Bröcker et al "Comments on 'Conditional Exceedance Probabilities'"

Bröcker, J., Siegert, S., & Kantz, H. (2011). Comments on “Conditional Exceedance Probabilities”. Monthly Weather Review, 139(10), 3322-3324.

Abstract

In a recent paper, Mason et al. propose a reliability test of ensemble forecasts for a continuous, scalar verification. As noted in the paper, the test relies on a very specific interpretation of ensembles, namely, that the ensemble members represent quantiles of some underlying distribution. This quantile interpretation is not the only interpretation of ensembles, another popular one being the Monte Carlo interpretation. Mason et al. suggest estimating the quantiles in this situation; however, this approach is fundamentally flawed. Errors in the quantile estimates are not independent of the exceedance events, and consequently the conditional exceedance probabilities (CEP) curves are not constant, which is a fundamental assumption of the test. The test would reject reliable forecasts with probability much higher than the test size.