A Common Framework for Approaches to Extreme Event Attribution
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The extent to which a given extreme weather or climate event is attributable to anthropogenic climate change is a question of considerable public interest. From a scientific perspective, the question can be framed in various ways, and the answer depends very much on the framing. One such framing is a risk-based approach, which answers the question probabilistically, in terms of a change in likelihood of a class of event similar to the one in question, and natural variability is treated as noise. A rather different framing is a storyline approach, which examines the role of the various factors contributing to the event as it unfolded, including the anomalous aspects of natural variability, and answers the question deterministically. It is argued that these two apparently irreconcilable approaches can be viewed within a common framework, where the most useful level of conditioning will depend on the question being asked and the uncertainties involved.
KeywordsClimate change Extremes Weather Dynamics Meteorology Attribution
Extreme weather and climate events are of great societal interest as they significantly affect people and property—usually adversely. They are also of public interest since they are unusual natural phenomena, which have scientific stories behind them. Just as weather is a topic of daily conversation, extreme weather events (including longer-duration climate extremes such as drought) provide a universal talking point. Whilst their proximate cause is meteorological, it is now inevitable that the question will be asked, “Was this event due to climate change?” This is a perfectly natural question to ask given that climate change is a reality and that in many cases, climate change will be felt most directly through its impact on extremes. (For example, sea level rise will generally impact society through storm surges leading to coastal inundation.) People relate to what they have experienced, so if extremes are the sharp edge of climate change, then it becomes important, from the standpoint of both communication and risk reduction, to address this question scientifically.
It is sometimes said that anthropogenic warming of the climate system will increase the energy of the atmosphere, which will lead to more storminess and thus more extreme behaviour. It is true that a warmer atmosphere can hold more moisture, which can provide more latent heat release in a convectively driven extreme event, and more precipitation in general. But atmospheric motions are driven by energy differences , not by energy itself, and the polar amplification that is a fundamental characteristic of global warming  will tend to reduce the pole-to-equator temperature gradient. Also, in a warming world, one would tend to expect a reduction in cold extremes. Thus, whilst climate change has undoubtedly affected weather and climate extremes, both the sign and the magnitude of the effect need to be assessed on a case-by-case basis. Although there may be general expectations based on global aspects of climate change, there can be local departures from that behaviour, and over any given time period, multi-decadal variability can also play a role in changes in extremes .
It has also to be recognized that an unprecedented event does not imply that climate has changed. Weather and climate records are of finite length, and as the record lengthens, new record-breaking events will continue to occur, even for stationary statistics. Thus, climate change is reflected in deviations from this behaviour . The temporal inhomogeneity that results from defining a reference period at the beginning of a time series can also lead to spurious trends in extremes when the reference period is short and the variability is normalized by that of the reference period ; several high-profile papers have fallen prey to this error, e.g. .
In general, there seem to be two basic (and at first sight orthogonal) approaches for determining the impact of one factor on an effect involving multiple factors. One is what will be called the ‘risk-based’ approach, where the change in likelihood of the effect arising from the presence of that factor is estimated. It is understood that the attribution is only probabilistic, much as smoking increases the risk of lung cancer but is neither a necessary nor a sufficient cause of lung cancer in any particular individual. This approach to extreme event attribution was introduced to the climate science community by  and applied by  to the European heat wave of 2003. The second is what will be called the ‘storyline’ approach, where the causal chain of factors leading to the event is identified, and the role of each assessed. This approach is exemplified in [13••]’s study of the 2011 Texas drought/heat wave.
The Risk-Based Approach
Implementing this approach involves several steps, which have both practical and philosophical implications. The first step is the event definition. The observed extreme event is unique, so it must be abstracted to a class of event amenable to statistical analysis. This requires a choice of physical variable and the spatial and temporal averaging used to define the event. There is obviously considerable freedom in this choice, yet any particular choice can have a strong effect on the result; in Fig. 3a, different choices would correspond to different locations of the grey lines, and the p1/p0 ratios will be quite sensitive to this choice. See [17•] for an explicit example.
