Changes between Initial Version and Version 1 of ImplementAnalysislenkfOmi


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Timestamp:
Nov 16, 2020, 3:38:55 PM (2 years ago)
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lnerger
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  • ImplementAnalysislenkfOmi

    v1 v1  
     1= Implementation of the Analysis step for the LEnKF (Localized Ensemble Kalman Filter) with OMI =
     2
     3{{{
     4#!html
     5<div class="wiki-toc">
     6<h4>Implementation Guide</h4>
     7<ol><li><a href="ImplementationGuide">Main page</a></li>
     8<li><a href="AdaptParallelization">Adaptation of the parallelization</a></li>
     9<li><a href="InitPdaf">Initialization of PDAF</a></li>
     10<li><a href="ModifyModelforEnsembleIntegration">Modifications for ensemble integration</a></li>
     11<li><a href="ImplementationofAnalysisStep">Implementation of the analysis step</a></li>
     12<ol>
     13<li><a href="ImplementAnalysisGlobal">Implementation for Global Filters</li>
     14<li><a href="ImplementAnalysisLocal">Implementation for Local Filters</a></li>
     15<li>Implementation for LEnKF</li>
     16</ol>
     17<li><a href="AddingMemoryandTimingInformation">Memory and timing information</a></li>
     18<li><a href="EnsembleGeneration">Ensemble Generation</a></li>
     19<li><a href="DataAssimilationDiagnostics">Diagnostics</a></li>
     20</ol>
     21</div>
     22}}}
     23
     24[[PageOutline(2-3,Contents of this page)]]
     25
     26With Version 1.16 of PDAF we introduced PDAF-OMI (observation module infrastructure). With OMI, a smaller number of routines needs to be supplied by the user than in the previous implementation approach.
     27
     28== Overview ==
     29
     30For the analysis step of the LEnKF different operations related to the observations are needed. These operations are requested by PDAF by calling user-supplied routines. Intentionally, the operations are split into separate routines in order to keep the operations rather elementary. This procedure should simplify the implementation. The names of the required routines are specified in the call to the routine `PDAF_put_state_lenkf_omi` for the fully-parallel implementation (or `PDAF_put_state_lenkf_omi` for the 'flexible' implementation). With regard to the parallelization, all these routines are executed by the filter processes (`filterpe=.true.`) only.
     31
     32For completeness we discuss here all user-supplied routines that are specified in the interface to `PDAF_put_state_lenkf_omi`. Thus, some of the user-supplied routines that are explained on the page explaining the modification of the model code for the ensemble integration are repeated here.
     33
     34The LEnKF implemented in PDAF follows the original LEnKF by Evensen (1994) including the correction for perturbed observations (Burgers et al. 1998). The LEnKF implemented in PDAF is reviewed by Nerger et al (2005) and described in more detail by Nerger (2004). The localization is covariance lozalization of PH^T and HPH^T as described in Houtekamer & Mitchell (2001) (See the [PublicationsandPresentations page on publications and presentations] for publications and presenations involving and about PDAF)
     35
     36In our studies (Nerger et al. 2005, Nerger et al. 2007), the EnKF showed performance deficiencies compared to the SEIK filter. Due to this, we focused more on the SEIK filter and the ETKF and ESTKF after these comparison studies. For real applications, we generally recommend using ESTKF or ETKF, or their local variants LESTKF or LETKF. However, the EnKF/LEnKF might have a good performance if very large ensemble can be used as this reduces the sampling errors.
     37
     38== `PDAF_assimilate_lenkf_omi` ==
     39
     40The 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. Here, we list once more the full interface of the routine. Subsequently, the full set of user-supplied routines specified in the call to `PDAF_assimilate_lenkf_omi` is explained.
     41
     42The interface when using the LEnKF is the following:
     43{{{
     44  SUBROUTINE PDAF_assimilate_lenkf_omi(U_collect_state, U_distribute_state, &
     45                                 U_init_dim_obs, U_obs_op, &
     46                                 U_prepoststep, U_localize, &
     47                                 U_next_observation, status)
     48}}}
     49with the following arguments:
     50 * [#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 `PDAF_get_state` as well as here.
     51 * [#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.
