The Minimum Spanning Tree Histogram as a Verification Tool for Multidimensional Ensemble Forecasts

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Abstract
The minimum spanning tree (MST) histogram is a multivariate extension of the ideas behind the conventional scalar rank histogram. It tabulates the frequencies, over n forecast occasions, of the rank of the MST length for each ensemble, within the group of such lengths that is obtained by substituting an observation for each of its ensemble members in turn. In raw form it is unable to distinguish ensemble bias from ensemble underdispersion, or to discern the contributions of forecast variables with small variance. The use of scaled and debiased MST histograms to diagnose attributes of ensemble forecasts is illustrated, both for synthetic Gaussian ensembles and for a small sample of actual ensemble forecasts. Also presented are adjustments to χ2 critical values for evaluating rank uniformity, for both MST histograms and scalar rank histograms, given serial correlation in the forecasts. Abstract The minimum spanning tree (MST) histogram is a multivariate extension of the ideas behind the conventional scalar rank histogram. It tabulates the frequencies, over n forecast occasions, of the rank of the MST length for each ensemble, within the group of such lengths that is obtained by substituting an observation for each of its ensemble members in turn. In raw form it is unable to distinguish ensemble bias from ensemble underdispersion, or to discern the contributions of forecast variables with small variance. The use of scaled and debiased MST histograms to diagnose attributes of ensemble forecasts is illustrated, both for synthetic Gaussian ensembles and for a small sample of actual ensemble forecasts. Also presented are adjustments to χ2 critical values for evaluating rank uniformity, for both MST histograms and scalar rank histograms, given serial correlation in the forecasts.