The emergence of heat and humidity too severe for human tolerance



The ability of humans to efficiently dissipate heat has allowed us to vary on all continents, but a wet bulb temperature (TW) of 35 ° C marks our upper physiological limit, and much lower values ​​have serious impacts on the health and productivity. Climate models project the first occurrences of 35 ° C TW by the middle of the 21st century. However, a complete evaluation of the data from weather stations shows that some coastal subtropical sites have already reported a TW of 35 ° C and that the extremely humid heat has on the whole more than doubled in frequency since 1979. Recent exceedances of 35 ° C in the maximum surface of the world sea the temperature provides additional support for the validity of these dangerously high TW values. We find that the most extreme moist heat is very localized both in space and in time and is therefore significantly underestimated in reanalysis products. Our results thus underscore the serious challenge posed by humid heat which is more intense than previously reported and increasingly severe.


Bipedal locomotion in humans, bare skin and sweat glands are components of a sophisticated cooling system (1). Despite these thermoregulatory adaptations, extreme heat remains one of the most dangerous natural hazards (2), with tens of thousands of deaths in the deadliest events of this century (3, 4). The additive effects of heat and humidity extend beyond direct health effects to include a reduction in individual performance in a range of activities, as well as large-scale economic impacts (57). The effects of heat and humidity have given rise to decades of study in military, sports and professional contexts (8, 9). However, the examination of the wet bulb temperature (TW) from the standpoint of climatology and meteorology has started more recently (ten, 11).

Some impacts of heat and humidity can be avoided through acclimatization and behavioral adaptation (12), there is an upper limit of survival in the event of prolonged exposure, even in idealized conditions of perfect health, total inactivity, full shade, absence of clothing and unlimited drinking water (9, ten). A normal internal human body temperature of 36.8 ° ± 0.5 ° C requires skin temperatures of approximately 35 ° C to maintain a gradient directing heat outward from the heart (ten, 13). Once the air temperature (dry bulb) (T) exceeds this threshold, metabolic heat can only be removed by latent cooling based on perspiration, and at TW exceeding about 35 ° C, this cooling mechanism loses its effectiveness. Since ideal physiological and behavioral assumptions are almost never met, the serious effects of mortality and morbidity generally occur at much lower values ​​- for example, the regions affected by the deadly 2003 heat waves in Europe and Russia in Russia have known TW values ​​not exceeding 28 ° C (fig. S1). In the literature to date, there have been no reports of TW observations exceeding 35 ° C and few reports exceeding 33 ° C (9, 11, 14, 15). The realization of a physiological limit has prompted modeling studies to ask themselves how soon it could be crossed. The results suggest that, under the scenario of maintaining the status quo of RCP8.5 emissions, TW could regularly exceed 35 ° C in parts of South Asia and the Middle East by the third quarter of the year. 21st century (1416).

Here we use quality guaranteed station observations from HadISD (17, 18) and high resolution reanalysis data from ERA-Interim (19, 20), checked against radiosondes and marine observations (see additional documents) (21, 22), to calculate TW base values, geographic patterns and recent trends. Uncertainties in TW of station data due to instrumentation and procedures are in the range of 0.5 ° to 1.0 ° C in all regions considered, an important consideration for proper interpretation of the results. Our approach to using TW and sea surface temperature observations (SST) as a guide for future TW projections provides a different source of evidence from previous research that used coupled or regional models without explicitly including historical station data.


Our study of climate recording from station data reveals numerous global TW exceedances of 31 ° and 33 ° C and two stations which have already reported several maximum daily TW values ​​greater than 35 ° C. These conditions, which approach or exceed prolonged human physiological tolerance, usually only occurring for one to two hours (Fig. S2). They are concentrated in South Asia, the coastal Middle East and the south-west of coastal North America, near extraordinarily high SST and intense continental heat which, together, favor the occurrence of heat extremely wet (2, 14). Along the coasts, the marine influence is manifested by abnormal low-level land winds during the midday and afternoon hours, and these changes in wind can cause a rapid increase in dew point temperature ( Td) in arid and semi-arid coastal areas (Figures S3 to S9). Consistent observational data at the regional level corroborate these intense values: stations located along the coast of the Persian Gulf with at least 50% of data available from 1979 to 2017, all have a 99.9th historic percentile of TW (the value has been exceeded about 14 times in 39 years) above 31 ° C (Fig. 1; see fig. S1 for the absolute maximum). In the ERA-Interim reanalysis, the highest values ​​are found in the same way in the Persian Gulf and the immediately adjacent land areas, as well as in certain parts of the Indus valley (fig. S10). The spatio-temporal average inherent in reanalysis products prevents ERA-Interim from representing short durations and small areas of critical thermal stress, which means that its extreme values ​​of TW are significantly lower than those of meteorological stations in tropical and subtropical regions. (fig. S11). In the Persian Gulf and the adjacent Gulf of Oman, these differences are systematically between −2 ° and −4 ° C (fig. S12). A larger but similar coherence bias is present along the eastern shore of the Red Sea, which provides a basis for future studies examining the reasons for this behavior, as well as other comparisons between station data and of the new analysis.

