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Irving I. Gringorten
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Irving I. Gringorten

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.

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Irving I. Gringorten

Abstract

After a review of the methods, advanced most recently, of estimating extreme values from data samples it is concluded that the straightforward method of moments offers the advantages of stability and simplicity without bias. The sample mean and standard deviation are computed, but the observations need not be ordered and the equation of estimate need not differ with sample size. A few charts are readily constructed, or used out of this text, to yield answers to the operational risks involved in a given period of time.

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Irving I. Gringorten

Abstract

The map is proposed for worldwide climatological statistics, to depict accurately the area covered by some specified meteorological condition or element. Since it is square, a grid overlay divides the map into small squares, each covering exactly the same amount of global area. The map is centered on the north pole where it is conformal. The parallels of latitude in each of the four quadrants of the square are represented by elliptical arcs that change from circular shape at either pole to a straight line at the equator.

Except for Antarctica no continent is split or divided in this projection. The Northern Hemisphere is presented without interruptions or discontinuities of direction. The map's four quadrants can be resembled to place the south pole and the whole of Antarctica at the center of the representation, as an interim step in the drawing of isopleths in the Southern Hemisphere.

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Irving I. Gringorten

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Irving I. Gringorten

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.

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Irving I. Gringorten

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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.

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Irving I. Gringorten

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.

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Irving I. Gringorten

Abstract

To test the skill of a forecaster the rule for the score S, for the quantitative forecast of Temperature or a similar variable, becomes S = −ln(1 − P 1 P 2 − 1 where P 1 is the cumulative climatic frequency of the forecast value T F, or the cumulative climatic frequency of the subsequently verified value T v, whichever is smaller. The value P 2 is the greater of these two frequencies. Such frequencies must be made conditional to the initial state of the weather in order to properly reward forecasters for recognizing future changes in the weather. For the quantitative forecast of precipitation, or similar variables, there are several alternate formulas for skill scores, each formula depending upon whether or not any precipitation is forecast or observed, or both forecast and observed.

This system of scoring assures that unskilled strategies, such as the forecasting of the mart frequent values, or persistence forecasting, will net the forecaster an expected average of zero. For individual accurate forecasts the rewards are greatest but still depend on the frequency or infrequency of the verified events. For inaccurate forecasts the rewards can be positive or negative, depending upon the sign and amount of change that is predicted, as well as the subsequent verification.

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Irving I. Gringorten

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.

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