Nonlinear increases in extreme temperatures paradoxically dampen increases in extreme humid-heat

Nonlinear increases in warm season temperatures are projected for many regions, a phenomenon we show to be associated with relative surface drying. However, negative human health impacts are physiologically linked to combinations of high temperatures and high humidity. Since the amplified warming and drying are concurrent, the net effect on humid-heat, as measured by the wet bulb temperature (TW), is uncertain. We demonstrate that globally, on the hottest days of the year, the positive effect of amplified warming on TW is counterbalanced by a larger negative effect resulting from drying. As a result, the largest increases in TW and Tx do not occur on the same days. Compared to a world with linear temperature change, the drying associated with nonlinear warming dampens mid-latitude TW increases by up to 0.5 °C, and also dampens the rise in frequency of dangerous humid-heat (TW > 27 °C) by up to 5 d per year in parts of North America and Europe. Our results highlight the opposing interactions among temperature and humidity changes and their effects on TW, and point to the importance of constraining uncertainty in hydrological and warm season humidity changes to best position the management of future humid-heat risks.


Introduction
Humid-heat extremes pose a severe risk to human health [1,2], and temperature extremes more broadly can reduce economic performance [3,4], damage crops and ecosystems [5][6][7], and harm infrastructure [8][9][10]. Climate change is increasing global mean temperature by altering the surface radiative balance, raising the chances of extreme heat events across the world [11][12][13][14]. At regional scales, land-atmosphere interactions among soil moisture and vegetation control the partitioning of energy into sensible and latent heat fluxes, playing a significant role in controlling extreme temperatures, drought, and heat wave statistics in the observational record and in climate models [15][16][17][18][19][20][21][22]. Further, recent research has identified soil drying and associated changes in surface energy partitioning to be a crucial driver of nonlinear temperature changes relative to the warm season mean [23].
In some regions, climate models project that extreme temperatures will increase an additional 1°C-2°C beyond warm season mean temperatures-indicating that mean changes alone cannot account for changes in the tails. This amplified warming of temperature extremes has been linked to declines in the fraction of total surface energy fluxes from latent heat, so that in regions where the surface is projected to dry, temperatures are projected to warm more rapidly as more energy is partitioned to sensible heating of the air [23].
While high temperatures have diverse and serious impacts on economies and ecosystems, human health is most tightly linked to the physiological consequences of extreme humid-heat [1]. Constraining uncertainty in the response of humid-heat to climate warming is an urgent task, as recent research has suggested that a critical threshold for human humid-heat tolerance could be approached or exceeded in parts of the world during the 21st century [24][25][26][27][28]. This threshold is defined using the wet bulb temperature (T W ), the saturation temperature of an air parcel. When T W exceeds the human skin temperature, approximately 35°C, evaporative cooling is no longer effective as a means of shedding body heat. Prolonged exposure to such conditions causes heat illness and eventually death [29]. In addition, much lower T W values between 27°C and 32°C have routinely caused tens of thousands of deaths and serious heat-related illnesses in recent decades [2], particularly among the world's most vulnerable populations. Uncertainty of a few degrees Celsius at the warm tail of the T W distribution is therefore essential to constrain, as the mortality risks it poses to people are considerable.
Recent research has shown that anomalously high specific humidity, rather than temperature, is often the dominant driver of present-day extreme humidheat events [30], while a dry land surface often accompanies the extreme temperature events projected in climate models [31,32]. Because T W is nonlinearly dependent on both temperature and humidity, it is not evident how the competing effects of temperature (and its associated surface drying) will combine with specific humidity to alter future risks of extreme humid-heat. Simultaneous changes in these quantities complicate estimates of the T W response, as temperature and specific humidity not only influence T W individually, but are also themselves interactive, responding in opposite directions to surface drying (temperature increases more, specific humidity increases less). These direct and indirect effects of temperature and humidity on T W suggest that surface drying could either increase or decrease humid-heat, depending on the balance of the two changes.
We use daily maximum temperature (T x ) amplification, the nonlinear change in temperature that results in the top half of the T x distribution warming more than the warm season average (or median) T x , which appear to be driven largely by land-atmosphere interactions, to assess whether they lead to nonlinear T W changes in a suite of global climate models. We investigate the relationships between T x amplification and its associated specific humidity change in the context of land-surface drying, and demonstrate the dependence of the magnitude and frequency of extreme T W on each at global and regional scales. We then illustrate how T x amplification-driven changes in T W affect the frequency of and population exposure to humid-heat extremes.

