1Decision-Making from Probability Forecasts using Calculations of Forecast ValueKenneth R. Mylne The Met. Office, Bracknell, UK (To be submitted to Meteorological Applications) How do I make a decision based on a probability forecast?Abstract: A method of estimating the economic value of weather forecasts for decision-making is described. The method may be applied equally to either probability forecasts or deterministic forecasts, and provides a forecast user with a direct comparison of the value of each in terms of money saved, which is more relevant to users than most standard verification scores. For a user who wishes to use probability forecasts to decide when to take protective action against a weather event, the method identifies the optimum probability threshold for action, thus answering the question of how to use probability forecasts for decision-making. The system optimises decision-making for any probability forecast system, whatever its quality, and therefore removes any need to calibrate the probability forecasts. The method is illustrated using site-specific probability forecasts generated from the ECMWF ensemble prediction system and deterministic forecasts from the ECMWF high-resolution global model. It is found that for most forecast events and most users the probability forecasts have greater user value than the deterministic forecasts from a higher resolution model.1. IntroductionA weather forecast, however skilful, has no intrinsic value unless it can be used to make decisions which bring some benefit, financial or otherwise, to the end user. Conventionally in most weather forecast services the forecast provider supplies the user with their best estimate of whether a defined event will occur (e.g. wind speed will or will not exceed 15ms-1), or of a value for a measurable parameter (e.g. maximum wind speed =18 ms-1). Decision- making is often based on whether a defined event is expected to occur or not. For example the owner of a small fishing boat may decide to seek shelter when the forecast wind speed exceeds 15 ms-1. The nature of atmospheric predictability is such that there is frequently a significant uncertainty associated with such deterministic forecasts. Forecast uncertainty can be expressed in many ways, either qualitatively or quantitatively, and where such information is included in a forecast this can aid the decision-maker who understands the potential impact of a wrong decision. However, uncertainty is most commonly estimated subjectively by a forecaster; such estimates are often inconsistent, and may be affected by factors such as forecasters “erring on the safe side”, which may not lead to optimal decision-making. In recent years there has been considerable development of objective methods of estimating forecast uncertainty, notably ensemble prediction systems (EPS) such as those operated by the European Centre for Medium Range Weather Forecasts (ECMWF) (Molteni et al, 1996, Buizza and Palmer 1998) and the US National Centers for Environmental 2Prediction (NCEP) (Toth and Kalnay, 1993). Output from an EPS is normally in the form of probability forecasts, and there is growing evidence (e.g. Molteni et al, 1996, Toth et al 1997) that these have greater skill than equivalent deterministic forecasts based on single high-resolution model forecasts, particularly on medium range time-scales. To make use of this additional skill, the decision-maker needs to know how to respond to a forecast such as There is a 30% probability that the wind speed will exceed 15 ms-1. This paper will describe a technique which estimates the economic value of a probability forecast system for a particular user based on verification of past performance, and use it to determine the users optimal decision-making strategy. The value of deterministic forecasts can be calculated in the same way, and this allows a direct comparison of the utility of probability and equivalent deterministic forecasts in terms which are clear and relevant to the user. 2. Background to Ensemble Probability ForecastsUncertainty in weather forecasts derives from a number of sources, in particular uncertainty in the initial state of the atmosphere and approximations in the model used to predict the atmospheric evolution. Errors in the analysis of the initial state result from observational errors, shortage of observations in some regions of the globe and limitations of the data assimilation system. Model errors are due to numerous approximations which must be made in the formulation of a model, most notably the many small-scale processes which cannot be resolved explicitly, and whose effect must therefore be represented approximately by parametrization. The non-linear nature of atmospheric evolution means that even very small errors in the model representation of the atmospheric state, whether due to the analysis or the model formulation, will be amplified through