# Elevated increases in human-perceived temperature under climate warming

## Abstract

Changes in air temperature (AT), humidity and wind speed (Wind) affect apparent temperature (AP), the human-perceived equivalent temperature1,2,3. Here we show that under climate warming, both reanalysis data sets and Global Climate Model simulations indicate that AP has increased faster than AT over land. The faster increase in AP has been especially significant over low latitudes and is expected to continue in the future. The global land average AP increased at 0.04 °C per decade faster than AT before 2005. This trend is projected to increase to 0.06 °C (0.03–0.09 °C; minimum and maximum of the ensemble members) per decade and 0.17 °C (0.12–0.25 °C) per decade under the Representative Concentration Pathway 4.5 scenario (RCP4.5) and RCP8.5, respectively, and reduce to 0.02 °C (0–0.03 °C) per decade under RCP2.6 over 2006–2100. The higher increment in AP in summer daytime is more remarkable than in winter night-time and is most prominent over low latitudes. The summertime increases in AT-based thermal discomfort are projected to balance the wintertime decreases in AT-based discomfort over low and middle latitudes, while the summertime increases in AP-based thermal discomfort are expected to outpace the wintertime decreases in AP-based thermal discomfort. Effective climate change mitigation efforts to achieve RCP2.6 can considerably alleviate the faster increase in AP.

## Main

Apparent temperature (AP), the human-perceived equivalent temperature, is commonly defined as a function of air temperature (AT), humidity, wind speed (Wind) and other climatic factors1,2,3. The contributions of these climatic factors to AP vary under different weather conditions. When AT is high, atmospheric humidity brings surplus heat stress to the human body. In this case, AP is represented by a heat index4,5,6. When AT is low, the chilling effect of strong wind can lower the AP by up to 20 °C or even more. To account for the effect of wind, a wind-chill equivalent temperature is usually used7. Extreme AP events (for example, heat waves and cold surges) associated with abnormally high or low AT combined with abnormal weather conditions can potentially lead to reduced labour capacity, temperature-related discomfort, stress, stroke, morbidity and even mortality8,9,10,11. On the other hand, even though non-extreme AP may not cause sudden impacts on human health, it could influence how humans perceive the effect of global warming, affect human comfort under normal conditions, and contribute to the substantially higher temperature-related mortality compared to extreme temperature12. Although past studies have demonstrated that global warming raises AP more than AT under extremely hot conditions4,9, possible changes in the long-term AP under both extreme and non-extreme conditions throughout the year have not been well studied. A better understanding of the long-term physiological impacts of global warming on human beings represented by AP under both extreme and non-extreme weather conditions is much needed for climate change adaptation. Previous observations have shown a historical U-shape or J-shape temperature–mortality relationship, with higher mortality under hot and cold conditions11,12,13,14. These relationships suggest increases in heat-related mortality and debatable decreases in cold-related mortality when temperature increases14,15,16. It is arguable how much future increases in heat-related mortality could be offset by the changes in cold-related mortality under global warming15. An investigation into changes in the seasonality of AP and AT, especially in summer/winter and extremely hot days/cold nights, is of great importance to improve the understanding of future changes in the balance of heat- and cold-related mortalities.

To estimate AP under all weather conditions, we combined a commonly used heat index for extremely hot conditions5,6, a wind-chill equivalent temperature for extremely cold conditions7, and a universal AP for normal conditions17 (see Methods for details). Near-surface AT, specific humidity at 2 m and Wind at 10 m from four reanalysis data sets, including ERA-Interim18, ERA4019, NCEP20 and NCEP221 and seven Global Climate Models (GCMs) participating in the Coupled Model Intercomparison Project Phase 5 (CMIP5) with available 3 h outputs, were used to compute daytime and night-time AP (see Methods and Supplementary Table 1)22. The outputs are based on the historical and three Representative Concentration Pathways (RCPs) scenarios, including RCP2.6, RCP4.5 and RCP8.5. The spatio-temporal patterns of AP, AT, relative humidity (RH) and Wind from individual GCMs and their multimodel ensemble means in the historical period are in good agreement with those from the reanalysis data sets, indicating that AP can be reliably computed from GCM outputs (Fig. 1 and Supplementary Figs. 131). A previous study demonstrated that it is more reliable to use AT and humidity from GCM outputs to compute heat indices under extremely hot weather than either AT or humidity alone10. These findings enhance our confidence in future projections of AP based on GCM outputs.