Data and methods
We utilize climate projections from a suite of 16 global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 5 (CMIP5) [33]. All models that provide the requisite variables for computing daily T W (daily maximum temperature (Tasmax), specific humidity (Huss), and sea level pressure (Psl)), as well as daily sensible (Hfss) and latent heat fluxes (Hfls), are used (supplementary material table 1). Sea level pressure is used as opposed to true surface pressure due to its greater availability in the CMIP5 ensemble; the difference in pressure is found to have a less than 0.2°C effect on global T W estimates, and a still smaller effect for T W extremes which occur almost exclusively in regions near sea-level. All model projections are made in the period 2061-2085 and are compared with historical simulations spanning 1981-2005. The Representative Concentration Pathway (RCP) 8.5 [34] emissions scenario is used to maximize the climate change signal. All model data are regridded using a linear interpolation procedure to a 2°×2°resolution to facilitate inter-model spatial comparison. This resolution is generally in the middle of the native CMIP5 model resolutions (see table 1) and ensures that the models are not all being unphysically downscaled. All analysis is conducted on the locally-defined warm season, estimated for each model and each grid cell as all unique months in which the annual maximum air temperature (TX x ) has occurred during the historical period. The regridding procedure has minimal effect on the model-estimated timing of the warm season (see supplementary material figure S1, which is available online at stacks.iop. org/ERL/14/084003/mmedia). Daily T W at the time of maximum air temperature is calculated between 60°S and 60°N using the algorithm presented in Davies-Jones, 2008 [35], implemented in HumanIndexMod [36], and ported to Matlab [37]. Estimating T W at the time of maximum air temperature rather than the true daily maximum T W creates a negligible downward bias in T W [24].
Changes in T x and T W decile thresholds are calculated for each grid cell and for each model. The resulting changes are averaged over all land grid cells between 60°S and 60°N. T x amplification is calculated for different percentiles. For example, T x amplification on the TX x (annual maximum daily temperature) day is calculated for each model and each grid cell as the projected change in TX x (averaged across all years) minus the projected change in the warm season 50th percentile T x (also averaged across all years). We denote this amplification using the following notation: where ΔTX x is the average change in TX x (i.e. 100th percentile of the annual T x distribution) and ΔT x 50 is the average change in the 50th percentile of the T x distribution. T W amplification on the T Ww day is calculated similarly as the change in the annual maximum T W minus the change in the warm season 50th percentile daily maximum T W . We similarly denote this amplification as: We note that our results are robust to the choice of defining amplification (ΔTX x −ΔT x 50 or ΔT Ww −ΔT W 50) as relative to the warm season 50th percentile or to the warm season mean.
T x amplification on the T Ww day is calculated as the projected change in T x on the day of the annual maximum T W minus the projected change in warm season 50th percentile T x . We denote this amplification as: x Ww x Similarly, T W amplification on the TX x day is calculated as the projected change in T W on the TX x day minus the projected change in the warm season 50th percentile T W , denoted as: T x amplification across the T W distribution is calculated as the mean projected change in T x on all days in each warm season T W decile (T W D, where D is the decile in which the calculation is being performed) minus the warm season 50th percentile change in T x : Similarly, T W amplification across the T x distribution is calculated as the mean projected change in T W on all days in each warm season T x decile minus the warm season 50th percentile change in T W : We also assess specific humidity (Huss) and evaporative fraction (EF) amplification across the T x and T W distributions. The EF is the ratio of the latent heat flux to the total heat flux, defined as: where Q E is the latent heat flux, and Q H is the sensible heat flux. As above, we denote these specific humidity and EF amplifications as: The specific humidity amplification across the T x distribution: Huss 50 .
x x The specific humidity amplification across the T W distribution: Huss 50 .

W W
The EF amplification across the T x distribution: The EF amplification across the To estimate the effect of T x amplification's temperature component on T W , for each model and for each grid cell, we calculate the T W change on days in each decile of the T x distribution using the decile's projected T x change and the specific humidity change at the T x median. To estimate the effect of T x amplification's specific humidity component on T W , we repeat the calculation using each T x decile's projected specific humidity change and median T x change. The total effect of T x amplification on T W change is estimated by repeating the calculation for each T x decile's projected specific humidity change and each decile's projected T x change. The components of T W change due to temperature and specific humidity change are calculated by subtracting the median T W change from the mean of the T W change across the top five T x deciles.
