Changes between Version 1 and Version 2 of ImplementAnalysisGlobal
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 Nov 16, 2020, 1:06:20 PM (9 days ago)
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ImplementAnalysisGlobal
v1 v2 1 = Implementation of the Analysis step for the global filters =1 = Implementation of the analysis step for the global filters = 2 2 3 3 {{{ … … 37 37 == Overview == 38 38 39 With Version 1. 8 of PDAF, the ESTKF [Error Subspace Transform Kalman Filter] algorithm has been introduced. The usersupplied routines required for the ESTKF are identical to those required for the SEIK filter and amost identical to those required for the ETKF method.39 With Version 1.16 of PDAF we introduced generic routines for the analysis step, which only distinguish global and local filters. These routines are used with OMI (observation module infrastrucutre, which has been introduced by version 1.16). This page describes the implementation of the analysis step for global filters. 40 40 41 For the analysis step of the ESTKF different operations related to the observations are needed. These operations are requested by PDAF by callback routines supplied by the user. Intentionally, the operations are split into separate routines in order to keep the operations rather elementary and efficient. This procedure should simplify the implementation. The names of the required routines are specified in the call to the routine `PDAF_assimilate_estkf` in the fullyparallel implementation (or `PDAF_put_state_estkf` for the 'flexible' implementation) that was discussed before. With regard to the parallelization, all these routines are executed by the filter processes (`filterpe=.true.`) only.41 For the analysis step of the global filters different operations related to the observations are needed. These operations are requested by PDAF by callback 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 `PDAF_assimilate_global` in the fullyparallel implementation (or `PDAF_put_state_global` for the 'flexible' implementation) that was discussed before. With regard to the parallelization, all these routines are executed by the filter processes (`filterpe=.true.`) only. 42 42 43 For completeness we discuss here all usersupplied routines that are specified in the interface to PDAF_assimilate_ estkf. Thus, some of the usersupplied routines that are explained on the page describing the modification of the model code for the ensemble integration are repeated here.43 For completeness we discuss here all usersupplied routines that are specified in the interface to PDAF_assimilate_global. Thus, some of the usersupplied routines that are explained on the page describing the modification of the model code for the ensemble integration are repeated here. 44 44 45 The ESTKF and the ETKF (Ensemble Transform Kalman Filter) are very similar. For this reason, the interface to the usersupplied 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.46 45 47 == `PDAF_assimilate_ estkf` ==46 == `PDAF_assimilate_global` == 48 47 49 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 subpage on [InsertAnalysisStep inserting the analysis step]. The routine is used in the fullyparallel 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 usersupplied routines specified in the call to `PDAF_assimilate_ estkf` is explained.48 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 subpage on [InsertAnalysisStep inserting the analysis step]. The routine is used in the fullyparallel 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 usersupplied routines specified in the call to `PDAF_assimilate_global` is explained. 50 49 51 The interface when using the ESTKFis the following:50 The interface when using one of the global filters is the following: 52 51 {{{ 53 SUBROUTINE PDAF_assimilate_estkf(U_collect_state, U_distribute_state, U_init_dim_obs, & 54 U_obs_op, U_init_obs, U_prepoststep, U_prodRinvA, & 55 U_init_obsvar, U_next_observation, status) 52 SUBROUTINE PDAF_assimilate_global(U_collect_state, U_distribute_state, U_init_dim_obs, & 53 U_obs_op, U_init_obs, U_prepoststep, U_next_observation, status) 56 54 }}} 57 55 with the following arguments: … … 60 58 * [#U_init_dim_obsinit_dim_obs_pdaf.F90 U_init_dim_obs]: The name of the usersupplied routine that provides the size of observation vector 61 59 * [#U_obs_opobs_op_pdaf.F90 U_obs_op]: The name of the usersupplied routine that acts as the observation operator on some state vector 62 * [#U_init_obsinit_obs_pdaf.F90 U_init_obs]: The name of the usersupplied routine that initializes the vector of observations63 60 * [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep]: The name of the pre/poststep routine as in `PDAF_get_state` 64 * [#U_prodRinvAprodrinva_pdaf.F90 U_prodRinvA]: The name of the usersupplied 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, ETKF, and ESTKF algorithms.65 * [#U_init_obsvarinit_obsvar_pdaf.F90 U_init_obsvar]: The name of the usersupplied routine that provides a mean observation error variance to PDAF (This routine will only be executed, if an adaptive forgetting factor is used)66 61 * [#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`. 67 62 * `status`: The integer status flag. It is zero, if `PDAF_assimilate_estkf` is exited without errors. 68 63 69 64 70 == `PDAF_put_state_ estkf` ==65 == `PDAF_put_state_global` == 71 66 72 When the 'flexible' implementation variant is chosen for the assimilation system, the routine `PDAF_put_state_ estkf` has to be used instead of `PDAF_assimilate_estkf`. 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_estkf` with the exception the specification of the usersupplied routines `U_distribute_state` and `U_next_observation` are missing.67 When the 'flexible' implementation variant is chosen for the assimilation system, the routine `PDAF_put_state_global` has to be used instead of `PDAF_assimilate_global`. 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_global` with the exception the specification of the usersupplied routines `U_distribute_state` and `U_next_observation` are missing. 