How to model greenhouse effect in calculating a planets temperature?
The basic principle is that the emissivity at the wavelengths the Earth radiates energy at is different from the emissivity it receives energy at. To do a thorough model, you’d also need to account for thermal gradients and heat transport in the atmosphere and a variety of other factors; it gets quite complex. A simplistic model would be to assume blackbody radiation with different values of e for input and output. Fudge the effective emissivities to make the numbers come out right. A more accurate model would integrate the radiation transfer over the spectrum, using the actual effective values of e at each wavelength. You could do this in a spreadsheet, iterating to converge on a solution. The wikipedia article on greenhouse effect might give you some ideas.
