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propagation (C) M. Ambaum

Atmospheric Nomogram

See also: Ambaum, M. H. P., 2007: A nomogram for the atmosphere. Weather, 62, 344-345. doi:10.1002/wea.141

... and also: the resources page for my Thermal Physics of the Atmosphere book for another version of an atmospheric nomogram.

A nomogram is a diagram that can be used to graphically perform a certain calculation. For example, given temperature and pressure, what is the potential temperature. We can get the calculator out and do this calculation or, if you are a bit more hard-core, log tables or a slide rule. Either way would work but it becomes rather cumbersome if you have to do it ten times in a row. In that case it might be more useful to write a little computer program or use a programmable calculator. Another way would be to produce a nomogram.

Click on the image to download your nomogram which can be printed on any laser printer. Read on for instructions.

A nomogram is a sheet of paper with graduated scales (for example for temperature, pressure, and potential temperature). We then put a ruler over the nomogram crossing the temperature scale at the given temperature value and the pressure scale at the given pressure value. Where the ruler crosses the potential temperature scale the potential temperature value can be read off. Of course this process can be generalized: given potential temperature and pressure we can read off the corresponding temperature. In this sense a nomogram is quite flexible.

The nomogram above contains four graduated scales: for potential temperature, density, pressure, and temperature. We can choose any two of these and read off the other two using the ruler. But there is more: the temperature scale also shows a saturated vapour pressure scale, and the pressure scale also shows a 1976 US standard atmosphere height scale, so these two quantities can be thrown in the mix as well. For good measure I included a Celcius-Fahrenheit converter, which consists of a seperate linear scale with two graduations, the simplest form of nomogram possible.

There are several books about construction of nomograms, most, if not all of them out of print. My nomogram consists of cleverly scaled and placed logarithmic scales. The devil is in the detail though: it took me quite a bit of time to work out the exact locations and optimal scalings. Making a basic nomogram is easy; making a nomogram with the right ranges which has readable scales and which incorporates two calculations at the same time is rather less easy.

In all, I hope you find it a useful tool to do some simple calculations commonly encountered in atmospheric science. I am open to any suggestions for improvement.

Instead of a ruler I found it useful to get an overhead transparancy and draw a straight coloured line on it and use this as the index line. This makes the reading off of the nomogram a bit easier.

And for the geeks out there: this nomogram was made through straight postscript programming. The postscipt code contains a bracketing routine to locate the saturated vapour pressure graduations on the temperature scale. Postscript printers are essentially big programmable RPN calculators and are ideally suited to produce graphics such as these: the locations of the scales and their graduations are calculated by the printer itself before they are plotted.

It is real a shame that it is nearly impossible to find simple RPN calculators these days (HP produces a few models.) In fact, it is difficult to find any simple scientific calculator anymore: most modern calculators have cumbersome, error-prone input methods (I see my students struggling with them) and have so many functions on them (none of which you will ever use) that you wonder if you can also fry an egg with them. Anyone who has aver used an RPN calculator, or who has done postscript programming, will realize that RPN notation is easy, intuitive, fast, and compact (see this page for a brief description.) Furthermore, you are much less likely to make errors. It is also not very difficult to learn, as you would expect from a truly intuitive system; when you know the basics, it takes about half a minute of practice. It is a shame that HP does not produce its old scientific RPN calculators anymore as legacy models. If anyone who is reading this owns an old HP-11C, HP-15C or HP-42S: I am interested in buying it!

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