Main program for performing data assimilation using one of the
following algorithms based on the incremental variational
approach:
3D-Var
3D- or 4D-EnVar
—
Algorithm
The incremental variational data assimilation approach uses
observations to compute a correction to the background state
(i.e. the analysis increment) while taking into account the
specified uncertainties for both the observations and the
background state (i.e. the R and B covariance matrices,
respectively). The analysis increment is computed by finding the
minimum value of a cost function. This cost function is a scalar
measure of the weighted departure of the corrected state from
both the background state and the observations. The minimization
is perfomed with a standard minimization algorithm (currently
the quasi-Newton algorithm) that employs the gradient of the
cost function to enable the minimum to be found (or at least
approximated with sufficient accuracy) with relatively few
iterations. The analysis increment is not assumed to be on the
same horizontal and vertical grid as the background state. In
addition, the temporal resolution of the background state and
analysis increment are not assumed to be equal.
–
In practical terms, the background state is used to compute the
“innovation” vector, that is, the difference between the
observations and the background state in observation space:
y-H(xb). The function H() represents the non-linear
observation operators that map a gridded state vector into
observation space. The innovation vector is used in the cost
function calculation. Versions of the observation operators that
are linearized with respect to the background state (or updated
background state when using the outer loop) are also used in the
cost function calculation to transform the analysis increment
into observation space. The gradient of the cost function is
computed using the adjoint of these linearized operators.
–
After the minimization, the analysis increment is spatially
interpolated to the same grid as the background state and then
added to this state to obtain the analysis. For some variables a
physical constraint is imposed on the analysis
(e.g. non-negative humidity or sea-ice concentration between 0
and 1) and then the analysis increment is recomputed.
–
File I/O
The required input files and produced output files can vary
according to the application. Below are tables of files for
typical NWP 4D-EnVar (e.g. GDPS) and sea ice or SST 3D-Var
applications.
–
Input and Output Files (NWP applicaton)
Description of file
flnml
In - Main namelist file with parameters user may modify
flnml_static
In - The “static” namelist that should not be modified
trlm_$NN (e.g. trlm_01)
In - Background state (a.k.a. trial) files for each timestep
analysisgrid
In - File defining grid for computing the analysis increment
bgcov
In - Static (i.e. NMC) B matrix file for NWP fields
bgchemcov
In - Static B matrix file for chemistry fields
ensemble/$YYYYMMDDHH_006_$NNNN
In - Ensemble member files defining ensemble B matrix
obsfiles_$FAM/obs$FAM_$NNNN_$NNNN
In - Observation file for each “family” and MPI task
obserr
In - Observation error statistics
obsinfo_chm
In - Something needed for chemistry assimilation?
preconin
In - Preconditioning file (Hessian of the cost function)
rebm_$MMMm (e.g. rebm_180m)
Out - Analysis increment on the (low-res) analysis grid
rehm_$MMMm
Out - Analysis increment on the (high-res) trial grid
anlm_$MMMm
Out - Analysis on the trial grid
obsfiles_$FAM.updated/obs$FAM_$NNNN_$NNNN
Out - Updated obs file for each “family” and MPI task
Remainder are files related to radiance obs:
stats_$SENSOR_assim
In - Satellite radiance observation errors of difference sensors
stats_tovs
In - Satellite radiance observation errors
stats_tovs_symmetricObsErr
In - User-defined symmetric TOVS errors for all sky
Cmat_$PLATFORM_$SENSOR.dat
In - Inter-channel observation-error correlations
ceres_global.std
In - High-res surface type and water fraction for radiance obs
rtcoef_$PLATFORM_$SENSOR.dat
In - RTTOV coefficient files
rttov_h2o_limits.dat
In - Min/max humidity limits applied to analysis
ozoneclim98
In - Ozone climatology
–
Input and Output Files (SST or Sea ice)
Description of file
flnml
In - Main namelist file with parameters user may modify
trlm_$NN (e.g. trlm_01)
In - Background state (a.k.a. trial) files for each timestep
analysisgrid
In - File defining grid for computing the analysis increment
sea_ice_obs-err
In - Observation error statistics (sea ice only)
bgstddev
In - Background error stddev
diffusmod.std
In - Normalization factor for diffusion operator correlations
obsfiles_$FAM/obs$FAM_$NNNN_$NNNN
In - Observation file for each “family” and MPI task
rebm_$MMMm (e.g. rebm_180m)
Out - Analysis increment on the (low-res) analysis grid
rehm_$MMMm
Out - Analysis increment on the (high-res) trial grid
anlm_$MMMm
Out - Analysis on the trial grid
obsfiles_$FAM.updated/obs$FAM_$NNNN_$NNNN
Out - Updated obs file for each “family” and MPI task
–
Synopsis
Below is a summary of the var program calling sequence:
Initial setups:
Setup horizontal and vertical grid objects for “analysis
grid” from analysisgrid file and for “trial grid” from
first trial file: trlm_01.
Setup obsSpaceData object and read observations from
files: inn_setupObs.
Setup columnData and gridStateVector modules (read
list of analysis variables from namelist) and allocate column
object for storing trial on analysis levels.
Setup the observation error statistics in obsSpaceData
object: oer_setObsErrors.
Allocate a stateVector object on the trial grid and then
read the trials: gio_readTrials.
