Diagonal Scores and Neighborhood: Definitions and Application to Idealized Cases

Abstract

Elementary diagonal score including neighborhood is presented as a new spatial verification tool for ensemble forecasts. It allows a spatial tolerance to be taken into account in the calculation of elementary diagonal scores by considering regional quantiles calculated from cumulative density functions computed on points in a spatial neighborhood. A climatology of the observed regional quantiles is required to define these diagonal scores. As in the case of the elementary diagonal scores without neighborhood, the relationship between error penalty rates and the level of the predicted regional quantile is fixed in order to have a proper score. In addition, this penalty rate is related to the climatological frequency of the event, to ensure an equitable score. The comparison of observations and ensemble forecasts is then summarized in a contingency table for this elementary diagonal score. An integral diagonal score including neighborhood can be calculated by averaging the elementary diagonal scores including neighborhood over a relevant sample of thresholds, as for the integral diagonal score without neighborhood. The properties of these diagonal scores have been illustrated on idealized cases including realistically spatially correlated fields.