= PDAFomi_set_localize_covar =

This page documents the routine `PDAFomi_set_localize_covar` of PDAF-OMI, which was introduced with PDAF V3.0.

The routine has to be called in `init_dim_obs_OBSTYPE` in each observation module if the localized EnKF or the ENSRF/EAKF with localization are used. It initializes the information for covariance localization.

||See the [wiki:OMI_observation_modules page describing PDAF-OMI observation modules] for the full documentation of OMI observation modules and the [wiki:ImplementAnalysislenkfOmi page on implementing the analysis step of the LEnKF] or the [wiki:ImplementAnalysisENSRFOmi page on implementing the analysis step of the ENSRF/EAKF] . ||

The interface is for isotropic localization:
{{{
  SUBROUTINE PDAFomi_set_localize_covar(thisobs, dim, ncoords, coords, &
       locweight, cradius, sradius)

    TYPE(obs_f), INTENT(inout) :: thisobs       ! Data type with full observation
    INTEGER, INTENT(in) :: dim                  ! State dimension
    INTEGER, INTENT(in) :: ncoords              ! Number of coordinate directions
    REAL, INTENT(in)    :: coords(dim,ncoords)  ! Coordinates of state vector elements
    INTEGER, INTENT(in) :: locweight            ! Localization weight type
    REAL, INTENT(in)    :: cradius              ! localization radius
    REAL, INTENT(in)    :: sradius              ! Support radius for weight functions
}}}

'''Notes:'''
 * The routine allows to specify the localization radius and support radius (`lradius`, `sradius`) and localization function (`locweight`) individually for each observation type. 
 * The coordinate array `coords` specifies the coordinates of each element in the state vector. The coordinate units have to be consistent with those used to specify the coordinates of observations.
 * The routine only supports a fixed localization radius throughout the domain.
 * One can also directly call the routine `PDAFomi_set_localize_covar_iso`, e.g. when calling from a program coded in C. 


== `PDAFomi_set_localize_covar` for non-isotropic localization ==

There is an alternative interface for non-isotropic localization. In this variant `cradius` and `sradius` are specified as vectors holding a value of the localization radius for each coordinate direction. This permits for non-isotropic localization.

{{{
  SUBROUTINE PDAFomi_set_localize_covar(thisobs, dim, ncoords, coords, &
       locweight, cradius, sradius)

    TYPE(obs_f), INTENT(inout) :: thisobs       ! Data type with full observation
    INTEGER, INTENT(in) :: dim                  ! State dimension
    INTEGER, INTENT(in) :: ncoords              ! Number of coordinate directions
    REAL, INTENT(in)    :: coords(dim,ncoords)  ! Coordinates of state vector elements
    INTEGER, INTENT(in) :: locweight            ! Localization weight type
    REAL, INTENT(in)    :: cradius(ncoords)     ! directional localization radii
    REAL, INTENT(in)    :: sradius(ncoords)     ! directional support radii for weight functions
}}}

**Note:**
 * One can also directly call the routine `PDAFomi_set_localize_covar_noniso`, e.g. when calling from a program coded in C. 




== `PDAFomi_set_localize_covar` for non-isotropic localization with different weight functions ==

There is also an alternative interface for non-isotropic localization which further allows to specify different weight functions for each direction. This allows, for example, to use a constant weight in the vertical direction, but smooth decaying weight in the horizontal directions. In this variant of the interface `cradius` and `sradius` are specified as vectors holding a value of localization radius for each coordinate direction. In addition `locweight` is specified as a vector holding the localization function index for each coordinate direction.

{{{
  SUBROUTINE PDAFomi_set_localize_covar(thisobs, dim, ncoords, coords, &
       locweight, cradius, sradius)

    TYPE(obs_f), INTENT(inout) :: thisobs       ! Data type with full observation
    INTEGER, INTENT(in) :: dim                  ! State dimension
    INTEGER, INTENT(in) :: ncoords              ! Number of coordinate directions
    REAL, INTENT(in)    :: coords(dim,ncoords)  ! Coordinates of state vector elements
    INTEGER, INTENT(in) :: locweight(ncoords)   ! directional localization weight types
    REAL, INTENT(in)    :: cradius(ncoords)     ! directional localization radii
    REAL, INTENT(in)    :: sradius(ncoords)     ! directional support radii for weight functions
}}}

**Note:**
 * One can also directly call the routine `PDAFomi_set_localize_covar_noniso_locweights`, e.g. when calling from a program coded in C.