Chris Colose suggests

(As part of Rabett Run's Gerlich and Tscheuschner project, Eli has started drafting parts of a response, which we will gift wrap in Bozo paper and send to some unsuspecting journal, but certainly arXiv. This second part comes from Chris Colose. The Editorial Board expresses its thanks=:> [Rabett Run has an exceedingly small Editorial Board] Suggestions for changes and additions are welcome. I think this makes much the same point as Joel Schor's model, with the advantage that it is somewhat clearer how it fits in with the sun/earth system. It might be substituted for it, after which we could place the section about the rotating earth and average temperatures. - Eli)

Request: I need a solar spectrum taken from space that extends to the IR preferably 10-4 microns, again, preferably in digital format. Resolution need not be high

UPDATE: Minor corrections 11:30 PM 3/24

All objects with a temperature emit energy according to the Planck radiation law. It has been shown above how objects of differing temperatures placed near each other must continue to radiate energy towards each other, and so cooler bodies must emit energy toward hotter ones. Gerlich and Tscheuschner (2009) believe that this state of affair represents a contradiction to thermodynamics. Above, we have looked at perhaps the simplest example that shows them to be wrong. The same logic can be applied to a simplified atmosphere represented by a number of blackbody layers which radiate energy in all directions.

This is not too far from how real radiative transfer codes work, with the caveat that here only two "gray" layers are considered. For simplicity, we assume that the atmospheric layers are opaque to infrared radiation, absorbing all terrestrial IR radiation, and emitting like a blackbody at their temperatures. This simplified atmosphere is also fully transparent to incoming solar radiation. An atmosphere with large infrared optical depth can be approximated with two layers centered at 0.5 and 2 km altitude (Goody and Walker 1972).

In this model, the amount of radiation absorbed on the surface equals the solar flux in W/m² at the top of the atmosphere, S, less that reflected back to space, the albedo, α, divided by 4, which accounts for the fact that the earth is spherical (for details see, for example, Insert Ref). The top layer (Layer 2) emits IR radiation that matches the solar radiation absorbed by the surface. In this simplified model, the temperature of the second layer is the effective temperature of the planet as observed from space. Below, we will consider a more complicated model for a rotating planet, again, reaching different conclusions than Gerlich and Tscheuschner, and again, will point out why their conclusions are in error. At equilibrium, each level must absorb and emit the same amount of radiation. This leads to three simple equations

(1) At the surface: S(1-α)/4 + σT1⁴ = σTsur⁴

(2) At Layer 1: σT2⁴ + σTsur⁴ = 2 σT1⁴

(3) At Layer 2: σT1⁴ = 2 σT2⁴

Starting with the observed solar flux at the top of the atmosphere, 1364 W/m², we can solve for

T2 = 255 K
T1 = 303 K
Tsur = 335 K

Because T_sur in Table 1 is too high, the assumption that only radiation governs the atmospheric thermal equilibrium has to be modified. In reality, evaporation of water from the surface and its condensation in the atmosphere, the latent and sensible heat fluxes, remove substantial amounts of energy from the surface. In the global, annual mean these terms equate to roughly 100 W/m² of energy removal from the surface and put in the atmosphere (Trenberth et al., 2009). Convection also plays a role

With or without considering convection or latent heats associated with the condensation of water vapor, the clear effect of the atmosphere is to make the surface temperature much higher than the effective temperature at which it radiates to space. These layers introduce another aspect to the supply of energy at the surface, which now is not only heated by the sun, but also by the downward emission of terrestrial radiation from the atmosphere. This term is larger than the incident solar radiation at the surface by a factor of roughly two in the global mean. Most of this terrestrial radiation originates in the lower atmosphere where water vapor is very abundant. As shown by the spectrum below the down welling radiation has been measured directly, again contrary to the assertions of Ref. 1. In this spectrum, taken at the pole, one sees the influence of water vapor as the sharp lines, mostly at the left, low frequency end, CO2 between 600 and 800 cm^-1, and ozone at about 1100 cm^-1.

