This paper is concerned with the value of climatological, categorical, probabilistic and perfect forecasts in the cost-loss ratio situation. Expressions are derived for the expense associated with these different types of forecasts, and measures of value and relative value are formulated in terms of these expressions. Some relationships among these expressions and measures are described, and these relationships are illustrated by examining both hypothetical and real sets of forecasts.
It is demonstrated that, if the probabilistic forecasts of concern are (completely) reliable, then the value of these forecasts is greater than the value of climatological and categorical forecasts for all activities or operations (i.e., for all values of the cost‐loss ratio C/L). On the other hand, if the forecasts are unreliable, then the value of climatological and/or categorical forecasts may be greater than the value of probabilistic forecasts for some values of C/L. However, examination of hypothetical and real sets of unreliable forecasts indicates that the relationships between the value of reliable probabilistic forecasts and the value of climatological and categorical forecasts are quite robust in the sense that these relationships appear to hold for most if not all values of C/L even for moderately unreliable forecasts.
The results presented in this paper have important implications for operational forecasting procedures and practices. These implications relate to the desirability of formulating and disseminating a wide variety of weather forecasts in probabilistic terms and of achieving and maintaining a high degree of reliability in probabilistic forecasts.