Bias Adjusted Precipitation Threat Scores

Abstract. Among the wide variety of performance measures available for the assessment of skill of deterministic precipitation forecasts, the equitable threat score (ETS) might well be the one used most frequently. It is typically used in conjunction with the bias score. However, apart from its mathematical definition the meaning of the ETS is not clear. It has been pointed out (Mason, 1989; Hamill, 1999) that forecasts with a larger bias tend to have a higher ETS. Even so, the present author has not seen this having been accounted for in any of numerous papers that in recent years have used the ETS along with bias "as a measure of forecast accuracy".

A method to adjust the threat score (TS) or the ETS so as to arrive at their values that correspond to unit bias in order to show the model's or forecaster's accuracy in \textit{placing} precipitation has been proposed earlier by the present author (Mesinger and Brill, the so-called dH/dF method). A serious deficiency however has since been noted with the dH/dF method in that the hypothetical function that it arrives at to interpolate or extrapolate the observed value of hits to unit bias can have values of hits greater than forecast when the forecast area tends to zero. Another method is proposed here based on the assumption that the increase in hits per unit increase in false alarms is proportional to the yet unhit area. This new method removes the deficiency of the dH/dF method. Examples of its performance for 12 months of forecasts by three NCEP operational models are given.