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# PROBABILITY ESTIMATES OF THE WEATHER IN RELATION TO OPERATIONAL DECISIONS

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• 1 Geophysics Research Directorate, Air Force Cambridge Research Center
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## Abstract

If an operation is influenced by the weather, each course of action should result in a profit, cost, or loss depending upon the subsequent development or state of the weather. To delve into the problem of relating the weather forecast to its operational usefulness, this paper defines an income matrix, which is essentially a table of numerical values of the utility of each course of action followed by each state of the weather. The probabilities of the several states of the weather, arranged in a single-columned matrix, are multiplied with the figures in the income matrix to give the expected gain or loss from each course of action. A decision, then, is generally the choice of that course of action whose expected mean operational value is a maximum. If one or more operations are not easily analyzed, the suggestion is advanced that the decision-making process is influenced by the increase of the probability of an event above its mean or climatic frequency.

Probability figures, however, are only estimates. It is desirable, therefore, to devise a forecasting scheme so as to minimize the effects of errors in these estimates. A least-squares method is applied to yield optimum probability estimates which are shown to be affected by the operation.

## Abstract

If an operation is influenced by the weather, each course of action should result in a profit, cost, or loss depending upon the subsequent development or state of the weather. To delve into the problem of relating the weather forecast to its operational usefulness, this paper defines an income matrix, which is essentially a table of numerical values of the utility of each course of action followed by each state of the weather. The probabilities of the several states of the weather, arranged in a single-columned matrix, are multiplied with the figures in the income matrix to give the expected gain or loss from each course of action. A decision, then, is generally the choice of that course of action whose expected mean operational value is a maximum. If one or more operations are not easily analyzed, the suggestion is advanced that the decision-making process is influenced by the increase of the probability of an event above its mean or climatic frequency.

Probability figures, however, are only estimates. It is desirable, therefore, to devise a forecasting scheme so as to minimize the effects of errors in these estimates. A least-squares method is applied to yield optimum probability estimates which are shown to be affected by the operation.

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