Implementation of the Analysis Step for the Local Filters with OMI without PDAFlocal

Overview

This documentation describes the implementation with OMI as it was standard since the introduction of PDAF-OMI in PDAF version 1.16 and until and including PDAF version 2.2.1. With PDAF 2.3 we introduced the PDAFlocal interface, which simplifies the implemenation of the local analysis. This approach is described on the current page on the Implementation for Local Filters.

PDAF-OMI provides generic routines for the analysis step, which only distinguish global and local filters. This page describes the implementation of the analysis step for domain-local filters (LESTKF, LETKF, LNETF, LSEIK).

For the analysis step of the local filters we need different operations related to the observations. 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 PDAFomi_assimilate_local in the fully-parallel implementation (or PDAFomi_put_state_local 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 PDAFomi_assimilate_local. Many of the routines are identical to those used for the global filters. Hence, when the user-supplied routines for the global filters have been already implemented, one can base on these routines to speed up the implementation. Due to this, it can also be reasonable to first fully implement a global filter version and subsequently implement the corresponding localized filter by modifying and extending the global routines.

PDAFomi_assimilate_local

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.

The interface for the routine PDAFomi_assimilate_local contains names for routines that operate on the local analysis domains (marked by the suffix _l). Further there are routines that convert between a local and a global model state vector (U_g2l_state and U_l2g_state). 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 local filters is the following:

  SUBROUTINE PDAFomi_assimilate_local(U_collect_state, U_distribute_state, &
                                  U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                                  U_prepoststep, U_init_n_domains, U_init_dim_l, &
                                  U_init_dim_obs_l_pdafomi, U_g2l_state, U_l2g_state, &
                                  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 and also 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_pdafomi: The name of the user-supplied routine that initializes the observation information and provides the size of observation vector
• U_obs_op_pdafomi: 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_init_n_domains: The name of the routine that provides the number of local analysis domains
• U_init_dim_l: The name of the routine that provides the state dimension for a local analysis domain
• U_init_dim_obs_l_pdafomi: The name of the routine that initializes the size of the observation vector for a local analysis domain
• U_g2l_state: The name of the routine that initializes a local state vector from the global state vector
• U_l2g_state: The name of the routine that initializes the corresponding part of the global state vector from the provided local state vector
• 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 PDAFomi_assimilate_local is exited without errors.

Note:

• The order of the routine names does not show the order in which these routines are executed. See the section on the order of the execution at the bottom of this page.

PDAFomi_put_state_local

When the 'flexible' implementation variant is chosen for the assimilation system, the routine PDAFomi_put_state_local has to be used instead of PDAFomi_assimilate_local. 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 PDAFomi_assimilate_local 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 local filters is the following:

  SUBROUTINE PDAFomi_put_state_local(U_collect_state, &
                                  U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                                  U_prepoststep, U_init_n_domains, U_init_dim_l, &
                                  U_init_dim_obs_l_pdafomi, U_g2l_state, U_l2g_state, &
                                  status)

User-supplied routines

Here, all user-supplied routines are described that are required in the call to PDAFomi_assimilate_local or PDAFomi_put_state_local. 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 tutorials in tutorial/ and in the template directory templates/ these routines exist without the prefix, but with the extension _pdaf. The files are named correspondingly. The user-routines relating to OMI are collected in the file callback_obs_pdafomi.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 (short for 'process'). This suffix indicates that the variable is particular to a model sub-domain, if a domain decomposed model is used. In addition, there will be variables with suffix _l (indicating 'local').

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_pdafomi (callback_obs_pdafomi.F90)

This is a call-back routine for PDAF-OMI initializing the observation information. The routine just calls a routine from the observation module for each observation type.

See the documentation on callback_obs_pdafomi.F90 for more information.

U_obs_op_pdafomi (callback_obs_pdafomi.F90)

This is a call-back routine for PDAF-OMI applying the observation operator to the state vector. The routine calls a routine from the observation module for each observation type.

See the documentation on callback_obs_pdafomi.F90 for more information.

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_init_n_domains (init_n_domains_pdaf.F90)

The interface for this routine is:

SUBROUTINE init_n_domains(step, n_domains_p)

  INTEGER, INTENT(in)  :: step        ! Current time step
  INTEGER, INTENT(out) :: n_domains_p ! Number of analysis domains for local model sub-domain

The routine is called during the analysis step before the loop over the local analysis domains is entered. It has to provide the number of local analysis domains. In case of a domain-decomposed model the number of local analysis domain for the model sub-domain of the calling process has to be initialized.

Hints:

• As a simple case, if the localization is only performed horizontally, the local analysis domains can be single vertical columns of the model grid. In this case, n_domains_p is simply the number of vertical columns in the local model sub-domain.

U_init_dim_l (init_dim_l_pdaf.F90)

The interface for this routine is:

SUBROUTINE init_dim_l(step, domain_p, dim_l)

  INTEGER, INTENT(in)  :: step        ! Current time step
  INTEGER, INTENT(in)  :: domain_p    ! Current local analysis domain
  INTEGER, INTENT(out) :: dim_l       ! Local state dimension

The routine is called during the loop over the local analysis domains in the analysis step. For PDAF it has to provide in dim_l the dimension of the state vector for the local analysis domain with index domain_p.

