One-dimensional radiative-convective (RC) climate models are very powerful diagnostic tools for understanding climatic sensitivity to changes in the physical and chemical structure of the Earth's atmosphere and surface. The usefulness of RC models stems from their relative simplicity and their ability to provide a quantitative estimate of climate change produced by variations in, for example, the atmospheric content of carbon dioxide or water vapour, changes in the solar flux and in the Earth's surface albedo. Most RC models incorporate the concept of a convective adjustment and parameterizations for solar and terrestrial radiation transfer, as discussed in Chapters 4 and 6. In RC models, the atmosphere is divided into two sections. The lower atmosphere or troposphere is taken to be in convective equilibrium and the upper atmosphere (stratosphere and mesosphere) is in radiative equilibrium. The upper boundary of the convective zone is determined by concepts of atmospheric stability.

### 11.3.1 Convective versus radiative equilibrium

We have seen in §2.3 that the atmospheric temperature gradient determines the stability of the atmosphere against convection. An atmosphere in radiative equilibrium (see Fig. 2.11) produces essentially a discontinuity (of about 20 K) between the Earth's surface temperature and the near-surface atmospheric temperature. This is a consequence of having a non-ideal blackbody atmospheric layer overlaying a blackbody surface. We can make an estimate of this discontinuity by considering the simple case of a grey atmosphere in radiative equilibrium (see §3.5.10). In the two-stream approximation the mean intensity is given by J = (I + +1-)/2 and the net upwelling flux, f, is constant in radiative equilibrium and given by f = n(I + — I-). Thus the mean intensity can be expressed as J = I + — f/2n. At the Earth's surface, with temperature Ts, I+ = B(Ts), where B(Ts) = aTS4/n, and we have seen that within the atmosphere, eqn (3.138),

where T(ts) is the near-surface atmospheric temperature. Now f/2n = B(To)

i where T0 is the atmospheric skin temperature, equal to (1/2)4 T®, where is the effective temperature of the Earth, so that the Earth's surface temperature can be calculated from