xr-x 8 272 Aug 22 17:13 da_etkf drwxr-xr-x 11 374 Aug 22 17:13 da_ffts drwxr-xr-x 16 544 Aug 22 17:13 da_gen_be drwxr-xr-x 13 442 Aug 22 17:13 da_geoamv drwxr-xr-x 16 544 Aug 22 17:13 da_gpspw drwxr-xr-x 13 442 Aug 22 17:13 da_gpsref drwxr-xr-x 8 272 Aug 22 17:13 da_grid_definitions drwxr-xr-x 11 374 Aug 22 17:13 da_interpolation drwxr-xr-x 19 646 Aug 22 17:13 da_main drwxr-xr-x 13 442 Aug 22 17:13 da_metar drwxr-xr-x 16 544 Aug 22 17:13 da_minimisation drwxr-xr-x 14 476 Aug 22 17:13 da_mtgirs drwxr-xr-x 18 612 Aug 22 17:13 da_obs drwxr-xr-x 24 816 Aug 22 17:13 da_obs_io drwxr-xr-x 36 1224 Aug 22 17:13 da_par_util drwxr-xr-x 69 2346 Aug 22 17:13 da_physics drwxr-xr-x 13 442 Aug 22 17:13 da_pilot drwxr-xr-x 13 442 Aug 22 17:13 da_polaramv drwxr-xr-x 13 442 Aug 22 17:13 da_profiler drwxr-xr-x 12 408 Aug 22 17:13 da_pseudo drwxr-xr-x 13 442 Aug 22 17:13 da_qscat drwxr-xr-x 17 578 Aug 22 17:13 da_radar drwxr-xr-x 10 340 Aug 22 17:13 da_radiance drwxr-xr-x 9 306 Aug 22 17:13 da_recursive_filter drwxr-xr-x 7 238 Aug 22 17:13 da_reporting drwxr-xr-x 13 442 Aug 22 17:14 da_satem drwxr-xr-x 28 952 Aug 22 17:14 da_setup_structures drwxr-xr-x 13 442 Aug 22 17:14 da_ships drwxr-xr-x 26 884 Aug 22 17:14 da_sound drwxr-xr-x 20 680 Aug 22 17:14 da_spectral drwxr-xr-x 84 2856 Aug 22 17:14 da_ssmi drwxr-xr-x 10 340 Aug 22 17:14 da_statistics drwxr-xr-x 14 476 Aug 22 17:14 da_synop drwxr-xr-x 46 1564 Aug 22 17:14 da_test drwxr-xr-x 74 2516 Aug 22 17:14 da_tools drwxr-xr-x 11 374 Aug 22 17:14 da_tracing drwxr-xr-x 12 408 Aug 22 17:14 da_transfer_model drwxr-xr-x 22 748 Aug 22 17:14 da_update_bc drwxr-xr-x 6 204 Aug 22 17:14 da_util drwxr-xr-x 3 102 Aug 22 17:14 da_varbc drwxr-xr-x 4 136 Aug 22 17:14 da_verif_anal drwxr-xr-x 5 170 Aug 22 17:14 da_verif_obs drwxr-xr-x 26 884 Aug 22 17:14 da_vtox_transforms -rwxr-xr-x 1 523 Aug 22 17:07 decode_l2_airs.make drwxr-xr-x 2 68 Aug 22 17:36 frame -rw-r--r-- 1 3969 Aug 22 17:07 gen_be.make drwxr-xr-x 2 68 Aug 22 17:36 inc drwxr-xr-x 40 1360 Aug 22 17:17 makedepf90-2.8.8 -rw-r--r-- 1 3150 Aug 22 17:17 makefile After compilation: a lot of files will appear in the directory WRFDA/var/da All source codes (*.F *.f90 and *.inc) are linked and *.f *.f90 *.o *.mod inc/*.inc *.exe are created

Minimize Cost Function WRFDA / var / da / da_main / da_solve.inc WRF-Var START Namelist File xb B0 yo Setup Frame Read Namelist Setup Background Setup Background Errors Setup Observations Compute Analysis Minimize Cost Function Calculate O-B “Outer Loop” Calculate Diagnostics Output Analysis Tidy Up Diagnostics File xa WRF-Var END

Setup Frame Reads grid dimensions from “namelist.input” file. Use WRF framework’s distributed memory capability to initialize tile, memory, patch dimensions, etc. Read Namelist Reads WRF-Var data assimilation options from “namelist.input” file. Performs consistency checks between namelist options.

