Quantitative projections are routinely made for the future statistics of climate variables,
such as the frequency and intensity of storms in the North Atlantic. The quantification
of uncertainty in these projections is particularly important if such results are
to be used for decision making. This thesis addresses the design, use, and interpretation
of models in climate science, using the behaviour of North Atlantic extratropical
storms as a detailed case study. Results from novel statistical models and state-of-the-art dynamical models are generated and evaluated, looking at the frequency and
intensity characteristics of storms in the eastern North Atlantic and the clustering
characteristics of the most intense storms. It is found that statistical models are extremely
limited by the shortness of the calibration data set of historical observations,
and therefore have little merit other than simplicity. Dynamical models are primarily
constrained by the accuracy of their dynamical assumptions, which cannot be easily
quantified. Some relevant properties of dynamical systems, including structural instability,
are discussed with reference to predictability in the North Atlantic and other
aspects of climate science. This thesis concludes that despite the existence of "statistically
significant" results from some individual models, there is little evidence that we
can correctly evaluate even the sign of 21st century change of North Atlantic storm
characteristics (frequency, intensity or spatial position). Although climate models do
suggest that the magnitude of overall change will be small, this could still result in very
large percentage changes to the tails of the distribution, given the nonlinear nature
of the climate system. In order to make more confident conclusions about the tails of
such distributions, much longer runs are needed than the 30 year slices requested by
the CMIP experiments. In addition, formal quantification of subjective opinions about
model error would benefit climate science, scientists, and decision-makers.