Groundwater modeling is an invaluable tool for the management of groundwater, for both understanding past occurrences and predicting future occurrences in the region. The insights and predictions obtained from modeling include 1) the effects of multiple pumping wells, 2) the availability of groundwater resources, both in terms of water quantity and quality, 3) the occurrence of natural compounds, and 4) the fate-and-transport of contaminants through time.

Groundwater modeling is a “synthesis (combining) of related but disparate (different and diverse types of) data”. As such, it has a mostly unfair reputation for being expensive, with much of the perceived cost actually being the cost of data acquisition, compilation, and management. Models need to be defined and calibrated with data. To understand any groundwater problem, even without modeling, the data usually need to be compiled anyway.

Groundwater modeling can range from very simple, inexpensive “back of the envelope” calculations to very complex, arguably expensive analyses that may include simulations on the computer. A groundwater model is a mathematical model constructed with a purpose in mind. Thus, the question of its purpose must be answered before beginning the project, to avoid misunderstandings and cost overruns. The more detailed a model, the more it can explain, but the greater the complexity the more information is required to define it and constrain the answer. The mathematics can be simplified, the solution made less expensive, the more that simplifying assumptions can be justified. The industry phrase for this is KISS: Keep It Simple Stupid.

Groundwater modeling is an exercise in deductive reasoning. It starts with an assumption of truth–namely the physics of groundwater flow and the existing field conditions for that flow–and derives its conclusions mathematically. If the assumptions of the truth change, so do the conclusions. Even professionals within the industry will joke about modeling, “What do you want the answer to be?” However, the question, “What do we observe that we need this model to explain?” can lead to many interesting discoveries. “Modeling guides the research.” (-Professor Mary Anderson, University of Wisconsin, Madison).

That is why groundwater modeling must be conducted by a seasoned professional like Dr. Hoaglund who understands and can defend both the initial assumptions and the limitations of its conclusions.

We tend to think deduction is the most powerful form of reasoning. Mathematics entices us to believe its predictions are infallible. After all, we landed the astronauts on the Moon with decimal point precisions using mathematical models of the physics. But the most powerful form of reasoning scientifically is actually induction: the reasoning of general conclusions from particular facts (i.e. data). And facts overrule models.

A single datum not in alignment with a model does not necessarily disprove the model.  The model may need to be refined to better match results within statistical error.  A groundwater model will never precisely reproduce all the data, but it can continue to make reasonable conclusions matching ordinary data. We can continue to refine the model in a process called calibration.  If the model is reasonable and robust in its explanations, it takes a significant finding to unseat it completely. To quote Carl Sagan, “Extraordinary claims require extraordinary evidence.”

Carl Sagan gave the example of Ptolemy’s model of the solar system, which stood the test of time and was used for over 1,000 years until Galileo’s extraordinary observations disproved it, in favor of the Copernican model.  If extraordinary evidence is found, we must be willing to reject a model and replace it with a new model, with new starting assumptions of truth.