= Implementation of the Analysis step for the SEIK filter = 

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== Overview ==

For the analysis step of the SEIK filter different 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_seik` that was discussed before. With regard to the parallelization, all these routines are executed by the filter processes (`filterpe=1`) only.

The user-supplied routines for the SEIK filter are 
 * 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 SEIK 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.


== `U_init_dim_obs` (init_dim_obs.F90) ==

This routine is used by all global filter algorithms (SEEK, SEIK, EnKF, ETKF).

The interface for this routine is:
{{{
SUBROUTINE init_dim_obs(step, dim_obs_p)

  INTEGER, INTENT(in)  :: step       ! Current time step
  INTEGER, INTENT(out) :: dim_obs_p  ! Dimension of observation vector
}}}

The routine is called at the beginning of each analysis step.  It has to initialize the size `dim_obs_p` of the observation vector according to the current time step. Without parallelization `dim_obs_p` will be the size for the full model domain. When a domain-decomposed model is used, `dim_obs_p` will be the size of the observation vector for the sub-domain of the calling process.

Some hints:
 * It can be useful if not only the size of the observation vector is determined at this point. One can also already gather information about the location of the observations, which will be used later, e.g. to implement the observation operator. An array for the locations can be defined in a module like `mod_assimilation`.

== `U_obs_op` ==

The interface for this routine is:
{{{
SUBROUTINE obs_op(step, dim_p, dim_obs_p, state_p, m_state_p)

  INTEGER, INTENT(in) :: step               ! Currrent time step
  INTEGER, INTENT(in) :: dim_p              ! PE-local dimension of state
  INTEGER, INTENT(in) :: dim_obs_p          ! Dimension of observed state
  REAL, INTENT(in)    :: state_p(dim_p)     ! PE-local model state
  REAL, INTENT(out) :: m_state_p(dim_obs_p) ! PE-local observed state
}}}

The routine is called during the analysis step. It has to perform the operation of the observation operator acting on a state vector that is provided as `state_p`. The observed state has to be returned in `m_state_p`.

For a model using domain decomposition, the operation is on the PE-local sub-domain of the model and has to provide the observed sub-state for the PE-local domain.

Hint:
 * If the observation operator involves a global operation, e.g. some global integration, while using domain-decompostion one has to gather the information from the other model domains using MPI communication.