     52 * [#U_init_dim_obscallback_obs_pdafomi.F90 U_init_dim_obs]: The name of the user-supplied routine that provides the size of observation vector
     53 * [#U_obs_opcallback_obs_pdafomi.F90 U_obs_op]: The name of the user-supplied routine that acts as the observation operator on some state vector
     54 * [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep]: The name of the pre/poststep routine as in `PDAF_get_state`
     55 * [#U_localizecallback_obs_pdafomi.F90 U_localize]: Apply covariance localization to the matrices HP and HPH^T^
     56 * [#U_next_observationnext_observation_pdaf.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`.
     57 * `status`: The integer status flag. It is zero, if `PDAF_assimilate_lenkf_omi` is exited without errors.
     58
     59== `PDAF_put_state_lenkf_omi` ==
     60
     61When the 'flexible' implementation variant is chosen for the assimilation system, the routine `PDAF_put_state_lenkf_omi` has to be used instead of `PDAF_assimilate_lenkf_omi`. 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 `PDAF_assimilate_lenkf_omi` with the exception the specification of the user-supplied routines `U_distribute_state` and `U_next_observation` are missing.
     62
     63The interface when using the LEnKF is the following:
     64{{{
     65  SUBROUTINE PDAF_put_state_lenkf_omi(U_collect_state, &
     66                                 U_init_dim_obs, U_obs_op, &
     67                                 U_prepoststep, U_localize, &
     68                                 status)
     69}}}
     70
     71
     72== User-supplied routines ==
     73
     74Here all user-supplied routines are described that are required in the call to `PDAF_assimilate_lenkf_omi`. For some of the generic routines, we link to the page on [ModifyModelforEnsembleIntegration modifying the model code for the ensemble integration].
     75
     76To indicate user-supplied routines we use the prefix `U_`. In the template directory `templates/` as well as in the example implementation in `testsuite/src/dummymodel_1D` 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.
     77
     78In 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.
     79
     80
     81=== `U_collect_state` (collect_state_pdaf.F90) ===
     82
     83This routine is independent of the filter algorithm used.
     84See the page on [InsertAnalysisStep#U_collect_statecollect_state_pdaf.F90 inserting the analysis step] for the description of this routine.
     85
     86
     87=== `U_distribute_state` (distribute_state_pdaf.F90) ===
     88
     89This routine is independent of the filter algorithm used.
     90See the page on [InsertAnalysisStep#U_distribute_statedistribute_state_pdaf.F90 inserting the analysis step] for the description of this routine.
     91
     92
     93=== `U_init_dim_obs` (callback_obs_pdafomi.F90) ===
     94
     95This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, NETF, PF) and by the LEnKF.
     96
     97The interface for this routine is:
     98{{{
     99SUBROUTINE init_dim_obs_pdafomi(step, dim_obs_p)
     100
     101  INTEGER, INTENT(in)  :: step       ! Current time step
     102  INTEGER, INTENT(out) :: dim_obs_p  ! Dimension of observation vector
     103}}}
     104
     105The routine is called at the beginning of each analysis step.  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.
     106
     107With PDAF-OMI, the routine just calls a routine from the observation module for each observation type.
     108
     109
     110=== `U_obs_op` (calllback_obs_pdafomi.F90) ===
     111
     112This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, NETF, PF) and the LEnKF.
     113
     114The interface for this routine is:
     115{{{
     116SUBROUTINE obs_op_pdafomi(step, dim_p, dim_obs_p, state_p, m_state_p)
     117
     118  INTEGER, INTENT(in) :: step               ! Currrent time step
     119  INTEGER, INTENT(in) :: dim_p              ! PE-local dimension of state
     120  INTEGER, INTENT(in) :: dim_obs_p          ! Dimension of observed state
     121  REAL, INTENT(in)    :: state_p(dim_p)     ! PE-local model state
     122  REAL, INTENT(out) :: m_state_p(dim_obs_p) ! PE-local observed state
     123}}}
     124
     125The 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`.
     126
     127For 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.
     128
     129With PDAF-OMI, the routine just calls a routine from the observation module for each observation type.
     130
     131
     132=== `U_prepoststep` (prepoststep_ens_pdaf.F90) ===
     133
     134The general aspects of this routines have already been described on the [ModifyModelforEnsembleIntegration#U_prepoststepprepoststep_ens_pdaf.F90 page on modifying the model code for the ensemble integration] for the SEIK filter. For completeness, the description is repeated specifically for the EnKF:
     135
     136The interface of the routine is identical for all filters, but sizes can vary. Also, the particular operations that are performed in the routine can be specific for each filter algorithm.
