Introduction to Environmental Modeling

Introduction

Nothing exists outside of its environment. For this reason alone, humans cannot ignore their environments. As civilizations have become more sophisticated in their ability to alter their environments, the need to understand chemical, biological, and physical activities within those environments has increased. One of the great challenges in gaining understanding is to determine how historical information can be used as a predictor of the future. It is not possible to simply extrapolate the past into the future because physical alteration of a region causes it to behave differently from its historical record. For example, deforestation alters the amount of water that is returned to the atmosphere by transpiration and evaporation in that region. Paving an agricultural region with asphalt impacts the amount of water that infiltrates into the subsurface. Removal of a predator from an ecosystem will alter populations within that system. Discharge of combustion products into the air will impact health. Thus, as the stock market analysts say, “Past performance is not necessarily an indication of future results.”

Although historical environmental data should not be ignored simply because it cannot be directly extrapolated to the future, we need tools that allow us to use this data wisely and effectively. These tools are mathematical models of processes, phenomena that occur in a system that contribute to its perceived behavior. Additionally, we will encounter regions or problems for which no data exists. If we are going to meaningfully study problems in those regions, we need a context in which questions can be asked. This context is provided by a mathematical model that describes relevant processes. Nevertheless, before embarking on a tour of some mathematical models, a disclaimer seems appropriate.

Mathematical models have developed a bit of an aura. They can be complex. Those who find the complexity to be overwhelming are inclined to accept the results of the model with minimal questioning. Complexity is equated to credibility! The fact that models can also produce striking color graphics and animations of simulated results adds to their credibility. However, it is important to emphasize that it is easier to misuse a model than to use one properly. Models are only, as the name states, “models” of reality. They are not reality; it is not possible to incorporate all elements of a real system into a model.