Verification of the Spatial Structure of Gridded Forecasts

A subset of methods developed for spatial verification involve clustering methods for identifying meteorological objects within gridded and forecast fields. The problem of comparing two fields which have been clustered is closely related to the problem of comparing different clusterings. Several clustering comparison techniques have already been developed in the machine learning community. This work examines various ways in which the clustering methods can be combined with the clustering comparison methods (e.g., optimal transportation and matching methods) for the purpose of better assessing the quality of the forecasts. Many of the existing clustering comparison methods involve quantities for which statistical tests exist, but some of those developed here do not have simple tests, and so, null distributions are developed by comparison with random gaussian fields.