Diversity in interpretations of probability:: Implications for weather forecasting

Over the last years, probability weather forecasts have become increasingly popular due in part to the development of ensemble forecast systems. Despite its widespread use in atmospheric sciences, probability forecasting remains a subtle and ambiguous way of representing the uncertainty related to a future meteorological situation. There are several schools of thought regarding the interpretation of probabilities, none of them without flaws, internal contradictions, or paradoxes. Usually, researchers tend to have personal views that are mostly based on intuition and follow a pragmatic approach. These conceptual differences may not matter when accuracy of a probabilistic forecast is measured over a long period (e.g., through the use of Brier score), which may be useful for particular objectives such as cost/benefit decision making. However, when scientists wonder about the exact meaning of the probabilistic forecast in a single case (e.g., rare and extreme event), the differences of interpretation become important. This work intends to describe this problem by first drawing attention to the more commonly accepted interpretations of probability, and then, the consequences of these assumptions are studied. Results suggest that without agreement on the interpretation, the usefulness of the probability forecast as a tool for single events-which include record-breaking events-remains unknown. An open discussion of this topic within the community would be useful to clarify the communication among researchers, with the public and with decision makers.