the Sahara was taken to be T0 = 320 K (very hot) and the surface temperature in Antarctica was taken to be T0 = 190 K (very cold). The surface pressure in the Sahara and the Mediterranean was taken to be p0 = 1013 hPa and the surface pressure in Antarctic was taken to be p0 = 677 hPa, low because of the high elevation of the ice surface, about 2.7 km above mean sea level. For convenience, we modeled the dependence of the water vapor concentrations C {i} on the height z above the surface as {i}
C {i} = C0 e−z/zw ,
(120) {i}
with a latitude-independent scale height zw = 5 km and with surface concentrations C0 = {i} {i} 31, 000 ppm for the Sahara, C0 = 12, 000 ppm for the Mediterranean, and C0 = 2, 000 ppm Antarctica. For the year 1970 when the satellite measurements were made, we used surface concentrations, in ppm, for CO2 , N2 O and CH4 of 326, 0.294 and 1.4, with the same relative altitude profile as those in Fig 2. The altitude profile of Fig. 2 for O3 was used for the Sahara, the Mediterranean and Antarctica. As can be seen from Fig. 22 the modeled spectral intensities can hardly be distinguished from the observed values. We conclude that our modeled spectral fluxes would also be close to observed fluxes, if a reliable way to measure spectral fluxes were invented.
8
Conclusions
The two goals of this review were: (1) to rigorously review the basic physics of thermal radiation transfer in the cloud-free atmosphere of the Earth; and (2) to present quantitative information about the relative forcing powers of the the naturally-occurring, greenhouse-gas molecules, H2 O, CO2 , O3 , N2 O and CH4 . Fig. 2 illustrates how the temperature T of the atmosphere and the concentrations C {i} of greenhouse gases of type i depend on the altitude z above the Earth’s surface. No matter how high the concentration of greenhouse gases, (46) shows that the TOA forcing of an isothermal atmosphere would be zero, since the brightness B̃ at each source altitude z would be equal to the surface brightness B̃0 , and the forcing increment, dF̃ ′ from molecules in the altitude interval z ′ to z ′ + dz ′ is proportional to (B̃ − B̃0 )dz ′ = 0. For radiation forcing, the atmospheric temperature profile is as important as greenhouse-gas concentrations. Modeling calculations were done with the integral forms of the fundamental radiation ˜ We transfer formulae, (44) for the spectral flux, Z̃, and (34) for the spectral intensity, I. showed that these follow directly from the Schwarzschild equation (27) for an atmosphere with gas molecules in local thermodynamic equilibrium. Greenhouse gas molecules absorb but do not scatter thermal radiation. Vibration-rotation energy imparted to a molecule by an absorbed infrared photon is lost in collisions with other molecules before it can be radiated away. Radiation transfer calculations are most conveniently done with the vertical optical depth τ of (21) as a measure of altitude z. We showed how the attenuation coefficient κ = ∂τ /∂z of (20), can be evaluated with the cross sections σ {i} of (20), expressed with (52) and (53) in terms of the line intensities and other parameters of the HITRAN data base[31]. In our modeling we included over 1/3 million lines from the HITRAN data base for the five most 48
