Theoretical environmental analysis

Lectures: 2 sessions / week, 1.5 hours / session

The course requires elementary physical reasoning, and therefore 8.01T Physics I is a prerequisite. The course also requires mathematical expertise at the level of 18.02SC Multivariable Calculus. Finally, 18.03SC Differential Equations is a corequisite.

This course analyzes cooperative processes that shape the natural environment, now and in the geologic past. It emphasizes the development of theoretical models that relate the physical and biological worlds, the comparison of theory to observational data, and associated mathematical methods. Topics include carbon cycle dynamics; ecosystem structure, stability and complexity; mass extinctions; biosphere-geosphere coevolution; and climate change. Employs techniques such as stability analysis; scaling; null model construction; time series and network analysis.

The principal objectives of this course are twofold. First, it provides students with an understanding of the mechanisms that underly the organization of the natural environment; i.e., how nature works. Second, it introduces students to methods of quantitative analysis that are useful for investigating how any system works. The course teaches students how to identify fundamental phenomena, how to formulate theoretical models, and how to quantitatively test models by comparison to observations. Students are provided with real datasets so that they can engage in these processes independently and creatively.

A secondary but no less important objective is to provide students with a unified view of environmental science. The unification is made possible by emphasizing aspects of earth, atmospheric, and planetary sciences that collectively act to create the natural environment, both physical and biological. We feature several of the great advances of 20th-century science (e.g., plate tectonics, climate cycles, and chaos theory) and introduce modern mathematical models of complex phenomena that remain to be understood. In so doing, we teach methods of analysis that are applicable throughout science and engineering.

The first part of the course (topics 1–3) is loosely organized around Earth's carbon cycle: The injection of CO2 into the atmosphere and oceans by volcanos and other tectonic processes, the exchange of CO2 between the atmosphere and oceans, and the runoff of dissolved carbon from rivers into the oceans. In each case, we emphasize the role of diffusion, perhaps the simplest and most important mode of transport in the natural environment.

In the second part of the course (topics 4–5) we focus on climate cycles, their foundation in orbital dynamics, and methods for the analysis of periodic phenomena in general. We learn how to compute and interpret power spectra, one of the most important tools used in the analysis of any system that evolves with time.

In the final part of the course (topics 6–7) we discuss the physical basis of ecological organization, the dynamics of ecological communities, and nonlinear dynamics in general. Here we meet concepts of scaling, stability, and the geometry of natural networks. The course ends with an introduction to the greatest intellectual achievement arising from the study of environmental dynamics: the theory of chaos.

There are quasi-weekly problem sets, a take-home midterm exam, and a take-home final exam due on the last day of classes. Students are welcome to collaborate on weekly problem sets but, if you do so, we ask that you list the names of the students with whom you have collaborated along with your own name. The take-home midterm and final exam must, however, be individual work. Students are not permitted to consult old solution sets.

Late problem sets will be accepted until the graded problems sets are returned. However, late problem sets will be penalized by 10% each day. Specifically, if the grade would have been s0 had the problem set been turned in on time, the effective grade Sn for a problem set handed in n days late is sn= s0 x 0.9n

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