View source for R4DVAR Observation Impact Tutorial 2010

<div class="title">R4D-Var Observation Impact 2010</div>


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<div style="float: left;margin: 0 20px 0 0;">{{4DVar Tut 2010 TOC}}</div>__TOC__

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==Introduction==
During this exercise you will apply the primal form of the dual form strong/weak constraint, 4-Dimensional Variational ('''4D-Var''') data assimilation observation impact based on the indirect representer algorithm to ROMS configured for the U.S. west coast and the California Current System (CCS). This configuration, referred to as [[WC13]], has 30 km horizontal resolution, and 30 levels in the vertical. While 30 km resolution is inadequate for capturing much of the energetic mesoscale circulation associated with the CCS, [[WC13]] captures the broad scale features of the circulation quite well, and serves as a very useful and efficient illustrative example of R4D-Var observation impacts.
{{#lst:4DVar_Tutorial_Introduction|setup}}

==Running R4D-Var Observation Impact==

To run this exercise, go first to the directory <span class="twilightBlue">WC13/R4DVAR_impact</span>. Instructions for compiling and running the model are provided below or can be found in the <span class="twilightBlue">Readme</span> file. The recommended configuration for this exercise is one outer-loop and 50 inner-loops, and <span class="twilightBlue">ocean_wc13.in</span> is configured for this default case. The number of inner-loops is controlled by the parameter [[Variables#Ninner|Ninner]] in <span class="twilightBlue">ocean_wc13.in</span>.

==Important CPP Options==
The following C-preprocessing options are activated in the [[build_Script|build script]]:
<div class="box">   [[W4DVAR_SENSITIVITY]]      R4D-Var observation sensitivity driver<br />   [[AD_IMPULSE]]              Force ADM with intermittent impulses<br />   [[OBS_IMPACT]]              Compute observation impact<br />   [[OBS_IMPACT_SPLIT]]        separate impact due to IC, forcing, and OBC<br />   [[WC13]]                    Application CPP option</div>

==Input NetCDF Files==
[[WC13]] requires the following input NetCDF files:
<div class="box">                       <span class="twilightBlue">Grid File:</span>  ../Data/wc13_grd.nc<br />          <span class="twilightBlue">Nonlinear Initial File:</span>  wc13_ini.nc<br />                 <span class="twilightBlue">Forcing File 01:</span>  ../Data/coamps_wc13_lwrad_down.nc<br />                 <span class="twilightBlue">Forcing File 02:</span>  ../Data/coamps_wc13_Pair.nc<br />                 <span class="twilightBlue">Forcing File 03:</span>  ../Data/coamps_wc13_Qair.nc<br />                 <span class="twilightBlue">Forcing File 04:</span>  ../Data/coamps_wc13_rain.nc<br />                 <span class="twilightBlue">Forcing File 05:</span>  ../Data/coamps_wc13_swrad.nc<br />                 <span class="twilightBlue">Forcing File 06:</span>  ../Data/coamps_wc13_Tair.nc<br />                 <span class="twilightBlue">Forcing File 07:</span>  ../Data/coamps_wc13_wind.nc<br />                   <span class="twilightBlue">Boundary File:</span>  ../Data/wc13_ecco_bry.nc<br /><br />        <span class="twilightBlue">Adjoint Sensitivity File:</span>  wc13_ads.nc<br />     <span class="twilightBlue">Initial Conditions STD File:</span>  ../Data/wc13_std_i.nc<br />                  <span class="twilightBlue">Model STD File:</span>  ../Data/wc13_std_m.nc<br />    <span class="twilightBlue">Boundary Conditions STD File:</span>  ../Data/wc13_std_b.nc<br />        <span class="twilightBlue">Surface Forcing STD File:</span>  ../Data/wc13_std_f.nc<br />    <span class="twilightBlue">Initial Conditions Norm File:</span>  ../Data/wc13_nrm_i.nc<br />                 <span class="twilightBlue">Model Norm File:</span>  ../Data/wc13_nrm_m.nc<br />   <span class="twilightBlue">Boundary Conditions Norm File:</span>  ../Data/wc13_nrm_b.nc<br />       <span class="twilightBlue">Surface Forcing Norm File:</span>  ../Data/wc13_nrm_f.nc<br/>               <span class="twilightBlue">Observations File:</span>  wc13_obs.nc<br />            <span class="twilightBlue">Lanczos Vectors File:</span>  wc13_lcz.nc</div>

