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might be adequate provided that diabatic heating and frictional dissipation were
included in a suitable manner. Phillips (1956) made the first attempt to model
the atmospheric general circulation numerically. His experiment employed a two-
level quasi-geostrophic forecast model modified so that it included boundary layer
friction and latitudinally dependent radiative heating. The heating rates chosen
by Phillips were based on estimates of the net diabatic heating rates necessary to
balance the poleward heat transport at 45
◦
N computed from observational data.
Despite the severe limitations of this model, the simulated circulation in some
respects resembled the observed extratropical circulation.
Phillips'experiment, although it was an extremely important advance in dynamic
meteorology, suffered from a number of shortcomings as a general circulation
model. Perhaps the gravest shortcoming in his model was the specification of
diabatic heating as a fixed function of latitude only. In reality the atmosphere
must to some degree determine the distribution of its own heat sources. This is
true not only for condensation heating, which obviously depends on the distri-
bution of vertical motion and water vapor, but also holds for radiative heating as
well. Both net solar heating and net infrared heating are sensitive to the distribu-
tion of clouds, and infrared heating depends on the atmospheric temperature as
well.
Another important limitation of Phillips' two-level model was that static stability
could not be predicted but had to be specified as an external parameter. This
limitation is a serious one because the static stability of the atmosphere is obviously
controlled by the motions.
It is possible to design a quasi-geostrophic model in which the diabatic heat-
ing and static stability are motion dependent. Indeed such models have been used
to some extent, especially in theoretical studies of the annulus experiments. To
model the global circulation completely, however, requires a dynamical frame-
work that is valid in the equatorial zone. Thus, it is desirable to base an AGCM
on the global primitive equations. Because of its enormous complexity and many
important applications, general circulation modeling has become a highly special-
ized activity that cannot possibly be covered adequately in a short space. Here
we can only give a summary of the primary physical processes represented and
present an example of an application in climate modeling. A brief discussion of
the technical aspects of the formulation of numerical prediction models is given
in Chapter 13.
10.8.2
Dynamical Formulation
Most general circulation models are based on the primitive equations in the
σ -coordinate form introduced in Section 10.3.1. As was pointed out in that sec-
tion, σ coordinates make it possible to retain the dynamical advantages of pressure
coordinates, but simplify the specification of boundary conditions at the surface.
