Implementation of the Analysis Step for 3DVar without using OMI
Implementation Guide
 Main page
 Adaptation of the parallelization
 Initialization of PDAF
 Modifications for ensemble integration
 Implementation of the analysis step
 Implementation for ESTKF
 Implementation for LESTKF
 Implementation for ETKF
 Implementation for LETKF
 Implementation for SEIK
 Implementation for LSEIK
 Implementation for SEEK
 Implementation for EnKF
 Implementation for LEnKF
 Implementation for NETF
 Implementation for LNETF
 Implementation for PF
 Implementation for 3DVar
 Implementation for 3D Ensemble Var
 Implementation for Hybrid 3DVar
 Memory and timing information
 Ensemble Generation
 Diagnostics
Contents of this page
 Overview

PDAF_assimilate_3dvar

PDAF_put_state_3dvar

Usersupplied routines

U_collect_state
(collect_state_pdaf.F90) 
U_distribute_state
(distribute_state_pdaf.F90) 
U_init_dim_obs
(init_dim_obs_pdaf.F90) 
U_obs_op
(obs_op_pdaf.F90) 
U_init_obs
(init_obs_pdaf.F90) 
U_prodRinvA
(prodrinva_pdaf.F90) 
U_cvt
(cvt_pdaf.F90) 
U_cvt_adj
(cvt_adj_pdaf.F90) 
U_obs_op_lin
(obs_op_lin_pdaf.F90) 
U_obs_op_adj
(obs_op_adj_pdaf.F90) 
U_prepoststep
(prepoststep_ens_pdaf.F90) 
U_next_observation
(next_observation_pdaf.F90)

 Execution order of usersupplied routines
Overview
With Version 2.0 with introduced 3D variational assimilation methods to PDAF. There are genenerally three different variants: parameterized 3DVar, 3D Ensemble Var, and hybrid (parameterized + ensemble) 3DVar.
This page describes the implementation of the analysis step for the parameterized 3DVar in the classical way (without using PDAFOMI).
For the analysis step of 3DVar we need different operations related to the observations. These operations are requested by PDAF by calling usersupplied routines. Intentionally, the operations are split into separate routines in order to keep the operations rather elementary as this procedure should simplify the implementation. The names of the required routines are specified in the call to the routine PDAF_assimilate_3dvar
in the fullyparallel implementation (or PDAF_put_state_3dvar
for the 'flexible' implementation) described below. With regard to the parallelization, all these routines (except U_collect_state
) are executed by the filter processes (filterpe=.true.
) only.
For completeness we discuss here all usersupplied routines that are specified in the interface to PDAF_assimilate_3dvar
. Thus, some of the usersupplied routines that are explained on the page describing the modification of the model code for the ensemble integration are repeated here.
PDAF_assimilate_3dvar
The general aspects of the filter (or solver) specific routines PDAF_assimilate_*
have been described on the page Modification of the model code for the ensemble integration and its subpage on inserting the analysis step. The routine is used in the fullyparallel implementation variant of the data assimilation system. When the 'flexible' implementation variant is used, the routines PDAF_put_state_*
is used as described further below. Here, we list the full interface of the routine. Subsequently, the usersupplied routines specified in the call is explained.
The interface for using the parameterized 3DVar is:
SUBROUTINE PDAF_assimilate_3dvar(U_collect_state, U_distribute_state, & U_init_dim_obs, U_obs_op, U_init_obs, U_prodRinvA, & U_cvt, U_cvt_adj, U_obs_op_lin, U_obs_op_adj, & U_prepoststep, U_next_observation, outflag)
with the following arguments:
 U_collect_state: The name of the usersupplied routine that initializes a state vector from the array holding the ensemble of model states from the model fields. This is basically the inverse operation to
U_distribute_state
used inPDAF_get_state
as well as here.  U_distribute_state: The name of a user supplied routine that initializes the model fields from the array holding the ensemble of model state vectors.
