Imperfect Forecasts Research Articles

On the Relationship between the Quality and Value of Forecasts in the Generalized Cost-Loss Ratio Situation

This paper investigates the relationship between the quality and value of forecast in the context of a generalized N-action, N-event model of the cost-loss ratio situation. The forecasts of interest are imperfect categorical forecasts, calibrated according to past performance and represented by multidimensional sets of conditional and predictive probabilities. Forecasts quality is measured by the ranked probability score (RPS), a natural measure of the accuracy of forecasts in the context of this model. The measure of value is the difference between the expected expense associated with climatological information and the expected expense associated with imperfect forecasts. Thus, climatological and perfect information define lower and upper bounds, respectively, on the quality and value of the imperfect forecasts. Quality-value relationships are explored in the three-action, three-event situation, using brute form and mathematical programming methods. Numerical results are presented for several specific cases. In all cases, the relationships are described by envelopes of values rather than by single-valued functions, indicating that a range of forecast value is generally associated with a given level of forecast quality (and vice versa). The existence of these envelopes reveals two important deficiencies in scalar (i.e., one-dimensional) measures of forecast quality, such as the RPS, when they an used as surrogates for measures of value: 1) these quality measures generally provide only imprecise estimates of forecast value and 2) increases in forecast quality, as reflected by such measures may actually be associated with decreases in forecast value.

Runoff volume forecasts conditioned on a total seasonal runoff forecast

Given an imperfect forecast of the total runoff volume for a season, it is useful to determine the distribution of the forecasted runoff volume in each subperiod. A method is developed for deriving the joint distribution of the subperiod flows and the total seasonal forecast. Historical subperiod flows and the corresponding total seasonal forecast are transformed to the Gaussian domain via three‐parameter lognormal transformations. The transformed subperiod flows and total seasonal forecast are then modeled as multivariate normal, from which the conditional distribution of the runoff volume in each subperiod, given the total seasonal forecast, is obtained.

Repetitive Decision Making and the Value of Forecasts in the Cost‐Loss Ratio Situation: A Dynamic Model

Abstract The purposes of this paper are to describe a dynamic model for repetitive decision‐making in the cost–loss ratio situation and to present some theoretical and numerical results related to the optimal use and economic value of weather forecasts within the framework of the model. This model involves the same actions and events as the standard (i.e., static) cost–loss ratio situation, but the former (unlike the latter) is dynamic in the sense that it possesses characteristics (e.g., decisions, events) that are related over time. We assume that the decision maker wants to choose the sequence of actions over an n‐occasion time period that minimizes the total expected expense. A computational technique known as stochastic dynamic programming is employed to determine this optimal policy and the total expected expense. Three types of weather information are considered in studying the value of forecasts in this context: 1) climatological information; 2) perfect information; and 3) imperfect forecasts. Cli...

The Impact of Meteorology on Aircraft Operating Efficiency: Notes on a Discussion

A symposium was held in London on 6 December 1982 under aegis of the Institute with the traffic management fuel conservation working group to discuss meteorological forecasting and its application in terms of fuel saving. The chairman was J. C. Morrall, Chief Scientist of the Civil Aviation working group. In the United States, the work of Dr R. Steinberg of NASA on the penalties of imperfect forecasts and possible benefits from an improvement was of considerable interest. V. W. Attwooll and L. Bennett of the CAA had also studied penalties from North Atlantic forecasts. Part of the UK civil avionics programme was concerned with the forecast of winds applied in particular to 4-D time-slot following; this was. described by R. C. Rawlings of RAE Bedford. Mr C. Flood, of the Meteorological Office, finally presented prospects for improved forecasts.

The Efficient Use of an Imperfect Forecast

This paper illustrates how individual forecasts and forecasting techniques may be evaluated by the use of established decision theory. Given the probability distribution of the forecast error, we first find the optimal strategy for a decision process, i.e., how to make the most efficient use of a forecast. After expressing the expected profit of the optimal strategies in terms of the probability of a correct forecast, we illustrate how to find (1) the value of an imperfect forecast, and (2) the value of a forecasting technique. With this information, we can then determine when to use a forecast, the maximum amount to pay for both a forecast and a forecasting method, and the conditions under which it is worthwhile to attempt to improve the accuracy of a forecasting method.

Rainfall in the Summer of 1911

ONE does not hear much of effort on the part of official meteorologists to supply long-range forecasts of months, seasons, c better to say, it cannot be done infallibly. My own experience leads me to think a beginning might now be made with what will no doubt some day be a familiar institution, like the useful but imperfect daily forecast.