The Unbearable Lightness of Probabilities

he use of probabilities in weather forecasting has become the most common way of conveying the chance of occurrence of a future event. Although accepted as a standard tool, the concept of probability involves a great deal of complexity that is sometimes not appreciated in our community. For years there have been several schools of thought regarding the interpretation of probability, and the debate includes fi elds of study as diverse as philosophy, risk theory, and artifi cial intelligence. Th ere are fundamental diff erences among these interpretations, and these are not dimin-ishing with our growing scientifi c understanding.Until a few years ago, most members of the me-teorological community were satisfi ed to think of probabilities as either the product of past knowledge projected into the future (as when a histogram of fre-quencies of occurrence is viewed as a probability dis-tribution), or as a personal degree of belief regarding the occurrence of the event (based on several sources of information, but ultimately a personal opinion). Although both interpretations satisfy the conditions of probability calculus, one could wonder (and many have wondered) if these two interpretations are really describing the same thing.Th e situation has not improved with the arrival of ensemble forecasting. Now, the probability of the occurrence of an event can be obtained as a direct result of numerical forecasting, suggesting that this probability may be linked to the intrinsic predict-ability of the event. Th is may make the meaning of probability an altogether diff erent thing. And, as is the case with any forecast variable, questions arise about the error or uncertainty associated with this predicted probability. For example, ensemble forecast systems of similar skill from diff erent weather offi ces routinely disagree over the probability of occurrence of some future events. What, then, is the uncertainty of our measure of uncertainty? Could it sometimes be as large as the entire [0,1] interval, the formulated probability value being therefore meaningless?This question is often only academic for three reasons: fi rst, for most common and recurrent events, past probabilities can be verifi ed against outcomes so as to give a sense of prediction skill. Second, the waiting time between the forecast and the event is normally too short to allow for a lengthy discussion or for predictability to become very poor; and third, because what is at stake to users may not be important or contentious enough to justify such a debate.However, forecasting is now being pushed to the limits of what we know, partly by pressures exerted by society for meteorologists to deliver increasingly accurate and timely forecasts, and here the use and meaning of probability becomes problematic. We can fi nd examples of this in the forecasting of rare ex-treme events (e.g., such as the prediction, by a member of an ensemble forecast system, of a hurricane landfall in an area usually free of these kinds of storms), but a clearer case emerges in climate change studies. Th e impact of CO

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