The second step is the construction of the factual likelihood distribution p1. This will generally be done with a climate model. The fundamental challenge is that in order to estimate the likelihood of an extreme event, one needs to perform many years of simulation—the more extreme the event, the larger the number of years. Yet, in order to do so, the model must be computationally cheap to run, which means that it may not be able to simulate credible facsimiles of the event in question. Even for cases where attribution seems easy, such as large-scale heat waves, land-surface feedbacks may involve mesoscale processes that are not adequately represented in models, and deficiencies in the representation of precipitation, let alone precipitation extremes, in coarse-resolution climate models are legion . Therefore, the appropriateness of the model for the study in question needs to be carefully assessed.
The third step is the construction of the counter-factual likelihood distribution p0. All the issues of model fidelity discussed above apply here as well of course, with the additional complication that the counter-factual observations do not exist with which one might evaluate the model. One might use historical observations instead, but those will be highly limited and perhaps nonexistent for the extreme of interest, and the assumption needs to be made that observed climate change is identical to anthropogenic climate change. If the climate model is coupled, then the attribution of differences between the factual and counter-factual climates is clear (assuming the imposed greenhouse gas changes are entirely anthropogenic), but to speed up computations, often the sea-surface temperatures (SSTs) are imposed in an atmosphere-only model. The typical choice is to use observed SSTs for the factual and define the counter-factual SSTs by subtracting an SST anomaly taken from coupled model simulations of climate change. Sensitivity to the choice of the latter must be assessed. Moreover, if the observed SSTs were important for inducing the particular extreme in question, then the attribution is conditional on this situation, and that too must be accounted for. See [17•] for an explicit example.
There are also philosophical issues. The risk-based approach uses concepts developed in epidemiology. In that context, attribution involves analysis of a population, and the question is asked whether the observed data are more consistent with an outbreak of an infectious disease (say) than with noise. That corresponds to the classic detection-attribution question in climate science. But if the attribution question concerns a single event, then the analogy with epidemiology is no longer there. Moreover, the observed event is only used to motivate the choice of event class, and confrontation with observations is not an intrinsic part of the analysis, as it is with detection-attribution. (Observations may be used to establish confidence in the climate model, but are not explicitly used for hypothesis testing.) The results therefore pertain very much to ‘model world’, and their physical connection to the actual event is not immediate. If there is a reliable long-term data record, this issue can be addressed by couching the event attribution within a more traditional detection-attribution framework, as illustrated by  for annual-mean Central England Temperature. However, this will generally constrain the spatiotemporal footprint of the event and will be limited to situations where such long-term records exist and exhibit attributable trends.
Dynamic and Thermodynamic Mechanisms
As discussed earlier, there is a striking difference between the robustness of purely thermodynamic aspects of climate change and of dynamic aspects involving the atmospheric or oceanic circulation. The former are quite certain, the latter highly uncertain [14•]. At the regional scale, the thermodynamic aspects are strongly modulated by the dynamic aspects so the latter must be taken into account. Part of the issue is the relatively small signal-to-noise of the circulation changes expected from models [23••]—although there are regional exceptions —and part is the general non-robustness of the circulation response in models (Fig. 4 of [14•], ). The difficulty is compounded by the fact that the forced circulation response can be expected to project on the modes of variability , so is difficult to separate from the noise using fingerprinting methods, and is not well constrained theoretically .
If an extreme event was mainly caused by purely thermodynamic processes, then the risk-based analysis using a climate model is probably reliable and a strong attribution statement can be made. If, on the other hand, an extreme event was caused in part by extreme dynamical conditions, then any risk-based analysis using a climate model also has to address the question of whether the simulated change in the likelihood or severity of such conditions is credible. Without attributed observed changes, or a theoretical understanding of what to expect, or a robust prediction from climate models, this would seem to be an extremely challenging prospect. And if plausible uncertainties are placed on those changes, then the result is likely to be ‘no effect detected’. This is indeed what tends to be concluded in event attribution studies of dynamically driven extremes . But absence of evidence is not evidence of absence. Can we do better?
