Anthropogenically-driven increases in the risks of summertime compound hot extremes

Compared to individual hot days/nights, compound hot extremes that combine daytime and nighttime heat are more impactful. However, past and future changes in compound hot extremes as well as their underlying drivers and societal impacts remain poorly understood. Here we show that during 1960–2012, significant increases in Northern Hemisphere average frequency (~1.03 days decade−1) and intensity (~0.28 °C decade−1) of summertime compound hot extremes arise primarily from summer-mean warming. The forcing of rising greenhouse gases (GHGs) is robustly detected and largely accounts for observed trends. Observationally-constrained projections suggest an approximate eightfold increase in hemispheric-average frequency and a threefold growth in intensity of summertime compound hot extremes by 2100 (relative to 2012), given uncurbed GHG emissions. Accordingly, end-of-century population exposure to compound hot extremes is projected to be four to eight times the 2010s level, dependent on demographic and climate scenarios.

The condition of k = 0 corresponds to the Type I case (Gumbel).
k > 0 corresponds to the Type II case (Fréchet), while k < 0 corresponds to the Type III case (Weibull).
We split the historical period of 1960-2012 into two sub-periods (1960-1985 and 1986-2012). The GEV fit is performed with respect to the former and the latter sub-periods, with fitted PDFs referred to as PDF0=f(µ0, σ0, k0) and PDF1= f(µ1, σ1, k1), respectively. For daily maximum/minimum temperatures in each grid-box, we keep the scale and shape parameters constant but shift the location parameter µ from µ0 to µ1 (i.e., PDFµ = f (µ1, σ0, k0)). We then obtain occurrence probabilities of hot days and nights in these two sub-periods by calculating proportions of threshold-exceeding (90 th percentile) days within PDF0 and PDFµ. By the derived probabilities, we use the bootstrapping technique to generate 100000 random samples of hot days and nights for two sub-periods, and then count the number of days registering hot days and nights simultaneously, i.e., the PDF-fitted frequency of compound hot extremes. The ratio of the difference between these PDF-fitted frequencies during two sub-periods in their observed counterpart is interpreted as the contribution from changing location parameter alone. Similarly, we quantify relative contributions from changing scale parameter alone (i.e., PDFσ = f (µ0, σ1, k0) vs. PDF0), changing shape parameter alone (i.e., PDFk = f (µ0, σ0, k1) vs. PDF0) and changing them both (i.e., PDFσ, k = f (µ0, σ1, k1) vs. PDF0).

Supplementary Note 2 Trends in dynamical conditions and its relationship with the frequency change of compound hot extremes
Both internal variability and anthropogenic warming may result in changes in atmospheric circulation patterns (refs. 29-31 in the main text). To account for both, we calculate trends for both sea level pressure (SLP) and 500hPa geopotential height (HGT) from the NCEP/NCAR R1

Reanalysis (National Centers for Environmental Prediction/National Center for Atmospheric
Research) 1 to generally represent regional changes in anticyclonic conditions, as recommended by ref. 29 in the main text.
We first apply a bilinear interpolation to re-grid the reanalysis data onto the HadGHCND's grids 34/53), we obtain the whole-period trend.
To better serve our purpose of explaining the spatial heterogeneity of trends for compound hot extremes, we divide the Northern Hemisphere continents into twenty nearly equal-area climate zones basically following the classification scheme proposed by ref. 4. The geographical realms of them are shown in Fig. 3a in the main text, with their acronyms and boundaries detailed in Supplementary Table 2. On this basis, we calculate regional-average trends for frequency of compound hot extremes, sea level pressure, and 500hPa geopotential height. We then use the ordinary least squares regression to quantify the statistical relationship between trends for dynamic conditions and frequency of compound hot extremes. We also compute the Pearson correlation coefficient between two variables and its corresponding p-values for the two-tailed test to determine its statistical significance, as presented in Fig. 3b-e in the main text.

Supplementary Note 3 Detection and attribution of observed changes in independent hot extremes
For summertime independent hot days, the simulated (multi-model ensemble-MME mean) frequency and intensity trends are slightly stronger than observed ( Supplementary Fig. 9a, b); while the simulated (MME mean) frequency and intensity changes in summertime independent hot nights are markedly weaker than observed ( Supplementary Fig. 9c, d). This seems to be partly associated with underestimation of the decreasing trend of diurnal temperature range in CMIP5 climate models 5 , which would have induced biased warming (cooling) trend in Tmax (Tmin), thus overestimating (underestimating) the frequency and intensity changes in independent hot days (nights).
Both the anthropogenic forcing (ANT) and natural forcing (NAT) signals can be detected in changes of independent hot days and nights ( Supplementary Fig. 10). The simulations tend to slightly overestimate (markedly underestimate) the human-induced frequency and intensity changes in independent hot days (nights). This agrees with previous studies on conventional univariate-based temperature extremes, which reported that CMIP5 models overestimated the frequency change of warm days, particularly in summer 6 . Such overestimation may artificially accelerate the transition of independent hot nights to compound hot extremes in summer in simulations (Supplementary Fig.   11e and Supplementary Fig. 12e). In the three-signal analysis, other anthropogenic forcings (OANT; i.e., anthropogenic aerosols and large-scale land use changes) fail to be detected in independent hot days' changes, while could be detected in changes of independent hot nights with relatively large uncertainties. This difference may be ascribed to misrepresentations of the diurnal variations of aerosols' influences and/or other forcings in models (e.g., the poorly-represented indirect effects of aerosols on clouds and precipitation). Amongst these three external forcers, the rise in greenhouse gases (GHG) is found to be the most dominant contributor to the frequency and intensity changes in independent hot days and nights, with a small offset from OANT forcings and negligible impacts from NAT forcings.

Supplementary Tables
Supplementary Table 1 The CMIP5 models used in the detection and attribution analysis.
Listed are the ensemble size of the ALL-forcing, NAT-forcing, GHG-forcing experiments, the chunks of pre-industrial (pi) control simulations, and the horizontal resolution of climate models.