Decide now or wait for the next forecast? Testing a decision framework using real forecasts and observations

Users of meteorological forecasts are often faced with the question of whether to make a decision now based on the current forecast or whether to wait for a later and hopefully more accurate forecast before making the decision. Imagine that you are the organiser of an event planned for Saturday. If the weather conditions at the start of the event are unsuitable then the event will have to be cancelled, leading to various expenses. Daily weather forecasts are available in the run-up to the event and you need to use them to decide whether to cancel in advance or not. Cancelling early could lead to only small cancellation charges, while cancelling shortly before leads to larger charges. Both sets of cancellation charges are lower than the potential loss due to last-minute cancellation on Saturday, and this leads to a nuanced set of decisions around when and whether to cancel. The general mathematical framework for understanding decisions of this type has been studied extensively, both in meteorology and in other fields such as economics. In order to understand our problem of whether to decide now or wait for the next forecast, we consider a special case of this general framework, that is also an extension of the well-known cost-loss model. We find that within this extended cost-loss model, the question of whether to decide now or wait depends on probabilities of probabilities. We develop a decision algorithm which we apply to real forecasts of temperature, and find that the algorithm leads to better decisions in most settings relative to three simpler alternative decision-making schemes. Our results have implications for the additional kinds of information that weather and climate forecasters could produce to facilitate good decision making based on their forecasts.