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# PDAF_assimilate_en3dvar_lestkf

This page documents the routine `PDAF_assimilate_en3dvar_lestkf`

of PDAF.

The routine is typically called in `assimilate_pdaf`

or directly in the model code.

The general aspects of the filter specific routines `PDAF_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 routines `PDAF_put_state_*' are used.

The interface is:

SUBROUTINE PDAF_assimilate_en3dvar_lestkf(U_collect_state, U_distribute_state, & U_init_dim_obs, U_obs_op, U_init_obs, U_prodRinvA, & U_cvt_ens, U_cvt_adj_ens, U_obs_op_lin, U_obs_op_adj, & U_init_dim_obs_f, U_obs_op_f, U_init_obs_f, U_init_obs_l, U_prodRinvA_l, & U_init_n_domains_p, U_init_dim_l, U_init_dim_obs_l, U_g2l_state, U_l2g_state, & U_g2l_obs, U_init_obsvar, U_init_obsvar_l, & U_prepoststep, U_next_observation, outflag)

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: The name of the user-supplied routine that provides the size of observation vector
- U_obs_op: The name of the user-supplied routine that acts as the observation operator on some state vector
- U_init_obs: The name of the user-supplied routine that initializes the vector of observations
- U_prodRinvA: 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. This operation occurs during the analysis step of the ETKF.
- U_cvt_ens: The name of the user-supplied routine that applies the ensemble control-vector transformation (square-root of the B-matrix) on some control vector to obtain a state vector.
- U_cvt_adj_ens: The name of the user-supplied routine that applies the adjoint ensemble control-vector transformation (with square-root of the B-matrix) on some state vector to obtain the control vector.
- U_obs_op_lin: The name of the user-supplied routine that acts as the linearized observation operator on some state vector
- U_obs_op_adj: The name of the user-supplied routine that acts as the adjoint observation operator on some state vector
- U_init_dim_obs_f: The name of the user-supplied routine that provides the size of the full observation vector
- U_obs_op_f: The name of the user-supplied routine that acts as the full observation operator on some state vector
- U_init_obs_f: The name of the user-supplied routine that initializes the full vector of observations
- U_init_obs_l: The name of the user-supplied routine that initializes the vector of observations for a local analysis domain
- U_prepoststep: The name of the pre/poststep routine as in
`PDAF_get_state`

- U_prodRinvA_l: 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_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: The name of the routine that initializes the size of the observation vector for a local analysis domain
- 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 the provided local state vector
- U_g2l_obs: The name of the routine that initializes a local observation vector from a full observation vector
- U_init_obsvar: The name of the user-supplied routine that provides a global mean observation error variance (This routine will only be executed, if an adaptive forgetting factor is used)
- U_init_obsvar_l: The name of the user-supplied routine that provides a mean observation error variance for the local analysis domain (This routine will only be executed, if a local adaptive forgetting factor is used)
- 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 the routine is exited without errors.

The user-supplied call-back routines are described on the page on implementing the analysis step of 3D-Var?.

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.