==Various Scripts and Include Files==
The following files will be found in <span class="twilightBlue">WC13/R4DVAR_impact</span> directory after downloading from ROMS test cases SVN repository:
<div class="box">   <span class="twilightBlue">Readme</span>                instructions<br />   [[build_Script|build.bash]]            bash shell script to compile application<br />   [[build_Script|build.sh]]              csh Unix script to compile application<br />   [[job_r4dvar_sen|job_r4dvar_sen.sh]]     job configuration script<br />   <span class="twilightBlue">ocean_wc13.in</span>         ROMS standard input script for WC13<br />   [[s4dvar.in]]             4D-Var standard input script template<br />   <span class="twilightBlue">wc13.h</span>                WC13 header with CPP options</div>

==Important parameters in standard input <span class="twilightBlue">ocean_wc13.in</span> script==
*Notice that this driver uses the following adjoint sensitivity parameters (see input script for details):
:<div class="box">       [[Variables#DstrS|DstrS]] == 0.0d0                      ! starting day<br />       [[Variables#DendS|DendS]] == 0.0d0                      ! ending day<br /><br />       [[Variables#KstrS|KstrS]] ==  1                         ! starting level<br />       [[Variables#KendS|KendS]] == 30                         ! ending level<br /><br />       [[Variables#Lstate|Lstate(isFsur)]] == T                 ! free-surface<br />       [[Variables#Lstate|Lstate(isUbar)]] == T                 ! 2D U-momentum<br />       [[Variables#Lstate|Lstate(isVbar)]] == T                 ! 2D V-momentum<br />       [[Variables#Lstate|Lstate(isUvel)]] == T                 ! 3D U-momentum<br />       [[Variables#Lstate|Lstate(isVvel)]] == T                 ! 3D V-momentum<br /><br />       [[Variables#Lstate|Lstate(isTvar)]] == T T               ! tracers</div>

*Both '''FWDNAME''' and '''HISNAME''' must be the same:
:<div class="box">       [[Variables#FWDname|FWDNAME]] == wc13_fwd.nc<br />       [[Variables#HISname|HISNAME]] == wc13_fwd.nc</div>

==Instructions==
To run this application you need to take the following steps:

