Water -- Pollution -- Mathematical models.
Sediment transport -- Mathematical models.
Turbulence -- Mathematical models.
Monte Carlo method.
Committee ChairFogel, Martin M.
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractA risk-based approach for addressing several non-structural stream quality management objectives is presented. To estimate risk, the input process, the stream contaminant transport, and the consequence of contamination are modeled mathematically. The transport of soluble contaminant introduced at a point into a turbulent stream medium is modeled as a boundary value problem in which the contaminant satisfies the Kolmogorov forward equation within the medium. Observed properties of turbulence are used to justify the adoption of this equation. The fundamental solution, as the probabilistic response of the stream to an instantaneous unit flux input, is derived and used as the kernel in a stochastic integral representation of the transport problem. The bulk input is used as the forcing function in the integral equation. It is modeled as a sequence of independent pulses with random magnitude and duration and also with random interval between the incidence of adjacent pulses ,. Stochastic simulation is used to construct the moments and the probability distribution of stream concentration and those of several variables associated with the exceedance of the concentration above a specified threshold. The variables include the dosage and the time to the first exceedance. The probability that an observed stream concentration exceeds the threshold within a given interval of time is also constructed. Generalizations of the Chebyshev inequality are extended to the case of a stochastic process. Upper bounds on the constructed probability distributions are calculated using these extensions. Based on previous studies, a rectangular hyperbolic relationship is assumed between dosage and consequence. The relationship is combined with the empirical dosage density function to obtain estimates of value risk of stream concentration for various thresholds. Given an acceptable risk, the corresponding threshold may be used as the stream standard. The reliability function, defined as the complementary density function of exceedance times, may be used as a gauge of the effectiveness of pollution abatement measures. Other illustrated areas of application include the construction of a minimum cost contaminant discharge policy and the determination of the optimal sampling interval for stream surveillance.
Degree NamePh. D.
Degree ProgramHydrology and Water Resources