Environmental Problems, Uncertainty and Mathematical Modeling

In this paper we discuss three rather special characteristics shared by many environmental problems. Namely, that (i) the environmental variables in which we are most interested constitute a stochastic process; (ii) the long-term or limiting behavior and the short-term or transient behavior are often both important; and (iii) the underlying probability distributions are likely to be influenced by the environmental policies or remedies that we choose to impose. This third characteristic implies the need to understand the impact of technologies and controls that influence the dynamics of the system. The control theoretic perspective of environmental engineering problems has, we believe, received less attention than it deserves in the literature. Consequently, after a brief discussion of the exogenous, control-independent case we focus on illustrating some special challenges and opportunities embedded in the control-dependent situations.