When record breaking heat waves should not surprise: skewness, heavy tails and implications for risk assessment

Abstract

Extreme heat waves beset western North America during 2021, including a 46.7°C (116°F) observation in Portland, Oregon, an astonishing 5°C above the previous record. Using Portland as an example we provide evidence for a latent risk of extreme heat waves in the Pacific Northwest (PNW) and along the west coast of the United States where a maritime climate and its intrinsic variations yield a positive skewness in summertime daily maximum temperatures. A generalized Pareto extreme value analysis yields a heavy tailed distribution with a return period of 300-1000 years, indicating that, while rare, the event was possible, contrary to prior claims that the event was "virtually impossible". We demonstrate that the extreme temperatures can be explained by the coincident extreme values of geopotential heights, and that the relationship between heights and extreme temperatures has not materially changed over the observational record. The dynamical nature of the event along with recent developments in stochastic theory justifies the use of skewed and heavy-tailed distributions which may provide the basis for a more proactive approach to managing the risk of future events.

Comparing Local Versus Hemispheric Perspectives of Extreme Heat Events

“…As discussed in Section 3.1, local temperatures exhibit well‐known and notable departures from the normal distribution on the extremes of frequency distributions (e.g., Bjarke et al., 2022; Huybers et al., 2014; Lewis & King, 2017; Loikith & Neelin, 2015; McKinnon & Simpson, 2022; Ruff & Neelin, 2012; Sardeshmukh et al., 2015; Schär et al., 2004; Sippel et al., 2015; Sura, 2011; Sura & Perron, 2010; Tamarin‐Brodsky et al., 2020). In the discussion of Figure 2a, we showed that the shapes of the temperature distributions significantly increase the incidence of heat events on the local scale ; in Figure 2b, we consider their effects on the hemispheric scale : For a given skewness and kurtosis, we generate 100 random time series (roughly the effective number of spatial degrees of freedom in the data) sampled from a Pearson distribution, and calculate the percent of days on which any of the random time series exceeds +4s.…”

“…The long‐term mean of all three indices is comparable to that in Figures 3a–3c, but the long‐term trends in all three indices are no longer significant. Hence, while changes in temperature variability and skewness may play a role in changes in extreme temperature anomalies over certain locations (Bjarke et al., 2022; Lewis & King, 2017; McKinnon & Simpson, 2022; McKinnon et al., 2016; Sardeshmukh et al., 2015; Schär et al., 2004; Schneider et al., 2015; Sippel et al., 2015; Tamarin‐Brodsky et al., 2020), changes in mean temperature clearly account for the preponderance of the hemispherically integrated changes in heat events (e.g., Amaya et al., 2023; Donat & Alexander, 2012; Hansen et al., 2012; Oliver et al., 2018; Rhines & Huybers, 2013; Seneviratne et al., 2021; Simolo et al., 2011; Thompson et al., 2022).…”

“…The increased incidence afforded by the hemispheric‐scale perspective is a well‐known consequence of the increased spatial degrees of freedom in the data and is markedly influenced by the shapes of the local frequency distributions (Figure 2), see, for example, Ruff and Neelin (2012) and Bjarke et al. (2022). Considering both skewness and kurtosis of the local temperature distributions increases the expected hemispheric incidence of heat events by more than an order of magnitude relative to what is expected from normal statistics.…”

“…Over land, where the decorrelation timescale of surface temperatures is on the order of a few days, the return time of +4s events is thus several centuries if the surface temperature is normally distributed. However, surface temperatures exhibit notable departures from the normal distribution, and the shape of the temperature distribution has an important effect on the likelihood of extreme temperature events (e.g., Bjarke et al, 2022;Huybers et al, 2014;Lewis & King, 2017;Loikith & Neelin, 2015;McKinnon & Simpson, 2022;Ruff & Neelin, 2012;Sardeshmukh et al, 2015;Schär et al, 2004;Sippel et al, 2015;Sura, 2011;Sura & Perron, 2010). Figure 2a summarizes both theoretical and observed effects of skewness and kurtosis on the local incidence of heat events in 2 m temperature from ERA5 reanalysis.…”

Foundations for Universal Non‐Gaussian Data Assimilation

“…Incorrectly applying Gaussian data assimilation in these cases can introduce biases in the forecast, or even predict values outside the physical bounds. Moreover, this assumption can have impacts on unbounded variables; for example, the likelihood of extreme events, such as heat waves, can be severely underestimated when assuming Gaussian statistics for the temperature (Bjarke et al, 2022;Sardeshmukh et al, 2015). Sophisticated techniques have been developed to deal with non-Gaussian errors, based largely on particle filters (van Leeuwen, 2009;van Leeuwen et al, 2019).…”