Andrea D. Pianta

Dartmouth College

Mathematics


1994

Mentor: L. David Meeker - Professor of Mathematicsh

Testing mathematical models that explain past and present climate dynamics

For the past thirty years, mathematicians and meteorologists have been working together to formulate mathematical models to duplicate past climate dynamics and also to, with a moderate amount of accuracy, predict future climatic changes. To date, five major climate models have been created. The most simplistic model which was the primary subject of this research project, is known as a zerodimensional energy balance model. While this model has existed since 1969, it has not yet been fully tested for its accuracy.

The main purpose of this research was to use computer simulation and statistical criteria to, by changing certain parameters of the model, test the accuracy and mathematical and meteorological validity of its results. First, the original, unchanged model was accurately simulated using the computer software Matlab. After the results of the unaltered model were recorded, statistical changes were made within the model. The most important parameter, the global mean solar radiative input (QO), was varied, as was the annually averaged temperature of the earth-atmosphere system. Then, some variability, or "noise" was added to the model. This noise was randomly chosen and kept within a certain standard deviation, which was a fraction part of Q(). The noise also collectively had mean zero.

Through these tests, it was verified that this model is, as expected, not very accurate. However, an interesting decrease in the average number of temperatures below a certain significant value (280K) was found when QO was increased by a factor of 1.20. It is, as of yet, unclear what is causing this decrease. Hopefully, further research will help to explain this variation. Finally, it is hoped that this research will be helpful in suggesting ways to create new, more statistically valid models which may allow meteorologists to better predict future weather trends.

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