There can be no question that Earth’s average temperature is increasing (Sánchez-Lugo et al. 2019). Reasons for this are well understood as a consequence of increasing greenhouse gases altering the global energy balance. Because regional climate change is not solely governed by radiative energy balance, there is less certainty about the extent to which changes in regional climate are the result of natural variability or changes in greenhouse gas concentrations. For example, ensembles of climate-model simulations with essentially the same global-warming trajectories can show significant regional variations in climate change among the individual members (Deser et al. 2012). Changes in extreme events are even harder to unambiguously attribute to global warming. For many phenomena, the observational record is inadequate for establishing baselines for their occurrence in the past and the extent to which they may be changing in the current climate. Ensembles of climate-model simulations are typically of limited use because extremes occur too infrequently to be well sampled by the ensemble. Moreover, many extreme events involve mesoscale processes that are particularly challenging to incorporate in climate simulations owing to limitations in numerical resolution and uncertainties in the physical parameterizations of clouds, precipitation, and boundary layer processes.
The science of extreme-event attribution has grown rapidly in an effort to address the challenge of quantifying the extent to which climate change is contributing to increases in the frequency or severity of extreme events and to potentially guide efforts toward mitigation and adaptation. Two approaches that have been used in the attribution of extreme events to climate change are the risk-based and the storyline approaches. In the risk-based approach, the goal is to quantify the extent to which anthropogenic influences have altered the probability of occurrence of a particular type of extreme event (e.g., Stott et al. 2016). In contrast, the storyline approach is not focused on the probabilistic estimation of the impact of climate change, but rather attempts to estimate the contribution of climate change to the various physical processes responsible for an extreme event (e.g., Shepherd 2016). Rather than being completely different methods, the risk-based and storyline approaches have also been regarded as limiting cases along a spectrum of event-attribution assessments in which conditional probabilities play an increasingly significant role as the method becomes closer to the storyline or Bayesian framework (Stott et al. 2017).
Using terminology from statistical hypothesis testing, a common null hypothesis in the risk-based approach is that a particular extreme event is the product of natural variability. Two types of errors can arise when testing this hypothesis. A type I error (rejection of a true null hypothesis) occurs when an extreme event is produced by natural variability and incorrectly attributed to climate change. A type II error (failure to reject a false null hypothesis) occurs when climate change is responsible for producing that extreme, but the evidence is deemed inadequate to reject the claim that it arose from natural variability. Because it is not possible to avoid both types of error, we must weigh the likelihood and seriousness of type I and type II errors in formulating our assessment. It has been suggested that using the risk-based approach to test the preceding hypothesis tends to understate anthropogenic contributions to extreme events (type II errors), whereas the storyline approach tends to overstate them (type I errors) (Lloyd and Oreskes 2018).
One way to avoid errors that arise from simple yes–no answers is to offer more nuanced probabilistic information. In the context of frequentist risk-based attribution, this can be provided by measures such as the risk ratio RR, which is the ratio of the probabilities of occurrence of events above a given threshold in the presence of, to that in the absence of, anthropogenic climate change, or alternatively, the fraction of attributable risk: 1 − RR‒1 (Stott et al. 2004; Stone and Allen 2005). Such numeric values, along with the associated probability distributions for extreme events in the baseline and current climates, might potentially be weighted by the estimated costs of reducing the risks from extremes to arrive at optimal strategies for mitigation and adaptation. Nevertheless, specific frameworks for environmental risk assessment are extremely difficult to formulate and implement for several reasons, including that the relevant probabilities and the costs are both poorly constrained (Jones 2001), and because the population that would most benefit from risk avoidance may be different from the population that bears its cost.
The political will to incur any cost is highly dependent on stakeholder perceptions of the risks from anthropogenic climate change. At present, the American public’s perception of these risks is still influenced by yes–no answers to the basic question: was a given extreme weather event made more likely or more severe by climate change? Even if scientists express their conclusions in probabilistic terms, the takeaway message conveyed to the public by the media is often simplified to “yes” or “no.” The provision of yes–no answers to a series of hypothesis tests also constituted a basic methodology used in a recent article in this journal on the detection and attribution of the influence of climate change on tropical cyclones (Knutson et al. 2019).
While being cognizant of its limitations, in the remainder of this paper we will therefore focus on considerations related to binary yes–no decision-making with the goal of highlighting connections between two problems that are nominally very different: the issuance of hazardous-weather warnings and the attribution of extreme weather events to climate change. An important goal in both cases is to properly alert the public about atmospheric phenomena that can have dramatic impacts on life and property.
Weather forecasters have long dealt with the tradeoffs between over- and under-warning for hazardous-weather events; forecasting metrics and historical performance data for U.S. National Weather Service (NWS) tornado warnings will, therefore, be presented in the second section. The application of similar metrics in the attribution of extreme high temperatures to climate change is examined in the third section, along with the relation between the weather-forecast metrics and other measures more traditionally used in extreme-event-attribution studies. Forecast metrics for warnings issued for other types of hazardous-weather events will be reviewed in the fourth section. The fifth section contains the conclusions.
The author has greatly benefited from conversations with Harold Brooks, Susan Solomon, Alexandra Anderson-Frey, Jane Baldwin, Brad Colman, Andrew DeLaFrance, and from comments by anonymous reviewers. NWS forecast verification metrics were kindly provided by Charles Kluepfel.
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The NWS issues warnings when the public should take action and there is imminent danger to life or property. Warnings should not be confused with watches, which are issued at a lower threat level and advise the public to be prepared for the possibility of a tornado.
The false alarm ratio should not be confused with terminology in signal detection theory (Mason 1982; Maxmillan and Creelman 1991), in which the probability of a false alarm is defined as the ratio of the nonevents for which warnings are issued to all nonevents or b/(b + d).
The POD data are from Brooks and Corriea (2018), and are for warnings issued before the appearance of a tornado; the complementary FAR data were provided by H. Brooks (2019, personal communication).
Longer-time-scale efforts at adaptation to tornadoes are not conditioned on tornado warnings themselves, but they can also have surprising parallels to political considerations that arise when proposing adaptions to climate change. For example, on 23 May 2014, one year and three days after seven children were killed when a tornado hit an elementary school in Moore, Oklahoma, the Oklahoma legislature rejected a proposal “for a statewide vote on allowing school districts, with local voter approval, to increase their bonding authority once to build tornado shelters” (Green 2014).