Implementation of the Analysis Step using the universal interface of PDAF3

Overview

This page describes the recommended implementation of the analysis step using the universal routines of the PDAF3 interface. The older approach calling PDAFomi_assimilate_local or PDAFomi_put_state_local is documented on the page on Implementing the Analysis Step for the Local Filters with OMI without PDAFlocal (until V2.2.1 of PDAF).

PDAF3 provides universal routines for the analysis step, which only distinguish whether the online or offline D mode is used.

For the analysis step 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 observation modules using PDAF-OMI. The names of the routines that are provided by the user are specified in the call to the assimilation routine PDAF3_assimilate.

For completeness we discuss here all user-supplied routines that are specified as arguments in the assimilation routines.

Assimilation routines

PDAF3_assimilate

This routine is used both in the fully-parallel and the flexible implementation variant of the data assimilation system. (See the page Modification of the model code for the ensemble integration for these variants)

The interface for the routine PDAF3_assimilate contains names for routines that operate on the local analysis domains (marked by the suffix _l). Here, we list the full interface of the routine. Subsequently, the user-supplied routines specified in the call are explained.

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

  SUBROUTINE PDAF3_assimilate(U_collect_state, U_distribute_state, &
                              U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                              U_init_n_domains, U_init_dim_l, U_init_dim_obs_l_pdafomi, &
                              U_prepoststep, U_next_observation, status)

with the following arguments:

• Routines to transfer between model fields and state vector:
  • 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_init_forecast 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.
• Observation routines using PDAF-OMI:
  • 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
• Routines only used for localization:
  • 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 and the index arrays used to map between the global state vector and the local state vector.
• Prepoststep and initialization for next forecast phase
  • U_prepoststep:
    The name of the pre/poststep routine as in PDAF_init_forecast
  • 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_init_forecast.
• Status flag
  • status:
    The integer status flag. It is zero, if the routine 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.

PDAF3_assim_offline

For the offline mode of PDAF, the routine PDAF3_assim_offline is used to perform the analysis step. The interface of the routine is identical with that of PDAF3_assimilate, except that the user-supplied routines U_distribute_state, U_collect_state and U_next_observation are missing.

The interface is:

  SUBROUTINE PDAF3_assim_offline( &
             U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
             U_init_n_domains, U_init_dim_l, U_init_dim_obs_l_pdafomi, &
             U_prepoststep, status)

PDAF3_put_state

This routine exists for backward-compatibility. In implementations that were done before the release of PDAF V3.0, a 'put_state' routine was used for the flexible parallelization variant and for the offline mode. When the 'flexible' implementation variant is chosen for the assimilation system, the routine. The routine PDAF3_put_state allows to port such implemnetations to the PDAF3 interface with minimal changes. The interface of the routine is identical with that of PDAF3_assimilate, except that 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 PDAF3_put_state(U_collect_state, &
                             U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                             U_init_n_domains, U_init_dim_l, U_init_dim_obs_l_pdafomi, &
                             U_prepoststep, status)

• If your code shows a call to PDAFomi_put_state_local, it uses the implementation variant without PDAFlocal. This is documented on the page on Implementing the Analysis Step for the Local Filters with OMI without PDAFlocal (until V2.2.1 of PDAF).

User-supplied routines

Here, all user-supplied routines are described that are required in the call to PDAF3_assimilate, PDAF3_assim_offline or PDAF3_put_state. 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 modifying the model code for the ensemble integration 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 modifying the model code for the ensemble integration for the description of this routine.

U_init_dim_obs_pdafomi (callback_obs_pdafomi.F90)

This is a call-back routine 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 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 modifying the model code for the ensemble integration for the description of this routine.

U_init_n_domains (init_n_domains_pdaf.F90)

This routine is only used for localization. It 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.

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

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 process-local model sub-domain.

U_init_dim_l (init_dim_l_pdaf.F90)

This routine is only used for localization.

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.

It provides in dim_l the dimension of the state vector for the local analysis domain with index domain_p to PDAF.

In the recommended implementation shown in the tutorial and template codes, there are two further initializations:

1. The routine has initialize the index array id_lstate_in_pstate containing the indices of the elements of the local state vector in the global (or domain-decomposed) state vector. Then it has to provide this array to PDAF by calling PDAFlocal_set_indices (see below).
2. The routine initializes an array coords_l containing the coordinates of the local analysis domain. This is shared with U_init_dim_obs_l_pdafomi via the module mod_assimilation.

Hints:

• The coordinates in coords_l have to describe one location in space that is used for localization 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.

The index array id_lstate_in_pstate is an integer array in form of a one-dimensional vector. One initializes this vector by determining the indices of the elements of the local state vector in the global, or domain decomposed, state vector. After initializing id_lstate_in_pstate, one has to provided it to PDAF by calling `PDAFlocal_set_indices'. The interface interface is:

SUBROUTINE PDAFlocal_set_indices(dim_l, id_lstate_in_pstate)

  INTEGER, INTENT(in) :: dim_l                          ! Dimension of local state vector
  INTEGER, INTENT(in) :: id_lstate_in_pstate(dim_l)     ! Index array for mapping

Hint for id_lstate_in_pstate:

• The initialization of the index vector id_lstate_to_pstate is analogous to a loop that directly performs the initialization of a local state vector. However, here only the indices are stored.
• See the PDAFlocal overview page for more information on the functionality of PDAFlocal.

U_init_dim_obs_l_pdafomi (callback_obs_pdafomi.F90)

This routine is only used for localization. It 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_next_observation (next_observation_pdaf.F90)

This routine is independent of the filter algorithm used.

See the page on modifying the model code for the ensemble integration 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, in U_init_dim_l we can prepare the index array that provides the information how to localize a global state vector.

Before the analysis step is called the following is executed:

1. U_collect_state (called once for each ensemble member)
2. U_prepoststep (Call to act on the forecast ensemble, called with negative value of the time step)

At the analysis time, the observations are initialized by the routines:

1. U_init_dim_obs_pdafomi
2. U_obs_op_pdafomi (Called dim_ens times; once for each ensemble member)

Now the analysis step is entered and the number of local analysis domain is initialized by calling:

1. U_init_n_domains

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

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 PDAF3_assimilate, the following routines are executed after the analysis step:

1. U_distribute_state
2. U_next_observation