Both GCM outputs for the 1950–2100 period and reanalysis data sets for the historical periods show consistent increases in the difference between AP and AT (AP–AT hereafter) over continents, suggesting faster increases in AP than in AT (Fig. 1a). The AP–AT values from the ERA-Interim, ERA40, NCEP and NCEP2 data sets exhibit statistically significant warming trends of 0.04 °C per decade, 0.07 °C per decade, 0.04 °C per decade and 0.04 °C per decade, respectively, which are similar to the corresponding trend based on GCM simulations for the historical scenario of 0.04 (0.01–0.06; minimum and maximum of the ensemble members) °C per decade. GCM-simulated AP–AT is projected to increase with trends of 0.06 (0.03–0.09) °C per decade and 0.17 (0.12–0.25) °C per decade under RCP4.5 and RCP8.5, respectively and decrease to 0.02 (0–0.03) °C per decade under RCP2.6 over the period 2006–2100. These differences in AP–AT under future scenarios suggest that high-mitigation efforts can considerably slow down the elevated increases in human-perceived equivalent temperature, AP. The changes in AP–AT in 2081–2100 relative to 1981–2000 (∆(AP–AT) hereafter) exhibit a strong latitudinal gradient (Fig. 1b,c). Under RCP8.5, multimodel ensemble simulations indicate an increment of AP–AT ranging from 3 to 6 °C over low latitudes (20° S–20° N), which is triple that over mid latitudes (20°–50° N and 20°–50° S). The magnitude of ∆(AP–AT) over the northern high latitudes (>50° N) is larger than that over mid latitudes. Under RCP2.6, ∆(AP–AT) is projected to drop below 1 °C in low latitudes and reach almost 0 °C over mid and high latitudes.

Summer daytime ∆(AP–AT) is projected to increase faster than winter night-time (Fig. 2). The zonal mean of summer daytime ∆(AP–AT) under RCP8.5 is >4 °C over low latitudes and decreases to 2 °C over mid latitudes (Fig. 2c). The highest winter night-time ∆(AP–AT) is 2 °C over the equator and high latitudes of the Northern Hemisphere (NH), but over the mid latitudes is <1 °C under RCP8.5, showing a pattern of Arctic amplification that can also be found under RCP4.523 (Fig. 2c). Under RCP2.6, summer daytime ∆(AP–AT) is consistently <1 °C at different latitudes, and the winter night-time changes are <0.5 °C. Summer daytime changes in AT (∆AT) are projected to be comparable to those of winter night-time, but summer daytime changes in AP (∆AP) are projected to be larger than those of winter night-time (Supplementary Fig. 38). Figure 2a shows that the summer daytime ∆(AP–AT) under RCP8.5 could reach 5–6 °C along the coastal areas in southeast Asia. The increase in extra heat stress is caused by high humidity in these areas (Supplementary Fig. 1).

Projected changes in the total degree of thermal discomfort (TDC) in summer daytime and winter night-time as a whole, TDCs+w (see Methods for details) based on AT under RCP2.6, RCP4.5 and RCP8.5, show the balance between summer daytime increases in TDC and winter night-time decreases in discomfort (Fig. 3b). However, TDCs+w computed from AP is about 1 °C and 3 °C over latitudes around 10° N under RCP4.5 and RCP8.5, respectively, and drops to almost 0 °C under RCP2.6, indicating an increase in the TDC caused by extra heat stress in AP under the more severe warming scenarios (Fig. 3a). Therefore, in contrast to the negligible net change in AT-based TDC in summer and winter as a whole, a positive change is expected in the AP-based TDC if humidity and other climatic variables are taken into consideration (Fig. 3a–c). The increase in TDC on extremely hot days and extremely cold nights (TDCh+c) based on AP is higher than the AT-based values over low latitudes (Fig. 3d–f). Higher AP values increase TDC and frequency of extremely hot days (TDCh and f h) considerably and hence lead to higher TDCh+c, with an increase of about 15 °C over low latitudes (Supplementary Fig. 41 and Fig. 3d). The occurrences of hot days and cold nights ∆f h+c based on AP and AT, respectively, are projected to increase, especially over low latitudes (Fig. 3g,h). In general, the increasing ∆f h+c is largely caused by a considerable increase in the occurrence of hot days f h (Supplementary Fig. 41). The increases in AP-based TDCh+c and ∆f h+c under RCP2.6 and RCP4.5 are as large as the corresponding increases in AT-based values under RCP4.5 and RCP8.5, respectively.

