Changes between Version 8 and Version 9 of OMI_nondiagonal_observation_error_covariance_matrices

Timestamp:

Sep 9, 2024, 2:27:13 PM (10 days ago)

Author:

lnerger

Comment:

--

OMI_nondiagonal_observation_error_covariance_matrices

@@ -248 +248 @@
  * Please see the further implementation hints for `prodRinvA_l_pdafomi`.
  * For diagonal **R** PDAF-OMI uses the routine `PDAFomi_likelihood_hyb_l` in `/src/PDAFomi_obs_l.F90` as the routine that is called within the observation module. This routine can serve as a template for an implementation by the user.
+
+== Hints ==
+
+For now, we do not have an example code that we could provide. However, for the implementation the follonig hints might be useful:
+ * The matrix **R** could be constructed e.g. from decorrelation length scales or by direct implementation. 
+ * The routine [wiki:PDAF_correlation_function] can be used to obtain values of a correlation function.
+ * The matrix **R** cannot be stored fully for larger numbers of observations. E.g. for 100 000 observations, the full matric **R** would have 10^10^ entries, which corresponds to 80 GB memory at double precision. Thus, one would need compressed ways of storing the matrix or one can implement the products with the inverse of **R** or the addition of **R** in form of oeprations.
+ * For the localized operations in `prodRinvA_l_pdafomi` and `likelihood_l_pdafomi` it should be possible to handle the part of **R** that relates only to the local observations used in a local analysis domain. However, the inverse of this local matrix part is not identical to the local part of the global inverse. The different might be mitigated by applying the localization weight to **R**.
+ * Examples of implementations are also available without PDAF-OMI, e.g. in the tutorial and in /models/lorenz96
+.