The Statistician’s extremes

Statistics are at the heart of climate studies. Starting with apparently chaotic data, it becomes possible to highlight profound changes in the climate system and to understand the causes of these changes. How extreme events, by definition improbable, are considered by statisticians?

While an extreme event can be defined by its intensity, duration or the resulting damages, for the statistician it remains one point, one piece of data among many others whose definition is purely linked to its probability. “The definition of an extreme event in statistics is very precise: an extreme is a very rare event”, explains Mathieu Vrac, research director at the Laboratory of Climate and Environmental Sciences (LSCE-IPSL). “In general a value is considered extreme when its probability of occurrence is under 1%, but even then, above one per thousand, it is not that rare,” he continues.

Thus, our climate is studied as a statistical object subject to variations, as would be a six-sided die. Historically, the approach of climate researchers has been to observe and analyse the long-term evolution of a variable in a defined geographical area, such as the average temperature in the northern hemisphere. Statistical analyses make it possible to see whether there is a discernible global trend and to determine if it is significant, i.e. if it can be due to something other than chance. This approach has the advantage of attributing the apparently random and chaotic appearance of extremes to identifiable trends over time.

Frontiers in event attribution

However, as climate change becomes more noticeable in recent years, a new question has emerged: “Is this event due to climate change?” It may seem similar to the previous ones but truly has a major difference: it is no longer a trend that is being questioned but a single occurrence. To Mathieu Vrac, the question is an odd one for a scientist: “an event cannot be solely due to climate change. From my point of view, the climate is a statistical object. In this context, a rare event always has a probability of occurring.” The question for researchers is rather whether the associated probability would be the same with fewer greenhouse gas emissions. Their approach is to compare the factual world ─ the one we live in ─ with the one that was, or could have been. In order to imagine worlds without human-related greenhouse gases, scientists have climate models and simulations at their disposal.

Moreover, attributing these events to climate change is not an end in itself, reminds Mathieu Vrac: “Extreme events are just the tip of the iceberg. Beyond, the whole atmospheric circulation can be modified and be the cause.” Most often, extremes are only the manifestations of less visible but equally important changes. On the flip side, gaining further insight on these events and knowing their probability is bound to increase encourages us to look at the problem differently: “A more societal way of defining the notion of extremes is the question of impacts. If you ask a farmer or a researcher in an office, the experience of what an extreme is will be very different.” This vision, just as relevant as the statistician’s, allows for the questioning of our ability to adapt as a society, lacking the possibility to prevent the occurrence of extreme events.

Translated from Marion Barbé for IPSL

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