The Storyline Approach
Since climate change is an accepted fact [15•], it should no longer be necessary to detect climate change; rather, the question (for extreme event attribution) is what is the best estimate of the contribution of climate change to the observed event. In this case, effect size is the more relevant question than statistical significance . Trenberth et al. [16••] argue that a physical investigation of how the event unfolded, and how the different contributing factors might have been affected by known thermodynamic aspects of climate change, is the more effective approach when the risk-based approach yields a highly uncertain outcome. This storyline approach, which is analogous to accident investigation (where multiple contributing factors are generally involved and their roles are assessed in a conditional manner), was employed by [13••] to investigate the 2011 Texas drought/heat wave. Although [13••] emphasized the dominance of natural variability, specifically the precipitation deficit associated with anomalous Pacific SSTs, they estimated that about 0.7 °C (20 %) of the heat-wave magnitude relative to the 1981–2010 mean was attributable to anthropogenic climate change. Thus, the storyline approach can quantify the magnitude of the anthropogenic effect, but only for that particular event. This could be useful for liability, or for planning if historical events are used as benchmarks for resilience. (It may be difficult to convince people to invest in defences against a hypothetical risk, but easier to do so if an event has previously occurred so clearly could occur again, but potentially with more impact.)
The risk-based approach estimates δP(E), or sometimes δP(E,D), the change in the joint occurrence of E and D (e.g. the combination of high temperature and anti-cyclonic circulation anomaly used by [8••] for the 2010 Russian heat wave). The dynamically conditioned attribution, in contrast, estimates δP(E|D); this is equivalent to the ‘circulation analogues’ approach described earlier and illustrated in Fig. 5, where anthropogenic changes in temperature for a particular extreme winter were estimated after conditioning on the circulation regime. The signal-to-noise of this estimate can be expected to be large, since the conditioning (especially if on a specific synoptic situation) eliminates most of the dynamical variability; the concept is illustrated in Fig. 3c. The product P(D) times δP(E|D) is simply the change in probability of the extreme event, assuming no change in occurrence of the dynamical situation that led to the event. The justification for the dynamically conditioned approach is that the latter change in occurrence, δP(D), is highly uncertain and best assumed to be zero unless there are strong grounds for assuming something else [16••]. In any case, its impact on δP(E) depends on the ratio of the signal-to-noise of the dynamical change, δP(D)/P(D), to that of the thermodynamic change, δP(E|D)/P(E|D). Since this ratio can generally be expected to be small, the neglect of this term is not unreasonable. There is also the last term in eq. 2, but assuming that D was a necessary condition for the occurrence of the extreme, it will be negligible. Since P(E,D) = P(E|D)P(D), neglect of the last term in eq. 2 is implicit in the risk-based approach when an event is defined by the joint occurrence P(E,D).
It may be noted that this approach is analogous to specifying the meteorology and quantifying the impact of a chemical change on atmospheric composition, which assumes that the composition change is too small to appreciably affect the meteorology. This was used by  to quantify the contribution of changes in ozone-depleting substances to the observed total-ozone record on a year-by-year basis, i.e. deterministically, rather than only statistically as would be the case with a free-running model.
As illustrated by Fig. 3c, conditioning on the dynamical situation leading to the event can convert necessary causation to sufficient causation, in which case even a single event can distinguish between alternative hypotheses. For example,  argued that the exceptionally warm European fall/winter of 2006/2007 could not have occurred, in conjunction with the observed circulation anomaly, without anthropogenic warming. This then ties the attribution directly to the observed event, rather than being only probabilistic. The direct confrontation with data as an essential component of the attribution is a very attractive feature of this approach, as is its emphasis on a physically based causal narrative.