 U_init_dim_obs: The name of the usersupplied routine that provides the size of observation vector
 U_obs_op: The name of the usersupplied routine that acts as the observation operator on some state vector
 U_init_obs: The name of the usersupplied routine that initializes the vector of observations
 U_prodRinvA: The name of the usersupplied routine that computes the product of the inverse of the observation error covariance matrix with some matrix provided to the routine by PDAF. This operation occurs during the analysis step of the ETKF.
 U_cvt: The name of the usersupplied routine that applies the controlvector transformation (squareroot of the Bmatrix) on some control vector to obtain a state vector.
 U_cvt_adj: The name of the usersupplied routine that applies the adjoint controlvector transformation (with squareroot of the Bmatrix) on some state vector to obtain the control vector.
 U_obs_op_lin: The name of the usersupplied routine that acts as the linearized observation operator on some state vector
 U_obs_op_adj: The name of the usersupplied routine that acts as the adjoint observation operator on some state vector
 U_prepoststep: The name of the pre/poststep routine as in
PDAF_get_state
 U_next_observation: The name of a user supplied routine that initializes the variables
nsteps
,timenow
, anddoexit
. The same routine is also used inPDAF_get_state
. status
: The integer status flag. It is zero, if the routine is exited without errors.
PDAF_put_state_3dvar
When the 'flexible' implementation variant is chosen for the assimilation system, the routine PDAF_put_state_3dvar
has to be used instead of PDAF_assimilate_3dvar
. The general aspects of the filter specific routines PDAF_put_state_*
have been described on the page Modification of the model code for the ensemble integration. The interface of the routine is identical with that of PDAF_assimilate_global
with the exception the specification of the usersupplied routines U_distribute_state
and U_next_observation
are missing.
The interface for using the parameterized 3DVar is:
SUBROUTINE PDAF_put_state_3dvar(collect_state_pdaf, & U_init_dim_obs, U_obs_op, U_init_obs, U_prodRinvA, & U_cvt, U_cvt_adj, U_obs_op_lin, U_obs_op_adj, & prepoststep_pdaf, outflag)
Usersupplied routines
Here all usersupplied routines are described that are required in the call to PDAF_assimilate_3dvar
. For some of the generic routines, we link to the page on modifying the model code for the ensemble integration.
To indicate usersupplied routines we use the prefix U_
. In the template directory templates/
as well as in the example implementation in testsuite/src/dummymodel_1D
these routines exist without the prefix, but with the extension _pdaf.F90
. In the section titles below we provide the name of the template file in parentheses.
In the subroutine interfaces some variables appear with the suffix _p
. This suffix indicates that the variable is particular to a model subdomain, if a domain decomposed model is used. Thus, the value(s) in the variable will be different for different model subdomains.
U_collect_state
(collect_state_pdaf.F90)
This routine is independent of the filter algorithm used.
See the page on inserting the analysis step for the description of this routine.
U_distribute_state
(distribute_state_pdaf.F90)
This routine is independent of the filter algorithm used.
See the page on inserting the analysis step for the description of this routine.
U_init_dim_obs
(init_dim_obs_pdaf.F90)
This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF) and the 3DVar methods.
The interface for this routine is:
SUBROUTINE init_dim_obs(step, dim_obs_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(out) :: dim_obs_p ! Dimension of observation vector
The routine is called at the beginning of each analysis step. It has to initialize the size dim_obs_p
of the observation vector according to the current time step. Without parallelization dim_obs_p
will be the size for the full model domain. When a domaindecomposed model is used, dim_obs_p
will be the size of the observation vector for the subdomain of the calling process.
Some hints:
 It can be useful to not only determine the size of the observation vector at this point. One can also already gather information about the locations of the observations, which will be used later, e.g. to implement the observation operator. An array for the locations can be defined in a module like
mod_assimilation
of the example implementation.
U_obs_op
(obs_op_pdaf.F90)
This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF) and the 3DVar methods.
The interface for this routine is:
SUBROUTINE obs_op(step, dim_p, dim_obs_p, state_p, m_state_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_p ! PElocal dimension of state INTEGER, INTENT(in) :: dim_obs_p ! Dimension of observed state REAL, INTENT(in) :: state_p(dim_p) ! PElocal model state REAL, INTENT(out) :: m_state_p(dim_obs_p) ! PElocal observed state
The routine is called during the analysis step. It has to perform the operation of the observation operator acting on a state vector that is provided as state_p
. The observed state has to be returned in m_state_p
.