#We need to run the model application for a period that is long enough to compute meaningful circulation statistics, like mean and standard deviations for all prognostic state variables ([[Variables#zeta|zeta]], [[Variables#u|u]], [[Variables#v|v]], [[Variables#T|T]], and [[Variables#S|S]]). The standard deviations are written to NetCDF files and are read by the 4D-Var algorithm to convert modeled error correlations to error covariances. The error covariance matrix, '''D'''=diag('''B<sub>x</sub>''', '''B<sub>b</sub>''', '''B<sub>f</sub>''', '''Q'''), is very large and not well known. '''B''' is modeled as the solution of a diffusion equation as in [[Bibliography#WeaverAT_2001a|Weaver and Courtier (2001)]]. Each covariance matrix is factorized as '''B = K &Sigma; C &Sigma;<sup>T</sup> K<sup>T</sup>''', where '''C''' is a univariate correlation matrix, '''&Sigma;''' is a diagonal matrix of error standard deviations, and '''K''' is a multivariate balance operator.<div class="para">&nbsp;</div>In this application, we need standard deviations for initial conditions, surface forcing ([[ADJUST_WSTRESS]] and [[ADJUST_STFLUX]]), and open boundary conditions ([[ADJUST_BOUNDARY]]). The standard deviations for the initial and open boundary conditions are in terms of the unbalanced error covariance ('''K B<sub>u</sub> K<sup>T</sup>''') since the balanced operator is activated ([[BALANCE_OPERATOR]] and [[ZETA_ELLIPTIC]]).<div class="para">&nbsp;</div>The balance operator imposes a multivariate constraint on the error covariance such that the unobserved variable information is extracted from observed data by establishing balance relationships (i.e., T-S empirical formulas, hydrostactic balance, and geostrophic balance) with other state variables ([[Bibliography#WeaverAT_2005a|Weaver ''et al.'', 2005]]).<div class="para">&nbsp;</div>These standard deviations have already been created for you:<div class="box"><span class="twilightBlue">../Data/wc13_std_i.nc</span>     initial conditions<br /><span class="twilightBlue">../Data/wc13_std_m.nc</span>     model error (if weak constraint)<br /><span class="twilightBlue">../Data/wc13_std_b.nc</span>     open boundary conditions<br /><span class="twilightBlue">../Data/wc13_std_f.nc</span>     surface forcing (wind stress and net heat flux)</div>
#Since we are modeling the error covariance matrix, '''D''', we need to compute the normalization coefficients to ensure that the diagonal elements of the associated correlation matrix '''C''' are equal to unity. There are two methods to compute normalization coefficients: exact and randomization (an approximation).<div class="para">&nbsp;</div>The exact method is very expensive on large grids. The normalization coefficients are computed by perturbing each model grid cell with a delta function scaled by the area (2D state variables) or volume (3D state variables), and then by convolving with the squared-root adjoint and tangent linear diffusion operators.<div class="para">&nbsp;</div>The approximate method is cheaper: the normalization  coefficients are computed using the randomization approach of [[Bibliography#FisherM_1995a|Fisher and Courtier (1995)]]. The coefficients are initialized with random numbers having a uniform distribution (drawn from a normal distribution with zero mean and unit variance). Then, they are scaled by the inverse squared-root of the cell area (2D state variable) or volume (3D state variable) and convolved with the squared-root adjoint and tangent diffusion operators over a specified number of iterations, Nrandom.<div class="para">&nbsp;</div>Check following parameters in the 4D-Var input script [[s4dvar.in]] (see input script for details):<div class="box">[[Variables#Nmethod|Nmethod]]  == 0             ! normalization method<br />[[Variables#Nrandom|Nrandom]]  == 5000          ! randomization iterations<br /><br />[[Variables#LdefNRM|LdefNRM]] == F F F F        ! Create a new normalization files<br />[[Variables#LwrtNRM|LwrtNRM]] == F F F F        ! Compute and write normalization<br /><br />[[Variables#CnormI|CnormI(isFsur)]] =  T       ! 2D variable at RHO-points<br />[[Variables#CnormI|CnormI(isUbar)]] =  T       ! 2D variable at U-points<br />[[Variables#CnormI|CnormI(isVbar)]] =  T       ! 2D variable at V-points<br />[[Variables#CnormI|CnormI(isUvel)]] =  T       ! 3D variable at U-points<br />[[Variables#CnormI|CnormI(isVvel)]] =  T       ! 3D variable at V-points<br />[[Variables#CnormI|CnormI(isTvar)]] =  T T     ! NT tracers<br /><br />[[Variables#CnormB|CnormB(isFsur)]] =  T       ! 2D variable at RHO-points<br />[[Variables#CnormB|CnormB(isUbar)]] =  T       ! 2D variable at U-points<br />[[Variables#CnormB|CnormB(isVbar)]] =  T       ! 2D variable at V-points<br />[[Variables#CnormB|CnormB(isUvel)]] =  T       ! 3D variable at U-points<br />[[Variables#CnormB|CnormB(isVvel)]] =  T       ! 