The spatial distribution of the 90th percentile of the HWMId and AHWI calculated at each grid point within the period 1979–2015 compares well between reanalysis (ERA-Interim and NCEP-2) and model data (see Supplementary Figs S2 and S3). Additionally, the HWMId, AHWI, and AT40C spatial patterns compare remarkably well across models (Supplementary Figs S4, S5 and S6, respectively) and strongly resemble the reanalysis (Supplementary Figs. S2a,b,d,e and S3a,b) and ensemble models patterns (Supplementary Figs S2c,f and S3c). These results confirm those of a recent study19 showing robust agreement in heat stress variables (based on temperature and relative humidity) in a set of CMIP5 models.

In some key regions, such as the Midwestern and Eastern US, China, Northern Latin America and Malaysia, both reanalysis and model data show that heat wave magnitude and peak temperature have been amplified by high relative humidity in the recent past. The selected heat waves of Chicago 1995 and Shanghai 2003 are clear examples of the contribution of relative humidity during a heat wave (Fig. 1a–d,i–n). On the contrary, the effect of relative humidity was negligible during the two famous heat waves that occurred in Central Europe in 2003 and in Russia in 2010 (Fig. 1e–h,o–r).

Figure 1 Historical heat waves and humid heat waves across world regions with different climates and their HWMId and AHWI spatial distribution. The panels (a,e,i,o) show time series of heat waves that occurred in specific locations reporting the values of HWMId, AHWI and the duration, calculated by means of the Warm Spell Duration Index (WSDI, see method). Black line is the 90th percentile daily threshold (see method). Open grey circles are the temperature values of the days. ﻿Full black circles﻿ are the days in the heat wave. Red open circles represent the apparent temperature values calculated, for each day composing the heat wave, by means of the Heat Index (see method). The maps in (b,f,l,p) and (c,g,m,q) represent the spatial distribution of the HWMId and AHWI, respectively. The maps in (d,h,n,r) show the spatial distribution of the differences between AHWI and HWMId. This figure has been produced using R version 3.3.2 (https://cran.r-project.org/). Full size image

In both humid and dry regions heat wave occurrence can be associated with persistent synoptic conditions such as: blocking patterns, reduced cloudiness and advection of warm air20, 21. However, in regions such as the Eastern US and China, where apparent temperature impacts are amplified by high relative humidity, the formation of a humid heat wave typically is due to hot and humid air being advected from the Gulf of Mexico or from tropical regions22, respectively. In contrast, across Europe and the Western US, the formation of a dry heat wave is often due to a blocking pattern and associated advection of hot dry air from desert areas. As an example the 2010 Russian heat wave resulted from a strong blocking anticyclone driving warm air from Africa23.

During the heat wave of 1995, Chicago was referred to as “the Urban Inferno24”. The heat wave had a high impact because extreme temperatures were made worse by high relative humidity, which made it difficult to sweat and cool off. From a physiological point of view, this short heat wave would not have been so extreme without high relative humidity25, 26 (Fig. 1a–d).

In the summer of 2003, two heat waves hit Europe21 and China27 (Fig. 1e–h,i–n, respectively). By comparing these two events, we see that the heat wave across central Europe was mainly due to extreme temperatures, whereas during the hottest summer of the past 50 years recorded in Shanghai in 2003 high relative humidity played an important role in exacerbating the heat wave impact27 (Fig. 1i–n).

Another example of extreme but not humid heat wave is represented by the heat wave that occurred in Russia in the summer of the 2010 (Fig. 1o–r). This heat wave is considered the most extreme one of the present era15, 21. For this heat wave the maximum magnitude exceeded the score of 60 (Fig. 1o–r), a value that, according to all our datasets, was never recorded during any other heat wave of the recent past period (1979–2015). Additionally, the HWMId and AHWI values calculated for the same recent past period from the CMIP5 models do not show any location exceeding a magnitude of 60. This threshold is used as reference to estimate the probability of occurrence of an extreme heat wave with magnitude greater than the one in Russia in 2010 (hereafter, RU2010).

In the coming decades, with increasing global mean temperature, the global land fraction with high probability of occurrence of humid heat waves with magnitude greater than RU2010 is expected to increase (Fig. 2). On a global scale, the near-surface absolute humidity of the air roughly follows the increasing temperatures according to the Clausius–Clapeyron relationship, and thus relative humidity remains roughly constant or slightly decreases over land28. However, locally the relative humidity may change due to circulation changes28. Moreover, the non-linear terms in the definition of AT amplify the impact of temperature changes even if relative humidity remains constant. The humidity-induced heat stress amplification is strongest in the regions that are warmest and most humid under present-day conditions19, 29 Our results are consistent with earlier studies showing that heat stress is projected to increase over all land regions along with rising temperatures19.