73 68 74 The interface when using the ESTKFis the following:69 The interface when using one of the global filters is the following: 75 70 {{{ 76 SUBROUTINE PDAF_put_state_ estkf(U_collect_state, U_init_dim_obs, U_obs_op, &77 U_ init_obs, U_prepoststep, U_prodRinvA, U_init_obsvar, status)71 SUBROUTINE PDAF_put_state_global(U_collect_state, U_init_dim_obs, & 72 U_obs_op, U_init_obs, U_prepoststep, status) 78 73 }}} 79 74 80 75 == Usersupplied routines == 81 76 82 Here all usersupplied routines are described that are required in the call to `PDAF_assimilate_ estkf`. For some of the generic routines, we link to the page on [ModifyModelforEnsembleIntegration modifying the model code for the ensemble integration].77 Here all usersupplied routines are described that are required in the call to `PDAF_assimilate_global`. For some of the generic routines, we link to the page on [ModifyModelforEnsembleIntegration modifying the model code for the ensemble integration]. 83 78 84 79 To indicate usersupplied 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. … … 140 135 141 136 142 === `U_init_obs` (init_obs_pdaf.F90) ===143 144 This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, ESTKF).145 146 The interface for this routine is:147 {{{148 SUBROUTINE init_obs(step, dim_obs_p, observation_p)149 150 INTEGER, INTENT(in) :: step ! Current time step151 INTEGER, INTENT(in) :: dim_obs_p ! PElocal dimension of obs. vector152 REAL, INTENT(out) :: observation_p(dim_obs_p) ! PElocal observation vector153 }}}154 155 The routine is called during the analysis step.156 It has to provide the vector of observations in `observation_p` for the current time step.157 158 For a model using domain decomposition, the vector of observations that exist on the model subdomain for the calling process has to be initialized.159 160 161 137 === `U_prepoststep` (prepoststep_ens_pdaf.F90) === 162 138 … … 195 171 196 172 197 === `U_prodRinvA` (prodrinva_pdaf.F90) ===198 199 This routine is used by all filter algorithms that use the inverse of the observation error covariance matrix (SEEK, SEIK, ETKF, ESTKF).200 201 The interface for this routine is:202 {{{203 SUBROUTINE prodRinvA(step, dim_obs_p, rank, obs_p, A_p, C_p)204 205 INTEGER, INTENT(in) :: step ! Current time step206 INTEGER, INTENT(in) :: dim_obs_p ! PElocal dimension of obs. vector207 INTEGER, INTENT(in) :: rank ! Rank of initial covariance matrix208 REAL, INTENT(in) :: obs_p(dim_obs_p) ! PElocal vector of observations209 REAL, INTENT(in) :: A_p(dim_obs_p,rank) ! Input matrix from analysis routine210 REAL, INTENT(out) :: C_p(dim_obs_p,rank) ! Output matrix211 }}}212 213 The 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`.214 215 For a model with domain decomposition, `A_p` contains the part of the matrix that resides on the model subdomain of the calling process. The product has to be computed for this subdomain, too.216 217 Hints:218 * The routine does not require that the product is implemented as a real matrixmatrix 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.219 * 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.220 * 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.)221 222 === `U_init_obsvar` (init_obsvar_pdaf.F90) ===223 224 This 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).225 226 The interface for this routine is:227 {{{228 SUBROUTINE init_obsvar(step, dim_obs_p, obs_p, meanvar)229 230 INTEGER, INTENT(in) :: step ! Current time step231 INTEGER, INTENT(in) :: dim_obs_p ! PElocal dimension of observation vector232 REAL, INTENT(in) :: obs_p(dim_obs_p) ! PElocal observation vector233 REAL, INTENT(out) :: meanvar ! Mean observation error variance234 }}}235 236 The routine is called in the global filters during the analysis or237 by the routine that computes an adaptive forgetting factor (PDAF_set_forget).238 The routine has to initialize the mean observation error variance.239 For the global filters this should be the global mean.240 241 Hints:242 * For a model with domaindecomposition one might use the mean variance for the model subdomain 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`).243 * 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.244 245 246 173 === `U_next_observation` (next_observation_pdaf.F90) === 247 174 … … 252 179 == Execution order of usersupplied routines == 253 180 254 For the ESTKF, the usersupplied routines are essentially executed in the order they are listed in the interface to `PDAF_assimilate_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`.181 The usersupplied routines are essentially executed in the order they are listed in the interface to `PDAF_assimilate_global`. The order can be important as some routines can perform preparatory work for later routines. For example, `U_init_dim_obs` prepares an index array that provides the information for executing the observation operator in `U_obs_op`. How this information is initialized is described in the documentation of OMI. 255 182 256 183 Before the analysis step is called the following routine is executed: … … 260 187 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the forecast ensemble, called with negative value of the time step) 261 188 1. [#U_init_dim_obsinit_dim_obs_pdaf.F90 U_init_dim_obs] 262 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (A single call to operate on the ensemble mean state) 263 1. [#U_init_obsinit_obs_pdaf.F90 U_init_obs] 264 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (`dim_ens` calls: one call for each ensemble member) 265 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)) 189 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (multiple calls for each ensemble members) 266 190 1. [#U_prodRinvAprodrinva_pdaf.F90 U_prodRinvA] 267 191 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the analysis ensemble, called with (positive) value of the time step) 268 192 269 In case of the routine `PDAF_assimilate_ estkf`, the following routines are executed after the analysis step:193 In case of the routine `PDAF_assimilate_global`, the following routines are executed after the analysis step: 270 194 1. [#U_distribute_statedistribute_state_pdaf.F90 U_distribute_state] 271 195 1. [#U_next_observationnext_observation_pdaf.F90 U_next_observation]