How is calculus used in hurricane formation and forecasting?

Question

I am looking for reference materials on how calculus can be used to explain the formation and behavior of a hurricane. I am also looking for examples of equations, or formulas used in the forecasting, or prediction of hurricanes. This is for a research project on a college level. All I have found so far is information on a grade school level that simplifies the answers. I really want the resources that the meteorologists use.
Thanks

Answer 1

Calculus is not routinely used in either the observation of developing tropical cyclones or their forecasting. Calculus and differential equations are far more useful in understanding mid and high latitude weather. In these regions, the primitive equations, a set of time dependent differential equations, useful in analysis and forecasting include the equation of state as derived from the first law of thermodynamics, the equation of continuity, the three equations of motion on a rotating earth, and the law of conservation of energy. This would be a simple set of five equations in five unknowns (the three vector components of motion u, v, and w together with pressure and density). It is difficult to obtain a set of equations like these that work near the equator where the coriolis accelerations go to zero.

Hurricane forecasting then is less of a science and more of an art similar to tornado forecasting. One major difficulty in addition to developing a numerical model is the scale of either of these phenomena. To forecast a hurricane forecasters look for sea surface temperature to be above 80F, so that there will be an easier transfer of moisture from the sea to the air. This moisture when condensed releases heat energy which can be use to fuel the hurricane. Another condition the forecaster looks for is the existance of monsoonal flow to the south of the easterlies. A good area for this in the Atlantic is off the coast of Africa, where the heat of the continent draws the wind back into a southeasterly flow. This flow together with easterly flow to the north helps generate cyclonic circulation. Another ingredient is little vertical shear in the wind. If there is shear (winds increase strongly with height) then the heat of condensation is removed and the anticyclonic flow required aloft are stymied. But if all of these conditions are present then a storm "may" form. Tropical meteorologists are still looking for a more suitable mathematical formualation for the tropics that will be as successful as the mid latitude models and be able to reveal the development of tropical cyclones. Finally, since surface and upper air observations are also scant over the tropical oceans, the forecaster must rely heavily on aircraft reconnaisance and satellite observations of storm genesis areas over the oceans. I hope this helps you understand this problem a little better. The science of meteorology is indeed a very complicated and sophisticated problem of scales(from dust devils to giant mid latitude cyclones and anticyclones), observation, physics, and mathematics.

Answer 2

Try the AMS journal search tool. Note that you can freely download PDFs of research papers that are at least five years old. For newer stuff, you'll have to subscribe or head to your library and go looking around for the journals.
http://ams.allenpress.com/perlserv/?request=search-simple

Other books to grab while you're at the library would be...
Atmospheric Science: An Introductory Survey (by Wallace & Hobbs)
An Introduction to Dynamic Meteorology (by Holton)

As for calculus used in hurricane forecasting & behavior, that would be primarily dealt with by folks working with atmospheric models and the "primitive equations" or "basic equations" of motion, thermodynamics, etc. As such, I did a quick search on the AMS journal search page and I found this paper.
http://ams.allenpress.com/archive/1520-0469/32/1/pdf/i1520-0469-32-1-25.pdf

Granted, there are going to be hundreds of papers like this out there, and they'll all have a relatively small scope in dealing with a certain scenario or a specific research topic. The nice thing is that when you see an equation in a paper like this, they'll usually explain what each term of the equation represents. In the textbooks above, you'll find more of a derivation process.

I'm certainly no expert on the calculus involved, but I do feel like I could get you away from the grade school stuff. Hope this helped.

Answer 3

When I glanced at your question I thought it said "How is calculus used in human fornication and forecasting."

Calculus is the "mathematics of change." It is useful for describing gradients and changes in velocity, pressure, temperature, humidity, etc. By setting up an equation with several partial diffs relative to time you could arrive at the probability of a particular result, such as a hurricane. Other than that I don't know. try NOAA.gov