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Keywords:

  • Dynamic programming;
  • Markov decision process;
  • Value of information;
  • Weather forecasts

Abstract

Some theoretical results concerning the nature of the relationship between the scientific quality and economic value of imperfect weather forecasts are obtained. A prototype multistage decision-making model is considered, involving only two possible actions and two possible states of weather. This particular form of model is motivated by a real-world application known as the fruit-frost problem. For an infinite-horizon, discounted version of this model it is shown that economic value remains zero below a forecast quality threshold and then rises monotonically but nonlinearly above this threshold. In particular, the relative sensitivity of economic value to changes in the quality of forecasts increases as perfect information is approached. This curve is compared with quality/value relationships that have been obtained for other versions of the model; namely, a single-stage model and a multistage, finite-horizon model.