An Information-Theoretical Score of Dichotomous Precipitation Forecast

This study presents an information-theoretical score (ITS) with an emphasis on desirable and undesirable mutual information between a series of dichotomous forecast and observation. As ITS makes use of the same contingency table as traditional scores, the performance of threat score (TS), equitable threat score (ETS), and true skill statistics (TSS) are compared with ITS using three different approaches. First, a hypothetical forecast setup is employed to investigate the responses of the scores to bias, phase error, and event frequency. It was found that the desirable mutual information portion of ITS (C+) is closer to TSS, and the undesirable mutual information portion of ITS (C-) reveals the presence of biases and random errors in the forecast. There is also a similarity between ITS and ETS. Second, the sensitivities of ITS and ETS to forecast bias tendency are examined analytically using the critical performance ratio (CPR). It is shown that ITS has a more dynamical response to incremental bias. By increasing the bias, the CPR value of ITS increases more rapidly than that of ETS indicating a higher resistance to hedging. Third, the skill scores on two sets of operational forecasts are applied with respect to a mosaic of observed radar reflectivity. The results show that ITS remains more consistent in its evaluation of skills at different thresholds compared to other scores.