The Little Ice Age – dated from the mid-14th century to the early 19th – plays a large role in historical analyses. Anthropologist Brian Fagan suggests that this climate swing demoralised the European peasantry, allowing for the rise of despotic leaders (Fagan 2000). British and Dutch canals and rivers frequently froze, allowing French land forces to invade the Netherlands while the Dutch fleet was ice-locked. But was it really an ice age, or have historians been “fooled by randomness” (Taleb 2005)?
In recent research we attempt to discover how much European weather actually worsened during the Little Ice Age. Our conclusion – using a variety of standard temperature reconstructions – is that there is little evidence that a European Little Ice Age ever occurred (Kelly and Ó Gráda 2014).
Figure 1. The European Little Ice Age as Slutsky Effect: Netherlands summer temperature, 1301-1980. The top panel shows the data smoothed with a twenty-five year moving average and gives the appearance of marked cold episodes between the 15th and 19th centuries. The lower panel shows the actual data which are almost entirely random with a constant mean and variance.
Instead, European weather between the 14th and 19th centuries resembles white noise: uncorrelated draws from a distribution with a constant mean and variance (although there are occasional decades of markedly lower summer temperature), with the same behaviour holding more tentatively back to the eleventh century. Our results suggest that the existing consensus over a Little Ice Age in Europe is a statistical artefact, where the standard climatological practice of smoothing what turn out to be random data prior to analysis gives the spurious appearance of irregular oscillations. This is an example of the ‘Slutsky effect’ where filtering of purely random variations can produce spurious cycles.
Climate cycles in history
The idea that human history is driven by fluctuations in climate is a tenacious one, with the collapse of most civilizations from Rome to Maya having been attributed at some time or another to the diminishing resources and increasing conflict caused by weather. While the implicit view of humanity as passive victims of meteorological circumstance – preferring starvation to adaptation as conditions change – led most mainstream historians to be sceptical of such stories, the growing popularity of ‘big history’ has led to a revival of climatic determinism, but the emphasis is decidedly on anecdote over formal analysis (see McNeill 2014 for an enthusiastic overview).
Thanks to concerns about global warming, an increasing number of annual winter and summer temperature reconstructions now exist:
- for Central Europe since 1500,
- for the Netherlands from 1201,
- for Switzerland from 1525, and
- for England from 1660.
These reconstructions offer the potential to assess the size and timing of major swings in European climate since the Middle Ages – assuming, of course, that they are more than figments of their authors’ imaginations. To assess the reliability of the earliest (and presumably most conjectural) reconstructions we compare the Netherlands estimates with known English wheat prices from 1211 to the beginning of the price revolution in 1500 and find a close match.
Given the widely-held belief that Europe experienced a Little Ice Age, the statistical behaviour of these temperature reconstructions comes as a surprise. In every case the mean and variance of the series remain almost constant until around 1900 when temperatures start to rise steadily (particularly winter temperatures). In no case do we find evidence of autocorrelation, trends, or structural breaks in mean temperature. Most importantly, an array of powerful martingale difference tests (portmanteau tests that look at the sum of autoregressive coefficients in the data, variance ratio tests that look at how the variance of a series grows as the number of observations rises, and spectral tests that look for departures from a straight line spectrum) do not reject the null that mean temperatures from the late middle ages to the late 19th century are constant.
Given the lack of evidence for any sustained trends or shifts in European temperatures before, 1900 how are we to account for the general belief among climatologists that Europe experienced a Little Ice Age? The answer probably lies in the practise in climatology of smoothing data using some sort of moving average before analysing it. If the underlying data are white noise, as European temperatures appear to be, then smoothing them will give the spurious appearance of irregular oscillations as the filter is distorted by runs of high or low values: a Slutsky effect. We illustrate this in Figure 1.
Creating an ice age with 25 year moving averages
The top panel of Figure 1 shows Low Countries’ summer temperatures from 1301, smoothed using a twenty-five year moving average. The Little Ice Age is immediately evident as a declining trend from the mid 15th to the early 19th centuries, with markedly cold episodes in the late 16th, late 17th, and early 19th centuries. But looking at the unsmoothed graph of summer temperatures in the panel below, the impression is one of randomness, without any major trends, cycles, or breaks: something that our statistical tests confirm.
