captured by a single number. In reality, of course, cloud reflectiveness varies, but
some reasonable estimate has to be given. Finding the best values for these
parameters in a way that is effective and is based on well-defined mathematical
and physical principles is extremely difficult.
Figure 7: Clouds vary in their reflectiveness, but in order to be computationally manageable,
climate models have to approximate their reflectiveness with a single number called a parameter.
Much mathematical work needs to be done to come up with the best values for these parameters.
Credit: Fred Roberts.
Once the models are built, they need to be analyzed so that they canprovide useful information. This is also tricky, since precise predictions are
impossible, but mathematicians can still pull out a qualitative understanding of
how the system behaves. For example, some systems have tipping points,
thresholds where the system suddenly starts acting very differently: With climate,
if global temperatures rise enough to melt the Greenland ice sheet, the climate
would be irreversibly changed; with infectious disease, if a virus spreads enough
to reach people who fly, it could become a global pandemic rather than a local
contagion; with fisheries, when fish populations dip below some threshold, the
entire species may disappear. Understanding when the tipping points can occur
within a system and identifying where those tipping points are, as precisely as
possible, is critical.
Pulling predictions from the model raises another set of mathematical andstatistical questions. Scientists have found that the “wisdom of the crowd” applies
to models as well as people: under the right conditions, when multiple models