Setup Background (First-Guess) WRFDA/var/da/da_setup_structures/da_setup_firstguess_wrf.inc Set up mapping information WRFDA/var/da/da_transfer_model/da_transfer_wrftoxb.inc Reads in the first-guess field. Extracts necessary fields. Creates background FORTRAN 90 derived data type “xb” e.g. xb % mix, xb % u(:,:,:), ….

WRFDA/var/da/da_transfer_model/da_transfer_wrftoxb.inc Vertical coordinate Derived fields grid%xb%sigmaf(kte+1) = grid%znw(kte+1) grid%xb%znw(kte+1) = grid%znw(kte+1) grid%xb%znu(kte+1) = 0.0 do k=kts,kte grid%xb%sigmah(k) = grid%znu(k) grid%xb%sigmaf(k) = grid%znw(k) grid%xb%znu(k) = grid%znu(k) grid%xb%znw(k) = grid%znw(k) grid%xb%dn(k) = grid%dn(k) grid%xb%dnw(k) = grid%dnw(k) end do grid%xb % ptop = ptop cvpm = - (1.0 - gas_constant/cp) cpovcv = cp / (cp - gas_constant) do k=kts,kte do i=its,ite ! The base specific volume (from real.init.code) ppb = grid%znu(k) * grid%mub(i,j) + ptop ttb = (base_temp + base_lapse*log(ppb/base_pres)) * & (base_pres/ppb)**kappa albn = (gas_constant/base_pres) * ttb * (ppb/base_pres)**cvpm qvf1 = 1.0 + grid%moist(i,j,k,P_QV) / rd_over_rv aln = -1.0 / (grid%mub(i,j)+grid%mu_2(i,j)) * & (albn*grid%mu_2(i,j) + grid%rdnw(k) * & (grid%ph_2(i,j,k+1) - grid%ph_2(i,j,k))) ! total pressure: grid%xb%p(i,j,k) = base_pres * & ((gas_constant*(t0+grid%t_2(i,j,k))*qvf1) / & (base_pres*(aln+albn)))**cpovcv ! total density grid%xb%rho(i,j,k)= 1.0 / (albn+aln) ! pressure purtubation: grid%p(i,j,k) = grid%xb%p(i,j,k) - ppb end do Constant fields grid%xb%map_factor(i,j) = grid%msft(i,j) grid%xb%cori(i,j) = grid%f(i,j) grid%xb%tgrn(i,j) = grid%sst(i,j) if (grid%xb%tgrn(i,j) < 100.0) & grid%xb%tgrn(i,j) = grid%tmn(i,j) grid%xb%lat(i,j) = grid%xlat(i,j) grid%xb%lon(i,j) = grid%xlong(i,j) grid%xb%terr(i,j) = grid%ht(i,j) grid%xb%snow(i,j) = grid%snowc(i,j) grid%xb%lanu(i,j) = grid%lu_index(i,j) grid%xb%landmask(i,j) = grid%landmask(i,j) grid%xb%xland(i,j) = grid%xland(i,j)

