WRF-Var Overview

- differences between V2.2-beta and V3

- setup and run

- code structures

http://www.mmm.ucar.edu/wrf/users/tutorial/tutorial_presentation.htm

WRF-Var Overview

WRF-Var System

http://www.mmm.ucar.edu/wrf/users/tutorial/200807/VAR/WRFVAR_Tutorial_overview.pdf

http://www.mmm.ucar.edu/wrf/users/tutorial/200807/VAR/wrfvar_system.pdf

Please see other related detailed tutorial presentations available at

WRF-VarObservation

Preprocessing(OBSPROC)

BackgroundError

(gen_be)

Forecast(WRF)

xb

xaUpdate Lateral& Lower BCs

(UPDATE_BC)

BackgroundPreprocessing(WPS , real)

xlbc

WRF-Var in the WRF Modeling System

Blue --> Supported by WRF-Var Team

Cycled Background

B0

yo , R

Cold-Start Background

Radar in ASCIIRadiance in BUFR

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

• 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

Major changes in WRF-Var V3.0

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

- 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

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.TBLln -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

&wrfvar1 /&wrfvar2 /&wrfvar3 /&wrfvar4 /&wrfvar5 /&wrfvar6 /&wrfvar7 /&wrfvar8 /&wrfvar9trace_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 /&wrfvar18analysis_date="2007-01-02_00:00:00.0000", /&wrfvar19 /&wrfvar20 /&wrfvar21time_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.)/&wrfvar22time_window_max="2007-01-02_03:00:00.0000", (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_max in obsproc namelist.3dvar_obs for your own reference.)/&wrfvar23 /

&time_controlstart_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/&domainse_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/

namelist.input

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

Setup and run

WRFDA / var / test / README

V3 wrfinputfloat 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 wrfinputfloat 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

dyn_opt

float ALBBCK(Time, south_north, west_east) ;float EDT_OUT(Time, south_north, west_east) ;float EMISS(Time, south_north, west_east) ;float HGT_SHAD(Time, 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 MAX_MSTFX(Time) ;float MAX_MSTFY(Time) ;float MF_VX_INV(Time, south_north_stag, west_east) ;float PRATEC(Time, south_north, west_east) ;float QNDROPSOURCE(Time, bottom_top, south_north, west_east) ;float SEAICE(Time, south_north, west_east) ;float XICEM(Time, south_north, west_east) ;

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 XICE(Time, south_north, west_east) ;

V2.2 wrfoutV3 wrfout

In case you have any applications using the variables that are available in V2.2 but not V3

Major difference is in stage0Previous stage0 versions:

gen_be

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_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:

gen_beFor 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_12:00:002008030700/wrfout_d01_2008-03-08_00:00:002008030712/wrfout_d01_2008-03-08_00:00:002008030712/wrfout_d01_2008-03-08_12:00:002008030800/wrfout_d01_2008-03-08_12:00:002008030800/wrfout_d01_2008-03-09_00:00:002008030812/wrfout_d01_2008-03-09_00:00:002008030812/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...

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...

V2

V3

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=trueexport RUN_GEN_BE_STAGE1=trueexport RUN_GEN_BE_STAGE2=trueexport RUN_GEN_BE_STAGE2A=trueexport RUN_GEN_BE_STAGE3=trueexport RUN_GEN_BE_STAGE4=trueexport RUN_GEN_BE_DIAGS=trueexport RUN_GEN_BE_DIAGS_READ=trueexport RUN_GEN_BE_MULTICOV=true

export WRFVAR_DIR=/karri/users/xinzhang/support/WRFDAexport FC_DIR=export STRIDE=

#t46 45km:export START_DATE=2007010200export END_DATE=2007013100export NUM_LEVELS=28export REGION=con200export EXPT=exptexport BIN_TYPE=5export 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

gen_be - scripts and namelists

WRFDA/var/scripts/gen_be>ls -lgen_be.kshgen_be_cov2d.kshgen_be_cov3d.kshgen_be_ensrf.cshgen_be_ep1.cshgen_be_ep2.cshgen_be_plot_wrapper.kshgen_be_set_defaults.kshgen_be_stage0_wrf.kshgen_be_stage4_global.kshgen_be_stage4_regional.kshgen_be_wrapper.ksh

