Changes between Initial Version and Version 1 of ImplementAnalysisestkf


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Jan 22, 2012, 10:38:47 AM (9 years ago)
Author:
lnerger
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  • ImplementAnalysisestkf

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     1= Implementation of the Analysis step for the SEIK filter =
     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>Implementation for SEIK</li>
     14<li><a href="ImplementAnalysislseik">Implementation for LSEIK</a></li>
     15<li><a href="ImplementAnalysisetkf">Implementation for ETKF</a></li>
     16<li><a href="ImplementAnalysisletkf">Implementation for LETKF</a></li>
     17<li><a href="ImplementAnalysisseek">Implementation for SEEK</a></li>
     18<li><a href="ImplementAnalysisenkf">Implementation for EnKF</a></li>
     19<li><a href="ImplementAnalysisestkf">Implementation for ESTKF</a></li>
     20<li><a href="ImplementAnalysislestkf">Implementation for LESTKF</a></li>
     21</ol>
     22<li><a href="AddingMemoryandTimingInformation">Memory and timing information</a></li>
     23</ol>
     24</div>
     25}}}
     26
     27[[PageOutline(2-3,Contents of this page)]]
     28
     29== Overview ==
     30
     31With Version 1.8 of PDAF, the ESTKF [Error Subspace Transform Kalman Filter] algorithm has been introduced. The user-supplied routines required for the ESTKF are identical to those required for the SEIK filter.
     32
     33For the analysis step of the ESTKF different operations related to the observations are needed. These operations are requested by PDAF by call-back routines supplied by the user. 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_estkf` that was discussed before. With regard to the parallelization, all these routines are executed by the filter processes (`filterpe=.true.`) only.
     34
     35For completeness we discuss here all user-supplied routines that are specified in the interface to PDAF_put_state_estkf. 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.
     36
     37The ESTKF and the ETKF (Ensemble Transform Kalman Filter) are very similar. For this reason, the interface to the user-supplied routines is almost identical. Depending on the implementation it can be possible to use identical routines for the ESTKF and the ETKF. Differences are marked in the text below.
     38
     39== `PDAF_put_state_estkf` ==
     40
     41The general espects of the filter specific routines `PDAF_put_state_*` have been described on the page [ModifyModelforEnsembleIntegration Modification of the model code for the ensemble integration]. Here, we list once more the full interface. Subsequently, the full set of user-supplied routines specified in the call to `PDAF_put_state_estkf` is explained.
     42
     43The interface when using the ESTKF is the following:
     44{{{
     45  SUBROUTINE PDAF_put_state_estkf(U_collect_state, U_init_dim_obs, U_obs_op, &
     46                                 U_init_obs, U_prepoststep, U_prodRinvA, U_init_obsvar, status)
     47}}}
     48with the following arguments:
     49 * [#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`
     50 * [#U_init_dim_obsinit_dim_obs_pdaf.F90 U_init_dim_obs]: The name of the user-supplied routine that provides the size of observation vector
     51 * [#U_obs_opobs_op_pdaf.F90 U_obs_op]: The name of the user-supplied routine that acts as the observation operator on some state vector
     52 * [#U_init_obsinit_obs_pdaf.F90 U_init_obs]: The name of the user-supplied routine that initializes the vector of observations
     53 * [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep]: The name of the pre/poststep routine as in `PDAF_get_state`
     54 * [#U_prodRinvAprodrinva_pdaf.F90 U_prodRinvA]: The name of the user-supplied routine that computes the product of the inverse of the observation error covariance matrix with some matrix provided to the routine by PDAF. This operation occurs during the analysis step of the SEIK filter.
     55 * [#U_init_obsvarinit_obsvar_pdaf.F90 U_init_obsvar]: The name of the user-supplied routine that provides a mean observation error variance to PDAF (This routine will only be executed, if an adaptive forgetting factor is used)
     56 * `status`: The integer status flag. It is zero, if `PDAF_put_state_estkf` is exited without errors.
     57
     58
     59== User-supplied routines ==
     60
     61Here all user-supplied routines are described that are required in the call to `PDAF_put_state_estkf`. For some of the generic routines, we link to the page on [ModifyModelforEnsembleIntegration modifying the model code for the ensemble integration].
     62
     63To 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.
     64
     65In 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.
     66
     67
     68=== `U_collect_state` (collect_state_pdaf.F90) ===
     69
     70This routine is independent of the filter algorithm used.
     71See the page [ModifyModelforEnsembleIntegration#U_collect_statecollect_state.F90 modifying the model code for the ensemble integration] for the description of this routine.
     72
     73
     74=== `U_init_dim_obs` (init_dim_obs_pdaf.F90) ===
     75
     76This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, ESTKF).
