= PDAFomi_assimilate_lenkf_nondiagR =

This page documents the routine `PDAF_assimilate_lenkf` of PDAF. The routine is used to execute the analysis step of the localized EnKF (LEnKF) with PDAF-OMI for the case of a non-diagonal observation error covariance matrix. This routine was introduced with PDAF V2.3. 

The routine is typically called in `assimilate_pdaf` or directly in the model code.

The general aspects of the filter specific routines `PDAFomi_assimilate_*` are described on the page [ModifyModelforEnsembleIntegration Modification of the model code for the ensemble integration] and its sub-page on [InsertAnalysisStep inserting the analysis step]. The routine is used in the fully-parallel implementation variant of the data assimilation system. When the 'flexible' implementation variant, the routine [wiki:PDADomi_put_state_lenkf_nondiagR PDAFomi_put_state_lenkf_nondiagR] is used. 

Here, we list the full interface of the routine. 

The interface when using the LEnKF is the following:
{{{
  SUBROUTINE PDAFomi_assimilate_lenkf_nondiagR(U_collect_state, U_distribute_state, &
                                 U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                                 U_prepoststep, U_localize_covar_pdafomi, &
                                 U_add_obs_err_pdafomi, U_init_obscovar_pdafomi, &
                                 U_next_observation, status)
}}}
with the following arguments:
 * `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_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_obs_pdafomi`: The name of the user-supplied routine that initializes the observation information and provides the size of observation vector
 * `U_obs_op_pdafomi`: The name of the user-supplied routine that acts as the observation operator on some state vector
 * `U_prepoststep`: The name of the pre/poststep routine as in `PDAF_get_state`
 * `U_localize_covar_pdafomi`: Apply covariance localization to the matrices HP and HPH^T^
 * `U_add_obs_err_pdafomi`: The name of the user-supplied routine that adds the observation error covariance matrix to the ensemble covariance matrix projected onto the observation space.
 * `U_init_obscovar_pdafomi`: The name of the user-supplied routine that initializes the observation error covariance matrix.
 * `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 this routine is exited without errors. 

For the EnKF, the user-supplied routines are essentially executed in the order they are listed in the interface to PDAFomi_assimilate_lenkf_nondiagR. 

The user-supplied call-back routines are described on the page on [ImplementAnalysislenkf implementing the analysis step of the local EnKF].

It is recommended that the value of `status_pdaf` is checked in the program after this routine is executed. Only if its value is 0 the initialization was successful.

PDAF also has a [PdafSimplifiedInterface Simplified Interface] providing the routine [wiki:PDAFomi_assimilate_lenkf_nondiagR_si PDAFomi_assimilate_lenkf_nondiagR_si]. In the simplified interface, the name of the user-supplied routines have predefined names and do not appear in the call to `PDAFomi_assimilate_lenkf_nondiagR_si`.  More information on the pre-defined names is provided in the [ImplementAnalysisLocal page on implementing the analysis step of the local filters].