Implementation of the Analysis Step for the Global Filters with OMI

Overview

With Version 1.16 of PDAF we introduced PDAF-OMI (observation module infrastructure). With OMI we provide generic routines for the analysis step, which only distinguish global and local filters. This page describes the implementation of the analysis step for global filters (ESTKF, ETKF, EnKF, NETF, PF).

For the analysis step of the global filters different operations related to the observations are needed. These operations are requested by PDAF by call-back routines supplied by the user and provided in the OMI structure. The names of the routines that are provided by the user are specified in the call to the routine PDAF_assimilate_global_omi in the fully-parallel implementation (or PDAF_put_state_global_omi for the 'flexible' implementation) that was discussed before. With regard to the parallelization, all these routines (except U_collect_state, U_distribute_state, and U_next_observation) are executed by the filter processes (filterpe=.true.) only.

For completeness we discuss here all user-supplied routines that are specified in the interface to PDAF_assimilate_global_omi. Thus, some of the user-supplied routines that are explained on the page describing the modification of the model code for the ensemble integration are repeated here.

PDAF_assimilate_global_omi

The general aspects of the filter specific routines PDAF_assimilate_* have been described on the page Modification of the model code for the ensemble integration and its sub-page on inserting the analysis step. The routine is used in the fully-parallel 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 user-supplied routines specified in the call is explained.

The interface when using one of the global filters is the following:

  SUBROUTINE PDAF_assimilate_global_omi(U_collect_state, U_distribute_state, &
                                 U_init_dim_obs, U_obs_op, U_init_obs, &
                                 U_prepoststep, U_next_observation, status)

with the following arguments:

• U_collect_state: The name of the user-supplied 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 in PDAF_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 user-supplied routine that initializes the observation information and provides the size of observation vector
• U_obs_op: The name of the user-supplied routine that acts as the 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, and doexit. The same routine is also used in PDAF_get_state.
• status: The integer status flag. It is zero, if PDAF_assimilate_global_omi is exited without errors.

PDAF_put_state_global_omi

When the 'flexible' implementation variant is chosen for the assimilation system, the routine PDAF_put_state_global_omi has to be used instead of PDAF_assimilate_global_omi. 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 user-supplied routines U_distribute_state and U_next_observation are missing.

The interface when using one of the global filters is the following:

  SUBROUTINE PDAF_put_state_global_omi(U_collect_state, &
                                 U_init_dim_obs, U_obs_op, U_init_obs, &
                                 U_prepoststep, status)

User-supplied routines

Here all user-supplied routines are described that are required in the call to PDAF_assimilate_global_omi. For some of the generic routines, we link to the page on modifying the model code for the ensemble integration.

To indicate user-supplied routines we use the prefix U_. In the template directory templates/ as well as in the tutorial implementations in tutorial/ 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 sub-domain, if a domain decomposed model is used. Thus, the value(s) in the variable will be different for different model sub-domains.

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 (callback_obs_pdafomi.F90)

The interface for this routine is:

SUBROUTINE init_dim_obs_pdafomi(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. For PDAF, 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 domain-decomposed model is used, dim_obs_p will be the size of the observation vector for the sub-domain of the calling process.

With PDAF-OMI, the routine just calls a routine from the observation module for each observation type.

U_obs_op (callback_obs_pdafomi.F90)

The interface for this routine is:

SUBROUTINE obs_op_pdafomi(step, dim_p, dim_obs_p, state_p, m_state_p)

  INTEGER, INTENT(in) :: step               ! Currrent time step
  INTEGER, INTENT(in) :: dim_p              ! PE-local dimension of state
  INTEGER, INTENT(in) :: dim_obs_p          ! Dimension of observed state
  REAL, INTENT(in)    :: state_p(dim_p)     ! PE-local model state
  REAL, INTENT(out) :: m_state_p(dim_obs_p) ! PE-local 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 PE-local sub-domain of the model and has to provide the observed sub-state for the PE-local domain.

With PDAF-OMI, the routine just calls a routine from the observation module for each observation type.

U_prepoststep (prepoststep_ens_pdaf.F90)

The routine has already been described on the page on modifying the model code for the ensemble integration. For completeness, the description is repeated:

The interface of the routine is identical for all filters. However, the particular operations that are performed in the routine can be specific for each filter algorithm.

The interface for this routine is

SUBROUTINE prepoststep(step, dim_p, dim_ens, dim_ens_p, dim_obs_p, &
                       state_p, Uinv, ens_p, flag)

  INTEGER, INTENT(in) :: step        ! Current time step
                         ! (When the routine is called before the analysis -step is provided.)
  INTEGER, INTENT(in) :: dim_p       ! PE-local state dimension
  INTEGER, INTENT(in) :: dim_ens     ! Size of state ensemble
  INTEGER, INTENT(in) :: dim_ens_p   ! PE-local size of ensemble
  INTEGER, INTENT(in) :: dim_obs_p   ! PE-local dimension of observation vector
  REAL, INTENT(inout) :: state_p(dim_p) ! PE-local forecast/analysis state
                                     ! The array 'state_p' is not generally not initialized in the case of SEIK/EnKF/ETKF/ESTKF.
                                     ! It can be used freely in this routine.
  REAL, INTENT(inout) :: Uinv(dim_ens-1, dim_ens-1) ! Inverse of matrix U
  REAL, INTENT(inout) :: ens_p(dim_p, dim_ens)      ! PE-local state ensemble
  INTEGER, INTENT(in) :: flag        ! PDAF status flag

The routine U_prepoststep is called once at the beginning of the assimilation process. In addition, it is called during the assimilation cycles before the analysis step and after the ensemble transformation. The routine is called by all filter processes (that is filterpe=1).

The routine provides for the user the full access to the ensemble of model states. Thus, user-controlled pre- and post-step operations can be performed. For example the forecast and the analysis states and ensemble covariance matrix can be analyzed, e.g. by computing the estimated variances. In addition, the estimates can be written to disk.

Hint:

• If a user considers to perform adjustments to the estimates (e.g. for balances), this routine is the right place for it.
• Only for the SEEK filter the state vector (state_p) is initialized. For all other filters, the array is allocated, but it can be used freely during the execution of U_prepoststep.
• The interface has a difference for ETKF and ESTKF: For the ETKF, the array Uinv has size dim_ens x dim_ens. In contrast it has size dim_ens-1 x dim_ens-1 for the ESTKF. (For most cases, this will be irrelevant, because most usually the ensemble array ens_p is used for computations, rather than Uinv. Only for the SEIK filter with fixed covariance matrix, Uinv is required to compute the estimate analysis error. The fixed covariance matrix mode is not available for the ETKF or ESTKF.)
• The interface through which U_prepoststep is called does not include the array of smoothed ensembles. In order to access the smoother ensemble array one has to set a pointer to it using a call to the routine PDAF_get_smootherens (see page on auxiliary routines)

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 user-supplied routines

The user-supplied routines are essentially executed in the order they are listed in the interface to PDAF_assimilate_global_omi. 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. How this information is initialized is described in the documentation of OMI.

Before the analysis step is called the following routine is executed:

1. U_collect_state

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:

1. U_prepoststep (Call to act on the forecast ensemble, called with negative value of the time step)
2. U_init_dim_obs
3. U_obs_op (multiple calls, one for each ensemble member)
4. U_prodRinvA
5. U_prepoststep (Call to act on the analysis ensemble, called with (positive) value of the time step)

In case of the routine PDAF_assimilate_global_omi, the following routines are executed after the analysis step:

1. U_distribute_state
2. U_next_observation