The cost of uncertainty in weather prediction: modelling quality-value relationships for yes/no forecasts

This paper investigates the relationship between the skill and economic value of forecasts using a modelling approach based on signal detection theory (SDT). The value of weather forecasts in a two-action, two-state decision situation can be modelled as a function of forecasting skill, decision threshold, climate and the economic parameters of the decision situation. In general the value of forecasts increases monotonically with increasing skill, measured by the SDT parameter d′. In some circumstances, however, reversal of the expected relationship between forecasting skill and economic value is found, so that forecast value decreases as skill increases. This is associated with use of suboptimal decision thresholds. Thresholds on skill are found for some decision situations, such that forecasts of lower quality have no economic value even though they have some positive skill and are applied optimally. These results reinforce the importance of using the optimal decision threshold in realising the full potential value of forecasts.