Weather forecasting and chaos^4
The science of chaos has developed rapidly since
the 1960s (when a meteorologist Edward Lorenz
was one of its pioneers) along with the power of
electronic computers.In this context, chaos is a
term with a particular technical meaning. A chaotic
system is one whose behaviour is so highly sensi-
tive to the initial conditions from which it started
that precise future prediction is not possible. Even
quite simple systems can exhibit chaos under some
conditions.For instance, the motion ofa simple
pendulum (Figure 5.7) can be ‘chaotic’ under some
circumstances, and, because of its extreme sensitiv-
ity to small disturbances, its detailed motion is not
then predictable.
A condition for chaotic behaviour is that the
relationship between the quantities which govern
the motion of the system be non-linear; in other
words, a description of the relationship on a graph
would be a curve rather than a straight line.^5 Since
the appropriate relationships for the atmosphere
are non-linear it can be expected to show chaotic
behaviour. This is illustrated in Figure 5.6, which
shows the improvement in predictability that can be
expected if the data describing the initial state are
improved. However, even with virtually perfect ini-
tial data, the predictability in terms of days ahead
only moves from about six days to about twenty
days, because the atmosphere is a chaotic system.
For the simple pendulum not all situations are
chaotic. Not surprisingly, therefore, in a system
as complex as the atmosphere, some occasions
are more predictable than others. A good illustra-
tion of an occasion with particular sensitivity to
the initial data and to the way in which the data
were assimilated into the model is provided by
the Meteorological Office forecasts for the storm
which hit southeast England in the early hours of
Friday, 16 October 1987.During this storm gusts of
over 90 knots (170 km h−^1 ) were recorded and ap-
proximately fifteen million trees were blown down.
Although as early as the previous Sunday forecasts
had given good early warning of a storm of un-
usualseverity, the model forecasts available during
15 October gave much poorer guidance than earlier
forecasts and failed to predict the intensity or the
correct track of the storm. The question was raised
at the time as to whether the numerical models used
were capable of the accurate prediction of such an
exceptional event. Figure 5.8 shows that, using all
the data which could have been available and bet-
ter assimilation procedures in the model, a good
forecast of the event can be achieved.Figure 5.7(a) Illustrating a simple pendulum consisting of a bob at the end of a string of length 10 cm
attached to a point of suspension which is moved with a linear oscillatory forcing motion at frequencies
near the pendulum’s resonance frequencyf 0. (b) and (c) show plots of the bob’s motion on a horizontal
plane, the scale being in centimetres. (b) For a forcing frequency just abovef 0 the motion of the bob
settles down to a simple, regular pattern. (c) For a forcing frequency just belowf 0 the bob shows
‘chaotic’ motion (although contained within a given region) which varies randomly and discontinuously
as a function of the initial conditions.