= Initialization of PDAF and the ensemble by PDAF_init = {{{ #!html

Implementation Guide

  1. Main page
  2. Adaptation of the parallelization
  3. Initialization of PDAF
  4. Modifications for ensemble integration
  5. Implementation of the analysis step
  6. Memory and timing information
}}} [[PageOutline(2-3,Contents of this page)]] == Overview == After the adaption of the parallelization, the initialization of PDAF has to be implemented. It is performed by the routine `PDAF_init`. This subroutine has several arguments. Typically, the initializations of all variables required for the call to `PDAF_init` can be collected into a single subroutine. This implementation strategy is useful, as only a single additional subroutine call has to be inserted to the model source code. In the example in `testsuite/src/dummymodel_1D` the routine in the file `init_pdaf.F90` collects all initializations for PDAF. The routine has no arguments. Likewise, the tutorial implementations use a routine `init_pdaf.F90`. The file `init_pdaf.F90` in `templates/` provides a commented template for this routine, which can be used as the basis of the implementation. `PDAF_init` itself calls a user-supplied routine to initialize the ensemble of model states through its interface. In the example there are separate routines for ensemble-based and mode-based filters. They are in the files `init_seik_pdaf.F90` (for SEIK, LSEIK, ETKF, LETKF), `init_enkf_pdaf.F90` (for EnKF), and `init_seek_pdaf.F90` (for SEEK). == Inserting `init_pdaf` == The right place to insert a routine like `init_pdaf` to the model code is in between the initialization part of the model and its time stepping loop. I.e. the regular model initialization should be completed, which allows PDAF to initialize the ensemble of model states. In the routine a number of variables have to be defined that are used in the call to `PDAF_init` as described in '[#RequiredargumentsforPDAF_init Required arguments for `PDAF_init`]' below. (Please note: All names of subroutines that start with `PDAF_` are core routines of PDAF, while subroutines whose name end with `_pdaf` are generally user-supplied interface routines) There are also a few variables that are initialized in `init_pdaf` but not used in the call to `PDAF_init`. These are variables that are specific for the data assimilation system, but only shared in between the user-supplied routines. For the example case, these variables are described in '[#Othervariablesfortheassimilation Other variables for the assimilation]' The example and tutorial implementations, as well as the template routines allow to parse all variables through a command line parser by call in `init_pdaf_parse.F90`. This method provides a convenient way to define an experiment and could also be used for other models. The parser module is provided as `templates/parser_mpi.F90`. Alternatively, one could implement an initialization of the variables with Fortran namelists or could just rely on hard-coded numbers in the source code. == Required arguments for `PDAF_init` == In `init_pdaf` the variables for the call to `PDAF_init` are set. The call to `PDAF_init` has the following structure: {{{ CALL PDAF_init(filtertype, subtype, step_null, & filter_param_i, length_filter_param_i, & filter_param_r, length_filter_param_r, & COMM_model, COMM_filter, COMM_couple, & task_id, n_modeltasks, filterpe, & U_init_ens, screen, status_pdaf) }}} The required variables are the following: * `filtertype`: An integer defining the type of filter algorithm. Available are * 0: SEEK * 1: SEIK * 2: EnKF * 3: LSEIK * 4: ETKF * 5: LETKF * 6: ESTKF * 7: LESTKF * 8: local EnKF * 9: NETF * 10: LNETF * [11: GENOBS (moved to 100 in PDAF V2.0)] * 12: PF * 100: GENOBS (generate synthetic observations - from PDAF V2.0) * 200: 3D-Var (introduced in PDAF V2.0) * `subtype`: An integer defining the sub-type of the filter algorithm (see the example code in `testsuite/src/dummymodel_1D` for choices). If `PDAF_init` is called with `subtype=-1` the available options are shown for the selected filter algorithm. * `step_null`: An integer defining the initial time step. For some cases it can use useful to set `step_null` larger to 0. * `filter_param_i`: Integer array collecting several variables for PDAF. The first two variables are mandatory and equal for all filters. Further variables are optional (see example code or use `subtype=-1` to display available options.). The mandatory variables are in the following order: * The size of the local state vector for the current process. * The ensemble size for all ensemble-based filters (or the rank of the state covariance matrix for mode-based filters like SEEK) * `length_filter_param_i`: An Integer defining the length of the array `filter_param_i`. The entries in the array are parsed up to this index. * `filter_param_r`: Array of reals collecting floating point variables for PDAF. The first variable is mandatory and equal for all filters. Further variables are optional (see example code in `testsuite/src/dummymodel_1D` or use `subtype=-1` to display available