| 36 | | This page describes the recommended implementation of the analysis step for the hybrid 3D-Var schemes using the PDAF3 interface of. |
| 37 | | |
| 38 | | || The interface for hybrid 3D-Var using the localized LESTKF for the transformation is the universal interface. If one intends to implement particularly for the variant using the global filter ESTKF, there is a separate interface for this special case. || |
| 39 | | |
| 40 | | For the analysis step of 3D-Var 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 assimilation routines. With regard to the parallelization, all these routines (except `collect_state_pdaf`, `distribute_state_pdaf`, and `next_observation_pdaf`) are executed by the filter processes (`filterpe=.true.`) only. |
| | 35 | This page describes the recommended implementation of the analysis step for the parameterized 3D-Var using the particular interface routines. |
| | 36 | |
| | 37 | || |
| | 38 | |
| | 39 | There are genenerally three different variants of 3D-Var provided by PDAF: parameterized 3D-Var, 3D Ensemble Var, and hybrid (parameterized + ensemble) 3D-Var. All can be called using the universal interface routines described here. |
| | 40 | |
| | 41 | For the analysis step of 3D-Var 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 `PDAF3_assimilate_3dvar_all` in the online mode of PDAF or `PDAF3_assim_offline_3dvar_all` for the offline mode. With regard to the parallelization, all these routines (except `collect_state_pdaf`, `distribute_state_pdaf`, and `next_observation_pdaf`) are executed by the filter processes (`filterpe=.true.`) only. |
| | 42 | |
| | 43 | The universal interface has more arguments than the specific interfaces for the parameterized 3D-Var or the 3D ensemble Var methods. It is useful if one implements both the 3D-Var with parameterized covariances and rhe 3D ensemble Var. The hybrid 3D-Var using the LESTKF is always called using this unversal interface. |
| 46 | | |
| 47 | | == Analysis Routines == |
| 48 | | |
| 49 | | The general aspects of the filter (or solver) specific routines `PDAF_assimilate_*` have been described on the page [OnlineModifyModelforEnsembleIntegration_PDAF3 Modification of the model code for the ensemble integration]. Here, we list the full interface of the routine. Subsequently, the user-supplied routines specified in the call is explained. |
| 50 | | |
| 51 | | There are two variants that either compute the transformataion of the ensemble transformation using the local LESTKF method, or the global ESTKF. |
| 52 | | |
| 53 | | === `PDAF3_assimilate_3dvar_all` === |
| 54 | | |
| 55 | | This universal routine can be used for the hybrid 3D-Var in both variants, using the local LESTKF or the global ESTKF for the transformation of the ensemble perturbations. |
| 56 | | |
| 57 | | 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) |
| 58 | | |
| 59 | | The interface is: |
| 60 | | {{{ |
| 61 | | SUBROUTINE PDAF3_assimilate_3dvar_all(collect_state_pdaf, distribute_state_pdaf, & |
| | 49 | == `PDAFomi_assimilate_3dvar` == |
| | 50 | |
| | 51 | This routine is used both in the ''fully-parallel'' and the ''flexible'' implementation variants of the data assimilation system. (See the page [OnlineModifyModelforEnsembleIntegration_PDAF3 Modification of the model code for the ensemble integration] for these variants) |
| | 52 | |
| | 53 | The interface for using the parameterized 3D-Var is: |
| | 54 | {{{ |
| | 55 | SUBROUTINE PDAF3_assimilate_3dvar(collect_state_pdaf, distribute_state_pdaf, & |
| 86 | | === `PDAF3_assim_offline_3dvar_all` === |
| 87 | | |
| 88 | | For the offline mode of PDAF, the routine `PDAF3_assim_offline_3dvar_all` is used to perform the analysis step. |
| 89 | | The interface of the routine is identical with that of `PDAF3_assimilate_3dvar_all`, except that the user-supplied routines `U_distribute_state`, `U_collect_state` and `U_next_observation` are missing. |