To better understand the reasons for the faster increase in AP than in AT, we project changes in the contributing factors under RCP4.5. AT shows a pattern of Arctic amplification with a projected increase of about 2–3 °C in most areas, but about 3–4 °C over high latitudes23 (Supplementary Fig. 45). The specific humidity is projected to increase most significantly over low latitudes by ≥1.6 g kg–1. However, RH, the ratio of partial pressure of water vapour (e a) to the saturation water vapour pressure (e s) at a given temperature is projected to undergo marginal changes because both e a and e s are expected to increase under warming, which is consistent with previous observations24. Given the same increases in AT and humidity, either a higher initial AT or a higher initial humidity would lead to a stronger heat stress (Supplementary Fig. 42)4. According to this relationship, because AT during 2081–2100 is projected to be higher than that during 1981–2000 but RH remains more or less the same, the heat stress to human beings under the impact of climate change is expected to increase in the future. The projected increases in AT alone under RCP4.5 could explain more than 90% of the increases in AP over high latitudes and about 60–70% over low latitudes (Fig. 4a). Although the projected ∆RH alone cannot cause significant impacts on ∆AP over high latitudes, ∆RH significantly contributes 20–30% increases in AP over low latitudes (Fig. 4b). Changes in Wind alone, the key contributing factor to AP under cold conditions, lead to insignificant changes in AP (Fig. 4c). The relationship between wind-chill equivalent temperature and AT is linear given the same Wind, indicating that wind-chill effect would decrease as AT increases (see Methods and Supplementary Fig. 43). Because AT is expected to increase in the twenty-first century, the cooling effect of wind should become weaker.

Overall, we anticipate a larger increase in AP than AT as a result of global warming, which means that human beings sense a larger increase in temperature than the increase in AT. This phenomenon is expected to be most prominent in low latitudes under the high-emission scenario. The increase in AT can balance the summertime increases in TDC and wintertime decreases in discomfort, while the summertime increases in AP-based TDC are expected to outpace the wintertime decreases in TDC. In other words, the increase in summer AT is projected to be comparable to that in winter over low and mid latitudes, but summer AP is projected to increase faster than winter AP. The TDC based on AP under extreme conditions increases at a higher rate than that based on AT. Our results are consistent with previous studies of extremely hot events9,25 and seasonal projections of AT26,27. Under RCP2.6, the difference between AP and AT is projected to be marginal and the projected increasing trend of the difference is even smaller than that under the historical period, indicating low future emissions are the key to mitigate harmful heat stress effects on human beings, especially those living in low latitudes.

## Methods

We estimated AP from AT, specific humidity at 2 m and Wind at 10 m above land surface. Under different weather conditions the contributions of various climatic factors to AP are different. Therefore, we combined three commonly used AP indices for three different conditions: the heat index under hot conditions5, wind-chill equivalent temperature under cold conditions3 and a universal AP index for normal conditions17. These indices have been used globally or regionally in many past studies.

In this study, the heat index was calculated by the Rothfusz regression in °C (refs 25,28):

$${\rm{HI}}\phantom{\rule{2.77626pt}{0ex}}=-8.7847{\rm{+}}1.6114{\rm{\times AT}}-0.012308{{\rm{\times AT}}}^{2}{\rm{+RH\times }}(2.3385-0.14612{\rm{\times AT}}{\rm{+}}2.2117{\rm{\times }}1{0}^{-3}{{\rm{\times AT}}}^{2}){{\rm{+RH}}}^{2}{\rm{\times }}(-0.016425+7.2546\times 1{0}^{-4}{\rm{\times AT}}-3.582{\rm{\times }}1{0}^{-6}{{\rm{\times AT}}}^{2})$$
(1)

where HI is the heat index (in °C), AT is the air temperature (in °C) and RH is the relative humidity (in %). For GCM outputs, NCEP and NCEP2, we estimated RH from the simulated specific humidity by using Tetens’ formula to estimate saturation specific humidity29. For the ERA-Interim and ERA40 reanalysis data, we derived RH from dew point temperature and AT (ref. 30). This equation will fail if the heat index is less than 26.67 °C and adjustment should be made under specified conditions (for example, RH < 13% and 26.67 °C ≤ AT ≤ 44.4 °C and RH > 85% and 26.67 °C ≤ AT ≤ 30.56 °C) (NOAA, http://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml). This heat index indicates the temperature perceived by human being under hot, shady and calm conditions.

We estimated wind-chill equivalent temperature based on the equation used by the United States National Weather Service and the Meteorological Service of Canada3,31:

$${\rm{WCT}}\phantom{\rule{2.77626pt}{0ex}}=13.12{\rm{+}}0.6215{\rm{\times AT}}-11.37{\rm{\times }}{v}^{0.16}{\rm{+}}0.3965{\rm{\times AT\times }}{v}^{0.16}$$
(2)

where WCT is the wind-chill equivalent temperature (in °C) and v is wind speed at 10 m (in km h−1). The WCT is only defined for an AT <10 °C and a Wind exceeding 4.8 km h–1 (NOAA, www.nws.noaa.gov/om/winter/faqs.shtml).

The heat index and wind-chill equivalent temperature defined above are only effective under hot or cold weather conditions. Therefore, under normal weather conditions, climatic variables will be out of the recommended range for estimating the heat index and wind-chill equivalent temperature. Steadman proposed a universal AP (UAP) for more general weather conditions17:

$${\rm{UAP}}\phantom{\rule{2.77626pt}{0ex}}=-2.7{\rm{+}}1.04{\rm{\times AT+}}2{\rm{\times }}P-0.65{\rm{\times }}v$$
(3)

where UAP is the universal AP and P is the water vapour pressure (in kPa) estimated from the specific humidity and AT. The AP defined in this study represents the human-perceived equivalent temperature in the shade, which means that solar radiation (both direct and diffuse radiation) is not considered.

