A STOCHASTIC APPROACH TO SPACE-TIME MODELING OF RAINFALL

Abstract

This study gives a phenomenologically based stochastic model of space -time rainfall. Specifically, two random variables on the spatial rainfall, e.g. the cumulative rainfall within a season and the maximum cumulative rainfall per rainfall event within a season are considered. An approach is given to determine the cumulative distribution function (c.d.f.) of the cumulative rainfall per event, based on a particular random structure of space -time rainfall. Then the first two moments of the cumulative seasonal rainfall are derived based on a stochastic dependence between the cumulative rainfall per event and the number of rainfall events within a season. This stochastic dependence is important in the context of the spatial rainfall process. A theorem is then proved on the rate of convergence of the exact c.d.f. of the seasonal cumulative rainfall up to the ith year, i > 1, to its limiting c.d.f. Use of the limiting c.d.f. of the maximum cumulative rainfall per rainfall event up to the ith year within a season is given in the context of determination of the 'design rainfall'. Such information is useful in the design of hydraulic structures. Special mathematical applications of the general theory are developed from a combination of empirical and phenomenological based assumptions. A numerical application of this approach is demonstrated on the Atterbury watershed in the Southwestern United States.