| 90 | | |
| 91 | | The interface when using one of the global filters is the following: |
| 92 | | {{{ |
| 93 | | SUBROUTINE PDAF3_assim_offline_3dvar_all(& |
| 94 | | U_init_dim_obs_pdafomi, U_obs_op_pdafomi, & |
| 95 | | U_cvt_ens, U_cvt_adj_ens, U_cvt, U_cvt_adj, & |
| 96 | | U_obs_op_lin_pdafomi, U_obs_op_adj_pdafomi, & |
| 97 | | U_init_n_domains_p, U_init_dim_l, U_init_dim_obs_l_pdafomi, & |
| 98 | | U_prepoststep, outflag) |
| 99 | | }}} |
| 100 | | |
| 101 | | === `PDAF3_put_state_3dvar_all` === |
| 102 | | |
| 103 | | 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. |
| 104 | | When the 'flexible' implementation variant is chosen for the assimilation system, the routine. The routine `PDAF3_put_state_3dvar_all` allows to port such implemnetations to the PDAF3 interface with minimal changes. |
| 105 | | The interface of the routine is identical with that of `PDAF3_assimilate_3dvar_all`, except that the user-supplied routines `U_distribute_state` and `U_next_observation` are missing. |
| 106 | | |
| 107 | | The interface when using one of the global filters is the following: |
| 108 | | {{{ |
| 109 | | SUBROUTINE PDAF3_put_state_3dvar_all(U_collect_state, & |
| 110 | | U_init_dim_obs_pdafomi, U_obs_op_pdafomi, & |
| 111 | | U_cvt_ens, U_cvt_adj_ens, U_cvt, U_cvt_adj, & |
| 112 | | U_obs_op_lin_pdafomi, U_obs_op_adj_pdafomi, & |
| 113 | | U_init_n_domains_p, U_init_dim_l, U_init_dim_obs_l_pdafomi, & |
| 114 | | U_prepoststep, outflag) |
| 115 | | }}} |
| 116 | | |
| 117 | | |
| 118 | | == Analysis Routines specific for using global ESTKF == |
| 119 | | |
| 120 | | === `PDAF3_assimilate_hyb3dvar_estkf` === |
| 121 | | |
| 122 | | This routine is particular for the ESTKF. One can use it if one exclusively uses the global filter. In the argument list of this routine, the call-back routine for localization are not present and hence the argument list is shorter than that of `PDAF3_assimilate_3dvar_all`. |
| 123 | | |
| 124 | | 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) |
| | 74 | |
| | 75 | == `PDAF3_assim_offline_3dvar` == |
| | 76 | |
| | 77 | This routine is used to perform the analysi step for the offline mode of PDAF. |
| | 78 | The interface of the routine is identical with that of `PDAF3_assimilate_3dvar`, except that the user-supplied routines `U_distribute_state`, `U_collect_state` and `U_next_observation` are missing. |
| 134 | | where all arguments, except the last one, are the names of call-back routines. See the description of the arguments for `PDAF3_assimilate_3dvar_all`. |
| 135 | | |
| 136 | | |
| 137 | | |
| 138 | | === `PDAF3_assim_offline_hyb3dvar_estkf` === |
| 139 | | |
| 140 | | This routine is particular for the ESTKF. One can use it if one exclusively uses the global filter. In the argument list of this routine, the call-back routine for localization are not present and hence the argument list is shorter than that of `PDAF3_assim_offline_3dvar_all`. |
| 141 | | |
| 142 | | This routine is used to perform the analysis step for the offline mode. |
| 143 | | The interface of the routine is identical with that of `PDAF3_assimilate_hyb3dvar_estkf`, except that the user-supplied routines `U_distribute_state`, `U_collect_state` and `U_next_observation` are missing. |
| | 88 | |
| | 89 | |
| | 90 | == `PDAF3_put_state_3dvar` == |
| | 91 | |
| | 92 | 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. |
| | 93 | When the 'flexible' implementation variant is chosen for the assimilation system, the routine. This routine allows to port such implementations to the PDAF3 interface with minimal changes. |
| | 94 | The interface of the routine is identical with that of `PDAF3_assimilate_3dvar`, except that the user-supplied routines `U_distribute_state` and `U_next_observation` are missing. |
