Climate science is inherently interdisciplinary, with every division in the sciences contributing to our understanding of various climate processes. Mathematical and computational techniques play an especially important role in climate studies, however, in that they are the mechanisms by which disparate climate processes are synthesized into mathematical models. These quantitative models constitute the "laboratory" of climate science. They give essential insight into the ways in which individual climate processes interact and help in understanding the possible responses of the climate system to various forcings.
This course will examine climate from the perspective of mathematical modeling. The goal of the course is to learn an array of techniques that are often useful when trying to quantify naturally occurring systems, and to investigate how these techniques may be used to model the interaction of climate processes.
The course material is loosely organized into three parts. The first part will cover the basics of climate physics. The second part will consist of investigations into a variety of simple climate models. There are an abundance of relatively simple climate models that are interesting not only for their mathematics, but for what they say about climate itself. Indeed, these simple models are often of much greater importance for clarifying the relative roles of individual climate processes than are the big general circulation models that are more oriented toward detailed simulation of observed phenomena. Finally, the course will culminate in the modeling of climate-glacier interaction.
Glaciers are sensitive indicators of climate change. In fact, some of the simplest glacier models parameterize this sensitivity by just two quantities: mean bed slope and atmospheric temperature lapse rate. Inverting this relationship yields an estimation of the historical change in the earth’s temperature as a function of glacier length. Thus, through even the simplest mathematical models of glaciers we obtain independent estimates of the changes in global temperature over the past 100 years.
The near polar regions (where many glaciers reside) have been called the "barometer of climate change" due to their extreme sensitivity to variations in climate. Even small increases in average temperature in these regions lead to dramatic changes in the form of retreating glaciers, shrinking ice fields, melting permafrost, migrating species, etc. The near-polar regions are also of central importance in climate modeling due to the enormous influence that planetary albedo (the solar reflectivity of the earth) has on global temperatures.
This course assumes familiarity with the material of Calculus I (derivatives, limits, integrals, and their use in modeling simple physical systems). More advanced topics in mathematics will be introduced as needed. These topics will include differential equations, numerical methods, matrix equations, spectral methods, finite-difference methods, etc. No special computing background is assumed. Mathematica, MATLab, and Vensim will be used frequently to simulate models and to aid in model visualization. Relevant syntax and programming features needed to utilize these software packages will be presented as needed.
If you are an OWU student who is interested in taking this course, please contact the instructor, Dr. Craig Jackson, at chjackso(at)owu.edu.
The following books will be the principle references for the course:
- Global Physical Climatology, Dennis L. Hartman, Academic Press, 1994. (amazon)(google)
- Minimal Glacier Models, Johannes Oerlemans, Igitur, Utrecht, 2008. (pdf)
Supplementary readings may be taken from:
- Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics, M. Ghil and S. Childress, Applied Mathematical Sciences (60), Springer, 1987.
- Mathematics, Climate and Environment, J.-I. Diaz and J.-L. Lions, Eds., Research Notes in Applied Mathematics (27), Masson, 1993.
- Physics of Climate, J. P. Peixoto and A. H. Oort, Springer-Verlag, 1992.
Further readings may also be taken from journal articles.
Accurate data is essential for parametrizing mathematical models and is important in verification of model output. In order to gain an appreciation for the realities of data collection in support of climate modeling, students and faculty will travel to Alaska for 9 days in May of 2012. While in the field, students will undertake a campaign to collect data relevant to glacier modeling and the modeling of climate/glacier interaction. We will also spend several days meeting with modelers and research scientists at the University of Alaska, Fairbanks.
The following is a tentative itinerary of the travel-learning component of the course:
- May 12, Columbus to Anchorage
- May 13-15, Seward: Exit glacier AWS, Harding icefield, tidewater glaciers, Sea Life Center
- May 16-19, Fairbanks: UAF, IARC, Geophysical Institute, National Weather Service
- May 20, Anchorage to Columbus
In all, we will travel about 1000 miles through coastal and interior Alaska.
Because we will be conducting fieldwork in remote glaciated environments, students will need to outfit themselves with appropriate gear and equipment. Many of the more technical items (ice axe, crampons, skis/snowshoes) can be rented in order to minimize expenses. Also, some basic required gear (backpack, sleeping bag/pad) can be rented if desired.
Please see here for a detailed gear check-list.
The following websites are good places to buy outdoor gear:
Below are some links describing the meteorological and scientific instrumentation we will use. Some instrumentation will be built by us, however.
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