*** 20th Anniversary: 2003 to 2023 ***

Weather math

by Josh
(Blacksburg, VA)

Log-Log example both axes with logarithmic scales

Log-Log example both axes with logarithmic scales

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 Po and the height z by this exponential (inverse log) relation:

P = Po 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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Thank you to my research and writing assistants, ChatGPT and WordTune, as well as Wombo and others for the images.

GPT-4, OpenAI's large-scale language generation model, helped generate this text.  As soon as draft language is generated, the author reviews, edits, and revises it to their own liking and is responsible for the content.