Theory and Applications of the Minimum Spanning Tree Rank Histogram

A minimum spanning tree (MST) rank histogram (RH) is a multidimensional ensemble reliability verification tool. The construction of debiased, decorrelated, and covariance-homogenized MST RHs is described. Experiments using Euclidean L2, variance, and Mahalanobis norms imply that, unless the number of ensemble members is less than or equal to the number of dimensions being verified, the Mahalanobis norm transforms the problem into a space where ensemble imperfections are most readily identified. Short-Range Ensemble Forecast Mahalanobis-normed MST RHs for a cluster of northeastern U.S. cities show that forecasts of the temperature–humidity index are the most reliable of those considered, followed by mean sea level pressure, 2-m temperature, and 10-m wind speed forecasts. MST RHs of a Southwest city cluster illustrate that 2-m temperature forecasts are the most reliable weather component in this region, followed by mean sea level pressure, 10-m wind speed, and the temperature–humidity index. Forecast reliabilities of the Southwest city cluster are generally less reliable than those of the Northeast cluster.