= Implementation of the Analysis step for the PF (Particle Filter) algorithm = {{{ #!html

Implementation Guide

  1. Main page
  2. Adapting the parallelization
  3. Initializing PDAF
  4. Modifications for ensemble integration
  5. Implementing the analysis step
    1. Implementation for ESTKF
    2. Implementation for LESTKF
    3. Implementation for ETKF
    4. Implementation for LETKF
    5. Implementation for SEIK
    6. Implementation for LSEIK
    7. Implementation for SEEK
    8. Implementation for EnKF
    9. Implementation for LEnKF
    10. Implementation for ENSRF/EAKF
    11. Implementation for NETF
    12. Implementation for LNETF
    13. Implementation for PF
    14. Implementation for 3D-Var
    15. Implementation for 3D Ensemble Var
    16. Implementation for Hybrid 3D-Var
  6. Memory and timing information
  7. Ensemble Generation
  8. Diagnostics
}}} [[PageOutline(2-3,Contents of this page)]] || This page describes the implementation of the analysis step using PDAF's full interface, i.e. without using PDAF-OMI. This approach is supported by all versions of PDAF. However, this approach is mainly used in older implementations of PDAF and can be seen as a expert-mode. Please see the [wiki:ImplementationofAnalysisStep_PDAF3 page on the analysis step in PDAF3] for the current implementation recommendation using the PDAF3 interface. The page also provides links to some other variants that were introduced in verisons of PDAF2. || The PF algorithm was added with Version 1.14 of PDAF. == Overview == The Particle Filter (PF) in PDAF is a standard particle filter with importance resampling (see, e.g. [wiki:PublicationsandPresentations Vetra-Carvalho et al., 2018]). There are different options to set perturbation noise or a stabilizing factor (`type_winf`, `limit_winf`) based on the effective sample size, see the [wiki:AvailableOptionsforInitPDAF#PFfiltertypePDAF_DA_PF12 Page on available options]. For the analysis step of the PF, 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_assimilate_pf` in the fully-parallel implementation (or `PDAF_put_state_pf` 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. For completeness we discuss here all user-supplied routines that are specified in the interface to `PDAF_assimilate_pf`. 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. The analysis step of the PF is is wide parts similar to that of filters like ETKF, and ESTKF filters and strongly related to the NETF method. For this reason, the interface to the user-supplied routines is almost identical, and in fact identical to the NETF. Depending on the implementation it can be possible to use identical routines for the PF and the ETKF with the exception of the routine `U_likelihood`. Differences are marked in the text below. However, the NETF and PF have the same interface, but there are some different options that can be set when PDAF_init is called. == `PDAF_assimilate_pf` == This routine is used both in the ''fully-parallel'' and the ''flexible'' implementation variants of the data assimilation system. (See the page [wiki:OnlineModifyModelforEnsembleIntegration_PDAF3 Modification of the model code for the ensemble integration] for these variants) Here, we list the full interface of the routine. Subsequently, the user-supplied routines specified in the call are explained. The interface is: {{{ SUBROUTINE PDAF_assimilate_pf(U_collect_state, U_distribute_state, & U_init_dim_obs, U_obs_op, U_init_obs, U_prepoststep, & U_likelihood, U_next_observation, status) }}} with the following arguments: * [#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. * [#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. * [#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 * [#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 * [#U_init_obsinit_obs_pdaf.F90 U_init_obs]: The name of the user-supplied routine that initializes the vector of observations * [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep]: The name of the pre/poststep routine as in `PDAF_get_state` * [#U_likelihoodlikelihood_pdaf.F90 U_likelihood]: The name of the user-supplied routine that computes the likelihood of the observations for an ensemble member provide when the routine is called. * [#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`. * `status`: The integer status flag. It is zero, if `PDAF_assimilate_pf` is exited without errors. == `PDAF_assim_offline_pf ` == This routine is used to perform the analysis step for the offline mode of PDAF. The interface of the routine is identical with that of the 'assimilate'-routine, except that the user-supplied routines `U_distribute_state`, `U_collect_state` and `U_next_observation` are missing. The 'assim_offline' routines were introduced with PDAF V3.0 to simplify the [wiki:OfflineImplementationGuide_PDAF3 implementation of the offline mode]. The interface is: {{{ SUBROUTINE PDAF_assim_offline_pf( & U_init_dim_obs, U_obs_op, U_init_obs, U_prepoststep, & U_likelihood, status) }}} == `PDAF_put_state_pf` == This routine exists for backward-compatibility. In implementations that were done for PDAF V2.3.1 and before, a 'put_state' routine was used for the [wiki:OnlineFlexible_PDAF3 'flexible' parallelization variant] and for the [wiki:OfflineImplementationGuide_PDAF3 offline mode]. This routine allows to continue using the previous implementation structure. The interface of the routine is identical with that of the 'assimilate'-routine, except that the user-supplied routines `U_distribute_state` and `U_next_observation` are missing. The interface is: {{{ SUBROUTINE PDAF_put_state_pf(U_collect_state, & U_init_dim_obs, U_obs_op, U_init_obs, U_prepoststep, & U_likelihood, status) }}} == User-supplied routines == Here all user-supplied routines are described that are required in the call to the analysis routine. For some of the generic routines, we link to the page on [wiki:OnlineModifyModelforEnsembleIntegration_PDAF3 modifying the model code for the ensemble integration]. To indicate user-supplied routines we use the prefix `U_`. In the tutorials in `tutorial/` and in the template directory `templates/` these routines exist without the prefix, but with the extension `_pdaf`. The files are named correspondingly. In the section titles below we provide the name of the template file in parentheses. In 