1. - 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
WRF-Var Overview
WRF-Var System

2. 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

3. 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

4. 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

5. WRFDA / README.VAR V3.0.1.1 Release Notes: -----------------------
Version has only limited bug fixes compared to version
- 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.
- For more information on WRF-Var release, visit WRF Users home page
For questions, send mail to
======================================
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

6. 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/ /wrfinput_d01 ./fg (link first guess file as fg)
ln -sf WRFDA/var/obsproc/obs_gts_ _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

7. 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=" _00:00: ",
&wrfvar19 /
&wrfvar20 /
&wrfvar21
time_window_min=" _21:00: ",
(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=" _03:00: ",
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

8. 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 $DAT_DIR/rc/ /wrfbdy_d01 ./wrfbdy_d01 (IMPORTANT: make a copy of wrfbdy_d01
as the wrf_bdy_file will be
overwritten by da_update_bc.exe)
vi param.in
&control_param
wrfvar_output_file = './wrfvar_output'
wrf_bdy_file = './wrfbdy_d01'
wrf_input = '$DAT_DIR/rc/ /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

9. 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

10. 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

11. 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 e001 where the date is perturbation valid time

12. 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:
/wrfout_d01_ _12:00:00
/wrfout_d01_ _00:00:00
/wrfout_d01_ _00:00:00
/wrfout_d01_ _12:00:00
/wrfout_d01_ _12:00:00
/wrfout_d01_ _00:00:00
/wrfout_d01_ _00:00:00
/wrfout_d01_ _12:00:00
diff has forecast difference from
( /wrfout_d01_ _00:00: /wrfout_d01_ _00:00:00)
diff has forecast difference from
( /wrfout_d01_ _12:00: /wrfout_d01_ _12:00:00)
diff has forecast difference from
( /wrfout_d01_ _00:00: /wrfout_d01_ _00:00:00)
diff has forecast difference from
( /wrfout_d01_ _12:00: /wrfout_d01_ _12:00:00)
and so on... V2
pert e001 has forecast difference from
( /wrfout_d01_ _00:00: /wrfout_d01_ _00:00:00)
pert e001 has forecast difference from
( /wrfout_d01_ _12:00: /wrfout_d01_ _12:00:00)
pert e001 has forecast difference from
( /wrfout_d01_ _00:00: /wrfout_d01_ _00:00:00)
pert e001 has forecast difference from
( /wrfout_d01_ _12:00: /wrfout_d01_ _12:00:00)
and so on... V3

13. 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=
export END_DATE=
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

14. 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

15. Before compilation
WRFDA/var/da>ls -l
total 56
-rw-r--r Aug 22 17:07 convertor.make
-rw-r--r Aug 22 18:06 da.make
drwxr-xr-x Aug 22 17:13 da_airep
drwxr-xr-x Aug 22 17:13 da_airsr
drwxr-xr-x Aug 22 17:13 da_bogus
drwxr-xr-x Aug 22 17:13 da_buoy
drwxr-xr-x Aug 22 17:13 da_control
drwxr-xr-x Aug 22 17:13 da_define_structures
drwxr-xr-x Aug 22 17:13 da_dynamics
drwxr-xr-x Aug 22 17:13 da_etkf
drwxr-xr-x Aug 22 17:13 da_ffts
drwxr-xr-x Aug 22 17:13 da_gen_be
drwxr-xr-x Aug 22 17:13 da_geoamv
drwxr-xr-x Aug 22 17:13 da_gpspw
drwxr-xr-x Aug 22 17:13 da_gpsref
drwxr-xr-x Aug 22 17:13 da_grid_definitions
drwxr-xr-x Aug 22 17:13 da_interpolation
drwxr-xr-x Aug 22 17:13 da_main
drwxr-xr-x Aug 22 17:13 da_metar
drwxr-xr-x Aug 22 17:13 da_minimisation
drwxr-xr-x Aug 22 17:13 da_mtgirs
drwxr-xr-x Aug 22 17:13 da_obs
drwxr-xr-x Aug 22 17:13 da_obs_io
drwxr-xr-x Aug 22 17:13 da_par_util
drwxr-xr-x Aug 22 17:13 da_physics
drwxr-xr-x Aug 22 17:13 da_pilot
drwxr-xr-x Aug 22 17:13 da_polaramv
drwxr-xr-x Aug 22 17:13 da_profiler
drwxr-xr-x Aug 22 17:13 da_pseudo
drwxr-xr-x Aug 22 17:13 da_qscat
drwxr-xr-x Aug 22 17:13 da_radar
drwxr-xr-x Aug 22 17:13 da_radiance
drwxr-xr-x Aug 22 17:13 da_recursive_filter
drwxr-xr-x Aug 22 17:13 da_reporting
drwxr-xr-x Aug 22 17:14 da_satem
drwxr-xr-x Aug 22 17:14 da_setup_structures
drwxr-xr-x Aug 22 17:14 da_ships
drwxr-xr-x Aug 22 17:14 da_sound
drwxr-xr-x Aug 22 17:14 da_spectral
drwxr-xr-x Aug 22 17:14 da_ssmi
drwxr-xr-x Aug 22 17:14 da_statistics
drwxr-xr-x Aug 22 17:14 da_synop
drwxr-xr-x Aug 22 17:14 da_test
drwxr-xr-x Aug 22 17:14 da_tools
drwxr-xr-x Aug 22 17:14 da_tracing
drwxr-xr-x Aug 22 17:14 da_transfer_model
drwxr-xr-x Aug 22 17:14 da_update_bc
drwxr-xr-x Aug 22 17:14 da_util
drwxr-xr-x Aug 22 17:14 da_varbc
drwxr-xr-x Aug 22 17:14 da_verif_anal
drwxr-xr-x Aug 22 17:14 da_verif_obs
drwxr-xr-x Aug 22 17:14 da_vtox_transforms
-rwxr-xr-x Aug 22 17:07 decode_l2_airs.make
drwxr-xr-x Aug 22 17:36 frame
-rw-r--r Aug 22 17:07 gen_be.make
drwxr-xr-x Aug 22 17:36 inc
drwxr-xr-x Aug 22 17:17 makedepf
-rw-r--r 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

16. 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

17. 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.

18. 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(:,:,:), ….

19. 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 = 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)

20. 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 

21. 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, ….

22. 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, ….

23. 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 ….

24. 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)

25. 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

26. ! 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

27. !---------------------------------------------------------------------------
! [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

28. !---------------------------------------------------------------------------
! [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)

29. ! ========================
! 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

30. 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.