On the Evaluation of Point Precipitation Probability Forecasts in Terms of Areal Coverage

Allan H. Murphy Environmental and Societal Impacts Group, National Center for Atmospheric Research, Boulder, CO 80307

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Abstract

Probability of precipitation (PoP) forecasts can often be interpreted as average point probability forecasts. Since the latter are equivalent to (unconditional) expected areal coverage forecasts, PoP forecasts can be evaluated in terms of observed areal coverages in those situations in which observations of precipitation occurrence are available from a network of points in the forecast area. The purpose of this paper is to describe a partition of the average Brier, or probability, score—a measure of the average accuracy of average point probability forecasts over the network of points of concern—that facilitates such an evaluation. The partition consists of two terms: 1) a term that represents the average squared error of the average point probability forecasts interpreted as areal coverage forecasts and 2) a term that represents the average variance of the observations of precipitation occurrence in the forecast area. The relative magnitudes of the terms in this partition are examined, and it is concluded (party on the basis of experimental data) that the variance term generally makes a significant contribution to the overall probability score. This result, together with the fact that the variance term does not depend on the forecasts, suggests that the squared error term (rather than the overall score) should be used to evaluate PoP forecasts in many situations. The basis for the interpretation of PoP forecasts as average point probability forecasts and some implications of the results presented in this paper for the evaluation of PoP forecasts are briefly discussed.

Abstract

Probability of precipitation (PoP) forecasts can often be interpreted as average point probability forecasts. Since the latter are equivalent to (unconditional) expected areal coverage forecasts, PoP forecasts can be evaluated in terms of observed areal coverages in those situations in which observations of precipitation occurrence are available from a network of points in the forecast area. The purpose of this paper is to describe a partition of the average Brier, or probability, score—a measure of the average accuracy of average point probability forecasts over the network of points of concern—that facilitates such an evaluation. The partition consists of two terms: 1) a term that represents the average squared error of the average point probability forecasts interpreted as areal coverage forecasts and 2) a term that represents the average variance of the observations of precipitation occurrence in the forecast area. The relative magnitudes of the terms in this partition are examined, and it is concluded (party on the basis of experimental data) that the variance term generally makes a significant contribution to the overall probability score. This result, together with the fact that the variance term does not depend on the forecasts, suggests that the squared error term (rather than the overall score) should be used to evaluate PoP forecasts in many situations. The basis for the interpretation of PoP forecasts as average point probability forecasts and some implications of the results presented in this paper for the evaluation of PoP forecasts are briefly discussed.

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