| 151 | | prepoststep_pdaf, outflag) |
| 152 | | }}} |
| 153 | | where all arguments, except the last one, are the names of call-back routines. See the description of the arguments for `PDAF3_assimilate_3dvar_all`. |
| 154 | | |
| 155 | | |
| 156 | | |
| 157 | | === `PDAF3_put_state_hyb3dvar_estkf` === |
| 158 | | |
| 159 | | 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. |
| 160 | | When the 'flexible' implementation variant is chosen for the assimilation system, the routine. The routine `PDAF3_put_state_hyb3dvar_estkf` allows to port such implemnetations to the PDAF3 interface with minimal changes. |
| 161 | | The interface of the routine is identical with that of `PDAF3_assimilate_hyb3dvar_estkf`, except that the user-supplied routines `U_distribute_state` and `U_next_observation` are missing. |
| 162 | | |
| 163 | | This routine is particular for the ESTKF. One can use it if one exclusively uses the global filter. In the argument list of this routine, the call-back routine for localization are not present and hence the argument list is shorter than that of `PDAF3_put_state_3dvar_all`. |
| 164 | | |
| 165 | | The interface is: |
| 166 | | {{{ |
| 167 | | SUBROUTINE PDAF3_assimilate_hyb3dvar_estkf(collect_state_pdaf, & |
| 168 | | init_dim_obs_pdafomi, obs_op_pdafomi, & |
| 169 | | cvt_ens_pdaf, cvt_adj_ens_pdaf, cvt_pdaf, cvt_adj_pdaf, & |
| 170 | | obs_op_lin_pdafomi, obs_op_adj_pdafomi, & |
| 171 | | prepoststep_pdaf, outflag) |
| 172 | | }}} |
| 173 | | where all arguments, except the last one, are the names of call-back routines. See the description of the arguments for `PDAF3_assimilate_3dvar_all`. |
| 174 | | |
| 175 | | |
| 176 | | |
| | 103 | prepoststep_pdaf, next_observation_pdaf, outflag) |
| | 104 | }}} |
| 197 | | 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. |
| 198 | | |
| 199 | | |
| 200 | | |
| 201 | | === `init_dim_obs_pdafomi` (callback_obs_pdafomi.F90) === |
| 202 | | |
| 203 | | This is a call-back routine initializing the observation information. The routine just calls a routine from the observation module for each observation type. |
| 204 | | |
| 205 | | See the [wiki:OMI_Callback_obs_pdafomi documentation on callback_obs_pdafomi.F90] for more information. |
| 206 | | |
| 207 | | |
| 208 | | |
| 209 | | === `obs_op_pdafomi` (callback_obs_pdafomi.F90) === |
| 210 | | |
| 211 | | 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. |
| 212 | | |
| 213 | | See the [wiki:OMI_Callback_obs_pdafomi documentation on callback_obs_pdafomi.F90] for more information. |
| 214 | | |
| 215 | | |
| 216 | | |
| 217 | | === `cvt_ens_pdaf` (cvt_ens_pdaf.F90) === |
| 218 | | |
| 219 | | The interface for this routine is: |
| 220 | | {{{ |
| 221 | | SUBROUTINE cvt_ens_pdaf(iter, dim_p, dim_ens, dim_cv_ens_p, ens_p, cv_p, Vcv_p) |
| 222 | | |
| 223 | | INTEGER, INTENT(in) :: iter ! Iteration of optimization |
| 224 | | INTEGER, INTENT(in) :: dim_p ! PE-local observation dimension |
| 225 | | INTEGER, INTENT(in) :: dim_ens ! Ensemble size |
| 226 | | INTEGER, INTENT(in) :: dim_cv_ens_p ! Dimension of control vector |
| 227 | | REAL, INTENT(in) :: ens_p(dim_p, dim_ens) ! PE-local ensemble |
| 228 | | REAL, INTENT(in) :: cv_p(dim_cv_ens_p) ! PE-local control vector |
| 229 | | REAL, INTENT(inout) :: Vcv_p(dim_p) ! PE-local state increment |
| 230 | | }}} |
| 231 | | |
| 232 | | The routine is called during the analysis step during the iterative minimization of the cost function. |
| 233 | | It has to apply the control vector transformation to the control vector and return the transformed result vector. Usually this transformation is the multiplication with the square-root of the background error covariance matrix '''B'''. For the 3D Ensemble Var, this square root is usually expressed through the ensemble. |
| 234 | | |