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. === `U_collect_state` (collect_state_pdaf.F90) === This routine is independent of the filter algorithm used. See the page on [wiki:OnlineModifyModelforEnsembleIntegration_PDAF3#collect_state_pdafcollect_state_pdaf.F90 modifying the model code for the ensemble integration] for the description of this routine. === `U_distribute_state` (distribute_state_pdaf.F90) === This routine is independent of the filter algorithm used. See the page on [wiki:OnlineModifyModelforEnsembleIntegration_PDAF3#distribute_state_pdafdistribute_state_pdaf.F90 modifying the model code for the ensemble integration] for the description of this routine. === `U_init_dim_obs` (init_dim_obs_pdaf.F90) === This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, NETF, PF). The interface for this routine is: {{{ SUBROUTINE init_dim_obs(step, dim_obs_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(out) :: dim_obs_p ! Dimension of observation vector }}} The 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. Some hints: * 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. === `U_obs_op` (obs_op_pdaf.F90) === This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, NETF, PF). The interface for this routine is: {{{ SUBROUTINE obs_op(step, dim_p, dim_obs_p, state_p, m_state_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_p ! PE-local dimension of state INTEGER, INTENT(in) :: dim_obs_p ! Dimension of observed state REAL, INTENT(in) :: state_p(dim_p) ! PE-local model state REAL, INTENT(out) :: m_state_p(dim_obs_p) ! PE-local observed state }}} The 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`. For 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. Hint: * 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. === `U_init_obs` (init_obs_pdaf.F90) === This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF, NETF, PF). The interface for this routine is: {{{ SUBROUTINE init_obs(step, dim_obs_p, observation_p) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_obs_p ! PE-local dimension of obs. vector REAL, INTENT(out) :: observation_p(dim_obs_p) ! PE-local observation vector }}} The routine is called during the analysis step. It has to provide the vector of observations in `observation_p` for the current time step. For a model using domain decomposition, the vector of observations that exist on the model sub-domain for the calling process has to be initialized. === `U_prepoststep` (prepoststep_ens_pdaf.F90) === The routine has already been described for modifying the model for the ensemble integration and for inserting the analysis step. See the page on [wiki:OnlineModifyModelforEnsembleIntegration_PDAF3#distribute_state_pdafdistribute_state_pdaf.F90 modifying the model code for the ensemble integration] for the description of this routine. === `U_likelihood` (likelihood_pdaf.F90) === This routine is used by the PF and NETF algorithms only. The interface for this routine is: {{{ SUBROUTINE U_likelihood(step, dim_obs_p, obs_p, residual, likely) INTEGER, INTENT(in) :: step ! Current time step INTEGER, INTENT(in) :: dim_obs_p ! PE-local dimension of obs. vector REAL, INTENT(in) :: obs_p(dim_obs_p) ! PE-local vector of observations REAL, INTENT(in) :: residual(dim_obs_p) ! Input vector holding the residual y-Hx REAL, INTENT(out) :: likely ! Output value of the likelihood }}} The routine is called during the analysis step. In the PF and NETF, as in other particle filters, the likelihood of the observations has to be computed for each ensemble member. The likelihood is computed from the observation-state residual according to the assumed observation error distribution. Commonly, the observation errors are assumed to be Gaussian distributed. In this case, the likelihood is '''exp(-0.5*(y-Hx)^T^*R^-1^*(y-Hx))'''. For a model with domain decomposition, `resid` contains the part of the matrix that resides on the model sub-domain of the calling process. The likelihood has to be computed for the global state vector. Thus some parallel communication might be required to complete the computation. Hints: * The routine is very similar to the routine [wiki:U_prodRinvA]. The main addition is the computation of the likelihood after computing '''R^-1^*(y-Hx)''', which corresponds to '''R^-1^*A_p''' in [wiki:U_prodRinvA]. * The information about the inverse observation error covariance matrix has to be provided by the user. Possibilities are to read this information from a file, or to use a Fortran module that holds this information, which one could already prepare in init_pdaf. * The routine does not require that the product is implemented as a real matrix-vector 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 inverse diagonal with the vector `resid` has to be implemented. * 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. === `U_next_observation` (next_observation_pdaf.F90) === This routine is independent of the filter algorithm used. See the page on [wiki:OnlineModifyModelforEnsembleIntegration_PDAF3#next_observation_pdafnext_observation_pdaf.F90 modifying the model code for the ensemble integration] for the description of this routine. == Execution order of user-supplied routines == For the PF, the user-supplied routines are essentially executed in the order they are listed in the interface to `PDAF_assimilate_pf`. 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`. Before the analysis step is called, the following routine is executed: 1. [#U_collect_statecollect_state_pdaf.F90 U_collect_state] The 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: 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (Call to act on the forecast ensemble, called with negative value of the time step) 1. [#U_init_dim_obsinit_dim_obs_pdaf.F90 U_init_dim_obs] 1. [#U_init_obsinit_obs_pdaf.F90 U_init_obs] 1. [#U_obs_opobs_op_pdaf.F90 U_obs_op] (`dim_ens` calls; one call for each ensemble member) 1. [#U_likelihoodlikelihood_pdaf.F90 U_likelihood] (`dim_ens` calls; one call for each ensemble member) 1. [#U_prepoststepprepoststep_ens_pdaf.F90 U_prepoststep] (call to act on the analysis ensemble, called with (positive) value of the time step) In case of the routine `PDAF_assimilate_pf`, the following routines are executed after the analysis step: 1. [#U_distribute_statedistribute_state_pdaf.F90 U_distribute_state] 1. [#U_next_observationnext_observation_pdaf.F90 U_next_observation]