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Stochastic integral equations and rainfall-runoff models. (English) Zbl 0702.60104
Berlin etc.: Springer-Verlag. xviii, 384 p. DM 138.00 (1989).
The usual approach used by rainfall-runoff modelers is to attempt to compute the expected value of the criterion variable under study (e.g., peak flow rate, pipe size for the design condition, etc.). However, with the acknowledged uncertainty in rainfall-runoff estimates, it may be more appropriate to compute the probabilistic distribution of the subject criterion variable given the past history of performance from the chosen rainfall-runoff model, and then use a confidence interval limit as the design objective. A method to include this uncertainty in runoff estimates is to use stochastic integral equations.
By means of stochastic integral equations, the rainfall-runoff model’s history of error (developed from prior rainfall-runoff data) can be used to develop the probable variations in predicted runoff estimates, given a hypothetical rainfall event. Any reasonable rainfall-runoff model can be used, no matter the level of complexity, and an appropriate stochastic integral equation developed which approximately represents the model’s performance in accurately estimating runoff.
With the stochastic integral equation approach to including modeling total error, essentially all rainfall-runoff modeling approaches are revitalized in that their respective capabilities in predicting runoff quantities can be rationally compared by the evaluation of the associated probabilistic distributions for the subject criterion variable. The frequency-distribution of the subject criterion variable can then be used to make rational decisions as to the proper design.

60K99 Special processes
60H20 Stochastic integral equations
60-02 Research exposition (monographs, survey articles) pertaining to probability theory