PDAF3_assimilate_hyb3dvar_lestkf_nondiagR

This page documents the routine PDAF3_assimilate_hyb3dvar_lestkf_nondiagR of PDAF which is used in 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 routines `PDAFomi_put_state_*' are used.

The interface is:

SUBROUTINE PDAF3_assimilate_hyb3dvar_lestkf_nondiagR(U_collect_state, U_distribute_state, &
                                 U_init_dim_obs_pdafomi, U_obs_op_pdafomi, U_prodRinvA_pdafomi, &
                                 U_cvt_ens, U_cvt_adj_ens, U_cvt, U_cvt_adj, &
                                 U_obs_op_lin_pdafomi, U_obs_op_adj_pdafomi, &
                                 U_init_n_domains_p, U_init_dim_l, U_init_dim_obs_l_pdafomi, 
                                 U_prodRinvA_l_pdafomi, 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 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. This routine is part of an OMI observation module.
• U_obs_op_pdafomi:
  The name of the user-supplied routine that acts as the observation operator on some state vector. This routine is part of an OMI observation module.
• U_prodRinvA_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_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_cvt:
  The name of the user-supplied routine that applies the control-vector transformation (square-root of the B-matrix) on some control vector to obtain a state vector.
• U_cvt_adj:
  The name of the user-supplied routine that applies the adjoint control-vector transformation (with square-root of the B-matrix) on some state vector to obtain the control vector.
• U_obs_op_pdafomi:
  The name of the user-supplied routine that acts as the observation operator on some state vector. This routine is part of an OMI observation module.
• U_obs_op_lin_pdafomi:
  The name of the user-supplied routine that acts as the linearized observation operator on some state vector. This routine is part of an OMI observation module.
• U_obs_op_adj_pdafomi:
  The name of the user-supplied routine that acts as the adjoint observation operator on some state vector. This routine is part of an OMI observation module.
• U_init_n_domains:
  The name of the user-supplied routine that provides the number of local analysis domains
• U_init_dim_l:
  The name of the user-supplied routine that provides the state dimension for a local analysis domain
• U_init_dim_obs_l_pdafomi:
  The name of the user-supplied 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 including localization.
• U_prepoststep:
  The name of the user-supplied pre/poststep routine as in PDAF_get_state
• U_next_observation:
  The name of the 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. 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.

Note:

• The difference to the routine PDAF3_assimilate_hyb3dvar_lestkf used for diagonal R-matrices is only in the additional arguments U_prodRinvA_pdafomi and U_prodRinvA_l_pdafomi.

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