Fig. 1 Global extreme humid heat observed.

The colored symbols represent the 99.9th percentile of the maximum daily TW observed for 1979-2017 for HadISD stations with at least 50% data availability over this period. The size of the marker is inversely proportional to the density of the station.

Other hot spots> 31 ° C in meteorological station records emerge by examining the 99.9th TW percentile highest in the world: the east of the Indian coast, Pakistan and the northwest of India, and the shores of the Red Sea, the Gulf of California, and the southern Gulf of Mexico (Fig. 1). All are located in the subtropical regions, along the coasts (generally of a semi-closed gulf or a shallow bay, limiting ocean circulation and favoring high SST), and near continental heat sources which , with sea air, constitute the combination necessary for the most exceptional TW (11). The fact that the subtropical ribs are hot spots for heat stress was previously noted (23, 24); our analysis highlights the large geographic extent but also the large intra-regional variations (Fig. 1). Southwest Asia is the main exception to this coastal rule, possibly due to efficient inland transport of moist air by the summer monsoon and large-scale irrigation (15, 25). Tropical forests and ocean areas generally experience TWs not exceeding 31 ° to 32 ° C, possibly a consequence of the high evapotranspiration potential and cloud cover, as well as the greater instability of the tropical atmosphere . However, more research is needed on the thermodynamic mechanisms that prevent these areas from reaching higher values.

Abrupt and statistically significant upward trends in the extreme frequency of TW (overshoots of 27 °, 29 °, 31 ° and 33 ° C) and amplitude are present at all weather stations worldwide (Figure 2). Each frequency trend represents more than a doubling of the occurrences of the corresponding threshold between 1979 and 2017. The trends of ERA-Interim are strongly correlated with those of HadISD but are smaller for the highest values ​​(Fig. 2), consistent with the ERA-Interim underestimation of extreme TW which is the greatest for the most extreme conditions (fig. S11). We also find an acute peak in the number of global TW extremes = 27 ° C and TW = 29 ° C during the strong El Niño events of 1998 and 2016. Linearly destroying this global time series of TW extremes reveals that the El Niño– The correlation of the southern oscillation (ENSO) is most important for TW values ​​which are high but not unusual (~ 27 ° to 28 ° C) across the tropics and subtropics (fig. S13). More work is needed to test to what extent this relationship can be linked to the effect of ENSO on hydrological extremes on a global scale, on average temperatures of the troposphere or on SST in particular basins, and the implications of these effects on the predictability of TW (26, 27). On the whole, the extremes TW in the tropics largely correspond on an inter-annual basis to the average TW (fig. S14), which indicates that the climatic forcings and the modes of internal variability leading to average temperature changes can modulate tropical extremes TW. This is also the case in the subtropics, although to a lesser extent.

Fig. 2 Global trends in extremely humid heat.

((A at re) Annual global accounts of TW exceedances above the thresholds indicated on the respective panel, from HadISD (black, straight axes, with station day units) and ERA-Interim grid points (gray, left axes, with units of grid-point days). We only consider HadISD stations with at least 50% data availability over the period 1979-2017. The correlations between the series are annotated at the top left of each panel, and the dotted lines highlight the linear trends. ((E) TW annual global maximum in ERA-Interim. ((F) The linear plot shows the anomalies in the global average annual temperature (compared to 1850-1879) according to HadCRUT4 (40), which we use to estimate the warming observed each year since the pre-industrial period; the circles indicate the occurrences of TW HadISD stations exceeding 35 ° C, with a radius linearly proportional to the overall annual count, measured in station days.