options.). The mandatory variable is: * The value of the forgetting factor controlling covariance inflation (required to be larger than zero; common are values between 0.9 and 1.0. For 1.0 the ensemble is not inflated.) * `length_filter_param_r`: An Integer defining the length of the array `filter_param_r`. The entries in the array are parsed up to this index. * `COMM_model`: The communicator variable `COMM_model` as initialized by `init_parallel_pdaf`. (Usually stored in the module `mod_assimilation`) * `COMM_filter`: The communicator variable `COMM_filter` as initialized by `init_parallel_pdaf`. (Usually stored in the module `mod_assimilation`) * `COMM_couple`: The communicator variable `COMM_couple` as initialized by `init_parallel_pdaf`. (Usually stored in the module `mod_assimilation`) * `task_id`: The index of the model tasks as initialized by `init_parallel_pdaf`. (Usually stored in the module `mod_assimilation`) * `n_modeltasks`: The number of model tasks as defined before the call to `init_parallel_pdaf`. (Usually stored in the module `mod_assimilation`) * `filterpe`: A logical flag showing whether a process belongs to `COMM_filter` as initialized by `init_parallel_pdaf`. (Usually stored in the module `mod_assimilation`) * `U_init_ens`: The name of the user-supplied routine that is called by `PDAF_init` to initialize the ensemble of model states. (See '[#User-suppliedroutineU_init_ensinit_ens_pdaf.F90 User-supplied routine U_init_ens]' * `screen`: An integer defining whether information output is written to the screen (i.e. standard output). The following choices are available: * 0: quiet mode - no information is displayed. * 1: Display standard information (recommended) * 2: as 1 plus display of timing information during the assimilation process * 3: Display detailed information for debugging * `status_pdaf`: An integer used as status flag of PDAF. If `status_pdaf` is zero upon exit from `PDAF_init` the initialization was successful. An error occurred for non-zero values. (The error codes are documented in the routine `PDAF_init`.) An overview of available options for each filter an be found on the [wiki:AvailableOptionsforInitPDAF overview page on options]. It is recommended that the value of `status_pdaf` is checked in the program after PDAF_init is executed. Only if its value is 0 the initialization was successful. PDAF also has a [PdafSimplifiedInterface Simplified Interface] providing the routine `PDAF_init_si`. In the simplified interface, the name of the user-supplied routine `U_init_ens` is predefined to `init_ens_pdaf` such that it does not appear in the call to `PDAF_init_si`. More information on the pre-defined names is provided in the [PdafSimplifiedInterface documentation of PDAF's simplified interface]. == Other variables for the assimilation == The routine `init_pdaf` in the example also initializes several variables that are not used to call `PDAF_init`. These variables control some functionality of the user-supplied routines for the data assimilation system and are shared with these routines through the Fortran module `mod_assimilation`. These variables are for example: * `delt_obs`: An integer specifying the number of time steps between two analysis steps * `rms_obs`: Assumed observation error * `cradius`: Localization cut-off radius in grid points for the observation domain * `sradius`: support radius, if observation errors are weighted (i.e. `locweight>0`) * `locweight`: Type of localizing weight It is useful to define variables like these at this central position. Of course, their definition has to be adapted to the particular model used. == User-supplied routine `U_init_ens` (init_ens_pdaf.F90) == The user-supplied routine the we named `U_init_ens` here, is called by PDAF through the defined interface described below. The routine is called by all MPI processes that compute the filter analysis step (i.e. those for which 'filterpe' is set to true. In the standard configuration of `init_parallel_pdaf` these are all processes of the first model task, i.e. task_id=1.) `U_init_ens_pdaf` is only called by `PDAF_init` if no error occurred before; thus the status flag is zero. The interface is the following: {{{ SUBROUTINE U_init_ens(filtertype, dim_p, dim_ens, & state_p, Uinv, ens_p, flag) }}} with * `filtertype`: The integer defining the type of filter algorithm as given in the call to `PDAF_init` * `dim_p`: An integer holding the size of the state dimension for the calling process as specified in the call to `PDAF_init` * `dim_ens`: An integer holding the size of the ensemble (or the rank of the state covariance matrix for SEEK) * `state_p`: A real array of size (`dim_p`) for the local model state of the calling process (Only relevant for mode-based filters) * `Uinv`: A real array of size (`dim_ens-1`, `dim_ens-1`) for the inverse of matrix '''U''' from the decomposition of the state error covariance matrix '''P''' = '''VUV^T^''' (Only relevant for mode-based filters like SEEK.) * `ens_p`: A real array of size (`dim_p`, `dim_ens`) the has to hold upon exit the ensemble of model