Hints:

• For sharing through the module mod_assimilation, we further initialize an array coords_l containing the coordinates that describe the local domain.
  • These coordinates have to describe one location in space that is used in the OMI observation modules to compute the distance from observations.
  • The coordinates in coords_l have the same units as those used for the observations
  • For geographic distance computations, the unit of the coordinates needs to be radian, thus (0, 2*pi) or (-pi,pi) for longitude and (-pi/2, pi/2) for latitude.
• Any form of local domain is possible as long as it can be describe as a single location.
  • If the local domain is a single grid point, dim_l will be the number of model variables at this grid point.
  • The local analysis domain can also be a single vertical column of the model grid if observations are only horizontally distributed (a common situation with satellite data in the ocean).
    • In this case, dim_l will be the number of vertical grid points at this location times the number of model fields that exist in the vertical, plus possible variables at e.g. the surface.
    • In this case only the horizontal coordinates are used in coords_l.
• Further, we recommend to initialize an array containing the indices of the elements of the local state vector in the global (or domain-decomposed) state vector (id_lstate_in_pstate in the template files). This array is also shared through 'mod_assimilation'.

U_init_dim_obs_l_pdafomi (callback_obs_pdafomi.F90)

This is a call-back routine for PDAF-OMI that initializes the local observation vector. The routine calls a routine from the observation module for each observation type.

See the documentation on callback_obs_pdafomi.F90 for more information.

U_g2l_state (g2l_state_pdaf.F90)

The interface for this routine is:

SUBROUTINE g2l_state(step, domain_p, dim_p, state_p, dim_l, state_l)

  INTEGER, INTENT(in) :: step           ! Current time step
  INTEGER, INTENT(in) :: domain_p       ! Current local analysis domain
  INTEGER, INTENT(in) :: dim_p          ! State dimension for model sub-domain
  INTEGER, INTENT(in) :: dim_l          ! Local state dimension
  REAL, INTENT(in)    :: state_p(dim_p) ! State vector for model sub-domain 
  REAL, INTENT(out)   :: state_l(dim_l) ! State vector on local analysis domain

The routine is called during the loop over the local analysis domains in the analysis step. It has to provide the local state vector state_l that corresponds to the local analysis domain with index domain_p. Provided to the routine is the state vector state_p. With a domain decomposed model, this is the state for the local model sub-domain.

Hints:

• In the simple case that a local analysis domain is a single vertical column of the model grid, the operation in this routine would be to take out of state_p the data for the vertical column indexed by domain_p.
• Usually, one can use the index array id_lstate_in_pstate, which is initialized in U_init_dim_l. The array holds the indices of the local state vector elements in the global state vector.

U_l2g_state (l2g_state_pdaf.F90)

The interface for this routine is:

SUBROUTINE l2g_state(step, domain_p, dim_l, state_l, dim_p, state_p)

  INTEGER, INTENT(in) :: step           ! Current time step
  INTEGER, INTENT(in) :: domain_p       ! Current local analysis domain
  INTEGER, INTENT(in) :: dim_p          ! State dimension for model sub-domain
  INTEGER, INTENT(in) :: dim_l          ! Local state dimension
  REAL, INTENT(in)    :: state_p(dim_p) ! State vector for model sub-domain 
  REAL, INTENT(out)   :: state_l(dim_l) ! State vector on local analysis domain

The routine is called during the loop over the local analysis domains in the analysis step. It has to initialize the part of the global state vector state_p that corresponds to the local analysis domain with index domain_p. Provided to the routine is the state vector state_l for the local analysis domain.

Hints:

• In the simple case that a local analysis domain is a single vertical column of the model grid, the operation in this routine would be to write into state_p the data for the vertical column indexed by domain_p.
• Usually, one can use the index array id_lstate_in_pstate, which is initialized in U_init_dim_l. The array holds the indices of the local state vector elements in the global state vector.

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 executed in the order listed below. The order can be important as some routines can perform preparatory work for routines executed later on during the analysis. For example, U_init_dim_l can prepare an index array that provides the information how to localize a global state vector. Some hints one the efficient implementation strategy are given with the descriptions of the routine interfaces above.

Before the analysis step is called the following is executed:

1. U_collect_state (called once for each ensemble member)

When the ensemble integration of the forecast is completed, the analysis step is executed. Before the loop over all local analysis domains, the following routines are executed:

1. U_prepoststep (Call to act on the forecast ensemble, called with negative value of the time step)
2. U_init_n_domains
3. U_init_dim_obs_pdafomi
4. U_obs_op_pdafomi (Called dim_ens times; once for each ensemble member)

In the loop over all local analysis domains, it is executed for each local analysis domain:

1. U_init_dim_l
2. U_init_dim_obs_l_pdafomi
3. U_g2l_state (Called dim_ens+1 times: Once for each ensemble member and once for the mean state estimate)
4. U_l2g_state (Called dim_ens+1 times: Once for each ensemble member and once for the mean state estimate)

After the loop over all local analysis domains, it is executed:

1. U_prepoststep (Call to act on the analysis ensemble, called with (positive) value of the time step)

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

1. U_distribute_state
2. U_next_observation