The Climate Machine: A simple global climate model


On average, the amount of sunlight absorbed by the Earth is equal to the infrared radiation emitted by the Earth. This balance is referred to as the global radiative balance.

The globally averaged solar insolation is given by the ratio of the total sunlight absorbed by the Earth to the area of the Earth. If Fs is the intensity of sunlight reaching the Earth (normal to the path of sunlight), and the total cross section of the Earth is PI*R2
The amount of sunlight absorbed by the Earth is Fs*(1-albedo).

The total area of the Earth is 4*PI*R2.

So this gives the global average solar insolation as Fs*(1-albedo)*PI*R2 / [4*PI*R2]
                =Fs*(1-albedo)/4
This is balanced by outgoing longwave radiation (sigmaT4) and an effective temperature of the planet can be found
                Te=[ Fs*(1-alpha)/(4*sigma)]1/4
(where sigma is the Stefan-Boltzmann constant)
Results from this model compare favorably for many of the solar system's planets.