ARTICLE | doi:10.20944/preprints202002.0217.v2
Subject: Environmental And Earth Sciences, Atmospheric Science And Meteorology Keywords: cost-loss; forecast change; forecast volatility; decision making; expected utility; probabilistic forecasts; ensemble forecasts
Online: 8 May 2020 (04:28:30 CEST)
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. One would imagine that the answer to this question should depend on the extent to which there is a benefit in making the decision now rather than later, combined with an understanding of how the skill of the forecast improves, and information about the possible size and nature of forecast changes. We extend the well-known cost-loss model for forecast-based decision making to capture an idealized version of this situation. We find that 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 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 relative to three simpler alternative decision-making schemes. Similar problems have been studied in many other fields, and we explore some of the connections.