On the crossing-point forecast

The crossing-point forecast (CPF) is a new concept in the field of probabilistic forecasting. A CPF is defined by the intersection between a forecast cumulative distribution and the corresponding climatology distribution. Focusing on this intersection point, a probabilistic forecast is summarized into a single number conveying information about a "probabilistic worst-case scenario" with respect to climatology. Is the predicted chance of suffering a loss, due to the occurrence of an (exceedance) event, higher than that event’s climatological frequency? The crossing-point forecast indicates the limit case for which the answer is positive.

The outcome corresponding to a CPF, called “crossing-point observation”, is directly related to the return period of the event that materializes. A simple error function that applies to the forecast and observed crossing-points is formulated. The resulting score is closely related to the diagonal score: it is proper and equitable which makes its application appealing for the comparison of competing forecasts. The proposed scoring function is consistent for the crossing-point forecast in a similar way as the root mean squared error is consistent for the distributional mean forecast or the mean absolute error is consistent for the 50%-quantile forecast.

In weather forecasting, the information provided by CPF could be highly relevant for vulnerable users and more generally for users with interest for high-impact events. We propose here a comparison with the Extreme Forecast Index (EFI) using the ensemble forecast of the Integrated Forecasting System run at ECMWF and the corresponding model climatology. The EFI is designed to provide forecasters with general initial guidance on potential extreme weather events. Both EFI and CPF are derived using the same ingredients which makes their comparison particularly relevant. Based on case studies and verification metrics, we illustrate the complementarity of the two types of forecasts.