What exactly is meant by the term “Effective Emission Height (EEH)”? It is often used to explain the greenhouse effect because, it is claimed, increased CO2 levels will raise the EEH to a slightly colder level, reducing OLR, and thereby “forcing” a surface temperature rise in order to restore energy balance. EEH is essentially some imaginary height in the atmosphere approximately where the temperature matches the effective temperature of Earth (255K). This is because a hypothetical black body at this temperature would produce the necessary 240 watts/m2 – to balance incoming absorbed solar radiation.

However the EEH still has no real physical meaning since radiation is escaping to space from all heights in the atmosphere, and also from the surface. Figure 1 shows the main sources of IR radiation reaching space, as least as far as I see it.



The surface radiates photons directly through the Infrared window in clear skies or via cloud tops otherwise. The IR window spans wavelengths 8.5 – 13.5 microns with a small ozone absorption band in the middle. The total average flux through the window is calculated to be currently ~99 watts/m2 but some will be absorbed and then re-emitted through clouds thereby losing some energy in the process. The values displayed in figure 1 are in watts/m2 and are based on the paper by Kiehl & Trenberth [1].

“In the clear sky case, the radiation in the window amounts to 99 W m-2, while in the cloudy case the amount decreases to 80 W m-2, showing that there is considerable absorption and re-emission at wavelengths in the so-called window by clouds.”

The IR window must act as a negative feedback to any rise in surface temperature since the flux through the window increases as T^4, independent of greenhouse gases. It is like pumping air into a tyre with a puncture. The harder you pump the faster the air escapes.

The second way the planet cools to space is through radiation by greenhouse gases in the atmosphere. The atmosphere gets roughly 2/3 of its heat through convection and latent heat and about 1/3 from radiative transfer. Together they maintain the lapse rate at ~ 6.5deg/km and kinetic energy is thermalized at each height. The simple greenhouse model described previously showed that currently about 37 watts/m2 are radiated to space by CO2 in the Earth’s atmosphere. The rest ~ 112 watts/m2 is radiated by water vapor mainly in the lower parts of the atmosphere.

At what height in the atmosphere does CO2 radiate then directly to space ? I have investigated this by calculating the net energy radiated directly to space using the model. For each 100m wide level in the atmosphere I calculate which fraction of the radiation makes it out to space without being absorbed. There are two effects determining this which work against each other. The lower levels are warmer, contain more net CO2 molecules and therefore emit (and absorb) higher fluxes of 13-15 micron photons. The higher levels are thiner and more photons from below are transmitted through it. However they are cooler and emit less photons even though there is a higher probability they reach space. By calculating the flux of radiation to space from each level we can visualize the “effective height of emission” for different CO2 concentrations in the atmosphere. The result is shown in Figure 2.

It is clearly seen that the peak emission height moves upwards as CO2 concentrations increase. However the total energy radiated to space changes only slightly. It falls by 2.7 watts/m2 increasing CO2 levels from 400ppm to 600 ppm in this simple radiation model. The AGW argument is that the surface temperature will then increase slightly to compensate. However this does not seem to be completely true at higher levels of CO2. To investigate this I calculated how the change in outgoing 13-15 micron radiation from the atmosphere varies with CO2 level for a fixed surface temperature of 288K. Figure 3 shows the result. Note that as the CO2 levels fall to zero the IR window would actually increase to slowly include the CO2 band. This is because the surface radiation directly to space dominates for CO2 levels less than ~100ppm.

The peak for atmospheric OLR occurs for ~ 300ppm which just happens to be that found on Earth naturally. Can this really be just a coincidence ? It is almost as if convection and evaporation act to generate a lapse rate which maximizes radiation cooling by CO2 to space. If this conjecture is true in general, then any surface warming due to a doubling of CO2 levels would be offset somewhat by a change in the average environmental lapse rate to restore the radiation losses in the main CO2 band. In this case the surface temperature would hardly change.

More fundamental is the question – what causes CO2 concentrations to be ~300 ppm in the first place ? Maximum entropy increase is ensured by maximum radiation loss to space and for CO2 today that just happens to coincide with 300 ppm ! Could it really be possible that planetary thermodynamics drives the carbon cycle ?

updated 5/1/13 to show surface and total OLR in Figure 3.

References

[1] Earth’s Annual Global Mean Energy Budget, J. T. Kiehl and Kevin E. Trenberth, 1997

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