Decide Now or Wait for the Next Forecast? A Decision Framework Based on an Extension of the Cost-Loss Model

Users of meteorological forecasts are often faced with the question of whether to make a decision now based on the current forecast or 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. We derive an algorithm for calculating these two probabilities for the case of normally distributed weather or climate forecasts and apply it to a series of synthetic weather forecasts of temperature. We find that the algorithm leads to better decisions relative to three simpler alternative decision-making schemes.