The number of days per warm season that exceed T W thresholds is estimated using our calculations of T x amplification-driven changes in T W . Model bias in absolute T W is removed via a percentile-matching procedure using the ERA-Interim reanalysis. For each selected T W threshold, the corresponding T W percentile is found for each grid cell in ERA-Interim T W data. The number of days per warm season that exceed this T W percentile is then calculated for each model and each grid cell in historical climate simulations. Next, future T W values including the effects of T x amplification are calculated for each model, grid cell, and decile by adding the decile-mean change to the model's historical decile-mean T W value, and the number of days exceeding the same T W percentile is calculated using this future T W distribution. Future T W values not including the effects of T x amplification are calculated for each model, grid cell, and decile by adding the 50th-decile-mean T W change to the model's historical decile-mean T W values in each decile, and the number of days exceeding the same T W percentile is calculated. Finally, the number of additional days exceeding the T W threshold due to T x amplification is calculated by subtracting the number of exceedances calculated without the effects of T x amplification from the number of exceedances calculated with the effects of T x amplification.
Population exposure to each T W threshold is estimated using spatially explicit population projections from the Shared Socioeconomic Pathways Project [38,39]. Results are shown using the SSP3 population trajectory, which is consistent with the RCP 8.5 emissions scenario. For each model and each grid cell, the population change averaged over 2060-2090 as compared to 2010 is multiplied by the change in the number of extreme T W exceedances at each T W threshold between 27°C and 31°C, giving humid-heat exposure in the units of person-days per year. These exposure totals are summed for all global grid cells.

Results and discussion
We define an amplification to be the projected change in T x , T W , or other climate variables at a particular point in the distribution relative to the projected change in that variable at the 50th percentile across the local warm season. Positive (negative) amplification is when the magnitude of the local warm season change in percentiles above the 50th percentile is greater (less) than the magnitude of change at the 50th percentile. Positive (negative) amplification implies that there is not simply a mean shift in the distribution, but also an increase (decrease) in the variance of the right tail.
Global-scale nonlinear increases in warm temperatures are apparent by 2061-2085 across the 16 CMIP5 models forced with RCP 8.5 (see Methods). T x changes are negatively amplified for percentiles below the local warm season's 50th T x percentile and positively amplified for percentiles above it ( figure 1(a)). In contrast, warm season T W changes show less variation across the T W distribution, suggesting a mean shift in response to forcing. The multi-model median globally-averaged T x amplification on the TX x day (the 100th T x percentile in each year; ΔTX x −ΔT x 50) is 0.34°C, bringing the total TX x change to over 4.5°C, but shows wide spatial variation, with parts of the eastern and southwestern US, northern Europe, and China exhibiting well over a degree of amplification ( figure 1(b)). This positively-amplified warming of high T x values at both global and regional scales has been linked to land-atmosphere coupling and land surface drying [23], which allows energy to be preferentially partitioned into sensible rather than latent heat flux. T W , despite having temperature as a contributing factor (along with humidity and atmospheric pressure), exhibits less amplification than T x across the globally-averaged distribution: the multi-model median annual maximum T Ww day (the 100th T w percentile in each year; ΔT Ww −ΔT W 50) rises 0.24°C more than the warm season 50th percentile T W ( figure 1(c)). Parts of North Africa and the Middle East have amplified T W of just under a degree Celsius, though the magnitudes and ubiquity of T W amplification ( figure 1(c)) is less than that for T x amplification ( figure 1(b)).
As global temperatures rise, the multi-model median projects that T x on the T Ww day (ΔT x | T Ww ) and T W on the TX x day (ΔT W | TX x ) will increase by 3°C-6°C and 2°C-4°C, respectively, as both heat and humidity intensify for the most extreme temperatures (figures 2(a), (b)). Because T x influences T W , changes in both variables interact across their distributions. For example, T x and T W are negatively amplified on the T Ww and TX x days, respectively, robustly showing less to no warming (−1°C to −0.5°C) as compared with their respective seasonal 50th percentile changes in parts of the subtropics and mid-latitudes (figures 2(c), (d)). This means that on the future days that have the year's hottest temperatures, the increase in humid-heat intensity is projected to be less than the median increase across the warm season. Thus the nonlinear increase in T x does not to appear drive a nonlinear increase in T W. Globally, this interactive negative amplification occurs across the top quartile of both the T x and T W distributions (figures 2(e), (f)).