Under global warming, it is expected that heat-related mortality will increase due to more frequent and more intense extremely hot days, but how cold-related mortality decreases due to less frequent extremely cold events and how the future changes in heat-related and cold-related mortalities affect the net changes in temperature-related mortality under global warming are still controversial15,16. Projections of changes in the seasonality of temperature, that is, AP or AT in summer/winter and extremely hot/cold events, are the basis for estimating the net change in future temperature-related mortalities. To quantify the net impacts of temperature increase on TDC that would increase under hot conditions and decrease under cold conditions, we defined the total degree of TDC for (1) summer and winter as a whole (TDCs+w) and (2) the extremely hot days and cold nights as a whole (TDCh+c) as

$${{\rm{TDC}}}_{{\rm{s+w}}}{\rm{=}}{T}_{{\rm{s}}}-{T}_{{\rm{w}}}\quad {\rm{and}}\quad {{\rm{TDC}}}_{{\rm{h+c}}}{\rm{=}}({T}_{{\rm{h}}}{\rm{\times }}{f}_{{\rm{h}}}-{T}_{{\rm{c}}}{\rm{\times }}{f}_{{\rm{c}}})/({f}_{{\rm{h}}}{\rm{+}}{f}_{{\rm{c}}})$$
(4)

where T s and T w (AP or AT in °C) are summer daytime temperature and winter night-time temperature, respectively, T h and T c (AP or AT in °C) are the temperature on extremely hot days and extremely cold nights, respectively, and f h and f c are the frequencies of extremely hot days and extremely cold nights, respectively. Higher values of changes in these two indices indicate larger net changes in TDC. An extremely hot day is defined as a day with daytime temperature greater than the 90th percentile of maximum AP/AT of the calendar day centred on a five-day window in 1981–2000, while an extremely cold night is defined as a night with night-time temperature less than the 10th percentile of minimum AP/AT of the calendar day centred on a five-day window in 1981–2000 (ref. 32). The sum of the average numbers of extremely hot days and extremely cold nights within a year is f h+c.

In this study, AP was first estimated from reanalysis data sets and GCM outputs at their original spatial resolutions (Supplementary Table 1) and then regridded to 2.5° × 2.5° resolution. Only GCMs with available outputs of 3 h AT, specific humidity and Wind in 1981–2000 and in 2081–2100 under RCP2.6, RCP4.5 and RCP8.5 were used. One ensemble member (r1i1p1) from each of the GCMs was used in the study. We used the geographic local time of each grid cell to calculate the daytime (6:00–18:00) and night-time (18:00–6:00) climate variables. The biases from GCMs as estimated with reference to the ERA-Interim data did not have fundamental impacts on the increasing trend of AP–AT (Supplementary Fig. 37). The faster increase in AP than in AT is even more prominent in the bias-corrected GCMs.

The significance of the trend in AP and AT was tested by the modified Mann–Kendall trend test, a non-parametric trend detection method considering autocorrelation in time series33. The differences of averages of climatic variables between two periods were tested by the two-sample t-test34.

### Data availability

CMIP5 model outputs are available in the Earth System Grid Federation (ESGF) Peer-to-Peer system (https://esgf-node.llnl.gov/projects/esgf-llnl/). ERA-Interim and ERA40 reanalysis data sets are available from the European Centre for Medium-Range Weather Forecasts (ECMWF) website (http://apps.ecmwf.int/datasets/). NCEP and NCEP2 reanalysis data sets are available from the NOAA/ESRL/PSD data portal (https://www.esrl.noaa.gov/psd/data/gridded/).

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## Acknowledgements

The authors acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and acknowledge the climate modelling groups for developing and making available their model output. For CMIP5, the US Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The work described in this Letter was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. HKBU22301916) and a Direct Grant of The Chinese University of Hong Kong (project no. 4052134).

## Author information

J.L. and Y.D.C. designed the study. J.L. conducted the analysis. J.L., Y.D.C., T.Y.G. and N.-C.L. discussed the results and jointly wrote the paper.

Correspondence to Yongqin David Chen.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

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## Supplementary information

### Supplementary Information

Supplementary Discussions 1–8, Supplementary Figures 1–45, Supplementary Methods, Supplementary Table 1, Supplementary References

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Li, J., Chen, Y.D., Gan, T.Y. et al. Elevated increases in human-perceived temperature under climate warming. Nature Clim Change 8, 43–47 (2018). https://doi.org/10.1038/s41558-017-0036-2

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