Under typical conditions, most of the outgoing longwave radiation originates in the troposphere at altitudes much colder than the surface. Again, this has been measured directly from space


When more greenhouse gases are added to the atmosphere, energy can only radiate from higher altitudes where the inflow of energy then becomes greater than the outgoing longwave flux at the top of the atmosphere. The greenhouse warming is thus (Hansen et al. 1981),

(4) Tsur = Teff + ΓH

where Gamma (Γ) is the lapse rate and H is the height above the surface. In this way, the increased atmospheric CO₂ restricts the outflow of thermal radiation, and the planetary surface temperature can only rise. This situation is illustrated in Figure 2.

Gerlich and Tscheuschner (2009) are correct to conclude that this greenhouse mechanism does not act in the way real greenhouse acts, whereby convection is restricted, however this is a strawman, a strawman that occupies over 20 pages in Ref 1. No serious explanation of the greenhouse effect neglect the role of radiation and how it is suppressed with increased infrared opacity. On Earth, absorption and re-radiation of infrared energy is the reason why the actual surface temperature is much higher than that of the effective temperature. Although scattering of infrared light is not a significant term for the Earth's atmosphere, it can matter in other planetary cases such as Venus or past conditions on Mars (e.g., Forget and Pierrehumbert 1997).

Gerlich and Tscheuschner (2009) conclude that most of the infrared absorption in the atmosphere is due to water vapor, and that because CO2 only absorbs in a small part of the total infrared spectrum, raising its partial pressure will have little effect. This claim is very misleading and especially if one does not have a working knowledge of the infrared spectrum of both molecules. There is no physical meaning in comparing CO2’s absorption to the “total infrared spectrum” since the boundaries between infrared and other areas of the electromagnetic spectrum are arbitrary. What is important is that CO2 absorbs very strongly near the peak emission at Earth-like temperatures, and renders the atmosphere completely opaque between 14 and 16 microns, and partially absorbing still some distance from those edges (Petty 2006). As CO2 builds up in the atmosphere, there will still be significant absorption away from the line center, in the wings of the absorption area. This is an area of the spectrum in which water vapor is a weak absorber, and because the atmosphere is so dry at the colder, higher altitudes where radiative balance is set, CO2 is not swamped by water vapor’s greenhouse effect.

Of the 33 K greenhouse effect, roughly 50% of the infrared opacity is due to water vapor, 25% due to clouds, 20% from CO2, and the remaining 5% from other non-condensable greenhouse gases such as ozone, methane, and nitrous oxide (Kiehl and Trenberth 1997). Although this often leads to popular statements such as “water vapor is the most important greenhouse gas,” a more complete picture is that those gases which do not precipitate from the atmosphere under Earth’s current temperature regime (including CO2, ozone, methane) provide the supporting framework for which the condensable substances (water vapor and clouds) can act. As such, if CO2 and the other non-condensable gases were to be removed from the atmosphere, the colder temperature would then result in a substantial reduction of water vapor and clouds, and a collapse of the terrestrial greenhouse effect. On the other hand, as one makes the planet warmer by adding CO2 to the atmosphere, the saturation pressure for water will increase and result in a substantial positive feedback to amplify warming (e.g., Held and Soden 2000).

Forget, F and Pierrehumbert RT 1997: Warming Early Mars with carbon dioxide clouds that scatter infrared radiation. 1273 - 1276

Goody, R.M., and J.C.G. Walker, 1972: Atmospheres. Prentice-Hall, Englewood Cliffs, NJ, 150 pp.

Hansen, J., D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind, and G. Russell, 1981: Climate impact of increasing atmospheric carbon dioxide. Science, 957-966

Held, M., and B. J. Soden, 2000: Water vapor feedback and global warming. Annual Review of Energy and the Environment, 441-475.

Kiehl, J. T., and K. E. Trenberth, 1997: Earth's annual global mean energy budget. Bull. Amer. Met. Soc. 78, 197-208

Petty, G, 2006: A First Course In Atmospheric Radiation 2nd Ed., Sundog Publishing, Madison, Wisconsin

Trenberth, K. E., J. T. Fasullo, and J. Kiehl, 2009: Earth's global energy budget. Bull. Amer. Meteor. Soc., doi: 10.1175/2008BAMS2634.1