Model uncertainty and model aggregation in environmental management

This paper presents dynamic programming formulations for addressing model and parameter uncertainty in environmental management problems. To address the inherent uncertainty surrounding the mathematical modelling of a physical system, we present ways to aggregate information from multiple simulation models into a dynamic programming framework. Aggregation methods are based on minimizing the extent or frequency of standard level violation, as predicted by the simulation models. Different formulations aggregate information from the multiple simulation models through extreme value, summation, risk averse and risk seeking approaches. A second basic type of uncertainty, parameter value uncertainty, is addressed by considering selected input parameters as random variables. Monte Carlo simulations are then performed to generate one-step Markov transition matrices for use in stochastic versions of the optimization models. In developing the optimization models, two types of problem feasibility are identified: nominal or first stage feasibility and secondary feasibility. Variants on the basic multiple model methodologies highlight subtleties in the definition of feasibility in multiple model cases. The methodologies are demonstrated in a water quality management example for the Schuylkill River in Pennsylvania.