We are grateful to Harold Brooks and Daniel S. Wilks for valuable comments. David Jones is acknowledged for providing the initial impetus for this work.
Berger, J. O., 1985: Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, 617 pp.
Drummond, C., , and Holte R. C. , 2006: Cost curves: An improved method for visualizing classifier performance. Mach. Learn., 65, 95–130.
Jolliffe, I. T., , and Stephenson D. B. , 2003: Forecast Verification: A Practitioner’s Guide in Atmospheric Science. John Wiley and Sons, 240 pp.
Katz, R. W., , and Murphy A. H. , 1997: Economic Value of Weather and Climate Forecasts. Cambridge University Press, 225 pp.
Keith, R., , and Leyton S. M. , 2007: An experiment to measure the value of statistical probability forecasts for airports. Wea. Forecasting, 22, 928–935.
Letson, D., , Sutter D. S. , , and Lazo J. K. , 2007: Economic value of hurricane forecasts: An overview and research needs. Nat. Hazards Rev., 8, 78–86.
Mason, I., 2004: The cost of uncertainty in weather prediction: Modelling quality-value relationships for yes/no forecasts. Aust. Meteor. Mag., 53, 111–122.
Milligan, M. R., , Miller A. H. , , and Chapman F. , 1995: Estimating the economic value of wind forecasting to utilities. Proc. Windpower ’95, Washington, DC, National Renewable Energy Laboratory.
Murphy, A. H., 1977: The value of climatological, categorical and probabilistic forecasts in the cost-loss ratio situation. Mon. Wea. Rev., 105, 803–816.
Murphy, A. H., 1993: What is a good forecast? An essay on the nature of goodness in weather forecasting. Wea. Forecasting, 8, 281–293.
Murphy, A. H., , and Ehrendorfer M. , 1987: On the relationship between the accuracy and value of forecasts in the cost-loss ratio situation. Wea. Forecasting, 2, 243–251.
Palmer, T. N., 2002: The economic value of ensemble forecasts as a tool for risk assessment: From days to decades. Quart. J. Roy. Meteor. Soc., 128, 747–774.
Provost, F., , and Fawcett T. , 1997: Analysis and visualization of classifier performance: Comparison under imprecise class and cost distributions. Proc. Third Int. Conf. on Knowledge Discovery and Data Mining, Newport Beach, CA, Association for the Advancement of Artificial Intelligence.
Richardson, D. S., 2000: Skill and relative economic value of the ECMWF Ensemble Prediction System. Quart. J. Roy. Meteor. Soc., 126, 649–667.
Roebber, P. J., , and Bosart L. F. , 1996: The complex relationship between forecast skill and forecast value: A real-world analysis. Wea. Forecasting, 11, 544–559.
Stewart, T. R., , Pielke R. Jr., , and Nath R. , 2004: Understanding user decision making and value of improved precipitation forecasts: Lessons from a case study. Bull. Amer. Meteor. Soc., 85, 223–235.
Taylor, K. E., 2001: Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res., 106 (D7), 7183–7192.
Teisberg, T. J., , Weiher R. F. , , and Khotanzad A. , 2005: The economic value of temperature forecasts in electricity generation. Bull. Amer. Meteor. Soc., 86, 1765–1771.
Thornes, J. E., , and Stephenson D. B. , 2001: How to judge the quality and value of weather forecast products. Meteor. Appl., 8, 307–314.
Wandishin, M. S., , and Brooks H. E. , 2002: On the relationship between Clayton’s skill score and expected value for forecasts of binary events. Meteor. Appl., 9, 455–459, doi:10.1017/S1350482702004085.
Wilks, D. S., 2006: Statistical Methods in the Atmospheric Sciences. Academic Press, 627 pp.
If Cl > 1, then no action should be taken, independently of p, because the expected cost associated with no action is always lower than that associated with action. But if 0 < Cl < 1, then the optimal decision depends on the value of p. For this reason, only 0 < Cl < 1 is examined here.
If both p and Cl are very small (i.e., p ≪ 1 and Cl ≪ 1), then R ~ Cl/p. With Lm = L, Cl becomes C/L. Some reported C/L ranges are as follows: for orchardists, 0.02–0.05 (Murphy 1977); loading of fuel for airplanes, 0.01–0.12 (Leigh 1995); and winter road gritting, 0.125 (Thornes and Stephenson 2001).
For small p and Cl, an R of 1.6 corresponds to p/Cl = 1/R = 0.625.
The less than sign in Eq. (10) may be changed to less than or equal to but not much is gained from that revision.
The means of the two normal distributions are −1.035 and +1.035, and both standard deviations are 1.