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# Mathematics and Weather

The Mathematics of Weather is Complicated!
The information below in the highlighted box is taken  from Wikipedia:

 In Meteorology, the primitive equations are a version of the Navier-Stokes equations that describe hydrodynamical flow on the sphere . . . Thus, they are a good approximation of global atmospheric flow and are used in most atmospheric models.One of 6 equations using 6 variables is shown below: $c_{v} \frac{dT}{dt} + p \frac{d\alpha}{dt} = q + f$

Another meteorologist stated "Any type of synoptic forecasting is based and rooted with the QG-Omega Equation."  The QG-Omega equation is shown below.

Do TV Meteorologists Work With These Mathematical Equations Each Day?
Actually, they don't, at least not directly.  The results of using these equations and many others, along with additional mathematics and statistics applied to large amounts of collected data, provide the computer models that weather forecasters use on a daily basis. The meteorologist explains the forecast and associated weather phenomena using terminology that the average viewer will understand.  The meteorologist must have a good understanding of how the atmosphere behaves in order to accurately explain this phenomena.

So Why Do Meteorologists Need So Much Math?
I joined a meteorology forum and asked this question.  Here are replies I received from some meteorologists.

"[Needed for] establishing a good understanding of the atmosphere while in college"

"For those who go into the research and modeling fields, this math tends to get used often."

"The primitive equations that are used as the basis for weather models are important to understand because it can help explain why the model output is showing what it does."

"The math education a meteorologist gets, which is part of a degree in meteorology, is important as it bridges into how the atmosphere works by pretty much quantifying it."

"I'm in research, and I use quite a bit of calculus, and there would be no way I could study what I study without a good understanding of calculus."

Undergraduate meteorologists typically are required to take 3 semesters of Calculus along with 1 semester of Differential Equations. Meteorologists continuing on in graduate degrees are typically required to also take Partial Differential Equations before beginning graduate studies. See Penn State Graduate Studies in Meteorology.