Summary1 of Simplest Climate Model

First, a much-delayed suggestion to go look at Atmoz's calculation of the effect of the earth being an oblate spheroid rather than a perfect sphere. More about that in a moment.

The simplest model discussion so far occupies a few posts:

• The Simplest Meaningful Climate Model
• Building the Simplest Meaningful Climate Model
• Analyzing the Simplest Meaningful Climate Model
• (From Atmoz blog) The Simplest Climate Model: Oblate Spheroid Edition

In making the correction for the earth being an oblate spheroid rather than a perfect sphere, Atmoz found the 4 in the original formula (simplest model) should be changed to 4.00449, at least when we're at the equinoxes. As the earth's orientation changes, it will present somewhat different areas to the sun. Imagine a pancake, as an example of an extremely oblate spheroid. Put a pencil through it (the short direction) and consider that the rotation axis of your very oblate planet. Have a friend hold it up and tilt it some from the vertical. As you walk around your friend, you'll see the pancake edge on (equinoxes) and then more of the top or bottom as you get to the solstices. The amount of tilt will affect how much your view varies. The more tilt, the more variation. The earth is tilted about 23.5 degrees from the sun.

Atmoz found about a 0.07 degree C difference for the earth's temperature for oblate (and at equinox) vs. perfect sphere. Probably something about that size too for the solstices too, though we need the computation to be sure.

Here I've used an albedo of 0.30 and solar constant of 1367 W/m^2. Atmoz preferred 0.29 and 1366, respectively. Thanks to our looking into the sensitivity of the model in the analysis note, we know that this amounts to only about a 1 K difference in computing the earth's temperature. That suggests a few things. One is, the surface temperature averaging 288 K is unlikely to be explainable by modest changes from the values we used. Another is that it'd be a good idea to chase down some good sources on what values should be used, exactly. Or that at least we'll want to find out what the levels of uncertainty are about these observable quantities.