# Almost everything you wanted to know about the greenhouse effect

Every once in a while it is worth reviewing the basic physics behind the greenhouse effect and global warming. Sometimes all the debate about global warming in the media loses focus of the fact that the world really is governed by the laws of physics. Unfortunately, many internet explanations get dumbed down to the point of having an atmosphere that serves as a single “slab” between the ground and space, and has a bunch of colorful arrows coming out of it and bouncing off it, etc. This is a useless explanation, and gives no justice to understanding what is happening. Two encounters in the outside world recently prompted me to do another post just to have a reference handy, and I’m using this to replace an older post which I entitled “just a few more molecules.” There’s also been an interesting episode with Dr. Andy Lacis from NASA GISS over at Dot Earth which I’d like to elaborate on.

We begin with the Planck function, which describes the radiation emitted from a blackbody at a specified wavelength and temperature:

$B_{\lambda}(T) = \frac{2hc^{2}}{\lambda^{5}} \frac{1}{exp[hc/kT \lambda] -1}$

This has physical dimensions of intensity (power per unit area per unit solid angle) per unit wavelength, often in W m-2 µm-1 steradian-1 (a steradian is essentially the 3-D analog of what angles are in two-space; there are 4π steradians in a sphere). h and k are constants, λ is the wavelength, and T is the temperature. An important note is that dB/dT > 0 for all wavelengths, which suggests that increasing the temperature increases the emission at each wavelength.

For review, the electromagnetic spectrum is presented below

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You will have to be pretty hardcore, with a real preference for Greek symbols in the math, to make it through this but if you stick through it, you will get a background explaining why greenhouse gases are so important for determining the temperature of the Earth. Without them, we would be a frozen snowball.

The more GHCs there are in in the atmosphere, the warmer the planet. That is mathematically certain.