     137
     138The interface for this routine is for the LEnKF
     139{{{
     140SUBROUTINE prepoststep(step, dim_p, dim_ens, dim_ens_p, dim_obs_p, &
     141                       state_p, Uinv, ens_p, flag)
     142
     143  INTEGER, INTENT(in) :: step        ! Current time step
     144                         ! (When the routine is called before the analysis -step is provided.)
     145  INTEGER, INTENT(in) :: dim_p       ! PE-local state dimension
     146  INTEGER, INTENT(in) :: dim_ens     ! Size of state ensemble
     147  INTEGER, INTENT(in) :: dim_ens_p   ! PE-local size of ensemble
     148  INTEGER, INTENT(in) :: dim_obs_p   ! PE-local dimension of observation vector
     149  REAL, INTENT(inout) :: state_p(dim_p) ! PE-local forecast/analysis state
     150                                     ! The array 'state_p' is not generally not initialized in the case of SEIK/EnKF/ETKF.
     151                                     ! It can be used freely in this routine.
     152  REAL, INTENT(inout) :: Uinv(1, 1)  ! Not used not LEnKF
     153  REAL, INTENT(inout) :: ens_p(dim_p, dim_ens)      ! PE-local state ensemble
     154  INTEGER, INTENT(in) :: flag        ! PDAF status flag
     155}}}
     156
     157The 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`).
     158
     159The 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.
     160
     161Hint:
     162 * If a user considers to perform adjustments to the estimates (e.g. for balances), this routine is the right place for it.
     163 * 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`.
     164 * The array `Uinv` is not used in the EnKF. Internally to PDAF, it is allocated to be of size (1,1).
     165 * Apart from the size of the array `Uinv`, the interface is identical for all ensemble filters (SEIK/ETKF/EnKF/LSEIK/LETKF/LEnKF). In general it should be possible to use an identical pre/poststep routine for all these filters.
     166 * 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 [AuxiliaryRoutines auxiliary routines])
     167
     168
     169
     170=== `U_localize` (callback_obs_pdafomi.F90) ===
     171
     172This routine is only used for the LEnKF.
     173
     174The interface for this routine is:
     175{{{
     176SUBROUTINE localize_covar_pdafomi(dim_p, dim_obs, HP, HPH)
     177
     178  INTEGER, INTENT(in) :: dim_p                 ! PE-local state dimension
     179  INTEGER, INTENT(in) :: dim_obs               ! Dimension of global observation vector
     180  REAL, INTENT(inout) :: HP(dim_obs, dim_p)    ! Matrix HP
     181  REAL, INTENT(inout) :: HPH(dim_obs, dim_obs) ! Matrix HPH^T^
     182}}}
     183
     184The routine is called during the analysis step and has to apply the element-wise Schur product for the covariance localization of the two matrices'''HP''' and '''HPH^T^''', which are provided as input/output arguments.
     185
     186With PDAF-OMI, the routine just calls a routine provided by PDAF-OMI.
     187
     188
     189=== `U_next_observation` (next_observation_pdaf.F90) ===
     190
     191This routine is independent of the filter algorithm used.
     192See the page on [InsertAnalysisStep#U_next_observationnext_observation_pdaf.F90 inserting the analysis step] for the description of this routine.
     193
     194
     195
     196== Execution order of user-supplied routines ==
     197
     198For the :EnKF, the user-supplied routines are essentially executed in the order they are listed in the interface to `PDAF_assimilate_lenkf_omi`. The order can be important as some routines can perform preparatory work for later routines. For example, `U_init_dim_obs` can prepare an index array that provides the information for executing the observation operator in `U_obs_op`.
     199
     200Before the analysis step is called the following routine is executed:
     201 1. [#U_collect_statecollect_state_pdaf.F90 U_collect_state]
     202
     203The 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:
     204 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the forecast ensemble, called with negative value of the time step)
     205 1. [#U_init_dim_obsinit_dim_obs_pdaf.F90 U_init_dim_obs]
     206 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (`dim_ens` calls: one call for each ensemble member)
     207 1. [#U_localizelocalize_covar_pdaf.F90 U_localize]
     208 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (`dim_ens` calls: one call for each ensemble member, repeated to reduce storage)
     209 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the analysis ensemble, called with (positive) value of the time step)
     210
     211In case of the routine `PDAF_assimilate_enkf_omi`, the following routines are executed after the analysis step:
     212 1. [#U_distribute_statedistribute_state_pdaf.F90 U_distribute_state]
     213 1. [#U_next_observationnext_observation_pdaf.F90 U_next_observation]