Using non-diagonal R matrices with OMI

This feature was introduced with PDAF V2.3.

The default mode of PDAF-OMI is to use a diagonal observation error covariance matrix R and specifying the observation error variances, i.e. the diagonalof R only. This is in line with the common choice in data assimilation to assume that observation errors are uncorrelated.

However, there are also observation types with significant observation error correlations, which should be represented by a non-diagonal observation error covariance matrix. With PDAF V2.3 support for such nondiagonal R matrices was added to OMI.

PDAF-OMI's support for nondiagonal R-matrices consists in given the user access to the routines that perform operations involve R. This differs with the filter type, e.g. in LESTKF and LETKF a produce of some matrix with the inverse of R ha sto be computed, while in the traditional, perturbed observations, EnKF the matrix R has to be added to some other matrix. For the particle filter and the NETF the computation of the likelihood involves R.

Routines to perform the analysis step

For using a nondiagonal R there is a modified variant of the PDAF-OMI routines PDAFomi_assimilate_* or PDAFomi_put_state_*. Compared to the case of a diagonal R, the routines are slightly less generic. Below we provide an overview of the routines including the links to the interface description of each. The last column gives the name of the additional routine(s) provided in the interface to implement the non-diagonal R-matrix.

Global Filter	diagonal R	non-diagonal R	additional routine(s)
EnKF	PDAFomi_assimilate_global PDAFomi_put_state_global	PDAFomi_assimilate_enkf_nondiagR PDAFomi_put_state_enkf_nondiagR	add_obs_err_pdafomi init_obscovar_pdafomi
ESTKF	PDAFomi_assimilate_global PDAFomi_put_state_global	PDAFomi_assimilate_global_nondiagR PDAFomi_put_state_global_nondiagR	prodRinvA_pdafomi
ETKF	PDAFomi_assimilate_global PDAFomi_put_state_global	PDAFomi_assimilate_global_nondiagR PDAFomi_put_state_global_nondiagR	prodRinvA_pdafomi
PF	PDAFomi_assimilate_global PDAFomi_put_state_global	PDAFomi_assimilate_nonlin_nondiagR PDAFomi_put_state_nonlin_nondiagR	likelihood_pdafomi
NETF	PDAFomi_assimilate_global PDAFomi_put_state_global	PDAFomi_assimilate_nonlin_nondiagR PDAFomi_put_state_nonlin_nondiagR	likelihood_pdafomi
SEIK	PDAFomi_assimilate_global PDAFomi_put_state_global	PDAFomi_assimilate_global_nondiagR PDAFomi_put_state_global_nondiagR	prodRinvA_pdafomi

Local Filter	diagonal R	non-diagonal R	additional routine(s)
LEnKF	PDAFomi_assimilate_lenkf PDAFomi_put_state_lenkf	PDAFomi_assimilate_lenkf_nondiagR PDAFomi_put_state_lenkf_nondiagR	add_obs_err_pdafomi init_obscovar_pdafomi
LESTKF	PDAFomi_assimilate_local PDAFomi_put_state_local	PDAFomi_assimilate_local_nondiagR PDAFomi_put_state_local_nondiagR	prodRinvA_l_pdafomi
LETKF	PDAFomi_assimilate_local PDAFomi_put_state_local	PDAFomi_assimilate_local_nondiagR PDAFomi_put_state_local_nondiagR	prodRinvA_l_pdafomi
LSEIK	PDAFomi_assimilate_local PDAFomi_put_state_local	PDAFomi_assimilate_local_nondiagR PDAFomi_put_state_local_nondiagR	prodRinvA_l_pdafomi
LNETF	PDAFomi_assimilate_local PDAFomi_put_state_local	PDAFomi_assimilate_lnetf_nondiagR PDAFomi_put_state_lnetf_nondiagR	likelihood_l_pdafomi
LKNETF	PDAFomi_assimilate_local PDAFomi_put_state_local	PDAFomi_assimilate_lknetf_nondiagR PDAFomi_put_state_lknetf_nondiagR	likelihood_l_pdafomi likelihood_hyb_l_pdafomi prodRinvA_l_pdafomi prodRinvA_hyb_l_pdafomi

3D-Var	diagonal R	non-diagonal R	additional routine(s)
3DVar	PDAFomi_assimilate_3dvar PDAFomi_assimilate_3dvar	PDAFomi_put_state_3dvar_nondiagR PDAFomi_put_state_3dvar_nondiagR	prodRinvA_pdafomi
En3DVar ESTKF	PDAFomi_assimilate_en3dvar_estkf PDAFomi_assimilate_en3dvar_estkf	PDAFomi_put_state_en3dvar_estkf_nondiagR PDAFomi_put_state_en3dvar_estkf_nondiagR	prodRinvA_pdafomi
En3DVar LESTKF	PDAFomi_assimilate_en3dvar_lestkf PDAFomi_assimilate_en3dvar_lestkf	PDAFomi_put_state_en3dvar_lestkf_nondiagR PDAFomi_put_state_en3dvar_lestkf_nondiagR	prodRinvA_l_pdafomi
hyb3DVar ESTKF	PDAFomi_assimilate_hyb3dvar_estkf PDAFomi_assimilate_hyb3dvar_estkf	PDAFomi_put_state_hyb3dvar_estkf_nondiagR PDAFomi_put_state_hyb3dvar_estkf_nondiagR	prodRinvA_pdafomi
hyb3DVar LESTKF	PDAFomi_assimilate_hyb3dvar_lestkf PDAFomi_assimilate_hyb3dvar_lestkf	PDAFomi_put_state_hyb3dvar_lestkf_nondiagR PDAFomi_put_state_hyb3dvar_lestkf_nondiagR	prodRinvA_l_pdafomi

Call-back routines handling observations

For the different filters and 3D-Var variants,