WRFDA/var/da/da_transfer_model/da_transfer_wrftoxb.inc do k=kts,kte do i=its,ite grid%xb%u(i,j,k) = 0.5*(grid%xa%u(i,j,k)+grid%xa%u(i+1,j,k)) grid%xb%v(i,j,k) = 0.5*(grid%xa%v(i,j,k)+grid%xa%v(i,j+1,k)) grid%xb%wh(i,j,k)= 0.5*(grid%xb%w(i,j,k)+grid%xb%w(i,j,k+1)) grid%xb%h(i,j,k) = 0.5*(grid%xb%hf(i,j,k)+grid%xb%hf(i,j,k+1)) grid%xb%q(i,j,k) = grid%moist(i,j,k,P_QV) theta = t0 + grid%t_2(i,j,k) grid%xb%t(i,j,k) = theta*(grid%xb%p(i,j,k)/base_pres)**kappa ! Convert to specific humidity from mixing ratio of water vapor: grid%xb%q(i,j,k)=grid%xb%q(i,j,k)/(1.0+grid%xb%q(i,j,k)) if (grid%xb%q(i,j,k) < 1.0e-6) & grid%xb%q(i,j,k) = 1.0e-6  grid%xb%psac(i,j) = grid%mub(i,j)+grid%mu_2(i,j) grid%xb%psfc(i,j) = grid%mub(i,j)+grid%p(i,j,kts)+grid%p_top if (grid%xb%tgrn(i,j) < 100.0) & grid%xb%tgrn(i,j) = grid%xb%t(i,j,kts)+ & 0.0065*(grid%xb%h(i,j,kts)-grid%xb%hf(i,j,kts)) end do Derived fields u10, v10, t2, q2 (used by sfc_assi_options=2) rh, td, slp 

Setup Background Errors (BE) WRFDA/var/da/da_setup_structures/da_setup_be_regional.inc Reads in background error statistics. Extracts necessary quantities – eigenvectors, eigenvalues, lengthscales, regression coefficients, etc. Creates background error FORTRAN 90 derived data type “be” e.g. be % v1 % evec(:,:), be % v2 % eval(:), etc, ….

Format depends on namelist variable “ob_format” Setup Observations WRFDA/var/da/da_setup_structures/da_setup_obs_structures_ascii.inc WRFDA/var/da/da_setup_structures/da_setup_obs_structures_bufr.inc WRFDA/var/da/da_obs_io/da_scan_obs_bufr.inc WRFDA/var/da/da_obs_io/da_read_obs_bufr.inc WRFDA/var/da/da_obs_io/da_scan_obs_ascii.inc WRFDA/var/da/da_obs_io/da_read_obs_ascii.inc Format depends on namelist variable “ob_format” 1 = BUFR, 2 = ASCII “WRF-Var” format. Reads in observations. Identifies Obs outside/inside the domain Variable transforms Creates observation FORTRAN 90 derived data type “ob” e.g. ob % metar(:), ob % sound(:) % u(:), etc, ….

Calculate Innovation Vector (O-B) WRFDA/var/da/da_synop/da_get_innov_vector_synop.inc Calculates “model equivalent” B of observation O through interpolation and change of variable. Computes observation minus first guess (O-B) value. Creates innovation vector FORTRAN 90 derived data type “iv” e.g. iv % metar(:), iv % qscat(:) % u, iv % sound(:) % u(:), etc ….

Minimize Cost Function Conjugate Gradient (a) Initializes analysis increments to zero. (b) Computes cost function (if desired). (c) Computes gradient of cost function. (d) Uses cost function and gradient to calculate new value of analysis control variable (v) Iterate (b) to (d)

Calculate: analysis = first-guess + analysis increment Compute Analysis Once WRF-Var has found a converged control variable, convert control variable to model space analysis increments Calculate: analysis = first-guess + analysis increment Performs consistency checks e.g. remove negative humidity etc. WRFDA/var/da/da_transfer_model/da_transfer_xatowrf.inc !--------------------------------------------------------------------------- ! Purpose: Convert analysis increments into WRF increments ! ! The following WRF fields are modified: ! grid%u_2 ! grid%v_2 ! grid%w_2 ! grid%mu_2 ! grid%mu0 (NOTE: not clear that this is needed.) ! grid%ph_2 ! grid%t_2 ! grid%moist

