The methodology of decision analysis is used to investigate the economic value of frost (i.e., minimum temperature) forecasts to orchardists. First, the fruit-frost situation and previous studies of the value of minimum temperature forecasts in this context are described. Then, after a brief overview of decision analysis, a decision-making model for the fruit-frost problem is presented. The model involves identifying the relevant actions and events (or outcomes), specifying the effect of taking protective action, and describing the relationships among temperature, bud loss, and yield loss. A bivariate normal distribution is used to model the relationship between forecast and observed temperatures, thereby characterizing the quality of different types of information. Since the orchardist wants to minimize expenses (or maximize payoffs) over the entire frost-protection season and since current actions and outcomes at any point in the season are related to both previous and future actions and outcomes, the decision-making problem is inherently dynamic in nature. As a result, a class of dynamic models known as Markov decision processes is considered. A computational technique called dynamic programming is used in conjunction with these models to determine the optimal actions and to estimate the value of meteorological information.
Some results concerning the value of frost forecasts to orchardists in the Yakima Valley of central Washington are presented for the cases of red delicious apples, bartlett pears, and elberta peaches. Estimates of the parameter values in the Markov decision process are obtained from relevant physical and economic data. Twenty years of National Weather Service forecast and observed temperatures for the Yakima key station are used to estimate the quality of different types of information, including perfect forecasts, current forecasts, and climatological information. The orchardist's optimal actions over the frost-protection season and the expected expenses associated with the use of such information are determined using a dynamic programming algorithm. The value of meteorological information is defined as the difference between the expected expense for the information of interest and the expected expense for climatological information. Over the entire frost-protection season, the value estimates (in 1977 dollars) for current forecasts were $808 per acre for red delicious apples, $492 per acre for bartlett pears, and $270 per acre for elberta peaches. These amounts account for 66, 63, and 47%, respectively, of the economic value associated with decisions based on perfect forecasts. Varying the quality of the minimum temperature forecasts reveals that the relationship between the accuracy and value of such forecasts is nonlinear and that improvements in current forecasts would not be as significant in terms of economic value as were comparable improvements in the past.
Several possible extensions of this study of the value of frost forecasts to orchardists are briefly described. Finally, the application of the dynamic model formulated in this paper to other decision-making problems involving the use of meteorological information is mentioned.