Evaluating probabilistic forecasts of extremes using continuous ranked probability score distributions
This addresses a critical issue in meteorology and climate science for improving forecast reliability during extreme events, representing an incremental advance in verification methodology.
The paper tackles the problem of verifying probabilistic forecasts for extreme events by showing that standard methods based on expected scores are unsuitable, and proposes using extreme value theory to analyze the continuous ranked probability score as a random variable, introducing an index to compare calibrated forecasts for extremes.
Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical verification methods tailored for extreme events, such as thresholded and weighted scoring rules, have undesirable properties that cannot be mitigated, and the well-known continuous ranked probability score (CRPS) is no exception. In this paper, we define a formal framework for assessing the behavior of forecast evaluation procedures with respect to extreme events, which we use to demonstrate that assessment based on the expectation of a proper score is not suitable for extremes. Alternatively, we propose studying the properties of the CRPS as a random variable by using extreme value theory to address extreme event verification. An index is introduced to compare calibrated forecasts, which summarizes the ability of probabilistic forecasts for predicting extremes. The strengths and limitations of this method are discussed using both theoretical arguments and simulations.