3D variable at V-points<br />[[Variables#CnormB|CnormB(isTvar)]] =  T T     ! NT tracers<br /><br />[[Variables#CnormF|CnormF(isUstr)]] =  T       ! surface U-momentum stress<br />[[Variables#CnormF|CnormF(isVstr)]] =  T       ! surface V-momentum stress<br />[[Variables#CnormF|CnormF(isTsur)]] =  T T     ! NT surface tracers flux</div>These normalization coefficients have already been computed for you ('''../Normalization''') using the exact method since this application has a small grid (54x53x30):<div class="box"><span class="twilightBlue">../Data/wc13_nrm_i.nc</span>     initial conditions<br /><span class="twilightBlue">../Data/wc13_nrm_m.nc</span>     model error (if weak constraint)<br /><span class="twilightBlue">../Data/wc13_nrm_b.nc</span>     open boundary conditions<br /><span class="twilightBlue">../Data/wc13_nrm_f.nc</span>     surface forcing (wind stress and<br />                                           net heat flux)</div>Notice that the switches [[Variables#LdefNRM|LdefNRM]] and [[Variables#LwrtNRM|LwrtNRM]] are all '''false''' (F) since we already computed these coefficients.<div class="para">&nbsp;</div>The normalization coefficients need to be computed only once for a particular application provided that the grid, land/sea masking (if any), and decorrelation scales ([[Variables#HdecayI|HdecayI]], [[Variables#VdecayI|VdecayI]], [[Variables#HdecayB|HdecayB]], [[Variables#VdecayV|VdecayV]], and [[Variables#HdecayF|HdecayF]]) remain the same. Notice that large spatial changes in the normalization coefficient structure are observed near the open boundaries and land/sea masking regions.
#Before you run this application, you need to run the standard [[R4DVAR_Tutorial|R4D-VAR]] ('''../R4DVAR''' directory) since we need the Lanczos vectors. Notice that in [[job_r4dvar_sen|job_r4dvar_sen.sh]] we have the following operation:<div class="box"><span class="red">cp -p ${Dir}/R4DVAR/wc13_mod.nc wc13_lcz.nc</span></div>In R4D-Var (observartion space minimization), the Lanczos vectors are stored in the output 4D-Var NetCDF file <span class="twilightBlue">wc13_mod.nc</span>.
#In addition, to run this application you need an adjoint sensitivity functional. This is computed by the following Matlab script:<div class="box"><span class="red">../Data/adsen_37N_transport.m</span></div>which creates the NetCDF file <span class="twilightBlue">wc13_ads.nc</span>. This file has already been created for you.<div class="para">&nbsp;</div>The adjoint sensitivity functional is defined as the time-averaged transport crossing 37N in the upper 500m.
#Customize your preferred [[build_Script|build script]] and provide the appropriate values for:
#*Root directory, <span class="salmon">MY_ROOT_DIR</span>
#*ROMS source code, <span class="salmon">MY_ROMS_SRC</span>
#*Fortran compiler, <span class="salmon">FORT</span>
#*MPI flags, <span class="salmon">USE_MPI</span> and <span class="salmon">USE_MPIF90</span>
#*Path of MPI, NetCDF, and ARPACK libraries according to the compiler. Notice that you need to provide the correct places of these libraries for your computer. If you want to ignore this section, comment out the assignment for the variable <span class="salmon">USE_MY_LIBS</span>.
#Notice that the most important CPP options for this application are specified in the [[build_Script|build script]] instead of <span class="twilightBlue">wc13.h</span>:<div class="box"><span class="twilightBlue">setenv MY_CPP_FLAGS "-DW4DVAR_SENSITIVITY"<br />setenv MY_CPP_FLAGS "${MY_CPP_FLAGS} -DAD_IMPULSE"<br />setenv MY_CPP_FLAGS "${MY_CPP_FLAGS} -DOBS_IMPACT"<br />setenv MY_CPP_FLAGS "${MY_CPP_FLAGS} -DOBS_IMPACT_SPLIT"</span></div>This is to allow flexibility with different CPP options.<div class="para">&nbsp;</div>For this to work, however, any '''#undef''' directives MUST be avoided in the header file <span class="twilightBlue">wc13.h</span> since it has precedence during C-preprocessing.
#You MUST use the [[build_Script|build script]] to compile.
#Customize the ROMS input script <span class="twilightBlue">ocean_wc13.in</span> and specify the appropriate values for the distributed-memory partition. It is set by default to:<div class="box">[[Variables#NtileI|NtileI]] == 2                               ! I-direction partition<br />[[Variables#NtileJ|NtileJ]] == 2                               ! J-direction partition</div>Notice that the adjoint-based algorithms can only be run in parallel using MPI. This is because of the way that the adjoint model is constructed.
#Customize the configuration script [[job_r4dvar_sen|job_r4dvar_sen.sh]] and provide the appropriate place for the [[substitute]] Perl script:<div class="box"><span class="twilightBlue">set SUBSTITUTE=${ROMS_ROOT}/ROMS/Bin/substitute</span></div>This script is distributed with ROMS and it is found in the ROMS/Bin sub-directory. Alternatively, you can define ROMS_ROOT environmental variable in your .cshrc login script. For example, I have:<div class="box"><span class="twilightBlue">setenv ROMS_ROOT /home/arango/ocean/toms/repository/trunk</span></div>
#Execute the configuration [[job_r4dvar_sen|job_r4dvar_sen.sh]] '''before''' running the model. It copies the required files and creates <span class="twilightBlue">r4dvar.in</span> input script from template '''[[s4dvar.in]]'''. This has to be done '''every time''' that you run this application. We need a clean and fresh copy of the initial conditions and observation files since they are modified by ROMS during execution.
#Run ROMS with data assimilation:<div class="box"><span class="red">mpirun -np 4 oceanM ocean_wc13.in > & log &</span></div>

==Results==
The <span class="twilightBlue">WC13/plotting/plot_r4dvar_impact.m</span> Matlab script will allow you to plot the R4D-Var observation impacts:

[[Image:r4dvar_impact.png|500px|thumb|center|<center>R4D-Var Observation Impact</center>]]
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