Abstract
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 the next and hopefully more accurate forecast before making the decision. Following previous authors, we analyse this question as an extension of the well-known cost-loss model. Within this extended cost-loss model the question of whether to decide now or wait depends on two specific aspects of the forecast, both of which involve probabilities of probabilities. For the special case of weather and climate forecasts in the form of normal distributions we derive a simple simulation algorithm, and equivalent analytical expressions, for calculating these two probabilities. We apply the algorithm to forecasts of temperature and find that the algorithm leads to better decisions in most cases relative to three simpler alternative decision making schemes, in both a simulated context and when we use reforecasts, surface observations and rigorous out-of-sample validation of the decisions. To the best of our knowledge, this is the first time that a dynamic multi-stage decision algorithm has been demonstrated to work using real weather observations. 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.