     77
     78The interface for this routine is:
     79{{{
     80SUBROUTINE init_dim_obs(step, dim_obs_p)
     81
     82  INTEGER, INTENT(in)  :: step       ! Current time step
     83  INTEGER, INTENT(out) :: dim_obs_p  ! Dimension of observation vector
     84}}}
     85
     86The 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.
     87
     88Some hints:
     89 * It can be useful to not only determine the size of the observation vector at this point. One can also already gather information about the locations of the observations, which will be used later, e.g. to implement the observation operator. An array for the locations can be defined in a module like `mod_assimilation` of the example implementation.
     90
     91
     92=== `U_obs_op` (obs_op_pdaf.F90) ===
     93
     94This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, ESTKF).
     95
     96The interface for this routine is:
     97{{{
     98SUBROUTINE obs_op(step, dim_p, dim_obs_p, state_p, m_state_p)
     99
     100  INTEGER, INTENT(in) :: step               ! Currrent time step
     101  INTEGER, INTENT(in) :: dim_p              ! PE-local dimension of state
     102  INTEGER, INTENT(in) :: dim_obs_p          ! Dimension of observed state
     103  REAL, INTENT(in)    :: state_p(dim_p)     ! PE-local model state
     104  REAL, INTENT(out) :: m_state_p(dim_obs_p) ! PE-local observed state
     105}}}
     106
     107The 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`.
     108
     109For 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.
     110
     111Hint:
     112 * If the observation operator involves a global operation, e.g. some global integration, while using domain-decomposition one has to gather the information from the other model domains using MPI communication.
     113
     114
     115=== `U_init_obs` (init_obs_pdaf.F90) ===
     116
     117This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, ESTKF).
     118
     119The interface for this routine is:
     120{{{
     121SUBROUTINE init_obs(step, dim_obs_p, observation_p)
     122
     123  INTEGER, INTENT(in) :: step             ! Current time step
     124  INTEGER, INTENT(in) :: dim_obs_p        ! PE-local dimension of obs. vector
     125  REAL, INTENT(out)   :: observation_p(dim_obs_p) ! PE-local observation vector
     126}}}
     127
     128The routine is called during the analysis step.
     129It has to provide the vector of observations in `observation_p` for the current time step.
     130
     131For a model using domain decomposition, the vector of observations that exist on the model sub-domain for the calling process has to be initialized.
     132
     133
     134=== `U_prepoststep` (prepoststep_ens_pdaf.F90) ===
     135
     136The routine has already been described on the [ModifyModelforEnsembleIntegration#U_prepoststepprepoststep_ens_pdaf.F90 page on modifying the model code for the ensemble integration]. For completeness, the description is repeated:
     137
     138The interface of the routine is identical for all filters. However, the particular operations that are performed in the routine can be specific for each filter algorithm. Here, we exemplify the interface on the example of the SEIK filter.
     139
     140The interface for this routine is
     141{{{
     142SUBROUTINE prepoststep(step, dim_p, dim_ens, dim_ens_p, dim_obs_p, &
     143                       state_p, Uinv, ens_p, flag)
     144
     145  INTEGER, INTENT(in) :: step        ! Current time step
     146                         ! (When the routine is called before the analysis -step is provided.)
     147  INTEGER, INTENT(in) :: dim_p       ! PE-local state dimension
     148  INTEGER, INTENT(in) :: dim_ens     ! Size of state ensemble
     149  INTEGER, INTENT(in) :: dim_ens_p   ! PE-local size of ensemble
     150  INTEGER, INTENT(in) :: dim_obs_p   ! PE-local dimension of observation vector
     151  REAL, INTENT(inout) :: state_p(dim_p) ! PE-local forecast/analysis state
     152                                     ! The array 'state_p' is not generally not initialized in the case of SEIK/EnKF/ETKF.
     153                                     ! It can be used freely in this routine.
     154  REAL, INTENT(inout) :: Uinv(dim_ens-1, dim_ens-1) ! Inverse of matrix U
     155  REAL, INTENT(inout) :: ens_p(dim_p, dim_ens)      ! PE-local state ensemble
     156  INTEGER, INTENT(in) :: flag        ! PDAF status flag
     157}}}
     158
     159The 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`).
     160
     161The 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.
     162
     163Hint:
     164 * If a user considers to perform adjustments to the estimates (e.g. for balances), this routine is the right place for it.
     165 * 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`.
     166 * The interface has a difference for ETKF and SEIK: For the ETKF, the array `Uinv` has size `dim_ens` x `dim_ens`. In contrast it has size `dim_ens-1` x `dim_ens-1` for the SEIK filter. (For most cases, this will be irrelevant, because most usually the ensemble array `ens_p` is used for computations, rather than `Uinv`. However, for the SEIK filter with fixed covariance matrix, `Uinv` is required to compute the estimate analysis error. The fixed covariance matrix mode is not available for the ETKF)
     167
     168
     169=== `U_prodRinvA` (prodrinva_pdaf.F90) ===
     170
     171This routine is used by all filter algorithms that use the inverse of the observation error covariance matrix (SEEK, SEIK, ETKF, ESTKF).
