Scientific models are a depiction of physical, chemical or biological processes that tells a story of what happens in the nature. We, as a human being, are spatially and temporally constricted, i.e. we cannot observe everything happening in the universe. Additionally, we do not know what had happened earlier or what is going to happen in the future. Modeling helps us generate the physical, conceptual or mathematical representation of a real phenomenon that is difficult to observe. Thus, we can get the information of some of its properties and behavior without measuring it physically. Moreover, we can see and predict how the system is going to behave in different conditions or, if it is in transient state, we could see its evolution with time. It can also be employed to back the possibility of the behavior of the system if there are uncertainties involved.
Model of a subsurface section showing presence of aquifers confined with unsaturated zone on top and basement rock at bottom
Where modeling fits:
Science started with observing patterns. We realized that everything we see happening around is not arbitrarily but is governed by some philosophy. Science emerged as we came up with the equations, law and quantification for the natural process. We did not remain mere a spectator in world, but could make a scientific hypothesis by observing the nature. And to test the authenticity of our hypothesis, we perform experiments. But often, the natural processes are complex and involves many scientific aspects and mathematical calculation. Thus, it becomes difficult to guess the behavior of a physical process. With the help of modeling, we can make a mathematically backed hypothesis which could involve complex physical systems at any possible scale. This is basically where modeling fits in the workflow of scientific investigation:
Type of models:
Static and dynamic: A Static model is a digital representation of a system. Here the properties of system does not change with time. Many physical systems are steady unless an external subject is not included and thus the static model can represent it correctly. But to study the behavior of a system which is transient or has an external subject we will have to implement the governing equations and make a dynamic model or also simulation.
Statistical and Demonstrative: Modeling involves uncertainties. We might not know all the parameters or even if we do, we might not have an equation relating them. Additionally, the system might be heterogeneous which is difficult to be taken it into account. So, we make a statistical model which gives many results each with a certain probability of being true. But when we know significantly about the system, and by making relevant assumptions, we could make the model closest to reality. That’s what we call a demonstrative model.
Forward and Inverse: To see how a system behaves, we take all the properties of it and with the help of equation, we predict its behavior. That’s called forward modeling. But sometimes, we know how it has behaved in a certain condition and we need to know what factors or properties govern it. So, we estimate it by inverse modeling.
“Essentially all models are wrong, some are helpful” – George E. P. Box
We aesthetically appreciate the beauty and complexity of nature and try to look what’s behind it through science. We can even paint the mountains and sea on the paper replicating the nature. But what we cannot do is to find the exact same color the mountains are made up of. So, we take a logical assumption that the mountain is made up of one single brown color that we have with us. Same goes for modeling. We can employ mathematical techniques and equations which could be very close to the physical system but may not be exact. All models we see are simplifications of the natural process. This is owed to the complex governing equation for the system whose analytical solution is difficult to find. But, it is useful in making an informed decision or better implementations of new technology in a system.
Scope of modeling:
The Sci-fi novel The Hitchhiker´s Guide to the Galaxy by Douglas Adams explains that we and the world we see are itself a part of a simulation controlled by the ‘real living being’. The enormous power of modeling by creating a virtual picture of the reality can make us sometimes wonder if the reality we perceive is true or not. However, modeling in the scientific world is not new and before the advent of computers, people have tried to use analogical models to explain a physical system. For instance, the flow of groundwater was used to be analogically replicated through electric circuits experiments. Owing to similar governing equations for both the system, scientist used to understand the movement of groundwater by tracing the current flow. Now with digital modeling, we are accomplishing the new heights in scientific investigations. It has escalated our ability of making a data driven hypothesis. In just a few hundred years, it has found its application in not just the field of science but also business, economics, psychology, social science. In future, modeling could answer all our inquisitive questions which we couldn’t discover due to our spatial and temporal constraint.
Application of modeling in groundwater contamination:
Groundwater remediation techniques are helpful in eliminating contaminants from aquifers physically or chemically. But before they are employed, it is indispensable to ascertain the spatial and temporal varying contaminant concentration in the system governed by both physical and chemical processes. This is where groundwater modeling comes in picture. With the help of field data, and the governing equations, the physical phenomenon are imitated digitally on the computer. Once built, we could study the fate of chemical species and assess the interaction of these particles with groundwater and host rocks. For instance, in my project Metal Aid, we are implementing the use of modeling in two ways: modeling before injection and modeling after injection. The groundwater system on which we are working is contaminated with chlorinated solvents. Before the injection of our product (various types of layered materials), we would like to know the physical and chemical behavior of groundwater of our site. For this an intensive field study is being done and with the help of field data, we can build up a predictive model which would tell us the evolution of groundwater and the extent of contamination the site would go through with time. This would require the knowledge of both physical and chemical processes in the form of mathematical equations which would govern the fate of the contaminants. Simultaneously, we would also build up geochemical models studying the reactivity and kinetics of the layered materials. With the help of these primarily models, we would simulate how the groundwater is going to behave once injection is done. This will be helpful in optimizing the injection of our product and estimate how efficient this remediation method would be. Additionally, the model would be modified once the injection has been done with the observation that we would get from field.
Bellomo, Nicola. “Modeling and Simulation in Science, Engineering and Technology.” (2009).
Box, George EP. “Robustness in the strategy of scientific model building.” Robustness in statistics 1 (1979): 201-236.