An analytic radiative-equilibrium model is formulated where both short
- and longwave radiation are treated as two-stream (down- and upward)
fluxes. An equilibrium state is defined in the model by the vertical t
emperature profile. The sensitivity of any such state to the model atm
osphere's optical properties is formulated analytically. As an example
, this general formulation is applied to a single-column Ii-layer mode
l, and the model's optical parameters are obtained from a detailed rad
iative parametrization of a general circulation model. The resulting s
imple column model is then used to study changes in the Earth-atmosphe
re system's radiative equilibrium and, in particular, to infer the rol
e of greenhouse trace gases, water vapor and aerosols in modifying the
vertical temperature profile. Multiple equilibria appear when a posit
ive surface-albedo feedback is introduced, and their stability is stud
ied. The vertical structure of the radiative fluxes (both short- and l
ongwave) is substantially modified as the temperature profile changes
from one equilibrium to another. These equilibria and their stability
are compared to those that appear in energy-balance models, which here
tofore have ignored the details of the vertical temperature and radiat
ion profiles.