Optimal control of lake pH for mercury bioaccumulation control

Mercury is recognized internationally as an important pollutant since mercury and its compounds are persistent, bioaccumulative and toxic, and pose human and ecosystem risks. A critical aspect of mercury cycling is its bioaccumulation, mainly as methylmercury, along the aquatic food web resulting in high risk of human exposure through contaminated fish consumption. Since lake acidity (pH) and mercury methylation are correlated, control of lake pH through lake liming is a possible option to mitigate mercury bioaccumulation. This work proposes to use optimal control theory to derive time-dependent lake liming strategies for a tighter control of lake pH. Since the behavior of the freshwater ecosystems such as lakes is often associated with considerable uncertainties, a robust and realistic analysis should incorporate such uncertainties. This work models the time-dependent uncertain variations in the basic lake pH value and derives the liming profiles in the presence of such seasonal pH fluctuations. Established techniques from real options theory are employed for modeling the uncertainty as a stochastic process, and stochastic optimal control is used for deriving liming profiles. The approach is critically evaluated through applications to various case study lakes. Considering the substantial costs associated with liming operations, the work formulates a multi-objective problem highlighting the tradeoff between accurate pH control and liming cost. The results of the control problem solution are also compared with heuristics based liming. The results, while highlighting the success of using time-dependent liming, put forth certain interesting aspects that might be helpful to a decision maker. The analysis is expected to make liming operation more reliable, thereby presenting one more tool to manage the harmful effects of mercury pollution.