New Math Model
Xun Zhu, a research scientist in the Department of Earth and
Planetary Sciences, has created a new mathematical technique that
will significantly increase the accuracy of computer models used
for studying global changes of Earth's environment, such as ozone
depletion and global warming caused by pollution.
Models currently in use have an error rate of up to 20 percent; the new technique reduces the error rate to 10 percent.
Such models work by using equations to study and predict atmospheric dynamics and the transfer of energy in the atmosphere. Usually, the solar energy absorbed by the Earth's atmosphere is calculated by comparing the number of photons entering one section of atmosphere with the number of photons exiting a second section. The difference is the number of photons absorbed.
Because the quantities of ozone and carbon dioxide are directly related to the amount of radiation energy--or photons-- absorbed, such models can be used to indicate and predict ozone and carbon dioxide levels, Zhu said. He presented a paper about the work on May 20, during the American Geophysical Union's Spring Meeting in Baltimore.
Environmental predictions are only as good as the models they are based on, so accuracy is critical. But the models currently in use are subject to a high degree of error. Zhu said that's because the number of photons absorbed is much smaller than the number of photons entering the atmosphere; just a slight miscalculation of the number of photons entering the atmosphere will result in a large error in photons absorbed.
If, for example, the calculation starts with 1,002 photons passing through the first section of atmosphere, and 1,000 photons passing through the second section, the difference is two photons, meaning two photons have been absorbed.
But suppose there is a small error in the number of photons entering the atmosphere; if the actual number of photons entering the first section is 1,001, instead of 1,002, the model's calculation of how much energy is being absorbed will be off by 50 percent.
Zhu has developed a mathematical solution to this problem. After five years of work, he has invented a computational method that directly calculates the number of photons absorbed in a given volume of atmosphere. That means there is no need to compare the number of photons passing through the two sections of atmosphere, eliminating a major source of error, he said.
Zhu also has applied the same idea to equations for studying atmospheric dynamics--analyzing the complex movements of air within the atmosphere.
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