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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.

Inhaltsverzeichnis

Frontmatter

1. Rainfall-Runoff Aproximation

Abstract
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 deterministic solution to the problem has not yet been found.
Theodore V. Hromadka, Robert J. Whitley

2. Probability and Statistics Review

Abstract
A probability model tells what the things are that can happen and what their probabilities are.
Theodore V. Hromadka, Robert J. Whitley

3. Introduction to Stochastic Integral Equations in Rainfall-Runoff Modeling

Abstract
In this chapter, we will begin to examine how the general approach to rainfall-runoff modeling can be analyzed with respect to uncertainty. Specifically, the underpinnings of the total rainfall-runoff modeling effort will be recast into a problem involving stochastic integral equations.
Theodore V. Hromadka, Robert J. Whitley

4. Stochastic Integral Equations Applied to a Multi-Linear Rainfall-Runoff Model

Abstract
In this chapter, a multilinear rainfall-runoff model is used to develop stochastic estimates of runoff hydrographs for the frequently occurring case where the uncertainty in the effective rainfall (rainfall less losses; rainfall excess) over the catchment dominates all other sources of modeling uncertainty. Indeed, just the uncertainty in the precipitation over the catchment appears to be a major obstacle in the successful development, calibration, and application, of all rainfall-runoff hydrologic models (e.g., Schilling and Fuchs, 1986; Loague and Freeze, 1985; Beard and Chang, 1979; Troutman, 1982). The coupling of the uncertainty in both the rainfall and loss rates results in an important source of uncertainty that should be included in runoff estimates
Theodore V. Hromadka, Robert J. Whitley

5. Rainfall-Runoff Model Criterion Variable Frequency Distributions

Abstract
The previous chapters include brief statements from several reports which conclude that the variability in the effective rainfall over the catchment is a dominant factor in the development, calibration, and application, of hydrologic models (e.g., Schilling and Fuchs, 1986, among others). Including this premise in hydrologic studies would indicate that hydrologic model estimates must be functions of random variables, and hence the estimates are random variables themselves. In this chapter, the distribution of the model estimates is considered in order to evaluate the annual T-year values.
Theodore V. Hromadka, Robert J. Whitley

6. Using the Stochastic Integral Equation Method

Abstract
The Stochastic Integral Equation Method (S.I.E.M.) provides a procedure for including uncertainty and approximation error in the prediction of runoff quantities, given rainfall data. Important modeling issues may now perhaps be more rationally examined, such as rainfall-runoff model structure improvement, calibration, development of confidence interval estimates, among others. In this chapter, we will also develop the S.I.E.M. using model output.
Theodore V. Hromadka, Robert J. Whitley

Backmatter

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