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Thomas A. Gleeson

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Thomas A. Gleeson

Abstract

In a statistical-dynamical study of the atmosphere, the dependent variables of the dynamic equations constitute the continuous coordinates of a phase space in which an ensemble of possible states develops with time, according to the equations. However, the prediction of precipitation requires upward, not downward, winds and saturated, not unsaturated, air. These dichotomous features introduce first-order discontinuities in the dynamics at the time of condensation. It is shown that these discontinuities do not prevent the continuous transformation of a model ensemble with time, so that theoretical probabilities of atmospheric states are still possible both before and after precipitation begins.

By means of the probability calculus, a model is developed to predict a theoretical probability of precipitation occurrence.

Examples are given to illustrate these methods.

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Thomas A. Gleeson

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Thomas A. Gleeson

Abstract

Solutions for the differential equation of heat flow as applied to the atmosphere and to the ground are related by surface boundary conditions. One condition represents a vertical energy balance involving annual variations of incoming solar radiation, albedo, surface heat loss due to evaporation, heat radiation from the surface to space, heat reradiation to the surface from clouds and water vapor, convective heat transport between air and the surface, and conductive heat transport between ground and the surface. Applied to climatological data, the solution for the atmosphere yields a coefficient of vertical heat exchange that is constant rather than variable with elevation, and also fairly close approximations to observed annual variations of potential temperatures near the surface at three widely separated continental stations. Poorer agreement between observed and theoretical variations at upper levels in the troposphere may be due to neglect of advection and localized heating and cooling aloft. Theoretical variations of temperature at various ground depths are quite close to observed variations.

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Thomas A. Gleeson

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A statistical theory developed previously is applied to two prediction techniques: graphical integration of Estoque's baroclinic model and numerical integration of a barotropic model. In both instances, synoptic observations are regarded as samplings of the actual state at observation time. Probabilities of forecast height values to occur in specified height intervals at 500 and 1000 mb are computed with graphical aids. Analogous probabilities are obtained at 500 mb with aid of numerical methods. These are limiting probabilities whose values depend in part on network density and initial synoptic analysis.

Forecast procedures are described. Examples of probability forecasts and verifications are presented. It is found that theoretical limiting probabilities compared successfully with empirical probabilities for several synoptic cases, showing closest agreement in the numerical technique. This and other results are discussed.

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Thomas A. Gleeson
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Thomas A. Gleeson

Abstract

An expression is obtained for the limit to certainty of perfect prediction, in terms of the amount of verification data and the detail of the predictand. Related expressions are developed for the number of effective predictors that may be combined in a given prediction method, and for the fineness of predictand detail that can be forecast.

Applications to evaluation of practical forecast problems are discussed by use of examples. Similar treatments are suggested for specification problems.

Because of the generality of their derivations, it is believed that these expressions would be useful in other fields, as well as in meteorology.

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Thomas A. Gleeson

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A relation is derived for the periodic valley wind as a function of time and elevation, in terms of the diurnal temperature variation, slope of the valley floor, eddy viscosity, the Coriolis force, and a pressure force representing the constraining effect of the valley walls. The theoretical wind is examined in several postulated situations. It is shown that more realistic representations of the valley wind are possible when effects of the Coriolis force are considered than when neglected.

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Thomas A. Gleeson

Abstract

No Abstract Available.

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Thomas A. Gleeson

Abstract

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