namelistsUnused variables removed

Registry Mechanics

%compile all_wrfvar

WRF-VAR sourceWRFDA/var/da/da_*/

*.f90

CPP ____________

Fortran90

da_wrfvar.exe

Registry/Registry

registry program:tools/registry

WRFDA/var/da/inc/*.inc

WRFDA/Registry/Registry.wrfvar

WRFDA/var/da>ls -ltotal 56-rw-r--r-- 1 1319 Aug 22 17:07 convertor.make-rw-r--r-- 1 11547 Aug 22 18:06 da.makedrwxr-xr-x 13 442 Aug 22 17:13 da_airepdrwxr-xr-x 14 476 Aug 22 17:13 da_airsrdrwxr-xr-x 13 442 Aug 22 17:13 da_bogusdrwxr-xr-x 13 442 Aug 22 17:13 da_buoydrwxr-xr-x 3 102 Aug 22 17:13 da_controldrwxr-xr-x 15 510 Aug 22 17:13 da_define_structuresdrwxr-xr-x 21 714 Aug 22 17:13 da_dynamicsdrwxr-xr-x 8 272 Aug 22 17:13 da_etkfdrwxr-xr-x 11 374 Aug 22 17:13 da_fftsdrwxr-xr-x 16 544 Aug 22 17:13 da_gen_bedrwxr-xr-x 13 442 Aug 22 17:13 da_geoamvdrwxr-xr-x 16 544 Aug 22 17:13 da_gpspwdrwxr-xr-x 13 442 Aug 22 17:13 da_gpsrefdrwxr-xr-x 8 272 Aug 22 17:13 da_grid_definitionsdrwxr-xr-x 11 374 Aug 22 17:13 da_interpolationdrwxr-xr-x 19 646 Aug 22 17:13 da_maindrwxr-xr-x 13 442 Aug 22 17:13 da_metardrwxr-xr-x 16 544 Aug 22 17:13 da_minimisationdrwxr-xr-x 14 476 Aug 22 17:13 da_mtgirsdrwxr-xr-x 18 612 Aug 22 17:13 da_obsdrwxr-xr-x 24 816 Aug 22 17:13 da_obs_iodrwxr-xr-x 36 1224 Aug 22 17:13 da_par_utildrwxr-xr-x 69 2346 Aug 22 17:13 da_physicsdrwxr-xr-x 13 442 Aug 22 17:13 da_pilotdrwxr-xr-x 13 442 Aug 22 17:13 da_polaramvdrwxr-xr-x 13 442 Aug 22 17:13 da_profilerdrwxr-xr-x 12 408 Aug 22 17:13 da_pseudodrwxr-xr-x 13 442 Aug 22 17:13 da_qscatdrwxr-xr-x 17 578 Aug 22 17:13 da_radar

drwxr-xr-x 10 340 Aug 22 17:13 da_radiancedrwxr-xr-x 9 306 Aug 22 17:13 da_recursive_filterdrwxr-xr-x 7 238 Aug 22 17:13 da_reportingdrwxr-xr-x 13 442 Aug 22 17:14 da_satemdrwxr-xr-x 28 952 Aug 22 17:14 da_setup_structuresdrwxr-xr-x 13 442 Aug 22 17:14 da_shipsdrwxr-xr-x 26 884 Aug 22 17:14 da_sounddrwxr-xr-x 20 680 Aug 22 17:14 da_spectraldrwxr-xr-x 84 2856 Aug 22 17:14 da_ssmidrwxr-xr-x 10 340 Aug 22 17:14 da_statisticsdrwxr-xr-x 14 476 Aug 22 17:14 da_synopdrwxr-xr-x 46 1564 Aug 22 17:14 da_testdrwxr-xr-x 74 2516 Aug 22 17:14 da_toolsdrwxr-xr-x 11 374 Aug 22 17:14 da_tracingdrwxr-xr-x 12 408 Aug 22 17:14 da_transfer_modeldrwxr-xr-x 22 748 Aug 22 17:14 da_update_bcdrwxr-xr-x 6 204 Aug 22 17:14 da_utildrwxr-xr-x 3 102 Aug 22 17:14 da_varbcdrwxr-xr-x 4 136 Aug 22 17:14 da_verif_analdrwxr-xr-x 5 170 Aug 22 17:14 da_verif_obsdrwxr-xr-x 26 884 Aug 22 17:14 da_vtox_transforms-rwxr-xr-x 1 523 Aug 22 17:07 decode_l2_airs.makedrwxr-xr-x 2 68 Aug 22 17:36 frame-rw-r--r-- 1 3969 Aug 22 17:07 gen_be.makedrwxr-xr-x 2 68 Aug 22 17:36 incdrwxr-xr-x 40 1360 Aug 22 17:17 makedepf90-2.8.8-rw-r--r-- 1 3150 Aug 22 17:17 makefile

