What SoD says. The effect is not only not linear, it’s logarithmic for doubling CO2. Most of the contribution CO2 (at pre-industrial levels) has on the GHE has already occurred, but doubling it still incrementally enhances it somewhat.

The magnitude of the enhancement so far as surface warming is debatable, but radiative transfer models estimate it to be approximately 3.7 W/m^2 before the system has adapted to the change or imbalance. That is -3.7 W/m^2 at the TOA, or a reduction in IR flux passing into space from around 240 W/m^2 to 236.3 W/m^2.

]]>*“So what I meant to say was that a doubling of GHGs (rather than CO2 specifically) would mean a doubling of DLR.”*

No, not even close to doubling DLR (at the surface). DLR is around 300 W/m^2! The surface radiates only around 390 W/m^2.

]]>Sure. For the strongest line absorbed by 400 ppm of CO2, the ERL is allegedly 1 m. Most of the photons emitted downward from CO2 below 1 meter with reach 1 m^2 of surface. 1 m^3 of atmosphere with 400 ppm provides the DLR. At 800 ppm, the ERL will be at 0.5 m and only 0.5 m^3 of atmosphere will provide the DLR. Since there is no temperature difference between 0.5 and 1 m, there will be no change in the spectral intensity of DLR from doubling at this wavelength.

Radiation of blackbody intensity is what is emitted after absorption and (temperature-dependent) emission have come into equilibrium with each other and absorber they are passing through. Planck’s Law was derived by assuming such an equilibrium and a material composed of “quantized oscillators. Hohlraums were devised to create such an equilibrium. For some wavelengths passing through our atmosphere, effective equilibrium can be reached within a few 10’s of meters in the lower atmosphere and temperature doesn’t change much over short distances. Those wavelengths have BB spectral intensity. Doubling the concentration of a GHG has no effect when absorption and emission are in equilibrium. The band is “saturated”. At other wavelengths, the temperature changes faster than equilibrium can be reached. Then DLR arriving at the surface has less that BB intensity for Ts. In the atmospheric window, no equilibrium occurs and DLR at these wavelengths has the spectral intensity for the source above the atmosphere. That is the microwave radiation left over from the Big Bang that fills “empty” space.

Playing with MODTRAN is the best way to develop a reliable intuition about radiation transfer. Until you understand why CO2 alone increasing from 0 to 1 to 2 to 4 … to 1024 ppm changes DLR as it does, you shouldn’t rely on intuition. Equations can be interpreted. Numerical integration of the differential equations of radiative transfer is a black box. The blackbody curves on the MODTRAN plots tell you when radiation has the spectral intensity for a blackbody at 300, 280, 260, 240 or 220. When CO2 emission from a tropical atmosphere (Ts = 300 K) has blackbody intensity, the ERL must be near the surface.

]]>To put it another way, you can find the answer to your question in the articles linked, but you probably haven’t bothered to read them.

]]>As SoD pointed out above, it’s not that simple. Sure, two molecules may, in principle, emit twice as much radiation as one. But there are problems. Thermodynamic temperature is not defined for a few molecules. They won’t follow the Boltzmann energy distribution, etc., etc.

In one cubic meter of air at standard temperature and pressure with a CO2 partial pressure of 0.0004 atmospheres, there are ~1E22 molecules of CO2. You can answer your own question by using MODTRAN or spectralcalc.com. I could do your homework for you by working out an example, but you’ll learn more if you do it yourself.

http://climatemodels.uchicago.edu/modtran/

Doubling CO2, even at fairly high climate sensitivity, won’t double the amount of water vapor, which is the primary source of DLR. So doubling the well mixed ghg’s other than water vapor won’t double DLR and won’t even double the DLR from the ghg’s. At high concentrations, the system isn’t linear, it’s logarithmic.

]]>“When CO2 is doubled, twice as many photons are emitted, but their mean free path before absorption is half as long. This means the same flux will reach the ground after a doubling – to a first approximation.”

I expect there is an “altitude” that is quite low to the ground that is analogous to the ERL where most of the radiation does reach the surface. Would you agree?

]]>When CO2 is doubled, twice as many photons are emitted, but their mean free path before absorption is half as long. This means the same flux will reach the ground after a doubling – to a first approximation.

This approximation is true for strongly absorbed wavelengths. At a weakly absorbed wavelength where the mean free path is 2 km, doubling CO2 will reduce the MFP to 1 km. After doubling, there will be slightly more photons reaching the surface because the average photon reaching the ground is now emitted from lower where it is warmer. .

You can watch DLR from increasing CO2 saturate using MODTRAN at

http://climatemodels.uchicago.edu/modtran/

Zero out all the GHGs and choose to look up from 0 kilometers (at the DLR arrive at the surface). Notice the baseline isn’t flat. Add 1(!) ppm of CO2 and keep doubling. Notice that saturation prevents a doubling of DLR even between 1 and 2 ppm. The differences between 200, 400, and 800 are subtle.

Blackbody spectral intensity (the colored curves) are what is present when absorption and temperature-dependent emission are frequent enough to reach equilibrium with the absorbing molecules they are traveling past.

]]>From my point of view it would seem so given that radiation is basically a probability.

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