OPTIMAL REGULATION OF EUTROPHYING LAKES, FJORDS AND RIVERS IN THE PRESENCE OF THRESHOLD EFFECTS

In a large number of practical environmental regulation problems, the damage done by pollutants depends on stocks and/or flows of pollutants exceeding certain thresholds. A typical example is eutrophication which occur when stocks of nutrients in a lake exceeds a certain threshold. The present paper presents a model of eutrophication that accounts for such thresholds. The paper does so by applying a novel technique in optimal control theory that allows for the analysis of systems where state-variables bounce back and forth over thresholds that take the form of functions of time and state-variables.