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Edward S. Epstein

Abstract

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Edward S. Epstein

Abstract

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EDWARD S. EPSTEIN

Abstract

The meaning of probabilistic weather forecasts is discussed from the point of view of a subjectivist concept, of probability. The prior degree of belief of probabilities of the weather in question, for a given forecast statement, is expressed analytically as a beta function. Bayes' theorem is used to modify this degree of belief in the light of experience, producing a posterior degree of belief which is also in the form of a beta function. By establishing an arbitary criterion that one should always be able to assign at least as much belief to the probability interval implied by the forecast as to any other equivalent interval, a method of quality control for probability forecasts is developed. Appropriate tables are given to permit application of the method, and the implications of the method, for both forecaster and forecast user, are discussed.

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Edward S. Epstein

Abstract

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Edward S. Epstein

Abstract

Appropriately defined goodness-or-fit statistics are shown to provide a reasonable and objective means to determine the optimum number of harmonies to represent an annual climatology. The method is described in terms of its application, with varying degrees of success, to 5-day temperature means, their standard deviations, and to 5-day means of daily maximum and minimum temperatures.

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EDWARD S. EPSTEIN

Abstract

The relationship between point and area precipitation probabilities is examined on the basis of a simple model in which circular precipitation cells of uniform size are distributed at random over an area that is large compared to the forecast area. From knowledge of the cell size and the number of cells per unit area it is then possible to state both the point and area precipitation probabilities. Formulas and graphs of these relationships are shown. When the cells are large, point and area precipitation probabilities are almost equal, but they differ markedly when the cells are small. Joint and conditional probabilities of precipitation at two or more stations are also examined. An extension of the model is presented in which uncertainty regarding the density of cells is expressed as an elementary probability density, and the effects of this on the expected point and area precipitation probabilities are shown.

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EDWARD S. EPSTEIN

Abstract

Vertical velocities have been computed for the lower stratosphere for two independent winter periods, by employing a form of the adiabatic method. The regions studied were in both cases outside the polar vortex. The flow pattern was divided into stationary (long-wave) and transient (short-wave) components. The vertical velocity pattern associated with the stationary long wave is precisely that described by Kochanski [3]; i.e., the air rises in moving from warm troughs to cold ridges. The pattern associated with the short waves is more complicated. There is a maximum of warm, advection in the vicinity of short-wave ridges, and cold advection near troughs. Local temperature changes, however, very nearly compensate the advection, with the net result that in the mean the vertical velocities associated with short-wave patterns are small, but tend to be positive near ridges and negative near troughs. Superimposition of the short and long wave, however, can lead to any conceivable combination of signs of advection, local temperature change, vertical velocity, and position with respect to ridge or trough.

The single parameter which is most useful in specifying the vertical velocity is the temperature advection.

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Edward S. Epstein

Abstract

A method is proposed for deriving daily climatological values that are consistent with a given set of monthly means or monthly totals. It involves making an adjustment to a harmonic analysis of the monthly values. The method appears to provide reasonable results even under difficult circumstances.

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Edward S. Epstein

Abstract

When the initial values, or the parameters, of prognostic equations are not known with certainty, there must also be errors in the solution. The initial conditions may be represented by an ensemble, each member of which is consistent with all available knowledge. The mean of this ensemble is a reasonable "best" solution to the prognostic equation. Following Gleeson, we have examined the behavior of the error in the forecast, as represented by the rms deviation of the ensemble members from their mean, for a few simple equations. We have further examined the time-dependent behavior of the ensemble mean, as opposed to the solution obtained by applying the prognostic equation to the original mean values. These are, in general, different. It is concluded that optimum procedures for forecasting, i.e., solving prognostic equations, require includingterms in the equations to represent the influence of the initial uncertainties. Since the nature of these uncertainties may also have profound influences on the error of the forecast, this aspect, too, must be taken into consideration.

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Edward S. Epstein

Abstract

The details of the weather are not predictable beyond one to two weeks. At longer time ranges, averages of the weather over space and time can be usefully predicted only to the extent that the variations of the averages exceed the “noise” produced by the omnipresent but unpredictable transient weather. This margin of potential predictability is not large, but parts of it are being exploited in routinely issued monthly and seasonal forecasts. The format and utilization of these forecasts, the methods by which they are routinely produced, and prospects for improvements are discussed.

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