MODEL UNCERTAINTY AND MODEL AGGREGATION IN ENVIRONMENTAL-MANAGEMENT

This paper presents dynamic programming formulations for addressing mo del and parameter uncertainty in environmental management problems. To address the inherent uncertainty surrounding the mathematical modelli ng of a physical system, we present ways to aggregate information from multiple simulation models into a dynamic programming framework. Aggr egation methods are based on minimizing the extent or frequency of sta ndard level violation, as predicted by the simulation models. Differen t formulations aggregate information from the multiple simulation mode ls through extreme value, summation, risk averse and risk seeking appr oaches. A second basic type of uncertainty, parameter value uncertaint y, is addressed by considering selected input parameters as random var iables. Monte Carlo simulations are then performed to generate one-ste p Markov transition matrices for use in stochastic versions of the opt imization 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 metho dologies highlight subtleties in the definition of feasibility in mult iple model cases. The methodologies are demonstrated in a water qualit y management example for the Schuylkill River in Pennsylvania.