Weather math

by Josh
(Blacksburg, VA)

This description moves a little too quickly and might use too many English idioms ("eyeballing it") for younger readers to follow along.

I do data visualization for a living - I write code, graphics come out, and so on. This page doesn't seem unreasonable for any (sufficiently advanced) math student, with one exception - the associated graph has lines that make it look like a logarithmic scale (vertically), but I can't be sure by looking at it, and I'm not sure if this is right or not. Is it possible to explain the graph a little more?

Barry's Response - I think it deserves it, and shall give it a thorough review. As you can tell, the bulk of the article is for the more advanced mathematical/physical sciences student or professional, while the simple conversion was tacked on at the beginning for the people looking for a Fahrenheit to Celsius conversion and vice-versa.

The chart on the temperature conversions page is called a
skew-T log-p diagram, it is designed so that non-linear thermodynamic calculations can be quickly and informally executed using graphical methods, an example of which is provided on the page.

I do not know for sure if the pressures (vertical scale) are placed exactly on a logarithmic scale, but it does look like it. Inversely related to each of those standard pressure levels is a standard height above sea level for which the specified pressure may typically be found.

Pressure P is a function of the sea level pressure P_o and the height z by this exponential (inverse log) relation:

P = P_o e ^(-z/H)

H is the scale height for reference, and it ranges from 6000 to over 8000m, depending on the temperature and humidity. A good average value is around 7640 m.

I explain more about it with a slightly different example on my
introductory atmospheric physics page.

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