Changes between Initial Version and Version 1 of ImplementAnalysisPDAF3UniversalLocal

Timestamp:

May 24, 2025, 5:56:06 PM (11 days ago)

Author:

lnerger

Comment:

--

ImplementAnalysisPDAF3UniversalLocal

@@ +1 @@
+= Implementation of the Analysis Step using the universal interface of PDAF3 with g2l/l2g_state = 
+
+{{{
+#!html
+<div class="wiki-toc">
+<h4>Implementation Guide - Analysis Step</h4>
+<ol><li><a href="ImplementationofAnalysisStep">Implementation of the analysis step</a></li>
+<ol>
+<li>Ensemble filters</li>
+<ol>
+<li> <a href="ImplementFilterAnalysisOverview"> General overview for ensemble filters</a></li>
+<li><a href="ImplementAnalysisPDAF3Universal">Universal interface</a></li>
+<li>Universal interface using g2l/l2g_state</li>
+<li><a href="ImplementAnalysisPDAF3UniversalGlobal">Interface for all global filters</a></li>
+</ol>
+<li> <a href="Implement3DVarAnalysisOverview"> General overview for 3D-Var methods</a></li>
+<ol>
+<li><a href="ImplementAnalysis_3DVar">Implementation for 3D-Var</a></li>
+<li><a href="ImplementAnalysis_3DEnVar">Implementation for 3D Ensemble Var</a></li>
+<li><a href="ImplementAnalysis_Hyb3DVar">Implementation for Hybrid 3D-Var</a></li>
+</ol>
+<li><a href="OMI_nondiagonal_observation_error_covariance_matrices">Using nondiagonal R-matrices</a></li>
+<li><a href="PDAF_OMI_Overview">PDAF-OMI Overview</a></li>
+</ol>
+<li><a href="AddingMemoryandTimingInformation">Memory and timing information</a></li>
+<li><a href="EnsembleGeneration">Ensemble Generation</a></li>
+<li><a href="DataAssimilationDiagnostics">Diagnostics</a></li>
+</ol>
+</div>
+}}}
+
+
+[[PageOutline(2-3,Contents of this page)]]
+
+== Overview ==
+
+This page describes the recommended implementation of the local analysis step using the universal routines of the PDAF3 interface in the variant where the provides routines for transfer between global and local state vectors (g2l_state_pdaf/l2g_state_pdaf) in local filters.
+
+PDAF3 provides universal routines for the analysis step, which only distinguish whether the online or offline 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_local`. 
+
+For completeness we discuss here all user-supplied routines that are specified as arguments in the assimilation routines.
+
+== Assimilation routines ==
+
+=== `PDAF3_assimilate_local` ===
+
+This routine is used both in the ''fully-parallel'' and the ''flexible'' implementation variants of the data assimilation system. (See the page [ModifyModelforEnsembleIntegration 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_gel_state, U_l2g_state, &
+                              U_prepoststep, U_next_observation, status)
+}}}
+with the following arguments:
+* Routines to transfer between model fields and state vector:
+ * [#U_collect_statecollect_state_pdaf.F90 U_collect_state]:[[BR]] 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_init_forecast PDAF_init_forecast] and also here.
+ * [#U_distribute_statedistribute_state_pdaf.F90 U_distribute_state]:[[BR]]  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_pdafomicallback_obs_pdafomi.F90 U_init_dim_obs_pdafomi]:[[BR]] 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]:[[BR]] 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_domainsinit_n_domains_pdaf.F90 U_init_n_domains]:[[BR]] 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]:[[BR]] 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]:[[BR]] 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_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep]:[[BR]] The name of the pre/poststep routine as in `PDAF_init_forecast`
+ * [#U_next_observationnext_observation.F90 U_next_observation]:[[BR]] 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`:[[BR]] 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 [#Executionorderofuser-suppliedroutines 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 [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 `PDAF3_assimilate`, `PDAF3_assim_offline` or `PDAF3_put_state`. 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 [ModifyModelforEnsembleIntegration#collect_state_pdafcollect_state_pdaf.F90 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 [ModifyModelforEnsembleIntegration#distribute_state_pdafdistribute_state_pdaf.F90 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 [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 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_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 [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 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 [wiki:OMI_Callback_obs_pdafomi 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_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 [ModifyModelforEnsembleIntegration#distribute_state_pdafdistribute_state_pdaf.F90 modifying the model code for the ensemble integration] 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 [ModifyModelforEnsembleIntegration#distribute_state_pdafdistribute_state_pdaf.F90 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_statecollect_state_pdaf.F90 U_collect_state] (called once for each ensemble member)
+ 1. [#U_prepoststepprepoststep_ens_pdaf.F90 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_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)
+
+Now the analysis step is entered and the number of local analysis domain is initialized by calling:
+ 1. [#U_init_n_domainsinit_n_domains_pdaf.F90 U_init_n_domains]
+
+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 `PDAF3_assimilate`, 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]