Before compilation

After compilation: a lot of files will appear in the directory WRFDA/var/daAll source codes (*.F *.f90 and *.inc) are linked and *.f *.f90 *.o *.mod inc/*.inc *.exe are created

ReadNamelist

xb

xa

yo

ComputeAnalysis

CalculateO-B

SetupFrame

SetupBackground

SetupBackground

Errors

Minimize Cost Function

SetupObservations

CalculateDiagnostics

OutputAnalysis

DiagnosticsFile

NamelistFile

Tidy Up

WRF-VarSTART

WRF-VarEND

“Outer Loop”

B0

WRFDA / var / da / da_main / da_solve.inc

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)

• 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_setup_structures/da_setup_firstguess_wrf.inc

• Set up mapping information

WRFDA/var/da/da_transfer_model/da_transfer_wrftoxb.inc

grid%xb%sigmaf(kte+1) = grid%znw(kte+1)grid%xb%znw(kte+1) = grid%znw(kte+1)grid%xb%znu(kte+1) = 0.0do 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 dogrid%xb % ptop = ptop

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)

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 doend do

Vertical coordinate

Constant fields

WRFDA/var/da/da_transfer_model/da_transfer_wrftoxb.inc

Derived fields

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

do i=its,ite 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 end do

u10, v10, t2, q2 (used by sfc_assi_options=2)rh, td, slp

WRFDA/var/da/da_transfer_model/da_transfer_wrftoxb.inc

Derived fields

Setup Background Errors (BE)

• 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, ….

WRFDA/var/da/da_setup_structures/da_setup_be_regional.inc

Setup Observations

• 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, ….

WRFDA/var/da/da_setup_structures/da_setup_obs_structures_ascii.incWRFDA/var/da/da_setup_structures/da_setup_obs_structures_bufr.incWRFDA/var/da/da_obs_io/da_scan_obs_bufr.incWRFDA/var/da/da_obs_io/da_read_obs_bufr.incWRFDA/var/da/da_obs_io/da_scan_obs_ascii.incWRFDA/var/da/da_obs_io/da_read_obs_ascii.inc

Calculate Innovation Vector (O-B)

• 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 ….

WRFDA/var/da/da_synop/da_get_innov_vector_synop.inc

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)

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 end do end do

!--------------------------------------------------------------------------- ! [1.0] Get the mixing ratio of moisture first, as it its easy. !---------------------------------------------------------------------------

do k=kts,kte do j=jts,jte do i=its,ite 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 end do end do end do

!--------------------------------------------------------------------------- ! [2.0] compute increments of dry-column air mass per unit area !---------------------------------------------------------------------------

do j=jts,jte do i=its,ite sdmd=0.0 s1md=0.0 do k=kts,kte sdmd=sdmd+q_cgrid(i,j,k)*grid%dnw(k) s1md=s1md+(1.0+grid%moist(i,j,k,P_QV))*grid%dnw(k) end do

mu_cgrid(i,j)=-(grid%xa%psfc(i,j)+grid%xb%psac(i,j)*sdmd)/s1md end do end do

!--------------------------------------------------------------------------- ! [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 = - qvf1 / ((1.0+qvf1_b)*(1.0+qvf1_b)) qvf2_b = 1.0/(1.0+qvf1_b) qvf1 = qvf1*qvf2_b + qvf1_b*qvf2 qvf1_b = qvf1_b*qvf2_b grid%xa%p(i,j,k) = grid%xa%p(i,j,k+1) & - (1.0/grid%rdn(k+1)) * & ((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)) end do end do 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 do j=jts,jte do i=its,ite q_cgrid(i,j,k) = grid%xa%q(i,j,k)/(1.0 - grid%xb%q(i,j,k))**2 end do end do end do

!--------------------------------------------------------------------------- ! [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 end do end do

! To compute the geopotential height increment:

do k=kts, kte+1 do j=jts,jte do i=its,ite ph_cgrid(i,j,k) = grid%ph_2(i,j,k) - ph_cgrid(i,j,k) end do end do end do

! ======================== ! 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 do i=its,ite 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 end if

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 end if

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 end if end do end do end do

Compute Diagnostics

• 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.

WRFDA/var/da/da_minimisation/da_write_diagnostics.inc