Initial Publication Date: October 7, 2016
Using numerical models to experiment with earth and environmental systems
Phillip G. Resor, Department of Earth and Environmental Sciences, Wesleyan UniversityOne of the challenges of earth and environmental sciences is that the physical and temporal scales of the systems often preclude direct experimentation. Scaled modeling, however, provides a means to conduct numerical or analog experiments in order to evaluate the interaction between components of a system and the effects of changes in external forcing (initial or boundary conditions).
In my own research I am interested in the interaction between fault geometry and deformation during the earthquake cycle. Numerical models are critical tools for exploring the earthquake cycle and fault systems, as we cannot directly observe key pieces of the system and we are interested in time scales that extend well beyond a human lifetime. Advances in geodesy have permitted us to observe deformation of the earth surface throughout the earthquake cycle with increasing temporal and spatial sampling and higher precision since the Great 1906 San Francisco Earthquake, which was observed by pre and post earthquake triangulation surveys (Reid, 1910). Inferring the sub-surface processes responsible for this deformation, however, requires modeling. In my research I use both finite element (FEM) and boundary element (BEM) models along with geophysical and geological observations to explore fault system behavior.
As my own experience illustrates, modeling has become an important tool in Earth and Environmental Science research; however, it has yet to become a standard component of our undergraduate curriculum. To help address this deficiency I introduced an upper level elective course for undergraduates at Wesleyan University in the spring of 2013 entitled Modeling the Earth and Environment. The layout of course topics and problem sets is based primarily on the text Mathematical Modeling of Earth's Dynamical Systems: A Primer by Slingerland and Kump (Slingerland and Kump, 2011). The course was over-subscribed in its first offering, suggesting that Wesleyan students also recognize the importance of modeling to their future as Earth and Environmental Scientists.
The philosophy of the course is to introduce students to the entire process of modeling from translating Earth systems into idealized mathematical models, applying numerical methods for solving the resulting equations, implementing these solutions in MATLAB, and using the models to conduct numerical experiments. Each week I introduce a case study on Monday and present the necessary theoretical background. On Wednesday we discuss issues of implementation in MATLAB and students work in class on an associated problem set. On Friday we discuss two papers that use models to address the topic of the week. Although this course could be taught with commercial modeling software, I think that it is important for students to gain experience developing their own code so that they can better understand and appreciate what's happening inside the black box of a commercial code.
The course was an overall success, based on student evaluations and assessments, but the learning curve was steep as students tried to learn MATLAB, finite difference methods, and modeling all at once. I hope that by taking a more intentional approach to introducing programming in MATLAB I can help to reduce some of the students' struggles and anxieties. I also plan to develop case studies for each modeling topic covered in the course so that students have a clearer picture of the systems we're trying to model and why we are trying to model them. The most compelling case study from my 2013 class was based on the Woburn superfund site made famous in the movie A Civil Action starring John Travolta (1998). This example provided a problem of clear societal relevance and a case study where modeling was critical to interpretation of the data. I hope that an improved course will help our majors to become better makers, users, and consumers of models
References
Reid, H. F., 1910, The California earthquake of April 18, 1906; the mechanics of the earthquake; Vol. II: Carnegie Inst. of Wash., v. 87, no. no.2, p. 192.
Slingerland, R. L., and Kump, L., 2011, Mathematical Modeling of Earth's Dynamical Systems: A Primer, Princeton, Princeton University Press, 231 p.:
Zaillian, S., Dir, 1998, A Civil Action, Buena Vista Pictures, film.