AN ADAPTIVE MANAGEMENT MODEL FOR BENTHIC ALGAE UNDER LARGE UNCERTAINTY AND ITS APPLICATION TO HII RIVER

Abstract

Environmental and ecological dynamics in rivers are often stochastic and uncertain. Such a situation is called “under incomplete information” in mathematical science. We propose a new stochastic control model under incomplete information for cost-effective management of river environment, focusing on harmful benthic algae in dam downstream. The goal of the model is to find the optimal intervention policy to suppress the algae growth. An innovative point of the model is that it can consider the learning process on the algae population dynamics by the manager of river environment. Finding the optimal policy is achieved through solving a nonlinear integro-differential equation: Hamilton-Jacobi-Bellman (HJB) equation. Model parameter values are identified for a downstream reach of Obara Dam in Hii River, Japan. The theoretical and numerical analyses on the HJB equation give the optimal threshold value of the algae population density above which the interventions to suppress algae growth should be carried out.