Optimal Water Pollution Control in River Streams

不同的模拟/优化模型可用于河流水质保护，可为河流点源污染物负荷控制提供最优策略。一种是确定性优化模型，可视为线性规划问题；另一种是随机优化模型(稳健优化模型)，它考虑了问题数学公式中涉及的参数的不确定性。两种模型均能在满足水质标准或BOD、DO目标水质约束的条件下，确定河流允许的最大污染物负荷及其空间分布。为了增强模型的通用性，采用有限元方法将偏微分式的流动与输运(BOD和DO)方程转化为代数形式的等式约束。确定性模型适用于复杂的环状和/或辫状网络河流。随机(稳健)模型可以将河流流量、水深、断面面积、水温、风速和盐度等参数的不确定性反映到优化解中，从而提供一些可行的解决方案。因此，这对于制定河流水质管理的替代策略是有用的，决策者可以从中选择一种有效的策略。

Different two simulation/optimization models useful for conservation of water quality in river streams have been developed that can provide optimal strategies for controlling pollutant loads from point sources along the stream. One is a deterministic optimization model that can be regarded as a linear programming problem, while the other is a stochastic optimization model (robust optimization model) that considers uncertainties of the parameters involved in the mathematical formulation of the problem. The results are summarized in terms of the characteristics of the models as follows.Taking into account the dynamics of water motion and water quality as equality constraints in the optimization process, both of the models developed are capable of determining allowable maximum pollutant loads and their spatial allocation along the streams under the constraints of the water quality standards or targeted water qualities given for BOD and DO.In order to enhance the versatility of the models, the finite element method is employed to cast the flow and transport (BOD and DO) equations of partial differential form into the equality constraints of algebraic form.The deterministic model is applicable to the complex looped and/or braided network streams with junctions, and enables determination of the allowable maximum amount of pollutants loaded from multiple point sources as well as its optimal allocation to each of these sources.The stochastic (robust) model can reflect uncertainties of the parameters such as river discharge, water depth, cross-sectional area, water temperature, wind speed and salinity to the solution of optimization, thus providing some feasible solutions. It is therefore useful for making up some alternative strategies for stream water quality management from which decision makers can select an efficacious one.