[spunkets]

" Actually, Co can be any base you want to apply within the log functions it's effective range, it is not limited to Co=285. It is just as accurate at Co=185ppmv doubling to 390ppmv, as it would be at Co = 500ppmv doubling to 1000ppmv. It is a general empirical relationship derived from spectroscopic Line by Line integrations.

It comes from the solution of the diff eq,

dEexcited = A*dc/C.

I= A*ln(C) -ln(C_o) + const

The constant is zero, and the absorbed watts is above what's absorbed at C_o. A is evaluated as a sum of the absorption coefficients, the path length, and contains a base I_o. It's ng if any of those change, or the validity of the sum of the absorption coeffs is violated.

"Only in a very general sense as Beer's law holds valid for only very low concentrations for a specified monochromatic wavelength where absorption is a linear function of concentrations (e.g. <10ppmv for CO2 in my experience."

Only, because only one absorption coefficient is considered. I gave the general form, which is generally valid anytime. The gen diff eq is,

dI/I = Σ_n α_ncx dc(or dx, depending)

Re: Increasing concentration provides more unexcited molecules to absorb radiation. More States are available.

" And the effect of that is different from saying:
Increasing concentration effectively broadens the spectral line allowing more absorption by weak lines and the skirts either side of the central spectral line which are not saturated.
how?"

Broadening of spectral lines is a real effect caused by pressure, Doppler effects, and temperature. Increasing the concentration just adds to the number of States available. The lower concentration had the same lines being filled. It's an equipartition of energy thing. A higher concentration just allows that much more energy into the same modes. The modes fill according to the probability of transition for that mode. That probability is quantified in the absorption coefficients. No mode is ever saturated in these cases. Their absorption coefficients are constants, and the probability of exciting a mode stays the same. There's a Boltzmann dist of excited States at any temp. Only certain transitions are allowed. So the effective concentration is always lower. That doesn't mean the strong peaks are "saturated". It's means the molecules are in another State, that doesn't allow a transition.

THanks for the links. I see GW as not amounting to anything significant, until after the condition of 2060 is reached, where the total E is still less than 1% greater than the good old days of watermelon delight. Any system will move to minimize the E in any path between equilibrium conditions. It's the endpoints that are important. There's nothing significantly different in the endpoints, nor is there any reason for wild occurrences to appear, that would not have appeared before the perturbation.

[ancient_geezer]

Re: Increasing concentration provides more unexcited molecules to absorb radiation. More States are available. No mode is ever saturated in these cases.

Of little relavance when flux is already being absorbed near extinction levels at high concentrations. When there is little more to be absorbed a linear increment in the number of molecules involved has less effect as concentration increases.

All increasing concentration can do is ultimately approach an asymtotic boundry set by the free flux left to be absorbed however marginal that might be.

The net effect at high concentrations is essentially absorption approaching a logarithmic relationship to concentration at modrately high concentrations, clearly at a declining rate as compared to the near linear increase in absorption with change in concentration that occurs at low concentrations.