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# PDAFlocalomi_assimilate_nondiagR

This page documents the routine `PDAFlocalomi_assimilate_nondiagR`

of PDAF using the PDAFlocal interface. The routine is used to execute the analysis step of the local ensemble filters LESTKF, LETKF and LSEIK 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 Modification of the model code for the ensemble integration and its sub-page on 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 PDAFomi_put_state_local_nondiagR is used.

The interface for the routine `PDAFlocalomi_assimilate_nondiagR`

contains names for routines that operate on the local analysis domains (marked by the suffix `_l`

).
Here, we list the full interface of the routine. Subsequently, the user-supplied routines specified in the call is explained.

The interface when using one of the local filters is the following:

SUBROUTINE PDAFlocalomi_assimilate_local_nondiagR(U_collect_state, U_distribute_state, & U_init_dim_obs_pdafomi, U_obs_op_pdafomi, & U_prepoststep, U_init_n_domains, U_init_dim_l, & U_init_dim_obs_l_pdafomi, U_prodRinvA_l_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 and also 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_init_n_domains`

: The name of the routine that provides the number of local analysis domains`U_init_dim_l`

: The name of the routine that provides the state dimension for a local analysis domain`U_init_dim_obs_l_pdafomi`

: The name of the routine that initializes the size of the observation vector for a local analysis domain`U_prodRinvA_l_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_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 the routine is exited without errors.

Notes:

- The order of the routine names does not show the order in which these routines are executed. See the section on the order of the execution on the page on implementing the analysis step of the local filter algorithms.
- The difference to the routine
`PDAFlocalomi_assimilate`

used for diagonal R-matrices is only in the additonal argument`U_prodRinvA_l_pdafomi`

. - The filter LNETF uses the separate routine PDAFlocalomi_assimilate_lnetf_nondiagR.
- he filter LKNETF uses the separate routine PDAFlocalomi_assimilate_lknetf_nondiagR

The user-supplied call-back routines are described on the page on implementing the analysis step of the local filters.

It is recommended that the value of `status_pdaf`

is checked in the program after the routine is executed. Only if its value is 0 the initialization was successful.

PDAF also has a Simplified Interface providing the routine `PDAFlocalomi_assimilate_local_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_local_nondiagR_si`

. More information on the pre-defined names is provided in the page on implementing the analysis step of the local filters.