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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

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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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

The problem of decision making in applied meteorology is approached from the point of view of decision theory and subjectivist statistics. The modern concept of “utility” is discussed, and optional rules for decision making based on the availability of a limited amount of meteorological data are presented and discussed. Bayes' theorem forms the basis for the statistical estimation of the frequencies of various alternative weather events. The method is applied to a single example for the purpose of illustration, but it is emphasized that the generality of these techniques is great and that they warrant further study.

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Edward S. Epstein

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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

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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

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

Using 5 years of daily initialized height fields from the National Meteorological Center, expressed as coefficients of spherical harmonies, a climatology of the annual cycle has been formulated for the 1000, 700, 500 and 250 mb surfaces. The global analyses were first separated into separate Northern and Southern Hemisphere analyses, with a rhomboidal truncation at wavenumber 12. The daily values of each of the spectral coefficients were fit with the first four annual harmonics. Only those harmonics and Spectral coefficients were retained which explain a statistically significant amount of variance in time and space. The resulting mean height fields for both the Northern and the Southern hemispheres compare very favorably with established climatologies in spite of the limited length of the record on which they are based and the use of operational analyses. The statistical selection of spatial and temporal harmonies which contribute significantly to the annual mean and the annual cycle offers a unique insight into the structure of the climate in the two hemispheres.

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