> Assume that [C]=400 ppm. The mean free path becomes 2.646m so that N=3024. The probability of returning to the Earth becomes p(1)=0.9997. A photon with frequ

> Assume that [C]=400 ppm. The mean free path becomes 2.646m so that N=3024. The probability of returning to the Earth becomes p(1)=0.9997. A photon with frequency or wavenumber near the centre of the absorption band is virtually certain to make the return to Earth. If the CO2 concentration is doubled, the probability doesn’t change much; it becomes p(1)=0.9998. Any CO2 increase has minor effect on the photons in the center of the absorption band. This part of the band is ‘saturated’. Ok, so as I'm thinking about this, and forgetting about the edges of the absorption bands -- in steady state, all the heat of the sun must be radiated out into space, otherwise the earth would be hot enough to have killed off all life millions of years ago. When you think about it, an IR photon that returns to earth is not really done, it doesn't get "stuck" to the earth. The surface of the earth either reflects it back up, or absorbs it and its energy, and then re-emits it some time later. Even with 0.9997 probability of returning to earth, if you try enough times, you'll eventually escape, and photons get a lot of tries, really fast. That 0.0003 probability matters, and if you change it to 0.0002, it seems to me like it's a really, really big deal. To take it the other way -- if any given IR photon had, say, a 50% chance of escaping the earth, my intuition says that it would let the earths temperature drop extremely drastically at night, like the moon or mercury. The sheer speed at which photons get "tries" to escape means that the greenhouse gas blanket has to absorb and send back almost all photons in order for the earth not to become icy every night.