In climate science, we are accustomed to strive for quantitative answers, but it is important to appreciate that being quantitative is not necessarily the same thing as being rigorous . In particular, it is essential to distinguish between quantifiable uncertainty and Knightian (i.e. deep) uncertainty . Uncertainty associated with sampling variance is quantifiable, e.g. through boot-strapping methods, but many of the uncertainties associated with climate change—especially the deep uncertainties associated with the atmospheric circulation response to climate change—are not easily quantifiable. Examining the sensitivity of a result to the choice of climate model, as is becoming common practice in risk-based approaches , is an important first step in determining robustness. However, model spread is not a quantification of model uncertainty because a multi-model ensemble does not represent a meaningful probability distribution . It has therefore been argued that the quest for more accurate climate model predictions is illusory and that instead we need to be using models for understanding, not prediction [42, 43].
The risk-based approach to extreme event attribution is inherently probabilistic and does not claim to attribute the specific event that inspired the study; indeed, in , the observed event was excluded from the analysis to avoid selection bias, and the results concerned observed changes prior to the event itself, and expected future changes, rather than the event itself. Such analyses are clearly useful for policy and planning, and potentially also for liability [11, 44], if they can be established to be credible. However, for weather-related extremes, converting a weather question into a climate question by abstracting the particular event to an event class (e.g. regarding the extreme precipitation across a GCM grid cell as a proxy for extreme precipitation in a mountain valley or canyon) could be seen as substituting a simple problem in place of a complex one , and thus as falling prey to Whitehead’s fallacy of ‘misplaced concreteness’ . If the quantitative estimates of altered risk are sensitive to the spatiotemporal footprint of the event, as they almost certainly will be, then the quantification provided by the climate model may not be relevant at the spatiotemporal scale of the extreme weather event itself. Furthermore, if dynamical aspects of climate change are crucial to the model result, the credibility of these changes needs to be established. The ideal situation is when a model can reliably simulate the dynamics leading to the extreme, and the modelled effect of climate change is mainly occurring through well-represented thermodynamic processes.
The storyline approach to event attribution has the merit of being strongly anchored in a physically based causal narrative, at the price of not addressing the potential change in likelihood of the dynamical situation leading to the event. It has been argued here that this apparent weakness may actually be a strength insofar as it explicitly distinguishes between quantifiable risk [through δP(E|D)] and Knightian uncertainty [through δP(D)]. In this respect, the storyline approach is not so much ignoring the possibility of a dynamical component to climate change, as treating it separately from the purely thermodynamic changes concerning which there is much higher confidence. [46•] have recently advocated a similar approach for climate projections, within a transdisciplinary framework. This has the further advantage that other anthropogenic factors (i.e. apart from climate change) can be explicitly included in the analysis. (This can be done in the risk-based approach too, of course, but the effects would be more challenging to isolate because of the lower signal-to-noise.) For example, rather than removing urban heat-island effects from the data in order to isolate the ‘true’ climate signal, would it not be more useful to include them in the analysis—since those effects do kill people—and understand how the different factors combine?
Of course, the two approaches to extreme event attribution are not mutually exclusive, and as argued here can be cast within a common framework; there is no reason why they could not be used in a complementary fashion, thereby bringing together climate-oriented and weather-oriented perspectives. Moreover, conditioning can be done to various degrees. Indeed, [17•] argue that for Africa, where inter-annual variability is strongly controlled by SSTs, an SST-conditioned attribution may in some cases be more useful to users than an unconditioned attribution since observed events serve as a benchmark for resilience, which people can relate to. Conditioning by SSTs is merely the first step towards conditioning by circulation, and ultimately by synoptic situation. The most useful level of conditioning will depend on the question being asked, and the confidence one has in the resulting answer.
The author acknowledges the support provided through the Grantham Chair in Climate Science at the University of Reading, and the numerous constructive comments provided by two anonymous reviewers.
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The author states that there is no conflict of interest.
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