For a model using domain decomposition, the operation is on the PElocal subdomain of the model and has to provide the observed substate for the PElocal domain.
Hint:
 If the observation operator involves a global operation, e.g. some global integration, while using domaindecomposition one has to gather the information from the other model domains using MPI communication.
U_init_obs
(init_obs_pdaf.F90)
This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF) and the 3DVar methods.
The interface for this routine is:
SUBROUTINE init_obs(step, dim_obs_p, observation_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_obs_p ! PElocal dimension of obs. vector REAL, INTENT(out) :: observation_p(dim_obs_p) ! PElocal observation vector
The routine is called during the analysis step.
It has to provide the vector of observations in observation_p
for the current time step.
For a model using domain decomposition, the vector of observations that exist on the model subdomain for the calling process has to be initialized.
U_prodRinvA
(prodrinva_pdaf.F90)
This routine is used by all filter algorithms that use the inverse of the observation error covariance matrix (SEEK, SEIK, and ETKF) and the 3DVar methods.
The interface for this routine is:
SUBROUTINE prodRinvA(step, dim_obs_p, dim_ens, obs_p, A_p, C_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_obs_p ! PElocal dimension of obs. vector INTEGER, INTENT(in) :: dim_ens ! Ensemble size REAL, INTENT(in) :: obs_p(dim_obs_p) ! PElocal vector of observations REAL, INTENT(in) :: A_p(dim_obs_p, dim_ens) ! Input matrix from analysis routine REAL, INTENT(out) :: C_p(dim_obs_p, dim_ens) ! Output matrix
The routine is called during the analysis step. In the algorithms the product of the inverse of the observation error covariance matrix with some matrix has to be computed. For the ETKF, this matrix holds the observed part of the ensemble perturbations. The matrix is provided as A_p
. The product has to be given as C_p
.
For a model with domain decomposition, A_p
contains the part of the matrix that resides on the model subdomain of the calling process. The product has to be computed for this subdomain, too.
Hints:
 The routine does not require that the product is implemented as a real matrixmatrix product. Rather, the product can be implemented in its most efficient form. For example, if the observation error covariance matrix is diagonal, only the multiplication of the diagonal with matrix
A_p
has to be implemented.  The observation vector
obs_p
is provided through the interface for cases where the observation error variance is relative to the actual value of the observations.  The interface has a difference for SEIK and ETKF: For ETKF the third argument is the ensemble size (
dim_ens
), while for SEIK it is the rank of the covariance matrix (usually ensemble size minus one). In addition, the second dimension ofA_p
andC_p
has sizedim_ens
for ETKF, while it isrank
for the SEIK filter. (Practically, one can usually ignore this difference as the fourth argument of the interface can be named arbitrarily in the routine.)
U_cvt
(cvt_pdaf.F90)
The interface for this routine is:
SUBROUTINE cvt_pdaf(iter, dim_p, dim_cvec, cv_p, Vv_p) INTEGER, INTENT(in) :: iter ! Iteration of optimization INTEGER, INTENT(in) :: dim_p ! PElocal observation dimension INTEGER, INTENT(in) :: dim_cvec ! Dimension of control vector REAL, INTENT(in) :: cv_p(dim_cvec) ! PElocal control vector REAL, INTENT(inout) :: Vv_p(dim_p) ! PElocal result vector (state vector increment)
The routine is called during the analysis step during the iterative minimization of the cost function. It has to apply the control vector transformation to the control vector and return the transformed result vector. Usually this transformation is the multiplication with the squareroot of the background error covariance matrix B.
If the control vector is decomposed in case of parallelization it first needs to the gathered on each processor and afterwards the transformation is computed on the potentially domaindecomposed state vector.
