Historical development

2.4.1 Climate statistics

“Normal” weather

Informal observations of climate statistics could be said to have been made for millions of years: the evolution of plant and animal species to take advantage of the seasonal cycle by timing in some way their flowering, reproduction or migratory patterns is an

example of inductive reasoning about the expected weather (i.e., climate). Similarly, the expectation of certain patterns of weather has always been an important part of human societies, from the annual inundations of the Nile to the British hope for a White Christmas. Many aspects of human societies are vulnerable to unexpected weather, primarily via direct impacts on food supply and shelter, which may result either from short term variability or from longer term shifts in climate, and may even have caused the downfall of ancient civilisations68. The prospect of “anthropogenic climate change” is not new either: the witch-hunts of the sixteenth and seventeenth centuries are well correlated with periods of climatic instability, reduced harvests and food insecurity23,216.

Even in a world of globalised commodity trading, societies are still vulnerable to lo- calised weather extremes such as the 2010 Russian heatwave which resulted in grain export bans and high global food prices and contributed to the factors of social unrest driving the so-called Arab Spring133.

Thus, the first understanding of “climate” and perhaps the most relevant is as the normal or expected weather for a certain place at a certain time of year (to which local species are adapted). It is not trivial to construct an understanding of this even in an intuitive sense, because the timescales of weather variation can exceed human lifetimes (although the relative importance of different types of variation depends on geographic location). Natural variability exists at all timescales, from the passage of weather fronts to the glacial/interglacial cycles.

Ad hoc statistical models

In a quantitative manner, the construction of a description of “normal weather” is still non-trivial, because it is always produced based on limited data, and conditional on a series of assumptions about stationarity (and therefore possibly irrelevant). Where long time series are available, statistical curve fitting is possible but again relies on

statistical assumptions which may be questioned†.

In climate science, the definition of climate as an average over some timescale is a pragmatic but arbitrary decision, and the resulting statistics are referred to as the

climatology of a region (often using a base period of 1961-1990, but this depends on

what observations are available). For example, the Met Office produce maps showing the distribution of mean monthly high and low temperatures.

Trend detection and attribution

In the last thirty or so years, since the general consensus that the climate is likely to be changing due to greenhouse gas emissions, the emphasis in statistical analysis of climate observations has shifted towards detection of trends rather than determina- tion of climatology. As I discuss later (Section 2.5.6), trend detection requires various assumptions about the nature of the underlying distribution of the weather variables, assumptions which can be made in different ways resulting in different answers. More recently, there has been interest in attribution of trends to natural or anthro- pogenic causes. Extreme events cannot themselves be directly attributed to increased greenhouse gas in the atmosphere because the natural variability of the unforced sys- tem is large; however, statistical methods can be used to compare observations with forced and unforced modelled climate.

One such method of trend attribution is the optimal fingerprinting108,109,5_approach,

which performs a linear regression against a set of spatial patterns (the “fingerprints” of different forcing agents), to find which ones have contributed to the change. The primary assumption is that the response to a given forcing has a constant spatial pattern, varying only in magnitude (and does not interact with others).

Alternatively, the relative frequencies of events in the forced and unforced climate can be compared to give an idea of the degree of increase (or decrease) in risk. This

requires assumptions both about the current distribution of extreme events and about the alternative distribution the simplest being a ceteris paribus approach6 _{by which}

the alternative hypothesis is simply a climate simulation with identical forcings apart from the change under consideration†.

The human influence on the risk of events such as the England and Wales floods210 of 2000, the European heatwave279 of 2003, and other climatic events276 has been quantified in these ways. The prospect of assigning responsibility in this way allows a more balanced quantification of future climate damages, but also opens a large discussion about legal implications6,8, past and future climate responsibility, and the possibility of restitution/compensation for climate events95, as well as a need for con- sensus about the appropriate treatment of uncertainty.

2.4.2 Climate simulation

Milestones in climate science

The recorded history of large-scale meteorology begins with the age of global explo- ration in sailing ships, prompting investigations such as those of George Hadley97, who presented to the Royal Society a theory of the “cause of the general trade-winds” in 1735. With further developments in the theory of gases and heat transfer, the global perspective was expanded in the nineteenth century by the work of polymath Joseph