Stochastic dynamic programming models for water quality management

Abstract

This paper presents optimization models for waste load allocation from multiple point sources which include both parameter (Type II) and model (Type I) uncertainty. These optimization models employ more sophisticated water quality simulation models, for example, in the case of dissolved oxygen modeling, QUAL2E and WASP4, than is typically the norm in studies on the optimization of waste load allocation. Variability in selected input parameters to the water quality simulation models gives rise to stochastic dynamic programming approaches. Two types of reliability and feasibility attributes are highlighted, associated with the management options that are generated. Several dissolved oxygen simulation models are incorporated into the optimization procedures to explore the effects of Type I uncertainty on control decisions. Information from simultaneous consideration of multiple simulation models is aggregated in the dynamic programming framework through two regret-based formulations. By accommodating both model and parameter uncertainty in the modeling framework, trade-offs can be generated between the two so as to assess their influence on control decisions. The models are applied to a waste load allocation problem for the Schuylkill River in Pennsylvania. Papernumber 93WR00182. 0043.1397/93/93WR-00182505.00 variability. Aggregate measures of these violations are then traded off against control cost. SYSTEMS APPLICATIONS TO THE WASTE LOaD ALLOCATION PROBLEM Numerous studies have applied systems techniques to surface water quality management and typically minimize the overall cost of pollution control at multiple point sources of pollution that are subject to constraints on water quality at selected points in the stream. The basic mathematical models, the physico-chemical simulation models [Ambrose et al., 1988; Thomann and Mueller, 1987; Beck, 1984] and the optimization models within which the simulation models are imbedded, usually employ reaches along a river, defined in such a way that the physical environment within a reach is homogeneous. The confluence of a tributary, the presence of a point source of pollution or a marked change in the physical environment typically define a new reach. Most efforts for modeling dissolved oxygen (DO) and biochemical oxygen demand (BOD) use the SP equations (with or without the Camp-Dobbins modifications) to simulate pollutant biodegradation and to map waste loads into downstream DO concentrations [Streeter and Phelps, 1925]. The early systems applications to waste load allocation include Kerri [1966], ReVelle et al. [1967], Loucks et al. [1967], ReVelle et al. [1968] and Anderson and Day [!968]. Later work includes Arbabi [1973], Arbabi et al. [1974], and Arbabi and Elzinga [19751. Stochastic Applications It is interesting that attempts to address the natural variability of the waste load allocation problem preceded the development of the deterministic models. Stochastic models, then as now, consider streamflow as a random variable and may add as random variables, reaeration ...

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