U_cvt_adj
(cvt_adj_pdaf.F90)
The interface for this routine is:
SUBROUTINE cvt_adj_pdaf(iter, dim_p, dim_cvec, Vv_p, cv_p) INTEGER, INTENT(in) :: iter ! Iteration of optimization INTEGER, INTENT(in) :: dim_p ! PElocal observation dimension INTEGER, INTENT(in) :: dim_cvec ! Dimension of control vector REAL, INTENT(in) :: Vv_p(dim_p) ! PElocal result vector (state vector increment) REAL, INTENT(inout) :: cv_p(dim_cvec) ! PElocal control vector
The routine is called during the analysis step during the iterative minimization of the cost function. It has to apply the adjoint control vector transformation to a state vector and return the control vector. Usually this transformation is the multiplication with transposed of the squareroot of the background error covariance matrix B.
If the state vector is decomposed in case of parallelization one needs to take care that the application of the trasformation is complete. This usually requries a comminucation with MPI_Allreduce to obtain a global sun.
U_obs_op_lin
(obs_op_lin_pdaf.F90)
This routine is used by all 3DVar methods.
The interface for this routine is:
SUBROUTINE obs_op_lin(step, dim_p, dim_obs_p, state_p, m_state_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_p ! PElocal dimension of state INTEGER, INTENT(in) :: dim_obs_p ! Dimension of observed state REAL, INTENT(in) :: state_p(dim_p) ! PElocal model state REAL, INTENT(out) :: m_state_p(dim_obs_p) ! PElocal observed state
The routine is called during the analysis step. It has to perform the operation of the linearized observation operator acting on a state vector increment that is provided as state_p
. The observed state has to be returned in m_state_p
.
For a model using domain decomposition, the operation is on the PElocal subdomain of the model and has to provide the observed substate for the PElocal domain.
Hint:
 If the observation operator involves a global operation, e.g. some global integration, while using domaindecomposition one has to gather the information from the other model domains using MPI communication.
U_obs_op_adj
(obs_op_adj_pdaf.F90)
This routine is used by all 3DVar methods.
The interface for this routine is:
SUBROUTINE obs_op_adj(step, dim_p, dim_obs_p, state_p, m_state_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_p ! PElocal dimension of state INTEGER, INTENT(in) :: dim_obs_p ! Dimension of observed state REAL, INTENT(in) :: m_state_p(dim_obs_p) ! PElocal observed state REAL, INTENT(out) :: state_p(dim_p) ! PElocal model state
The routine is called during the analysis step. It has to perform the operation of the adjoint observation operator acting on a vector in observation space that is provided as m_state_p. The resulting state vector has to be returned in m_state_p
.
For a model using domain decomposition, the operation is on the PElocal subdomain of the model and has to provide the observed substate for the PElocal domain.
Hint:
 If the observation operator involves a global operation, e.g. some global integration, while using domaindecomposition one has to gather the information from the other model domains using MPI communication.
U_prepoststep
(prepoststep_ens_pdaf.F90)
The routine has already been described for modifying the model for the ensemble integration and for inserting the analysis step.
See the page on inserting the analysis step for the description of this routine.
U_next_observation
(next_observation_pdaf.F90)
This routine is independent of the filter algorithm used.
See the page on inserting the analysis step for the description of this routine.
Execution order of usersupplied routines
The usersupplied routines are essentially executed in the order they are listed in the interface to PDAF_assimilate_3dvar
. The order can be important as some routines can perform preparatory work for later routines. For example, U_init_dim_obs
prepares an index array that provides the information for executing the observation operator in U_obs_op
.
Before the analysis step is called the following routine is executed:
The analysis step is executed when the ensemble integration of the forecast is completed. During the analysis step the following routines are executed in the given order:
 U_prepoststep (Call to act on the forecast ensemble, called with negative value of the time step)
 U_init_dim_obs
 U_obs_op
 U_init_obs
Inside the analysis step the interative optimization is computed. This involves the repeated call of the routines:
After the iterative optimization the following routines are executes to complte the analysis step:
 U_cvt (Call to the control vector transform to compute the final state vector increment
 U_prepoststep (Call to act on the analysis ensemble, called with (positive) value of the time step)
In case of the routine PDAF_assimilate_3dvar
, the following routines are executed after the analysis step: