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# PDAFomi_assimilate_lknetf_nondiagR

This page documents the routine `PDAFomi_assimilate_lknetf_nondiagR`

of PDAF. The routine is used to execute the analysis step of the local nonlinear ensemble transform filter LKNETF 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_lknetf_nondiagR is used.

The interface for the routine `PDAFomi_assimilate_lknetf_nondiagR`

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

). Further there are routines that convert between a local and a global model state vector (`U_g2l_state`

and `U_l2g_state`

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

The interface when using the LKNETF is the following:

SUBROUTINE PDAFomi_assimilate_lknetf_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_prodRinvA_hyb_l_pdafomi, & U_likelihood_l_pdafomi, U_likelihood_l_pdafomi, & U_g2l_state, U_l2g_state, & 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_prodRinvA_hyb_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 including the hybrid weight.`U_likelihood_l_pdafomi`

: The name of the user-supplied routine that computes the local likelihood of an ensemble state.`U_likelihood_hyb_l_pdafomi`

: The name of the user-supplied routine that computes the local likelihood of an ensemble state including the hybrid weight.`U_g2l_state`

: The name of the routine that initializes a local state vector from the global state vector`U_l2g_state`

: The name of the routine that initializes the corresponding part of the global state vector from the provided local state vector`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.

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
`PDAFomi_assimilate_local`

used for diagdonal R-matrices is in the additonal arguments`U_likelihood_l_pdafomi`

,`U_likelihood_hyb_l_pdafomi`

,`U_prodRinvA_l_pdafomi`

,`U_prodRinvA_hyb_l_pdafomi`

. - The local filters LESTKF, LETKF, and LSEIK use the separate routine PDAFomi_assimilate_local_nondiagR.
- The filter KNETF uses the separate routine PDAFomi_assimilate_lnetf_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 PDAFomi_assimilate_lknetf_nondiagR is executed. Only if its value is 0 the initialization was successful.

PDAF also has a Simplified Interface providing the routine `PDAFomi_assimilate_lknetf_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_lknetf_nondiagR_si`

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