Environmental Modeling - Mathematics and Statistics for the Environment - page 77

3 Environmental Modeling
Who has measured the waters in the hollow of the hand, or with the breadth of his hand marked off the
heavens? Who has held the dust of the earth in a basket, or weighed the mountains on the scales and
the hills in a balance?
—Isaiah 40:12
3.1 INTRODUCTION
There is a growing interest in the field of environmental monitoring and quantitative assessment of
environmental problems. For some years now, the results of environmental models and assessment
analyses have been influencing environmental regulation and policies. These results are widely
cited by politicians in forecasting consequences of such greenhouse gas emissions as carbon dioxide
(CO 2 ) and in advocating dramatic reductions of energy consumption at local, national, and inter-
national levels. For this reason, and because environmental modeling is often based on extreme
conceptual and numerical intricacy and uncertain validity, environmental modeling has become
one of the most controversial topics of applied mathematics.
Having said this, environmental modeling continues to be widely used in environmental practice,
with its growth limited only by the imagination of the modelers. Environmental problem-solving
techniques incorporating the use of modeling are widely used in watershed management, surface
water monitoring, flood hazard mapping, climate modeling, and groundwater modeling, among
others. It is important to keep in mind, however, that modelers often provide models for product
developers who use the results to describe what their products are based on and why.
This chapter does not provide a complete treatment of environmental modeling. For the reader
who desires such a treatment, we highly recommend Nirmalakhandan (2002) and NIST (2012).
Much of the work presented in this chapter is modeled after these works. Here, we present an over-
view of quantitative operations implicit to environmental modeling processes.
3.2 BASIC STEPS FOR DEVELOPING AN EFFECTIVE MODEL
The basic steps used for model building are the same across all modeling methods. The details vary
somewhat from method to method, but an understanding of the common steps, combined with the
typical underlying assumptions needed for the analysis, provides a framework in which the results
from almost any method can be interpreted and understood. The basic steps of the model-building
process are
1. Model selection
2. Model fitting
3. Model validation
These three basic steps are used iteratively until an appropriate model for the data has been devel-
oped. In the model selection step, plots of the data, process knowledge, and assumptions about the
process are used to determine the form of the model to be fit to the data. Then, using the selected
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