On evaluation of ensemble forecast calibration using the concept of data depth

Multivariate rank histograms provide insightful information about the misspecification of genuinely multivariate features such as the correlation between various variables in a multivariate ensemble. However, the interpretation of patterns in a multivariate rank histogram should be handled with care.

The purpose of this paper is to focus on multivariate rank histograms designed based on the concept of data depth and outline some important considerations that should be accounted for when using such multivariate rank histograms. To generate correct multivariate rank histograms using the concept of data depth, the datatype of the ensemble should be taken into account to define a proper preranking function. This paper demonstrates how and why some preranking functions might not be suitable for multivariate or vector-valued ensembles and proposes preranking functions based on the concept of simplicial depth that are applicable to both multivariate points and vector-valued ensembles.