| 235 | | If the control vector is decomposed in case of parallelization it first needs to the gathered on each processor and afterwards the transformation is computed on the potentially domain-decomposed state vector. |
| 236 | | |
| 237 | | |
| 238 | | === `cvt_adj_pdaf` (cvt_adj_pdaf.F90) === |
| 239 | | |
| 240 | | The interface for this routine is: |
| 241 | | {{{ |
| 242 | | SUBROUTINE cvt_adj_ens_pdaf(iter, dim_p, dim_ens, dim_cv_ens_p, ens_p, Vcv_p, cv_p) |
| 243 | | |
| 244 | | INTEGER, INTENT(in) :: iter ! Iteration of optimization |
| 245 | | INTEGER, INTENT(in) :: dim_p ! PE-local observation dimension |
| 246 | | INTEGER, INTENT(in) :: dim_ens ! Ensemble size |
| 247 | | INTEGER, INTENT(in) :: dim_cv_ens_p ! PE-local dimension of control vector |
| 248 | | REAL, INTENT(in) :: ens_p(dim_p, dim_ens) ! PE-local ensemble |
| 249 | | REAL, INTENT(in) :: Vcv_p(dim_p) ! PE-local input vector |
| 250 | | REAL, INTENT(inout) :: cv_p(dim_cv_ens_p) ! PE-local result vector |
| 251 | | }}} |
| 252 | | |
| 253 | | The routine is called during the analysis step during the iterative minimization of the cost function. |
| 254 | | It has to apply the adjoint control vector transformation to a state vector and return the control vector. Usually this transformation is the multiplication with transpose of the square-root of the background error covariance matrix '''B'''. or the 3D Ensemble Var, this square root is usually expressed through the ensemble. |
| 255 | | |
| 256 | | If the state vector is decomposed in case of parallelization one needs to take care that the application of the trasformation is complete. This usually requries a comminucation with MPI_Allreduce to obtain a global sun. |
| 257 | | |
| 258 | | |
| 259 | | |
| 260 | | === `cvt_pdaf` (cvt_pdaf.F90) === |
| | 126 | See the page on [InsertAnalysisStep#U_distribute_statedistribute_state_pdaf.F90 inserting the analysis step] for the description of this routine. |
| | 127 | |
| | 128 | |
| | 129 | === `U_init_dim_obs_pdafomi` (callback_obs_pdafomi.F90) === |
| | 130 | |
| | 131 | 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. |
| | 132 | |
| | 133 | See the [wiki:OMI_Callback_obs_pdafomi documentation on callback_obs_pdafomi.F90] for more information. |
| | 134 | |
| | 135 | |
| | 136 | |
| | 137 | === `U_obs_op_pdafomi` (callback_obs_pdafomi.F90) === |
| | 138 | |
| | 139 | 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. |
| | 140 | |
| | 141 | See the [wiki:OMI_Callback_obs_pdafomi documentation on callback_obs_pdafomi.F90] for more information. |
| | 142 | |
| | 143 | |
| | 144 | |
| | 145 | |
| | 146 | === `U_cvt` (cvt_pdaf.F90) === |
| 314 | | |
| 315 | | === `init_n_domains_pdaf` (init_n_domains_pdaf.F90) === |
| 316 | | |
| 317 | | 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. |
| 318 | | |
| 319 | | The interface for this routine is: |
| 320 | | {{{ |
| 321 | | SUBROUTINE init_n_domains_pdaf(step, n_domains_p) |
| 322 | | |
| 323 | | INTEGER, INTENT(in) :: step ! Current time step |
| 324 | | INTEGER, INTENT(out) :: n_domains_p ! Number of analysis domains for local model sub-domain |
| 325 | | }}} |
| 326 | | |
| 327 | | Hints: |
| 328 | | * 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. |
| 329 | | |
| 330 | | |
| 331 | | === `init_dim_l_pdaf` (init_dim_l_pdaf.F90) === |
| 332 | | |
| 333 | | This routine is only used for localization. |
| 334 | | |
| 335 | | The interface for this routine is: |
| 336 | | {{{ |
| 337 | | SUBROUTINE init_dim_l_pdaf(step, domain_p, dim_l) |
| 338 | | |
| 339 | | INTEGER, INTENT(in) :: step ! Current time step |
| 340 | | INTEGER, INTENT(in) :: domain_p ! Current local analysis domain |
| 341 | | INTEGER, INTENT(out) :: dim_l ! Local state dimension |
| 342 | | }}} |
| 343 | | |
| 344 | | The routine is called during the loop over the local analysis domains in the analysis step. |
| 345 | | |
