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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

The likelihood ratio of the data for a hypothesis of some change, relative to the hypothesis of no change, is a suitable statistical measure for the detection of climate change. Likelihood ratios calculated on the basis of Angell and Korshover's (1977) global mean temperature, updated through 1980, do not show convincing evidence of recent climate change. It is possible to calculate probabilities of obtaining future values of likelihood ratios, depending on the postulated future climate change. A modest but significant climate change, such as that expected to occur from an increase of atmospheric carbon dioxide, is likely to be detected from global mean surface temperatures within ten years. The joint behavior of the troposphere and stratosphere is more likely to discriminate between climate change and no change than are surface temperatures. In this case, a climate change that can be attributed to carbon dioxide increase should be detectable by 1986.

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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

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Edward S. Epstein

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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

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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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