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# Implementation of the Analysis step for the SEIK filter

#### Implementation Guide

#### Contents of this page

## Overview

For the analysis step of the LSEIK filter several operations related to the observations are needed. These operations are requested by PDAF by calling user-supplied routines. Intentionally, the operations are split into separate routines in order to keep the operations rather elementary. This procedure should simplify the implementation. The names of the required routines are specified in the call to the routine `PDAF_put_state_lseik`

described below. With regard to the parallelization, all these routines are executed by the filter processes (`filterpe=1`

) only.

The following user-supplied routines for the SEIK filter are described on this page. (For completeness, we also repeat the generic routines that were described on the page Modification of the model core for the ensemble integration.

- U_init_dim_obs_full: The name of the user-supplied routine that provides the size of observation vector
- U_obs_op_full: The name of the user-supplied routine that acts as the observation operator on some state vector
- U_init_obs_full: The name of the user-supplied routine that initializes the vector of observations
- U_prodRinvA_local: 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 LSEIK filter.
- U_init_obsvar: The name of the user-supplied routine that provides a mean observation error variance to PDAF (This routine will only be executed, if an adaptive forgetting factor is used)

Below the names of the corresponding routines in the template directory are provided in parentheses. The the routines in the example implementation have the same name but include '`_dummy_D`

' in the name.

## PDAF_put_state_lseik

The general espects of the filter specific routines `PDAF_put_state_*`

have been described on the page Modification of the model core for the ensemble integration.
The interface for the routine `PDAF_put_state_lseik`

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

at then end of the routine name), as well as routines that consider all available observations to be considered within some sub-domain of the model (marked by `_f`

('full') at then end of the routine name). In case of a serial execution of the assimilation program, this will be all available observation. However, if the program is execute with parallelization, this might be a limited number of observations.

The interface when using the LSEIK filter is the following:

SUBROUTINE PDAF_put_state_lseik(U_collect_state, U_init_dim_obs_f, U_obs_op_f, & U_init_obs_f, U_init_obs_l, U_prepoststep, U_prodRinvA_l, U_init_n_domains, & 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, 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 ensembel of model states from the model fields. This is basically the inverse operation to`U_distribute_state`

used in`PDAF_get_state`

`U_init_dim_obs_f`

: The name of the user-supplied routine that provides the size of observation vector`U_obs_op_f`

: The name of the user-supplied routine that acts as the observation operator on some state vector`U_init_obs_f`

: The name of the user-supplied routine that initializes the 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. This operation occurs during the analysis step of the SEIK filter.`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 domains 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 part of the global state vector corresponding to the provided local state vector`U_g2l_obs`

: The name of the routine that initialized 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 to PDAF (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 to PDAF (This routine will only be executed, if an adaptive forgetting factor is used)`status`

: The integer status flag. It is zero, if PDAF_get_state is exited without errors.

## User-supplied routines

Here all user-supplied routines are described that are required in the call to `PDAF_put_state_lseik`

. For some of the generic routines, we link to the page on modifying the model code for the ensemble integration.

To indicate user-supplied routines we use the prefix `U_`

. In the template directory `templates/`

these routines are provided in files with the routines name without this prefix. In the example implementation in `testsuite/src/dummymodel_1D`

the routines exist without the prefix, but with the extension `_dummy_D.F90`

. In the section titles below we provide the name of the template file in parentheses.

`U_collect_state`

(collect_state.F90)

See here for the description of this routine.

`U_prepoststep`

(prepoststep_seik.F90)

See here for the description of this routine.