Relationship between Precipitation Forecast Errors and Skill Scores of Dichotomous Forecasts

Abstract

In this paper, the sensitivities of the equitable threat score (ETS) and the true skill score (TSS), obtained with a 2 ? 2 contingency table, to continuous precipitation forecast errors are investigated. Two idealized error models are adopted to describe the difference between forecasts and perfect observations. The observations consist of a time series generated by a multiplicative cascade model. The forecasts are constructed by adding the modeled errors to the observations. Two examples that are representative of two precipitation regimes are considered. Monte Carlo simulations of the modeled errors are performed to compute the score uncertainties. Monotonic relationships between the precipitation forecast errors and the two skill scores are found. It is shown that the precipitation regime and the event frequency influence these relationships and the score uncertainties. The score uncertainties also depend on the forecast errors. Furthermore, it is shown that a relationship exists between the ETS and TSS when the forecast errors are very large. Results suggest that more information should be provided together with the scores and their uncertainties in order to provide a complete picture of the forecast performance.