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also include equations describing the processes that transfer momentum,
energy, and mass into and out of the atmosphere from oceans and continents,
and the energy incoming to the atmosphere as shortwave radiation from the
Sun and outgoing as longwave radiation to deep space. Aspects of these
processes were discussed in earlier chapters. GCMs also include in their
code equations that describe the evolution with time of atmospheric constitu-
ents. This may require description of chemical reactions but much more
commonly it requires that the phase changes for atmospheric constituents are
described, the description of the phase changes of water being the most
important need.
When describing the computational mechanics that GCMs use to describe the
atmosphere, it is helpful first to draw an analogy with the computer programs
that are set up to manage bank accounts. GCMs manage atmospheric bank
accounts for volumes of atmosphere each of which is defined by the area of the
Earth's surface it overlies (specified as lying between latitude and longitude limits)
and by a height range above the ground. Although not strictly cubes, one might
visualize these volumes as being equivalent to bricks which when cemented
together form the whole atmosphere. The bank accounts maintained by the GCM
for each volume of atmosphere contain wealth in several different 'currencies, the
most important being the energy, momentum, and mass of atmospheric
constituents.
Extending the bank account analogy one step further, at regular intervals a
banking program would update the bank accounts it maintains to reflect changes
in the amount held in each currency in each account as a result of financial
transactions between them, and the interest earned on deposits and value lost by
inflation. In a broadly similar way, having built this basic descriptive framework
for the atmosphere, at regular intervals GCMs represent how much energy,
momentum, and mass is moved between the volumes of atmosphere it has defined
and the extent to which there are internally generated increases or decreases
within the volume.
Figure 8.1 illustrates how a GCM might partition the atmosphere into
segments and some of the exchanges and internal processes that are represented
in the model. The size of the areas of atmosphere represented in each column
of air, which is usually called the grid scale of the GCM, and the height range of
each volume within each column are mainly determined by computational
constraints. The computer memory available to store values of atmospheric
variables for each volume element in part determines the size of the volume
elements selected. However, just as important, if the computer program is to
remain stable, the time step at which updates are made to the variables in each
volume element falls rapidly as the grid scale and height ranges decrease.
Hence, the run time of atmospheric simulations also rapidly increases as the
grid scale and height ranges decrease. In practice, for stable operation a time
step of 20-30 minutes is required when GCMs have a grid scale of a few hundred
kilometers.
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