states. * `flag`: Status flag for PDAF. It is 0 upon entry and can be set by in the user-supplied routine, depending on the success of the ensemble initialization. Preferably, values above 102 should be used for failures to avoid conflicts with the error codes defined within PDAF_init. === Defining the state vector === The ensemble initialization routine is the first location at which the user has to fill a state vector (or array of state vectors). A state vector is the collection of all model fields that are handled in the analysis step of the assimilation procedure into a single vector. Usually one concatenates the different model fields as complete fields. Thus, the vector could contain a full 3-dimensional temperature field, followed by the salinity field (in case of an ocean model), and then followed by the 3 fields of the velocity components. The logical definition of the state vector will also be utilized in several other user-supplied routines. E.g. in routines that fill model fields from a state vector or in the routine providing the observation operator. === Initialization for ensemble-based filters === In the initialization routine `U_init_ens_pdaf` one has to distinguish between ensemble-based and mode-based filters. The only mode based filter supplied with PDAF is SEEK, while all other methods are ensemble-based. Generally, the filters SEIK, LSEIK, EnKF, ETKF, LETKF, ESTKF, and LESTKF are ensemble-based filters. For these filters only the array `ens_p` needs to be initialized by the ensemble of model states. If a parallel model with domain decomposition is used, the full ensemble for the local sub-domain of the MPI process has to be initialized. The arrays `state_p` and `Uinv` are allocated to their correct sizes because they are used during the assimilation cycles. They are not yet initialized and it is allowed to use these arrays in the initialization. An exception from this is EnKF for which `Uinv` is allocated only with size (1,1), because `Uinv` is not used for EnKF. === Initialization for mode-based filters === The only mode-based filter supplied with PDAF is currenly the SEEK filter. For this filter the initialization bases on the decomposition of the state error covariance matrix in the form '''P''' = '''VUV^T^'''. According to this decomposition, the array `ens_p` has to be initialized to hold the modes from matrix '''V''' and `Uinv` holds the inverse of matrix '''U'''. In addition `state_p` has to be initialized with the initial state estimate. If a parallel model with domain decomposition is used, the part of all modes for the local sub-domain of the MPI process and the corresponding part of the state vector has to be initialized. ```Uinv``` will be identical for all MPI processes. == Testing the PDAF initialization == The PDAF initialization can be tested by compiling the program and executing it. The Makefile of the model has to be extended to include the additional files. The core part of PDAF can be compiled separately as a library and can then simply be linked to the model code. This is the strategy followed in the PDAF-package. '''Remark:''' For the compilation with a real MPI library, one has to ensure that MPI-module (`USE MPI`) of the MPI-library is USED for both the model and PDAF. (Thus in the include file for make in `make.arch`, one might have set `MPI_INC` to the directory holding the module.) At this stage it will not be meaningful to perform an actual model time stepping. However, one can test whether the initialization in PDAF_init is successful and whether the ensemble array is correctly initialized. Standard output from PDAF_init should look like the following: {{{ PDAF ++++++++++++++++++++++++++++++++++++++++++++++++++++++ PDAF +++ PDAF +++ PDAF +++ Parallel Data Assimilation Framework +++ PDAF +++ +++ PDAF +++ Version 2.1 +++ PDAF +++ +++ PDAF +++ Please cite +++ PDAF +++ L. Nerger and W. Hiller, Computers and +++ PDAF +++ Geosciences, 2013, 55, 110-118, +++ PDAF +++ doi:10.1016/j.cageo.2012.03.026 +++ PDAF +++ when publishing work resulting from using PDAF +++ PDAF ++++++++++++++++++++++++++++++++++++++++++++++++++++++ PDAF: Initialize filter PDAF +++++++++++++++++++++++++++++++++++++++++++++++++++++++ PDAF +++ Local Error Subspace Transform Kalman Filter +++ PDAF +++ (LESTKF) +++ PDAF +++ +++ PDAF +++ Domain-localized implementation of the ESTKF by +++ PDAF +++ Nerger et al., Mon. Wea. Rev. 140 (2012) 2335 +++ PDAF +++ doi:10.1175/MWR-D-11-00102.1 +++ PDAF +++++++++++++++++++++++++++++++++++++++++++++++++++++++ PDAF LESTKF configuration PDAF filter sub-type = 0 PDAF --> Standard LESTKF PDAF --> Transform ensemble with deterministic Omega PDAF --> Use fixed forgetting factor: 1.00 PDAF --> ensemble size: 50 PDAF: Initialize Parallelization PDAF Parallelization - Filter on model PEs: PDAF Total number of PEs: 1 PDAF Number of parallel model tasks: 1 PDAF PEs for Filter: 1 PDAF # PEs per ensemble task and local ensemble sizes: PDAF Task 1 PDAF #PEs 1 PDAF N 50 }}} The correctness of the ensemble initialization in `U_init_ens` should be checked by the user.