On the verification of the crossing-point forecast

The crossing-point forecast is defined by the intersection between a forecast (conditional) and a climate (unconditional) cumulative probability distribution function. It is interpreted as the probabilistic worst-case scenario with respect to climatology. This article discusses a scoring function consistent for the crossing-point forecast where both forecasts and verifying observations are expressed in terms of a climatological probability level. Scores defined in 'probability space' are commonly used for the verification of deterministic forecasts and this concept is here generalised to ensemble forecast verification. Practical challenges for its application as well as the sensitivity of the score to ensemble size (number of ensemble members) and to climatology definition (number of used climate quantiles) are illustrated and discussed.