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Viewing Single Post From: The giant space ship example
Chris Ho-Stuart
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I've been busy and had limited time to work on this; but for the time being here's a slightly updated version 2.2.

Download link: Starship-v2.2.xls. Minor clean up applied.

My major reference for much of the theory I am applying is Principles of Planetary Climate by Ray Pierrehumbert. The integration sheet now includes also an additional column for an alternative calculation of the all-troposphere grey atmosphere using evaluation of a direct integral. There's a comment on the page describing how this works. It gives the same result as my original more direct layer by layer method, which is reassuring that I have the maths correct.

There are a couple of interesting points. For an atmosphere that is optically thick (a high k value, as is used for the Dwarf sample atmosphere) there is a theoretical dividing line between a deep troposphere and a shallow troposphere with the gamma value of the atmosphere at 4/3

Above 4/3, and the tropopause is low in the atmosphere. This is the expected case, with the bulk of the atmosphere as nitrogen and oxygen, which are around 1.4.

Try this. Alter the value for gamma on the first sheet, using the Dwarf example. By default, it is 1.4. Try entering 1.32, and then 1.34, and observe the sudden change in the height of the tropopause. This is another indication I am on about the right track; this is a theoretically expected behaviour.
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The giant space ship example · Physical theory for climate