Changes between Version 4 and Version 5 of PDAFomi_additional_functionality

Timestamp:

Sep 19, 2024, 12:33:12 PM (2 months ago)

Author:

lnerger

Comment:

--

PDAFomi_additional_functionality

@@ -171 +171 @@
 
 This function only supports geographic coordinates given in radians.
+
+== Determining observation localization weights ==
+
+When using non-diagonal observation error covariance matrices **R**, one has to code the localization weighting in the user-supplied routines. To obtain the localization weight according to the distance between the local analysis domain and the observation, one can utilize the routine `PDAFomi_observation_localization_weights, which ensures that the OMI-internal information is correctly handled.
+
+=== PDAFomi_observation_localization_weights ===
+
+This routine was introduced with PDAF V2.3.
+
+This routine returns a vector of observation localization weights computed according to the localization specifications in `thisobs_l` and observation coordinates in `thisobs`. The routine can be called in `prodRinvA_l_pdafomi` or `likelihood_l_pdafomi` in order to obtain the localization weights for observations. For diagonal observation error covariance matrices, the weighting is computed by OMI internally, but for nondiagonal R-matrices, the use had to implement the application of the localization. 
+
+The interface is the following:
+{{{
+  SUBROUTINE PDAFomi_observation_localization_weights(thisobs_l, thisobs, ncols, &
+             A_l, weight, verbose)
+
+    TYPE(obs_l), INTENT(inout) :: thisobs_l  ! Data type with local observation
+    TYPE(obs_f), INTENT(inout) :: thisobs    ! Data type with full observation
+    INTEGER, INTENT(in) :: ncols             ! Rank of initial covariance matrix
+    REAL, INTENT(in) :: A_l(:, :)            ! Input matrix, size (thisobs_l%dim_obs_l, ncols)
+    INTEGER, INTENT(in) :: verbose           ! Verbosity flag
+    REAL, INTENT(out) :: weight(thisobs_l%dim_obs_l) ! Localization weights
+}}}
+
+
+Notes:
+ * Array `A_l` is usually the input argument to the routine [wiki:prodRinvA_l_pdaf prodRinvA_l_pdaf]. It is only used when the regulated localization is used. 
+ * The regulated localization computes an alternative localization function based on the ration of state error variances to observation error variances. the regulated localization method is described in the paper Nerger et al. (Quarterly Journal of the Royal Meteorological Society, 138 (2012) 802-812; see [wiki:PublicationsandPresentations publications].)
+