Stochastic methods in hydraulics and hydrology of streamflow

Abstract

Stochastic methods in hydraulics and hydrology of streamflow are presented. The hydraulics part consists of mechanics of streamflow and sediment transport. A technique presented herein enables one to analyze a limited amount of field data to determine the stochastic structure of irregular stream geometry so that cross-sections and slopes of a stream may be simulated wherever, or as many as, needed. It provides the rational basis of efficient use, interpolation, and extrapolation of field data of irregular stream geometry for any studies to understand and control transport processes in streams. Stochastic modelings of motion of a single sediment particle, either in suspension or on the stream bed, help in understanding the complex mechanism governing sediment transport and, hence, improving techniques for calculating the spatial distribution and transport rate of sediment. For practical applications, however, the technique combining the stochastic and deterministic methods should be most effective.

In the hydrology part, Markov and non-Markov models are presented which may be used to simulate streamflow data. Markov models, which dominated stochastic hydrology in the past, have short memories and, therefore, cannot preserve or simulate long-term persistence characterizing physiscal streamflows. Non-Markov models which are currently being developed, and may or may not belong to the Brownian domain, have very long or infinite memories.

This paper is dedicated to the idea of coupling the stochastic and deterministic methods in hydraulics and hydrology, so that the two methods may contribute their strengths while complementing each other for their weaknesses.