Our above analysis highlights that conditions associated with T x amplification dampen increases in T W on days at high T x percentiles (figures 2(d), (f)), while conditions associated with T W amplification dampen increases in T x on days at high T W percentiles (figures 2(c), (e)). These results suggest that nonlinear increases in extreme temperatures alone are insufficient to cause nonlinear increases in humid-heat extremes. We explore this result by demonstrating how interactions between T x and T W are mediated by changes in the evaporative fraction (EF), defined as the ratio of the latent heat flux to the total heat flux, and specific humidity. Prior work has linked T x amplification to land surface drying and associated declines in EF [23]. We confirm this result, showing that EF has a more negative change (drying) on days above the 50th T x percentile, and a more positive change on days below it (figures 3(a); S2(a)). In addition, relative EF change across the T W distribution is generally more positive on days above the 50th T W percentile (figures 3(b); S2(b)). Together, these results suggest that the highest T x days will become relatively drier while the highest T W days will become relatively wetter, and highlight the fact that the hottest days often are not the same as those with the highest T W values [30].
Specific humidity responds directly to warming due to the ability of warmer air to hold more moisture. At the same time, however, humidity is shaped by the surface drying that is tightly associated with T x amplification. Concurrent with the relative changes in EF across the T x and T W distributions described above are corresponding changes in specific humidity: when EF change is more positive, specific humidity change is also more positive, a direct result of increased moisture available for evaporation. Accordingly, across the T x distribution, specific humidity change is more negative on days above the 50th T x percentile and more positive on days below it ( figure 3(c)). In contrast, across the T W distribution, specific humidity change is more positive on days above the 50th T W percentile and more negative on days below it ( figure 3(d)). Thus within the confines of local landatmosphere coupling, the linkages between T x amplification and T W change center around land surface drying, as indicated by declines in EF. As the surface dries, EF declines, energy is preferentially partitioned to sensible rather than latent heat flux, and temperatures rise more. At the same time, the lack of surface moisture for evaporation dampens the increase in specific humidity, creating a drier but hotter environment on days in the top half of the T x distribution. The opposite effect occurs on days in the top half of the T W distribution. Figure 4 shows the total effect of T x amplification on T W change on days above the 50th T x percentile relative to T W change at the 50th T x percentile, encompassing the combined effects of temperature and humidity. There is model agreement on the negative amplification of T W change associated with T x amplification in North America, Europe, and Central Asia, regions where the specific humidity component of T x amplification is projected to strongly dampen T W ( figure S5(b)), and its temperature component is projected to have weak effects on T W ( figure S5(a)). Here, T W increases are projected to be less than they would be in a world with only linear temperature and specific humidity changes. In much of the rest of the world, there is not model agreement on the direction of T W change associated with T x amplification. In these regions, the generally positive effect of the temperature component and the negative effect of the specific humidity component on T W balance out, making the magnitude of T W amplification small and its sign uncertain. However, the individual effects of the temperature and specific humidity components of T x amplification on T W change are large, meaning that small differences in either component could strongly affect T W change ( figure S5).
Because T x amplification can contribute to the magnitude of T W increases in some regions, we seek to clarify the implications of T x amplification-induced T W changes on people. We do this by examining how T x amplification contributes to changes in the frequency of T W days above critical wet bulb thresholds. T W proxies the effectiveness of evaporative cooling for people, and global mean climate warming will increase the frequency of extreme humid-heat events everywhere. The number of days with a T W above 27°C, a level above which mortality is observed to rise in cities across the United States ( figure S6), is projected to increase by 5-50 or more days per year in much of the tropics and mid-latitudes, irrespective of T x amplification ( figure 5(a)). Such a response causes increases in global population exposure to T W thresholds from 27°C to 31°C of 25 to 150 billion person days per year, respectively ( figure 5(b)) under a scenario of population growth consistent with RCP 8.5 (see Data and methods).
The T W change due to T x amplification generally reduces the occurrence of extreme humid-heat events above a T W of 27°C in eastern North America and Europe (−2 to −4 d per year) and has little effect on their occurrence in the tropics ( figure 5(c)). These reductions in occurrence as compared to a world with linear temperature and specific humidity change make a substantial contribution (−10 to −50%; figure S7) to the overall changes in the frequency of humid-heat extremes in Europe and eastern North America shown in figure 5(a). Because most of the highest T W values occur in the tropics where T x amplification has uncertain and near zero effect on T W change, the globallyaveraged effect of T x amplification is to slightly reduce the number of extreme T W days exceeding thresholds ranging from 27°C to 31°C by 0.1 to 1 day per year, respectively ( figure 5(d)). Additionally, because many of the regions where the effect of T x amplification on T W change is uncertain are also densely populated, T x amplification is projected to result in −3 to +2.5 billion more annual person-days per year of exposure to T W values above 27°C.

