## Models

In class we heard how models are defined and used within both Dr. Weiss’s and Dr. Zobel’s discipline. Dr. Weiss used mainly physical models based on Newton Mechanics and laws of motion and mathematical models that use mathematical processes and equations to represent a physical process. Dr. Zobel used an optimization model for his research on pre-positioning supplies before hazards occur. In my discipline of Environmental and Water Resources Engineering we focus more on quantitative and physical models to help us discuss things that are happening in the real world and come up with quantitative analysis for things like pollutants, contaminants, global warming, and other environmental hazards.

Environmental and Water Resources Engineering has many smaller disciplines that fall under our department, and different models that accompany each discipline. On the water side, we have hydrology and fluid dynamics, and models like Hec-Ras and Modflow used for predicting the likelihood and/or quantifying water ex, flooding, storm surge, sea level rise etc. These models are limited in that they rely on assumptions that allow us to use equations to solve them quantitatively.

Here’s an example of a static quantitative model from my class notes in hydrology:

As you can see the equation that is being used to model snow-melt is limited in that it relies on having data that is representative of a large spectrum to calibrate and find a rate constant. The model is static and quantitative in that it accounts for how much snow has melted, but does not account for the water moving downhill. This static model would need to be paired with a fluid dynamic and a soil infiltration model if you wanted to know not only how much snow is expected to melt based on different temperatures each day, but also where that melted snow would go, and if it would perhaps flood a town, flow to a river or ocean, or be absorbed by the soil.

On the Environmental side, we have a lot of different types of disciplines that come together often for just one profession. For instance if you want to become a professional in Water Treament (either for drinking water or wastewater) you need to understand models from the fields of microbiology, chemistry, and physics so that you can design unit operations that will treat the water. You need to understand microbial kinetics models, to estimate how microbes react in chemical processes. You need to understand mass flux models to be able to estimate how aeration, or another unit operation will effect concentrations of chemicals in your water. And you need to understand water quality models to understand how hydraulic forces and sediment and other components of lakes and natural waters interact, so that you can understand your water source. In my program we take Principles of Environmental Engineering, which is essentially a class about modeling physical processes and using physical laws, like conservation of mass, to track concentrations and components of different systems. Here’s an example from my notes of modeling the effect sunlight and heat has on large water bodies:

All of these models have limitations in that you have to make assumptions to create the equations you use to make the model. For instance, will you assume that no flux (or air-water exchange) is happening in the model? If you do this then you would cross out a term in your model, but if you’re trying to mimic reality and flux is happening, perhaps at a low level, that term may or may not be important. Additionally, it can be hard to account for all the things that are happening within one model, for example, to model sea level rise, you need models on snow melt, models on fluid dynamics to find out where the water is flowing, models on soil infiltration, evaporation, transpiration etc. to find out if water is lost, models on water quality and potential stratification of large bodies of water to see how the temperature differentials impact sea currents and water movement. There are so many equations and models that must be used within other models, that the assumptions made could have a large impact. Dr. Zobel had a similar experience where he was building a model to figure out where to place red cross trailers, and within his model he used an equation- or a mathematical model- to determine risk. If that equation had a simplifying assumption that was untrue for the scope of Dr. Zobel’s larger model, then his using that method of calculating risk for his model could potentially impact the results of his findings. Just because most model’s components are actually smaller models, does not mean that modeling is inherently flawed, in no way am I suggesting that models should be thrown into the post modern science category with no way to prove their worth. The fact that most models are built from smaller models is both a limitation to their use, and also a great system that allows us to get closer and closer to capturing reality. We just have to be careful that the components of the model support and agree with the model and that underlying assumptions made throughout the model do not contradict themselves.