Sage worksheet on energy balance model

Attached is a Sage worksheet on the simplest global energy balance model. An energy balance model looks at energy in and energy out:

change in temperature = energy in - energy out

Pretty straightforward, eh? Let Q be the incoming solar radiation (insolation) and \alpha be albedo (percentage of sunlight the earth reflects) -- our "energy in" will be Q(1-\alpha) . Then we can use Boltzmann's black-body radiation to get "energy out" -- it's  \sigma T^4 , where T is our global average surface temperature in kelvins and \sigma is Boltzmann's constant. So we get the equation

\frac{dT}{dt} = Q(1-\alpha)-\sigma T^4

It is not too hard to use calculus to find a linearization near the equilibrium point of this equation and then do some analysis.

The attached worksheet can be loaded into if you want to work through it without installing Sage:

MAA-NCS Climate Modeling -- Boltzmann

I'm trying to figure out how to put up a full interactive worksheet; it's not so hard to put up cells, but I'm not sure about a whole Sage file... let me know if you know!

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  1. Pingback: Snowball earth… last talk at climate model summer course | Earth Calculus

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