     172
     173The interface for this routine is:
     174{{{
     175SUBROUTINE prodRinvA(step, dim_obs_p, rank, obs_p, A_p, C_p)
     176
     177  INTEGER, INTENT(in) :: step                ! Current time step
     178  INTEGER, INTENT(in) :: dim_obs_p           ! PE-local dimension of obs. vector
     179  INTEGER, INTENT(in) :: rank                ! Rank of initial covariance matrix
     180  REAL, INTENT(in)    :: obs_p(dim_obs_p)    ! PE-local vector of observations
     181  REAL, INTENT(in)    :: A_p(dim_obs_p,rank) ! Input matrix from analysis routine
     182  REAL, INTENT(out)   :: C_p(dim_obs_p,rank) ! Output matrix
     183}}}
     184
     185The routine is called during the analysis step. In the algorithms the product of the inverse of the observation error covariance matrix with some matrix has to be computed. For the ESTKF this matrix holds the observed part of the ensemble perturbations. The matrix is provided as `A_p`. The product has to be given as `C_p`.
     186
     187For a model with domain decomposition, `A_p` contains the part of the matrix that resides on the model sub-domain of the calling process. The product has to be computed for this sub-domain, too.
     188
     189Hints:
     190 * The routine does not require that the product is implemented as a real matrix-matrix product. Rather, the product can be implemented in its most efficient form. For example, if the observation error covariance matrix is diagonal, only the multiplication of the diagonal with matrix `A_p` has to be implemented.
     191 * The observation vector `obs_p` is provided through the interface for cases where the observation error variance is relative to the actual value of the observations.
     192 * The interface has a difference for ESTKF and ETKF: For ETKF the third argument is the ensemble size (`dim_ens`), while for the ESTKF it is the rank (`rank`) of the covariance matrix (usually ensemble size minus one). In addition, the second dimension of `A_p` and `C_p` has size `dim_ens` for ETKF, while it is `rank` for the ESTKF.  (Practically, one can usually ignore this difference as the fourth argument of the interface can be named arbitrarily in the routine.)
     193
     194=== `U_init_obsvar` (init_obsvar_pdaf.F90) ===
     195
     196This routine is used by the global filter algorithms SEIK, ETKF, and ESTKF as well as the local filters LSEIK, LETKF, ad LESTKF. The routine is only called if the adaptive forgetting factor is used (`type_forget=1` in the example impementation).
     197
     198The interface for this routine is:
     199{{{
     200SUBROUTINE init_obsvar(step, dim_obs_p, obs_p, meanvar)
     201
     202  INTEGER, INTENT(in) :: step          ! Current time step
     203  INTEGER, INTENT(in) :: dim_obs_p     ! PE-local dimension of observation vector
     204  REAL, INTENT(in) :: obs_p(dim_obs_p) ! PE-local observation vector
     205  REAL, INTENT(out)   :: meanvar       ! Mean observation error variance
     206}}}
     207
     208The routine is called in the global filters during the analysis or
     209by the routine that computes an adaptive forgetting factor (PDAF_set_forget).
     210The routine has to initialize the mean observation error variance. 
     211For the global filters this should be the global mean.
     212
     213Hints:
     214 * For a model with domain-decomposition one might use the mean variance for the model sub-domain of the calling process. Alternatively one can compute a mean variance for the full model domain using MPI communication (e.g. the function `MPI_allreduce`).
     215 * The observation vector `obs_p` is provided to the routine for the case that the observation error variance is relative to the value of the observations.
     216
     217
     218== Execution order of user-supplied routines ==
     219
     220For the ESTKF, the user-supplied routines are essentially executed in the order they are listed in the interface to `PDAF_put_state_estkf`. 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`.
     221
     222Before the analysis step is called the following routine is executed:
     223 1. [#U_collect_statecollect_state_pdaf.F90 U_collect_state]
     224
     225The 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:
     226 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the forecast ensemble, called with negative value of the time step)
     227 1. [#U_init_dim_obsinit_dim_obs_pdaf.F90 U_init_dim_obs]
     228 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (A single call to operate on the ensemble mean state)
     229 1. [#U_init_obsinit_obs_pdaf.F90 U_init_obs]
     230 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (`dim_ens` calls: one call for each ensemble member)
     231 1. [#U_init_obsvarinit_obsvar_pdaf.F90 U_init_obsvar] (Only executed, if the adaptive forgetting factor is used (`type_forget=1` in the example implemention))
     232 1. [#U_prodRinvAprodrinva_pdaf.F90 U_prodRinvA]
     233 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the analysis ensemble, called with (positive) value of the time step)
     234