! To keep the background PH perturbation: do j=jts,jte do i=its,ite do k=kts, kte+1 ph_cgrid(i,j,k) = grid%ph_2(i,j,k) end do !--------------------------------------------------------------------------- ! [1.0] Get the mixing ratio of moisture first, as it its easy. do k=kts,kte if ((grid%xb%q(i,j,k)+grid%xa%q(i,j,k)) < 0.0) then q_cgrid(i,j,k) =-grid%xb%q(i,j,k)/(1.0 - grid%xb%q(i,j,k))**2 else q_cgrid(i,j,k) = grid%xa%q(i,j,k)/(1.0 - grid%xb%q(i,j,k))**2 end if ! [2.0] compute increments of dry-column air mass per unit area sdmd=0.0 s1md=0.0 sdmd=sdmd+q_cgrid(i,j,k)*grid%dnw(k) s1md=s1md+(1.0+grid%moist(i,j,k,P_QV))*grid%dnw(k) mu_cgrid(i,j)=-(grid%xa%psfc(i,j)+grid%xb%psac(i,j)*sdmd)/s1md

!--------------------------------------------------------------------------- ! [3.0] compute pressure increments ! Tangent linear code for grid%xa%p (based on WRF "real.init.code") ! developed by Y.-R. Guo 05/13/2004: do j=jts,jte do i=its,ite k = kte qvf1 = 0.5*(q_cgrid(i,j,k)+q_cgrid(i,j,k)) qvf1_b = 0.5*(grid%moist(i,j,k,P_QV)+grid%moist(i,j,k,P_QV)) qvf2 = - qvf1 / ((1.0+qvf1_b)*(1.0+qvf1_b)) qvf2_b = 1.0/(1.0+qvf1) qvf1 = qvf1*qvf2_b + qvf1_b*qvf2 qvf1_b = qvf1_b*qvf2_b grid%xa%p(i,j,k) = (-0.5/grid%rdnw(k)) * & ((mu_cgrid(i,j)+qvf1*grid%mub(i,j)) / qvf2_b & -(grid%mu_2(i,j)+qvf1_b*grid%mub(i,j))*qvf2/(qvf2_b*qvf2_b)) do k = kte-1,1,-1 qvf1 = 0.5*(q_cgrid(i,j,k)+q_cgrid(i,j,k+1)) qvf1_b = 0.5*(grid%moist(i,j,k,P_QV)+grid%moist(i,j,k+1,P_QV)) qvf2_b = 1.0/(1.0+qvf1_b) grid%xa%p(i,j,k) = grid%xa%p(i,j,k+1) & - (1.0/grid%rdn(k+1)) * & end do ! Adjust grid%xa%q to makte grid%xb%q + grid%xa%q > 0.0 if (check_rh == check_rh_tpw) then ! Shu-Hua~s TPW conservation: call da_check_rh(grid) else if (check_rh == check_rh_simple) then ! Simple resetting to max/min values: call da_check_rh_simple(grid) end if do k=kts,kte q_cgrid(i,j,k) = grid%xa%q(i,j,k)/(1.0 - grid%xb%q(i,j,k))**2

