Stochastic Integral Equations and Rainfall-Runoff Models

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.

Klappentext

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.

Inhalt
1: Rainfall-Runoff Approximation.- 1.1. Introduction.- 1.2. Stormflow Determination Methods.- 1.3. Method for Development of Synthetic Flood Frequency Estimates.- 1.4. Watershed Modeling Uncertainty.- 1.5. Hypothetical Floods, Balanced Floods, and Design Storm Methods.- 1.6. A Preview of the Rainfall-Runoff Model Prediction Problem.- 1.7. An Overview of Rainfall-Runoff Model Structures.- Study Problems.- 2: Probability and Statistics Review.- 2.1. Probability Spaces.- 2.2. Random Variables.- 2.3. Moments.- 2.4. Two Random Variables.- 2.5. Several Random Variables.- 2.6. Parameter Estimation.- 2.7. Confidence Intervals.- Study Problems.- 3: Introduction to Stochastic Integral Equations in Rainfall-Runoff Modeling.- 3.1. Introduction.- 3.2. Introduction to Analysis of Rainfall-Runoff Model Structures.- 3.3. Application of Stochastic Integral Equations to Rainfall-Runoff Data.- 3.4. Another Look at Probabilistic Modeling: Assuming Mutually Independent Parameters.- Study Problems.- 4: Stochastic Integral Equations Applied to a Multi-Linear Rainfall-Runoff Model.- 4.1. Stochastic Integral Equation Method.- 4.2. Sensitivity of Functional Operator Distributions to Sampling Error.- 4.3. A Multilinear Rainfall-Runoff Model.- 4.4. An Application of the S.I.E.M..- Study Problems.- 5: Rainfall-Runoff Model Criterion Variable Frequency Distributions.- 5.1. Probabilistic Distribution Concept.- 5.2. The Distribution of the Criterion Variable.- 5.3. Sequence of Annual Model Inputs.- 5.4. Model Input Peak Duration Analysis.- 5.5. Criterion Variable Distribution Analysis.- 5.6. Estimation of T-Year Values of the Criterion Variable.- 5.7. T-Year Estimate Model Simplifications.- 5.8. Discussion of Results.- 5.9. Computational Problem.- 5.10. Computational Program.- Study Problems.- 6: Using the Stochastic Integral Equation Method.- 6.1. Introduction.- 6.2. Problem Setting.- 6.3. Stochastic Integral Equation Method (S.I.E.M.).- 6.4. Approximation of Criterion Variable Confidence Intervals, Using the S.I.E.M..- 6.5. Rainfall-Runoff Models, and the Variance in the Criterion Variable Estimates.- 6.6 Rainfall-Runoff Model Calibration.- 6.7. Confidence Interval Estimates.- 6.8. Unit Hydrographs as a Multivariate Normal Distribution.- Study Problems.- References.- Author Index.