= Implementation of the Analysis Step for the Local Filters with OMI = {{{ #!html

Implementation Guide

  1. Main page
  2. Adaptation of the parallelization
  3. Initialization of PDAF
  4. Modifications for ensemble integration
  5. Implementation of the analysis step
    1. General overview for ensemble filters
      1. Implementation for Global Filters
      2. Implementation for Local Filters
      3. Implementation for LEnKF
    2. General overview for 3D-Var methods
      1. Implementation for 3D-Var
      2. Implementation for 3D Ensemble Var
      3. Implementation for Hybrid 3D-Var
    3. PDAF-OMI Overview
  6. Memory and timing information
  7. Ensemble Generation
  8. Diagnostics
}}} [[PageOutline(2-3,Contents of this page)]] == Overview == This page describes the recommended implementation of the analysis step of local filters with OMI using the PDAFlocal interface that was introduced with PDAF V2.3. The older approach calling PDAFomi_assimilate_local or PDAFomi_put_state_local is documented on the page on [wiki:ImplementAnalysisLocal Implementing the Analysis Step for the Local Filters with OMI without PDAFlocal (until V2.2.1 of PDAF)]. 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. == `PDAFlocalomi_assimilate_local` == The general aspects of the filter-specific routines `PDAF_assimilate_*` have been described on the page [ModifyModelforEnsembleIntegration Modification of the model code for the ensemble integration] and its sub-page on [InsertAnalysisStep 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 PDAFlocalomi_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_next_observation, status) }}} with the following arguments: * [#U_collect_statecollect_state_pdaf.F90 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 [ModifyModelforEnsembleIntegration#PDAF_get_state PDAF_get_state] and also here. * [#U_distribute_statedistribute_state_pdaf.F90 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_pdafomicallback_obs_pdafomi.F90 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_pdafomicallback_obs_pdafomi.F90 U_obs_op_pdafomi]: The name of the user-supplied routine that acts as the observation operator on some state vector * [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep]: The name of the pre/poststep routine as in `PDAF_get_state` * [#U_init_n_domainsinit_n_domains_pdaf.F90 U_init_n_domains]: The name of the routine that provides the number of local analysis domains * [#U_init_dim_linit_dim_l_pdaf.F90 U_init_dim_l]: The name of the routine that provides the state dimension for a local analysis domain * [#U_init_dim_obs_l_pdafomicallback_obs_pdafomi.F90 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. * [#U_next_observationnext_observation.F90 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 [#Executionorderofuser-suppliedroutines section on the order of the execution] at the bottom of this page. * If your code shows a call to `PDAFomi_assimilate_local`, it uses the implementation variant without PDAFlocal. This is documented on the page on [wiki:ImplementAnalysisLocal Implementing the Analysis Step for the Local Filters with OMI without PDAFlocal (until V2.2.1 of PDAF)]. == `PDAFlocalomi_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 [ModifyModelforEnsembleIntegration 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 PDAFlocalomi_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, & 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 [wiki:ImplementAnalysisLocal 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 `PDAFomi_assimilate_local` or `PDAFomi_put_state_local`. For some of the generic routines, we link to the page on [ModifyModelforEnsembleIntegration 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 [InsertAnalysisStep#U_collect_statecollect_state_pdaf.F90 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 [InsertAnalysisStep#U_distribute_statedistribute_state_pdaf.F90 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 [wiki:OMI_Callback_obs_pdafomi 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 [wiki:OMI_Callback_obs_pdafomi 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 [InsertAnalysisStep#U_prepoststepprepoststep_ens_pdaf.F90 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`. In addition, for PDAFlocal the routine has to provide the index array containing the indices of the elements of the local state vector in the global (or domain-decomposed) state vector to PDAFlocal by calling `PDAFlocal_set_indices'. (in the template files, this array is called `id_lstate_in_pstate`) 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`. 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 PDAFlocal 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 `map` is analogous to a loop that directly performs the initialization of a local state vector. However, here only the indices are stored. * See the [wiki:PDAFlocal_overview PDAFlocal overview page] for more information on the functionality of PDAFlocal. === `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 [wiki:OMI_Callback_obs_pdafomi 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 [InsertAnalysisStep#U_next_observationnext_observation_pdaf.F90 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_statecollect_state_pdaf.F90 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_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the forecast ensemble, called with negative value of the time step) 1. [#U_init_n_domainsinit_n_domains_pdaf.F90 U_init_n_domains] 1. [#U_init_dim_obs_pdafomicallback_obs_pdafomi.F90 U_init_dim_obs_pdafomi] 1. [#U_obs_op_pdadfomicallback_obs_pdafomi.F90 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_linit_dim_l_pdaf.F90 U_init_dim_l] 1. [#U_init_dim_obs_l_pdafomiinit_dim_obs_l_pdaf.F90 U_init_dim_obs_l_pdafomi] After the loop over all local analysis domains, it is executed: 1. [#U_prepoststepprepoststep_ens_pdaf.F90 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_statedistribute_state_pdaf.F90 U_distribute_state] 1. [#U_next_observationnext_observation_pdaf.F90 U_next_observation]