Glaciers can be seen as a physical embodiment of the Slutsky effect: their extent represents a moving average process of temperature and precipitation over preceding years, and can show considerable variation through time even though the annual weather processes that drive them are random. For example, while annual Swiss winter temperatures and precipitation are close to random until the late 19th century, Swiss glaciers fluctuate notably, expanding from the mid-15th century until 1650, contracting until 1750, and then expanding again until 1850.
A word of caution
Note when interpreting our results that local weather conditions are a noisy signal of global ones. Just as the fact that European temperatures did not rise much during the twentieth century does not imply that global temperatures were constant (rises were concentrated in the Arctic and Siberia), so their constancy between the 14th and 19th centuries does not imply that global average temperatures did not experience notable falls during this time associated primarily with known falls in solar output.
While sustained shifts in climate do not appear to have occurred in northern Europe since the late middle ages, and more tentatively (using German data that categorizes each year as good, average, or bad) since AD 1000, there have been decades of notably poor weather. Using a Bayesian changepoint procedure – which is robust to runs of outliers that distort most filters and lead to Slutsky effects – we can identify in Figure 2 decades of noticeably poor summer weather – in particular the 1690s when harvests failed repeatedly across Europe, and the 1810s. None of the European series, or recent Northern Hemisphere temperature reconstructions for that matter, shows evidence of any decline in the period 1635-1665 which the excitable but influential study of Parker (2013) claims to have been a period of “catastrophic” weather.
Figure 2. Historical series of central European, Netherlands, Swiss, and English summer temperatures, showing mean estimated by a Bayesian change point procedure.
The anecdotal evidence
In Kelly and Ó Gráda (2013) we examine some of the anecdotal evidence used to support claims of a European Little Ice Age.
- The freezing of the Thames – which for most people is the most salient fact about the Little Ice Age – was caused by Old London Bridge, whose twenty arches effectively acted as a dam, creating a large pool of still water that froze twelve times between 1660 and 1815.
Tidal stretches of the river have not frozen since the bridge was replaced with five-arched one in 1831 – even during 1963, which was the third coldest winter since records begin in 1660 (after 1684 and 1740).
- Grape growing in England was uncommon in the eleventh century – a lot of confusion stems from mistaking the word vivarium (fish pond) for vinarium (vineyard) – and disappeared entirely after Bordeaux passed to the English crown in 1152, suggesting that comparative advantage may have played a larger role than climate.
Similarly, the decline of wheat and rye cultivation in Norway from the 13th century may owe more to lower German cereal prices than temperature change.
- Regarding Greenland’s Viking settlements, competition for resources with the indigenous Inuit, the decline of Norwegian trade in the face of an increasingly powerful German Hanseatic League, the greater availability of African ivory as a cheaper substitute for walrus ivory, overgrazing, plague, and marauding pirates probably all played some role in their demise.
Most importantly, the fact that the colony had survived previous episodes of cold weather points to the insufficiency of the standard explanation that the Vikings there simply ‘got cold and died’.
While the idea that Europe experienced a Little Ice Age is widespread, its statistical basis is at best exiguous, and appears to stem from inappropriate efforts to smooth data that are actually random. At the same time, most of the anecdotal evidence admits more simple explanations than climate change.
Fagan, B (2000), The Little Ice Age: How Climate Made History, 1300–1850, New York: Basic Books.
Kelly, M and C Ó Gráda, (2013), “The Waning of the Little Ice Age”, Journal of Interdisciplinary History 44(2):301—325.
Kelly, M and C Ó Gráda (2014), “Change Points and Temporal Dependence in Reconstructions of Annual Temperature: Did Europe Experience a Little Ice Age?”, Annals of Applied Statistics 8(3):1372—1394.
Mahon, J and P Davies (2009), “The Meaning of Slutsky”, https://www.minneapolisfed.org/publications/the-region/the-meaning-of-slutsky.
McNeill, J R (2014), Changing Climates of History, Public Books.
Parker, G N (2013), Global Crisis: War, Climate Change and Catastrophe in the Seventeenth Century, New Haven: Yale University Press.
Taleb, N N (2005), Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, Random House.
 As Mahon and Davies (2009) put it: “Slutsky demonstrated that random numbers subjected to statistical calculations similar to those used to reveal trends in economic time-series formed wavelike patterns indistinguishable from business cycles.”