Integrated mathematical models for drinking water reservoirs and constructed wetlands as a tool for restoration planning

Abstract

In this work, we propose the integration of mechanistic models for eutrophic reservoirs and constructed wetland within a dynamic optimization framework for the optimal design of wetlands for water quality restoration purposes. A partial differential equation system results from dynamic mass balances for the main biogeochemical variables in both reservoir and wetland. The integrated model is formulated as an optimal control problem within a control vector parameterization approach. The optimization model includes wetland areas as design variables and the fractions of tributaries that are diverted through the wetlands as control variables. The objective function is the minimization of the sum of the integral of the quadratic difference between total phosphorus concentration and a desired value below eutrophication limits and the integral of the quadratic difference between total nitrogen concentration and a desired value below eutrophication limits, along a twelve-year time horizon. The case of study is the eutrophic Paso de las Piedras Reservoir which supplies drinking water to two cities in Argentina, and it has two tributaries which run through an important agricultural area in the region. Numerical results provide: a) the optimal areas for constructed wetlands next to tributaries, b) optimal temporal profiles for diverted fraction of tributaries through wetlands, and c) temporal profiles of the main biogeochemical variables within the lake and the wetlands. The integrated model, which constitutes a useful management tool for a more rational planning of water quality restoration.