Climate and Climate-System Modelling - Environmental Modelling: Finding Simplicity in Complexity - page 147

discussion of the interactions between and within the
various components of the climate system can be found
in Chapter 2 of Harvey (2000).
In building computer models of the climate system,
as with any system, there are a number of basic consid-
erations. The first involves the number of components
to be included. The various components of the climate
system change at different time scales. For example, at
the decade to century timescale, changes in the extent of
the large ice caps (Greenland, Antarctica) can be ignored.
There would thus be no need to include models of these
components for simulation of 100 years or less; rather,
the observed present-day distribution can be simply pre-
scribed as a lower boundary condition on the atmosphere.
Similarly, changes in the geographical distribution of the
major terrestrial biomes can be ignored at this time scale.
However, at longer time scales, changes in biomes and
in ice sheets, and their feedback effects on the atmo-
sphere and oceans, would need to be considered. Thus,
the comprehensiveness of a climate model (the number
of components retained) depends in part on the timescale
under consideration. The comprehensiveness is also dic-
tated in part by the particular purpose for which one is
building the climate model.
The flip side to comprehensiveness is model complex-
ity. Generally, more comprehensive models tend to be
less complex - that is, each component represents fewer
of the processes that occur in reality, or represents them in
a more simplified manner. This simplification is because
the more comprehensive models tend to be used for
longer time scales, so limitations in computing power
require that less detailed calculations be performed for a
given period of simulated time. Furthermore, the addi-
tion of more climate system components also tends to
increase the overall computational requirements, which
can be offset by treating each component in less detail.

important elements of the climate system (such as clouds,
land-surface variation) have scales much smaller than
this. Detailed models at high resolution are available for
such processes by themselves, but these are computation-
ally too expensive to be included in a climate model, and
the climate model has to represent the effect of these sub-
grid-scale processes on the climate system at its coarse
grid-scale. A formulation of the effect of a small-scale pro-
cess on the large scale is called a parameterization. All cli-
mate models use parameterizations to some extent. Some
parameterizations inevitably include constants that have
been tuned to observations of the current climate, and
which might not be entirely valid as the climate changes
(see Chapter 2 for further approaches to model parame-
terization and Chapter 5 for issues of parameter scaling).
Another kind of simplification used in climate mod-
els is to average over a complete spatial dimension.
Instead of, for instance, a three-dimensional longitude-
latitude-height grid, one might use a two-dimensional
latitude-height grid in models of the atmosphere or
oceans, with each point being an average over all lon-
gitudes at its latitude and height (examples include Peng
et al ., 1982; Yao and Stone, 1987, and Stone and Yao,
1987 for the atmosphere; and Wright and Stocker, 1991,
for the ocean). Another choice is to average in both
horizontal dimensions, retaining only the vertical dimen-
sion, as in one-dimensional radiative-convective models
that have been used in the detailed simulation of the
vertical transfer of solar and infrared radiation and in
studies of the effects of changes in the composition of the
atmosphere (examples include Manabe and Wetherald,
1967; Lal and Ramanathan, 1984; Ko et al ., 1993) and
the one-dimensional upwelling-diffusion ocean model
that has been used to study the role of oceans in
delaying the surface-temperature response to increas-
ing greenhouse-gas concentrations (Hoffert et al ., 1980;
Harvey and Schneider, 1985). A third choice is to average
vertically and in the east-west direction but to retain the
north-south dimension, as in the classical energy-balance
climate models. These models have provided a number
of useful insights concerning the interaction of horizon-
tal heat transport feedbacks and high-latitude feedbacks
involving ice and snow (e.g. Held and Suarez, 1974).
When the dimensionality is reduced, more processes have
to be parameterized but less computer time is required.
The equations used in climate models are a mixture of
fundamental principles that are known to be correct (such
as Newton's laws of motion and the First Law of Thermo-
dynamics), and parameterizations. Parameterizations are
empirical relationships between model-resolved variables

9.2 Finding the simplicity

Nature varies continuously in all three spatial dimensions,
thus comprising an infinite number of infinitesimally
close points. However, due to the finite memory capacity
of computers, it is necessary to represent variables at a
finite number of points, laid out on a grid of some sort.
The calculations are performed only at the grid points.
The spacing between the grid points is called the model
resolution. In global atmospheric models the typical hor-
izontal resolution is 200 to 400 km. In ocean models the
resolution can be as fine as tens of kilometres. Many