Setup the B matrices: bmat_setup.
Setup the gridVariableTransforms and minimization
modules.
Outer loop (only 1 iteration when no outer loop is used)
during which the analysis increment is computed to correct the
current “updated state” which is used to compute the
innovation and serve as the starting point for the
minimization of the following outer loop iteration:
Impose RTTOV humidity limits on updated state (initially the
trial) on trial grid: qlim_rttovLimit.
Use the updated state on trial grid to setup the reference
state used by gridVariableTransforms module for height
calculations.
Compute columnTrlOnTrlLev and columnTrlOnAnlIncLev from
updated state: inn_setupColumnsOnTrlLev,
inn_setupColumnsOnAnlIncLev
Compute innovation from updated state:
inn_computeInnovation.
Use the updated state on trial grid to setup the reference
state used by gridVariableTransforms module for LQ
to HU calculations.
Do the minimization for this outer loop iteration:
min_minimize to obtain controlVectorIncr.
Update sum of all computed increment control vectors:
controlVectorIncrSum(:) which is needed in the
background cost function for outer loop.
Compute stateVectorIncr (on analysis grid) from
controlVectorIncr: inc_getIncrement.
Interpolate and add stateVectorIncr to the updated
state: inc_computeHighResAnalysis.
If requested, impose saturation and RTTOV humidity limits on
the updated state.
Write increment (or sum of increments when outer loop used)
to file: inc_writeIncrement.
End of outer loop.
Final steps, after the outer loop:
If requested, compute final cost function value using
non-linear observation operators.
Write the final analysis and recomputed complete increment on
the trial grid: inc_writeincAndAnalHighRes.
Various final steps, including: write the Hessian to binary
file (min_writeHessian), update the observation files
(obsf_writeFiles).
The use of an outer loop is controlled by the namelist block
&NAMVAR read by the var program.
The choice of 3D-Var vs. EnVar is controlled by the weights given
to the climatological (i.e. static) and ensemble-based background
error covariance (i.e. B matrix) components. The weights for all
B matrix components are zero be default and can be set to a
nonzero value through the namelist variable SCALEFACTOR in
the namelist block for each corresponding fortran module.
Either algorithm can be used in combination with “First guess at
appropriate time” (i.e. FGAT) which is controlled by the namelist
variable DSTEPOBS (in NAMTIME) that specifies the length
of time (in hours) between times when the background state is
used to compute the innovation (i.e. O-B).
Similarly, the choice between 3D-EnVar and 4D-EnVar is controlled
by the namelist variable DSTEPOBSINC (also in &NAMTIME)
which specifies the length of time (in hours) between times when
the analysis increment is computed. In the context of EnVar, if
this is less than the assimilation time window, then the
ensembles used to construct the ensemble-based B matrix component
will be used at multiple times within the assimilation window to
obtain 4D covariances (i.e. 4D-EnVar).
Some of the other relevant namelist blocks used to configure the
variational analysis are listed in the following table:
Module
Namelist
Description of what is controlled
minimization_mod
NAMMIN
maximum number of iterations, convergence criteria and many
additional parameters for controlling the minimization
timeCoord_mod
NAMTIME
assimilation time window length, temporal resolution of
the background state and increment
bMatrixEnsemble_mod
NAMBEN
weight and other parameters for ensemble-based B matrix
component
bMatrixHI_mod
NAMBHI
weight and other parameters for the climatological B matrix
component based on homogeneous-isotropic covariances
represented in spectral space
Other B matrix modules
various
weight and other parameters for each type of B matrix
Needed modules
version_mod: MODULE version_mod (prefix=’ver’ category=’8. Low-level utilities and constants’)
codeprecision_mod: MODULE codePrecision_mod (prefix=’pre’ category=’8. Low-level utilities and constants’)
ramdisk_mod: MODULE ramDisk_mod (prefix=’ram’ category=’8. Low-level utilities and constants’)
utilities_mod: MODULE utilities_mod (prefix=’utl’ category=’8. Low-level utilities and constants’)
midasmpi_mod: MODULE midasMpi_mod (prefix=’mmpi’ category=’8. Low-level utilities and constants’)
message_mod: MODULE message_mod (prefix=’msg’ category=’8. Low-level utilities and constants’)
mathphysconstants_mod: MODULE mathPhysConstants_mod (prefix=’mpc’ category=’8. Low-level utilities and constants’)
horizontalcoord_mod: MODULE horizontalCoord_mod (prefix=’hco’ category=’7. Low-level data objects’)
verticalcoord_mod: MODULE verticalCoord_mod (prefix=’vco’ category=’7. Low-level data objects’)
humiditylimits_mod: MODULE humidityLimits_mod (prefix=’qlim’ category=’4. Data Object transformations’)
timecoord_mod: MODULE timeCoord_mod (prefix=’tim’ category=’7. Low-level data objects’)
obsspacedata_mod: MODULE obsSpaceData_mod (prefix=’obs’ category=’6. High-level data objects’)
columndata_mod: MODULE columnData_mod (prefix=’col’ category=’6. High-level data objects’)
gridstatevector_mod: MODULE gridStateVector_mod (prefix=’gsv’ category=’6. High-level data objects’)
gridstatevectorfileio_mod: MODULE gridStateVectorFileIO_mod (prefix=’gio’ category=’4. Data Object transformations’)
