Summary. Here we continue a discussion that we began in [1.2.4], by extending our treatment of some aspects of the art of forecast evaluation. We describe statistics that can be used to assess the skill of categorical and quantitative forecasts in Sections 18.1 and 18.2. The utility of the correlation skill score is discussed by illustrating that it can be interpreted as a summary statistic that describes properties of the probability distribution of future states conditional upon the forecast. The Murphy–Epstein decomposition is used to explain the relationships between commonly used skill scores (Section 18.3). Some of the common pitfalls in forecast evaluation problems are discussed in Section 18.4.

The Ingredients of a Forecast. In this section, we consider the problem of quantifying the skill of a forecast such as that of monthly mean temperature at a certain location. We use the symbols Fτ (t) to denote the forecast for the time t with a lead time of τ (e.g., in units of months) and P(t) to denote the verifying observations, or the predictand at time t. We generally omit the suffix (t) and the index τ in our notation unless they are needed for clarity.

Note that in some applications there may be substantial differences between P and the true observations. These differences might arise from biases induced by analysis systems or from errors induced by observing systems. An example of the latter are the various biases that are inherent in the many different rain gauge designs used throughout the world [247].