On producing probability forecasts

We present a method to produce probability forecasts from model-generated forecasts. A common scenario is this: a model-based forecast, such as a point high temperature forecast, or an ensemble of forecasts for some field, is made. This model-based forecast must then be transformed to a probability forecast for the observable of interest. Note that the observable of interest need not be the same variable which was forecast: it is only required that the forecast variable and the observable are not probabilistically independent.

The theory behind the re-forecasting method of Hamill et al. (2005), various classical and Bayesian modeling approaches, and the method of Briggs and Wilks (1996) are compared in their ability to produce these probability forecasts. The similarities and differences of these methods are laid out, and a general approach to follow is given.