Figure 2 Probability of occurrence of extreme humid heat waves at different warming levels relative to 1861–1880. (a), Simulated global mean surface temperature increase as a function of time. Decadal model median over the historical period (1860–2010) are represented by black crosses. Decadal model median over the future period (2011–2100) for the three Representative Concentration Pathway (RCP2.6, RCP4.5 and RCP8.5) scenarios are represented by black squares, circle and triangles, respectively. (b–d), Probability of occurrence of heat waves with magnitude greater than the maximum magnitude detected in Russia in 2010 (HWMId > 60) calculated at each grid point for all model years with global mean temperature anomaly relative to 1861–1880 between 1.4° and 1.6° (1.5° warming level, see method), 1.9°–2.1° (2° warming level) and 3.9°–4.1° (4° warming level), respectively. e-g, as b-d but for humid heat waves and the relative Apparent Heat Wave Index (AHWI > 60). This figure has been produced using R version 3.3.2 (https://cran.r-project.org/). Full size image

At 1.5 °C and 2 °C warming above pre-industrial levels, the probability of occurrence of a RU2010 heat wave is zero almost everywhere if measured with the HWMId (Fig. 2b,c). On the contrary, this probability is different than zero, although still very small, in the Eastern US, China, Central West Africa and Northern Latin America when measured by means of the AHWI, which takes into account both temperature and relative humidity (Fig. 2e,f). At 4 °C warming the yearly probability of occurrence of a heat wave with magnitude greater than the RU2010 will be greater than 10% in Central Europe, India, and across many African regions. The Eastern US, Northern Latin America and China are expected to experience such type of heat waves with a annual probability greater than 50%, corresponding to an average return period of two years (Fig. 2g). This probability is greater than the one projected in the hottest world regions, such as the Arabian Peninsula, Australia and other dry-deserts (see Fig. 2d,g).

Similar results are found for the occurrence of heat waves with AT40C and AT55C peaks. The percentage of global land area with a high probability of occurrence of heat waves with AT40C and AT55C increases with increasing warming levels (Fig. 3). Across the hottest world regions and the regions where relative humidity amplifies the heat wave magnitude, the probability of annual occurrence of a heat wave with a AT40C peak show annual values exceeding 50% and 90% at a warming level of 2 °C and 4 °C, respectively (Fig. 3b,c). These probability values are much smaller if measured only with temperature (see supplementary Fig. S7a–c). Highly populated regions, such as the Eastern US and China, are expected to experience the warmest AT peak values of the world (see Supplementary Fig. S8), with an occurrence of a AT55C peak on a two year basis (probability greater than 50%, see Fig. 3f). Due to the high expected apparent temperature values these regions are projected to have high number of deaths among people older than 65 years in 205030, without assuming adaptation effects. Note that, as for the heat wave magnitude across these regions, all warming levels show a probability of occurrence of AT55C equal to or greater than the one of the warmest world regions such as dry-deserts (Fig. 3d–f). Without considering relative humidity, the probability that heat wave temperature peaks exceed 55 °C is equal or very close to zero almost everywhere at all warming levels (see Fig. S7d–f).

Figure 3 Annual probability of occurrence of a heat waves with apparent temperature peaks greater than 40 °C and 55 °C. (a–c), Probability of occurrence of heat waves with AT peak ≥ 40 (AT40C) calculated at each grid point for all model years with global mean temperature anomaly relative to 1861–1880 at 1.5, 2, and 4 degrees warming (see Fig. 2), respectively. (d–f), as (a–c) but for occurrence of heat waves with AT peak ≥ 55 (AT55C). This figure has been produced using R version 3.3.2 (https://cran.r-project.org/). Full size image

The occurrence of heat waves with AT55C, never recorded in our data records in the recent past, is likely to cause heat strokes by limiting the human thermoregulation. The exceedance of this apparent temperature across these regions is in agreement with other measures accounting for the combined effect of temperature and relative humidity. As an example, the wet-bulb temperature peak during a heat wave is expected to exceed the value of 35 °C (see Supplementary Fig. S9), a threshold likely to induce hyperthermia in humans and other mammals as dissipation of metabolic heat becomes impossible25, 31 While this never happens in the present climate, and it is unlikely at 1.5 °C and 2 °C, it would occur on a regular basis in many highly populated regions with global-mean warming of about 4 °C, questioning the habitability of some of these regions.