## Mathematics and ClimateAs April ushers in Mathematics Awareness Month, with this year's theme ofMathematics and Climate, what insights can mathematics offer into climate, and on a smaller time scale, the weather?...Joseph Malkevitch
## IntroductionWhen all else fails in making "small talk," one can always fall back on the weather. For those of us used to living where there is a discernible change in seasons, one can chat about it being too cold, too hot, too wet, or, despite how lovely the snow is, how much of a pain it has become to shovel so much of it recently. The changeability of the weather is one constant fact of life. However, what about climate? ## Mathematical tools to study climateAlthough mathematics grows because it attempts to solve problems that arise outside of mathematics (e.g. Newton developed calculus in part to help understand gravity and the motion of the planets, Euler wrote a paper concerning where to optimally position the masts of a sailing ship), it also grows because mathematicians enjoy looking for patterns of all kinds for their own sake. Though, in part, the theory of games was developed to understand questions arising in economics and political science, once it was born it took off on its own, developing methods and ideas that were independent of applications settings. It might not seem that game theory has much to say about Mathematics and Climate, but the tools of game theory are being employed to try to help the world deal better with earthly issues that affect the climate. Because of its ability to abstract and generalize, mathematics is a unique tool for getting insight into the increasingly large number of domains that it is being applied to. Climate issues are just one of these.
y = 4s^{2}t^{3}then
## AlbedoAs a simple window into how complex it becomes to probe questions about climate, let us consider the concept of albedo is derived from the Latin word albus, which means white. We are all familiar with the idea that when light hits a mirror, most of it is reflected by the mirror but when the same light hits a fabric which you might be wearing, little is reflected. The way that light or other energy is reflected from a surface depends on the nature of the surface. The concept of albedo is to generalize this situation. The idea is to get a way of measuring how much electromagnetic radiation, from the sun or more generally from space (in fact, any source), is reflected back off the surface of a planetary body such as Earth, our moon, or Mars.The origins of ideas that are related to albedo go back surprisingly far, and show the fact that mathematical insight and talent is not the monopoly of any particular country. There are various attributions but there is no "harm" in calling attention to mathematical pioneers of work being carried out today. If light, or some other form of electromagnetic radiation, hits the "surface" of a planet's atmosphere, a river, a corn field, a glacier, or an ice flow, a certain portion of this energy is absorbed and a certain amount is reflected. If the energy is reflected off the atmosphere it is bounced back into space. If it bounces off a corn field or a glacier it may or may not be trapped by Earth's atmosphere and go into warming Earth, or it too may be released back into space. Thus, the amount of energy from outside Earth's "energy system" that becomes trapped by Earth is a very complex issue to understand. The attempt to understand what happens to light as it goes from one "medium" to another seems to have started with the work of Pierre Bouguer.
## Climate modelsUltimately, nearly all of the energy involved in understanding Earth's climate comes from the sun or, to a much lesser extent, from other stars. This energy comes in the form of light or other kinds of electromagnetic energy. What happens to this energy once it "arrives" at Earth? This is a very complicated question because energy that arrives at a portion of Earth covered by clouds has a different fate from energy that hits a large tract of dark land or a large tract of sea ice. Quite early in the history of mathematics and science, scholars have been trying to understand this issue. This led to the concept of albedo and all its complications hinted at in our discussion above. In addition to the consequences for climate driven by the sun (which has energy cycles and complex behavior of its own), there are some terrestrial features that drive climate. (Courtesy of Paul Ginoux, Geophysical Fluid Dyamics Laboratory, Princeton)
(Courtesy of Paul Ginoux, Geophysical Fluid Dyamics Laboratory, Princeton)
## References:Daley, R., Atmospheric Data Analysis, Cambridge U. Press, Cambridge, 1993. Joseph Malkevitch Those who can access JSTOR can find some of the papers mentioned above there. For those with access, the American Mathematical Society's MathSciNet can be used to get additional bibliographic information and reviews of some these materials. Some of the items above can be accessed via the ACM Portal , which also provides bibliographic services. |
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