| 346 | | It provides in `dim_l` the dimension of the state vector for the local analysis domain with index `domain_p` to PDAF. |
| 347 | | |
| 348 | | In the recommended implementation shown in the tutorial and template codes, there are two further initializations: |
| 349 | | 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). |
| 350 | | 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`. |
| 351 | | |
| 352 | | Hints: |
| 353 | | * The coordinates in `coords_l` have to describe one location in space that is used for localization to compute the distance from observations. |
| 354 | | * The coordinates in `coords_l` have the same units as those used for the observations |
| 355 | | * 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. |
| 356 | | * Any form of local domain is possible as long as it can be describe as a single location. |
| 357 | | * If the local domain is a single grid point, `dim_l` will be the number of model variables at this grid point. |
| 358 | | * 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). |
| 359 | | * 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. |
| 360 | | * In this case only the horizontal coordinates are used in `coords_l`. |
| 361 | | |
| 362 | | 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: |
| 363 | | |
| 364 | | {{{ |
| 365 | | SUBROUTINE PDAFlocal_set_indices(dim_l, id_lstate_in_pstate) |
| 366 | | |
| 367 | | INTEGER, INTENT(in) :: dim_l ! Dimension of local state vector |
| 368 | | INTEGER, INTENT(in) :: id_lstate_in_pstate(dim_l) ! Index array for mapping |
| 369 | | }}} |
| 370 | | |
| 371 | | Hint for `id_lstate_in_pstate`: |
| 372 | | * 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. |
| 373 | | * See the [wiki:PDAFlocal_overview PDAFlocal overview page] for more information on the functionality of PDAFlocal. |
| 374 | | |
| 375 | | |
| 376 | | === `init_dim_obs_l_pdafomi` (callback_obs_pdafomi.F90) === |
| 377 | | |
| 378 | | 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. |
| 379 | | |
| 380 | | See the [wiki:OMI_Callback_obs_pdafomi documentation on callback_obs_pdafomi.F90] for more information. |
| 381 | | |
| 382 | | |
| 383 | | === `prepoststep_pdaf` (prepoststep_ens_pdaf.F90) === |
| | 199 | === `U_prepoststep` (prepoststep_ens_pdaf.F90) === |
| 417 | | 1. [#cvt_ens_pdafcvt_pdaf.F90 cvt_pdaf] (Call to the parameterized part of the control vector transform to compute the final state vector increment) |
| 418 | | 1. [#cvt_ens_pdafcvt_ens_pdaf.F90 cvt_ens_pdaf] (Call to the eensemble-part of the control vector transform to compute the final state vector increment) |
| 419 | | 1. [#prepoststep_pdafprepoststep_ens_pdaf.F90 prepoststep_pdaf] (Call to act on the analysis ensemble, called with (positive) value of the time step) |
| 420 | | |
| 421 | | The iterative optimization abovve computes an updated ensemble mean state. Subsequently, the ensemble perturbations are updated using the LESTKF or ESTKF. The execution of the routines for these filters is described on the [wiki:ImplementAnalysisPDAF3Universal page on implementing the local filter analysis step] . |
| 422 | | |
| 423 | | In case of the routine `PDAF3_assimilate_3dvar_all`, the following routines are executed after the analysis step: |
| 424 | | 1. [#distribute_state_pdafdistribute_state_pdaf.F90 distribute_state_pdaf] |
| 425 | | 1. [#next_observation_pdafnext_observation_pdaf.F90 next_observation_pdaf] |
| | 232 | 1. [#U_cvtcvt_pdaf.F90 U_cvt] (Call to the control vector transform to compute the final state vector increment |
| | 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 | |
| | 235 | In case of the routine `PDAFomi_assimilate_3dvar`, the following routines are executed after the analysis step: |
| | 236 | 1. [#U_distribute_statedistribute_state_pdaf.F90 U_distribute_state] |
| | 237 | 1. [#U_next_observationnext_observation_pdaf.F90 U_next_observation] |
