A common fallacy in thinking about the effect of doubled CO2 on climate is to assume that the additional greenhouse gas warms the surface by leaving the atmospheric temperature unchanged, but increasing the downward radiation into the surface by making the atmosphere a better infrared emitter. A corrollary of this fallacy would be that increasing CO2 would not increase temperature if the lower atmosphere is already essentially opaque in the infrared, as is nearly the case in the Tropics today, owing to the high water vapor content of the boundary layer. This reasoning is faulty because increasing the CO2 concentration while holding the atmospheric temperature fixed reduces the OLR. This throws the top-of-atmosphere budget out of balance, and the atmosphere must warm up in order to restor balance. The increased temperature of the whole troposphere increases all the energy fluxes into the surface, not just the radiative fluxes. Further, if one is in a regime where the surface fluxes tightly couple the surface temperature to the overlying air temperature, there is no need to explicitly consider the surface balance in determining how much the surface warms. Surface and overlying atmosphere simply warm in concert, and the top-of-atmosphere balance rules the roost.
Arrhenius properly took both the top-of-atmosphere and surface balances into account in his estimate of the effect of doubling CO2 , though he did so using a crude one-layer model of the atmosphere. Guy Stewart Callendar (1938) and Gilbert Plass (1959) employed more sophisticated multilevel models, but when it came to translating their radiation results into surface temperature change both got mired in the surface budget fallacy. The prime importance of the top-of-atmosphere balance was emphasized with crystal clarity in Manabe's work of the early 1960's, but one still encounters the surface budget fallacy in discussions of global warming from time to time even today.
Figure 6.3 shows how the budgets change when CO2 is doubled from 300 ppmv. The case shown is typical fo the present Earth's tropics, for which water vapor makes the boundary layer optically thick. The system starts off in balance, at a surface temperature of 300K. If CO2 is immediately doubled, the downward radiation into the surface increases by a mere 1.2 W/m2. However the OLR goes down by over 4 W/m2. The atmosphere-ocean system is receiving more solar energy than it is losing, and so it warms up. The top-of-atmosphere balance is restored when the surface air temperature has warmed to 302K. This increases the radiation into the ground by an additional 7.3 W/m2. Part of this increase comes from the fact that the warmer boundary layer contains more water vapor, and therefore is closer to an ideal blackbody. Most of the increase, however, comes about simply because the low level air temperature Tsa increases, and hence aT4a increases along with it. This increase occurs even if the boundary layer is an ideal blackbody -i.e. completely opaque to infrared. In addition, the increase of Tsa would increase the latent and sensible heat fluxes into the surface if the surface temperature were to stay fixed, and this increase also contributes to the warming of the surface.
There are a few situations in which the detailed surface balance could have a significant effect on surface warming. This can only happen in the weakly-coupled regime. In that regime AT can be fairly large, and changes in AT can add to whatever warming is directly caused by the atmospheric warming that comes from satisfying the top-of-atmosphere budget. For example, if land dries out, the loss of evaporation will cause AT to increase. Conversely, if a formerly dry area becomes moist, AT would decrease, moderating the surface warming. The weakening of the low-level inversion in Antarctica can play a crucial role in Antarctic surface climate change. Finally, it should be noted that when the atmosphere is optically thick, AT does not affect the OLR. However, when the atmosphere is somewhat transparent to infrared from the surface, an increase in AT increases the OLR a bit, so that the atmosphere doesn't have to warm up quite as much as one thought in order to bring the top-of-atmosphere budget into balance.
The relative roles of the surface budget and the top-of-atmosphere budget in determining surface temperature change upon doubling of CO2 are further explored in Problems ?? and ??.
Doubled CO2, out of equilibrium
Doubled CO2, out of equilibrium
Figure 6.3: Changes in top-of-atmosphere and surface radiative fluxes upon doubling CO2. Calculations were carried out with the ccm radiation model assuming the atmosphere to be on a moist adiabat patched to an isothermal 180 K stratosphere. The low level relative humidity is fixed at 80%, while the relative humidity in the free troposphere is 50%.
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