Statistics of extreme events with application to climate

The statistical theory of extreme events is applied to observed global average temperature records and to simplified models of climate. Both hands of records exhibit behavior in the tails of the distribution that would be expected from a random variable having a a normal distribution. A simple nonlinear model of climate due to Lorenz is used to demonstrate that the physical dimensions of the underlying attractor, determined by applicable conservation laws, limits the range of extremes. These limits are not reached in either observed series or in more complex models of climate. The effect of a shift in mean on the frequency of extremes is discussed with special reference to possible thresholds for damage to climate variability.