= PDAFomi_assimilate_global_nondiagR =

This page documents the routine `PDAFomi_assimilate_global_nondiagR` of PDAF. The routine is used to execute the analysis step of all global ensemble filters ESTKF, ETKF, and SEIK 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:PDAFomi_put_state_global_nondiagR PDAFomi_put_state_global_nondiagR] is used. 

Here, we list the full interface of the routine. 

The interface for using the global filters is:
{{{
  SUBROUTINE PDAFomi_assimilate_global_nondiagR(U_collect_state, U_distribute_state, &
                                 U_init_dim_obs_pdafomi, U_obs_op_pdafomi, &
                                 U_prodRinvA_pdafomi, &
                                 U_prepoststep, 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_prodRinvA_pdafomi`: The name of the user-supplied routine that computes the product of the inverse of the observation error covariance matrix with some matrix provided to the routine by PDAF.
 * `U_prepoststep`: The name of the pre/poststep routine as in `PDAF_get_state`
 * `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 `PDAFomi_assimilate_global_nondiagR` is exited without errors.

Notes:
 * The difference to the routine `PDAFomi_assimilate_global` used for diagonal R-matrices is only in the additonal argument `U_prodRinvA_pdafomi`.
 * The filter EnKF uses the separate routine [wiki:PDAFomi_assimilate_enkf_nondiagR PDAFomi_assimilate_enkf_nondiagR].
 * The filters NETF and PF use the separate routine [wiki:PDAFomi_assimilate_nonlin_nondiagR PDAFomi_assimilate_nonlin_nondiagR].

The user-supplied call-back routines are described on the page on [ImplementAnalysisGlobal implementing the analysis step of the global filters].

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

PDAF also has a [PdafSimplifiedInterface Simplified Interface] providing the routine `PDAFomi_assimilate_global_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_global_nondiagR_si`.  More information on the pre-defined names is provided in the [ImplementAnalysisGlobal page on implementing the analysis step of the global filters].