!--------------------------------------------------------------------------- ! [4.0] Convert temperature increments into theta increments ! Evaluate also the increments of (1/rho) and geopotential do j=jts,jte do i=its,ite ph_full = grid%ht(i,j) * gravity ph_xb_hd = grid%ht(i,j) * gravity do k = kts, kte ! To obtain all of the full fitelds: t, p, q(mixing ratio), rho t_full = grid%xa%t(i,j,k) + grid%xb%t(i,j,k) p_full = grid%xa%p(i,j,k) + grid%xb%p(i,j,k) q_full = grid%moist(i,j,k,P_QV) + q_cgrid(i,j,k) ! Note: According to WRF, thits its the dry air density used to ! compute the geopotential height: rho_full = p_full / (gas_constant*t_full*(1.0+q_full/rd_over_rv)) ! To compute the theta increment with the full fitelds: grid%t_2(i,j,k) = t_full*(base_pres/p_full)**kappa - t0 ! The full fiteld of analysis ph: ph_full = ph_full & - grid%xb%dnw(k) * (grid%xb%psac(i,j)+mu_cgrid(i,j)) / rho_full ! background hydrostatic phi: ph_xb_hd = ph_xb_hd & - grid%xb%dnw(k) * grid%xb%psac(i,j) / grid%xb%rho(i,j,k) ! The analysis perturbation = Hydro_ph - base_ph + nonhydro_xb_ph: grid%ph_2(i,j,k+1) = ph_full - grid%phb(i,j,k+1) & + (grid%xb%hf(i,j,k+1)*gravity - ph_xb_hd) end do ! To compute the geopotential height increment: do k=kts, kte+1 ph_cgrid(i,j,k) = grid%ph_2(i,j,k) - ph_cgrid(i,j,k)

! ======================== ! Write out the increment: if (write_increments) then write(unit=stdout,fmt='(/"Write out increment for plotting......")') call da_write_increments (grid, q_cgrid, mu_cgrid, ph_cgrid) end if ! CONVERT FROM A-GRID TO C-GRID  !--------------------------------------------------------------------------- ! [5.0] add increment to the original guess and update "grid" do j=jts,jte do i=its,ite grid%mu_2(i,j) = grid%mu_2(i,j) + mu_cgrid(i,j) grid%mu0(i,j) = grid%mub(i,j) + grid%mu_2(i,j) grid%w_2(i,j,kte+1)= grid%w_2(i,j,kte+1) + grid%xa%w(i,j,kte+1) end do do k=kts,kte grid%u_2(i,j,k) = grid%u_2(i,j,k) + u_cgrid(i,j,k) grid%v_2(i,j,k) = grid%v_2(i,j,k) + v_cgrid(i,j,k) grid%w_2(i,j,k) = grid%w_2(i,j,k) + grid%xa%w(i,j,k) grid%moist(i,j,k,P_QV) = grid%moist(i,j,k,P_QV) + q_cgrid(i,j,k) ! makte sure qv its positive. if (num_pseudo == 0 .and. grid%moist(i,j,k,P_QV) < 1.0e-6) & grid%moist(i,j,k,P_QV) = 1.0e-6 if (size(grid%moist,dim=4) >= 4) then grid%moist(i,j,k,p_qc) = grid%moist(i,j,k,p_qc) + grid%xa%qcw(i,j,k) grid%moist(i,j,k,p_qr) = grid%moist(i,j,k,p_qr) + grid%xa%qrn(i,j,k) if (grid%moist(i,j,k,p_qc) < 0.0) grid%moist(i,j,k,p_qc) = 0.0 if (grid%moist(i,j,k,p_qr) < 0.0) grid%moist(i,j,k,p_qr) = 0.0 if (size(grid%moist,dim=4) >= 6) then grid%moist(i,j,k,p_qi) = grid%moist(i,j,k,p_qi) + grid%xa%qci(i,j,k) grid%moist(i,j,k,p_qs) = grid%moist(i,j,k,p_qs) + grid%xa%qsn(i,j,k) if (grid%moist(i,j,k,p_qi) < 0.0) grid%moist(i,j,k,p_qi) = 0.0 if (grid%moist(i,j,k,p_qs) < 0.0) grid%moist(i,j,k,p_qs) = 0.0 if (size(grid%moist,dim=4) >= 7) then grid%moist(i,j,k,p_qg) = grid%moist(i,j,k,p_qg) + grid%xa%qgr(i,j,k) if (grid%moist(i,j,k,p_qg) < 0.0) grid%moist(i,j,k,p_qg) = 0.0

Compute Diagnostics WRFDA/var/da/da_minimisation/da_write_diagnostics.inc Compute O-B, O-A statistics for all observation types and variables. Compute A-B (analysis increment) statistics for all model variables and levels. Statistics include minimum, maximum (and their locations), mean and root mean square.