Discussion and conclusions
Our results show that in the global mean, nonlinear T x increases are counterbalanced by the dampened increases in specific humidity associated with T x amplification, resulting in near-linear changes in the T W distribution (figures 1(a), 3(c), (d)). This globalscale linearity, however, belies important variations in T x -amplified T W changes at the regional scale: T x amplification generally dampens the warm season mean T W increase in mid-latitudes where warm season moisture is limited (figure 4), and has little or uncertain effect on T W change in the tropics. This response of T W is tightly coupled to the specific humidity change that is projected on hot days ( figure 3(c)). Globally averaged, T x amplification serves to slightly reduce the frequency of extreme T W values of 27°C or higher as compared to a world with only linear temperature and specific humidity change, a result dominated by eastern North America and Europe where robust warm season mean drying is projected. Because models suggest that declines in surface moisture (proxied by the evaporative fraction) are associated with amplified warming of the hottest temperatures, our results show that more warming of hot extremes can paradoxically reduce the occurrence of humid-heat extremes in some mid-latitude regions.
Land-atmosphere feedbacks play a role in controlling temperature extremes [23,40], and our results demonstrate that such feedbacks also exert an important influence over the change in T W extremes. On extreme T W days, specific humidity is the primary driver of T W change, while temperature is the primary driver of T W change on extreme T x days (figure S8). Accordingly, within the context of land-atmosphere feedbacks, the extent to which T x amplification modifies extreme T W change largely depends on how strongly specific humidity responds to surface drying. At the same time, we note that recent work [41] has detailed the importance of atmospheric dynamics and moisture advection in controlling continental humidity; such processes will also influence the changes in humid-heat.
These results emphasize the need for more research investigating the interactions among precipitation, soil moisture, vegetation, and surface heat fluxes, along with their representations in climate models [22]. In particular, the most extreme T W events often occur along coastlines, making the model parameterizations of sub-grid scale and coastal processes of particular interest. Future increases in model resolution may enable study of these coastal regions with strong temperature and humidity gradients. In this work, we focus on the thermodynamic drivers of nonlinear temperature and T W change. However, changes in atmospheric circulation patterns have been shown to influence the occurrence frequency of extreme temperature events in the historical record [42], and it is likely that dynamical changes may influence T W extremes as well.
We have estimated this relationship between T x amplification and its associated specific humidity change in 16 global climate models and four climate regions, but the extent to which T x changes vary within and across simulations may have a substantial effect on T W change. There is evidence that models may misrepresent the strength of land-atmosphere coupling in some contexts [32], and thus also misrepresent the relationships among evaporative fraction, temperature, and specific humidity that drive T x amplification. Further, because of the dynamical processes that determine moisture advection from the ocean to the land, uncertainty in both ensemble and model representations of internal variability and surface processes will shape uncertainty in how humid such heat extremes become. Because T x amplification generally has a negative influence on T W , an overestimation of the strength of this amplification could result in realworld T W values increasing more than projected.
Such structural and dynamical uncertainties, however, are crucial to preserve in the diagnosis of the risks posed by humid-heat events. While the magnitude of projected extreme T W increases across the CMIP5 model ensemble are smaller than for T x due to the countervailing effects of temperature and humidity change [43], human physiology and health is far more sensitive to small changes in the tails of T W than in temperature alone. This suggests that small uncertainties in T W projections can translate into large uncertainties in the risks of health impacts from humid-heat extremes. Accordingly, it is important that impactsfocused research recognize and present the wide range of projected extreme heat and humid-heat outcomes to best position effective climate risk management [44]. It is equally important to consider the spatial heterogeneity of extreme humid-heat and human mortality across the world. In the United States, where air conditioning is widely accessible and most people do not work outdoors, daily mortality begins to sharply increase above T W values of approximately 27°C (figure S6). While there may be variation in the mortality response to humid-heat in regions in the tropics and subtropics that regularly experience heat stress, human tolerance to high T W values is constrained by physiology [1,29]. Additionally, in regions where baseline health is lower, air conditioning is more expensive or unavailable, and a higher fraction of people perform outdoor physical labor, mortality could respond more sharply to humid-heat than in the US. A more detailed understanding of the regional variation in mortality responses to humid-heat is constrained by health data availability. Given the potential for T W values to approach the theoretical limits of human tolerance (35°C), more research is urgently needed to bound the health risks posed by frequent, unprecedented humid-heat in densely populated parts of the world.
W interpreted the results. E D C and J S M wrote the manuscript with contributions from R M H and J M W.