23. Analytical Approach for Sustainable Multi-Objective Management of Sediment-Algae Dynamics

We propose an analytical framework for sustainable management of sediment-algae dynamics in dam-downstream river environment. The problem considered in this short paper is an optimization of the dynamics by sediment replenishment schemes having multiple objectives: cost-efficient sediment supply and prevention of the bloom of nuisance benthic algae. We apply an Ergodic long-run stochastic control model to this problem, and show that it can be solved analytically being different from many other multi-objective optimization models. The sediment storage and algae population dynamics follow ordinary differential equations perturbed randomly by the sediment replenishment. We show that the most cost-efficient policy, namely the optimal sediment replenishment policy, is of a threshold type that is implementable in the real world. We analytically lead to a practical sustainability criterion that is based only on the biological and physical parameters, which can be specified prior to implementing a replenishment scheme. Our model is simple, but can give useful and practical insights into sustainable river environmental management.