Stochastic Integral Equations and Rainfall-Runoff Models - Tapa blanda

The subject of rainfall-runoff modeling involves a wide spectrum of topics. Fundamental to each topic is the problem of accurately computing runoff at a point given rainfall data at another point. The fact that there is currently no one universally accepted approach to computing runoff, given rainfall data, indicates that a purely deter­ ministic solution to the problem has not yet been found. The technology employed in the modern rainfall-runoff models has evolved substantially over the last two decades, with computer models becoming increasingly more complex in their detail of describing the hydrologic and hydraulic processes which occur in the catchment. But despite the advances in including this additional detail, the level of error in runoff estimates (given rainfall) does not seem to be significantly changed with increasing model complexity; in fact it is not uncommon for the model's level of accuracy to deteriorate with increasing complexity. In a latter section of this chapter, a literature review of the state-of-the-art in rainfall-runoff modeling is compiled which includes many of the concerns noted by rainfall-runoff modelers. The review indicates that there is still no deterministic solution to the rainfall-runoff modeling problem, and that the error in runoff estimates produced from rainfall-runoff models is of such magnitude that they should not be simply ignored.

The uncertainty in rainfall-runoff modeling predictions has become a topic of recent key interest. In this book, the uncertainty problem is approached by use of stochastic integral equations. Various aspects of the rainfall-runoff modeling process are scrutinized by use of probabilistic models, such that when combined, a stochastic integral equation results. Uncertainty in single even runoff estimates, as well as return frequency event outcomes are analyzed. Use of example problems demonstrate the application of stochastic integral equations in addition to explaining the underlying concepts. Computer program source code is also provided which can be used to solve both theoretical and real-world problems. The generous supply of chapter problems enables the book to be used as an applied textbook in stochastic integrals.