Accession Number : AD0600835

Title :   A SIMPLIFIED MODEL FOR THE FORMATION, MOVEMENT, AND DISSIPATION OF FAIR WEATHER CUMULUS CLOUDS.

Descriptive Note : Scientific rept. no. 1

Corporate Author : MICHIGAN STATE UNIV EAST LANSING

Personal Author(s) : Fox,Martin

Report Date : 29 MAY 1964

Pagination or Media Count : 22

Abstract : A stochastic model for the temporal evolution of the contribution to cloud cover by fair weather cumuli is presented. A differential equation is obtained for a probability generating function. The general solution of the differential equation is obtained and this is used to obtain the probability generating function for the number of clouds at time t given the number at time O. It is noted that the real interest is in the joint probability generating function for the numbers of clouds at times t sub 1,...,t sub n given that at time O there are no clouds. The methods of obtaining this joint probability generating function is exemplified by the solution for the case n=2. A Mathematical Appendix at the end of this report carries out certain of the derivations in greater detail. The definition and some properties of probability generating functions are also included there.

Descriptors :   (*MATHEMATICAL MODELS, CUMULUS CLOUDS), (*CUMULUS CLOUDS, MATHEMATICAL MODELS), (*METEOROLOGICAL PHENOMENA, MATHEMATICAL MODELS), CLOUD COVER, STOCHASTIC PROCESSES, DIFFERENTIAL EQUATIONS, PROBABILITY

Distribution Statement : APPROVED FOR PUBLIC RELEASE