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- Author or Editor: Irving I. Gringorten x
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Abstract
General expressions for the expected score for accuracy, score for skill and for operational value of the forecasts are developed and discussed. The expressions are then applied to the special case of two-class predictors and predictand, and an example is given to illustate how one set of probability forecasts can meet the operational requirements better than another set, even though both sets of forecasts are equally accurate and equally skillful.
Abstract
General expressions for the expected score for accuracy, score for skill and for operational value of the forecasts are developed and discussed. The expressions are then applied to the special case of two-class predictors and predictand, and an example is given to illustate how one set of probability forecasts can meet the operational requirements better than another set, even though both sets of forecasts are equally accurate and equally skillful.
Abstract
Single-station climatic probability of a meteorological condition can be estimated from a set of observations taken at the station. The probability, however, of the same condition prevailing along a line of sight or line of travel or in an area or fraction thereof is not so readily obtained. The aproach to this problem has been to model the spatial variability and to determine the values of model parameters. In the absence of an analytical solution a simulation technique involving random number generation was used to obtain answers that are presented in graphical form. Two models have been developed, one effective with upper air temperature fields. The other, and more interesting model, is effective with mesoscale phenomena (such as rainfall) in areas ranging from a few hundred square kilometers up to 100 000 km2.
Abstract
Single-station climatic probability of a meteorological condition can be estimated from a set of observations taken at the station. The probability, however, of the same condition prevailing along a line of sight or line of travel or in an area or fraction thereof is not so readily obtained. The aproach to this problem has been to model the spatial variability and to determine the values of model parameters. In the absence of an analytical solution a simulation technique involving random number generation was used to obtain answers that are presented in graphical form. Two models have been developed, one effective with upper air temperature fields. The other, and more interesting model, is effective with mesoscale phenomena (such as rainfall) in areas ranging from a few hundred square kilometers up to 100 000 km2.
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.
Abstract
Previous models for estimating the conditional probability of an event have used, as the condition, an initial categorized event such as no rain or overcast at time zero. But initial conditions frequently are observed and known in greater detail, and these observed values can replace the categories in determining conditional probabilities. A model that has as its underlying assumption the “Ornstein-Uhlenbeck” process is applicable to this problem. It uses the antecedent quantitatively without loss of information and with surprising simplicity.
Abstract
Previous models for estimating the conditional probability of an event have used, as the condition, an initial categorized event such as no rain or overcast at time zero. But initial conditions frequently are observed and known in greater detail, and these observed values can replace the categories in determining conditional probabilities. A model that has as its underlying assumption the “Ornstein-Uhlenbeck” process is applicable to this problem. It uses the antecedent quantitatively without loss of information and with surprising simplicity.
Single-heading flight is a relatively new and simple system of navigation which generally saves flying time and fuel. To date its use has been restricted to regions where geostrophic winds prevail. The present article presents the theoretical derivation of the formula for single heading and a method for plotting the expected track of the airplane. The use of single-heading flight may be extended over the whole earth, and for variable airspeeds and altitude of flight. This article shows under what circumstances this type of flight planning will yield the path of shortest flying time.
Single-heading flight is a relatively new and simple system of navigation which generally saves flying time and fuel. To date its use has been restricted to regions where geostrophic winds prevail. The present article presents the theoretical derivation of the formula for single heading and a method for plotting the expected track of the airplane. The use of single-heading flight may be extended over the whole earth, and for variable airspeeds and altitude of flight. This article shows under what circumstances this type of flight planning will yield the path of shortest flying time.
Abstract
The article is limited to consideration of a forecasting program in which a forecaster chooses as his forecast one event out of a finite group of well-defined, mutually exclusive events, for example, “rain” or “no rain.” If a table of scores is prepared, from which a forecaster's score can be obtained for each of his forecasts, the sum total of a set of scores will become normally distributed as the number of forecasts is made large. It is possible to set confidence limits on the score total or on the difference of two score totals. But it is necessary to assume that the forecasts by which a forecaster's performance is judged are independent of each other and that the days constitute a fair sample of the climatology of his station.
Abstract
The article is limited to consideration of a forecasting program in which a forecaster chooses as his forecast one event out of a finite group of well-defined, mutually exclusive events, for example, “rain” or “no rain.” If a table of scores is prepared, from which a forecaster's score can be obtained for each of his forecasts, the sum total of a set of scores will become normally distributed as the number of forecasts is made large. It is possible to set confidence limits on the score total or on the difference of two score totals. But it is necessary to assume that the forecasts by which a forecaster's performance is judged are independent of each other and that the days constitute a fair sample of the climatology of his station.
Abstract
Three distinct purposes for the verification and scoring of forecasts have been generally recognized: determination of the accuracy of the forecasts, their operational value, and, lastly, the skill of the forecaster. Although the question most frequently asked is “How accurate?,” the answer, “usually about 85%,” is the most trivial. The operational value of forecasts is much more interesting and significant, but difficult or impossible to determine. The skill of the forecaster, however, is a tractable subject. It is defined as “The ability of the forecaster to sort or group the weather situations so that within any group the probability of one out of several mutually exclusive subsequent events is increased above its climatic frequency.” A set of scores can be designed to reward the forecaster for skilled grouping or sorting of weather patterns and to permit no advantage to an unskilled strategy. Such a scoring system was described more than 10 years ago, but it is not popularly accepted, partly because there never has been a set of uniform goals for verification.
Abstract
Three distinct purposes for the verification and scoring of forecasts have been generally recognized: determination of the accuracy of the forecasts, their operational value, and, lastly, the skill of the forecaster. Although the question most frequently asked is “How accurate?,” the answer, “usually about 85%,” is the most trivial. The operational value of forecasts is much more interesting and significant, but difficult or impossible to determine. The skill of the forecaster, however, is a tractable subject. It is defined as “The ability of the forecaster to sort or group the weather situations so that within any group the probability of one out of several mutually exclusive subsequent events is increased above its climatic frequency.” A set of scores can be designed to reward the forecaster for skilled grouping or sorting of weather patterns and to permit no advantage to an unskilled strategy. Such a scoring system was described more than 10 years ago, but it is not popularly accepted, partly because there never has been a set of uniform goals for verification.
Abstract
In recognition of the fact that a weather forecast is rarely 100 per cent accurate, this paper considers the value of figures for the probability of a meteorological event in meeting specified operational requirements. An objective method is presented for deciding between alternative meteorological predictors. It is emphasized that there is no essential qualitative difference between this technique and the methods normally applied in a more subjective manner.
Abstract
In recognition of the fact that a weather forecast is rarely 100 per cent accurate, this paper considers the value of figures for the probability of a meteorological event in meeting specified operational requirements. An objective method is presented for deciding between alternative meteorological predictors. It is emphasized that there is no essential qualitative difference between this technique and the methods normally applied in a more subjective manner.