We also observe modulation on a seasonal scale, taking as an illustrative example the monsoon region of South Asia. There, the timing of the TW peak varies with the advance of the summer monsoon (15). By dividing South Asia into “early monsoon” and “late monsoon” sub-regions, we find that the number of TW ends is greatest at the time of the start date of the local climatological monsoon. (figure 3). Although equivalent extreme values ​​of TW are possible before, during and after the monsoon rains in a given year, they are different in character; especially in the northern and western parts of the subcontinent, they are becoming increasingly humid and have lower dry bulb temperatures as summer progresses. All over the world, these variations in temperature and humidity occur in a well-defined bivariate space (Fig. S15). The fact that these variations are systematically associated with the summer monsoon in South Asia underlines the important role of humidity and weather systems on synoptic to sub-seasonal time scales to control extreme TW (15, 28). Our results highlight the diversity of conditions that can lead to extremely humid heat in the same place at different times, suggesting that strategies for adapting to impacts could benefit from taking this recognition into account. Such intra-seasonal variability in TW is also important for physiological acclimatization, which requires time scales of several days to develop (29); The character TW is particularly relevant when considering effects on human systems that vary in their sensitivity to humidity and temperature – for example, thermoregulation and the demand for energy for artificial cooling are strongly affected by TW, while the materials that make up the built environment are mainly affected by temperature alone (13, 30).

Fig. 3 Seasonality modulated by the monsoon of extremely humid heat.

((A) Early monsoon areas (light orange shading; B) (Continuous line) Average annual number of TW exceedances of 31 ° C per station, per pentade, in the areas of the early monsoon. (Dotted line) Average relative humidity associated with these exceedances. The division between the brown and blue sections represents the start date of the weighted average climatological monsoon by station. ((VS) Same as (B), but for late monsoon areas.

Although our analysis of weather stations indicates that TW has already been reported to have exceeded 35 ° C in limited areas for short periods, this has not yet happened at the regional level represented by the reanalysis data, which is also the approximate scale of the projections of the TW extreme future model taken into account in previous studies (14, 15). To increase the comparability of our station results with these model projections, we are implementing an analysis of generalized extreme values ​​(GEV) to estimate the amount of global warming from the pre-industrial period until TW regularly exceeds 35 ° C on the hottest ERA-Interim grid in the world. cells, currently all located in the Persian Gulf region (Fig. 4). Full details of this procedure can be found in Materials and Methods. In short, we adapt a non-stationary GEV model to the grid cells with the highest TW values, the GEV localization parameter being a function of the annual average air temperature anomaly. This allows us to quantify the amount of global warming necessary for a maximum annual TW ≥ 35 ° C to become at most an event over 30 years in any cell of the grid. We perform this analysis only for grid cells where the non-stationary GEV model is significantly (P 6, ten, 31).

Fig. 4 Extremely humid heat projections exceeding the physiological survival limit.

((A) The shading shows the amount of global warming (since the pre-industrial period) until TW = 35 ° C should become at least one event over 30 years at each cell of the grid according to a non-stationary GEV model. In virgin areas, more than 4 ° C warming is necessary. The black dots indicate the cells of the ERA-Interim grid with a maximum TW (1979-2017) in 0.1% of the hottest grid cells in the world. ((B) Total area with TW of at least 35 ° C, depending on the annual average temperature variation 〈T〉 From the pre-industrial period. The vertical red (green) lines highlight the lowest 〈T〉 For which there are non-zero zones on land (sea) – the respective ToE. ((VS) ToE bootstrap estimates. See text for details of this definition and calculation.

Our method gives a ToE of 1.3 ° C on the waters of the Persian Gulf (90% confidence interval, 0.81 ° to 1.73 ° C) and 2.3 ° C for the cells of the terrestrial network at proximity (1.4 ° to 3.3 ° C) (Fig. 4). The adjustment of these figures for the robust differences of the Persian Gulf of ERA-Interim of around −3 ° C for the extreme TWs (fig. S12) confirms the conclusion of the station’s observations that the recent warming has increased exceedances. of TW = 35 ° C, but that this threshold very probably reached on occasion throughout the observation recording (Fig. 2). The strong marine influence on these values ​​is also apparent in Figure 1.

To better assess the physical realism of our GEV extrapolation, we also examine the maximum annual SST (monthly average) observed. An atmospheric boundary layer fully balanced with the ocean surface would be at saturation and have the same temperature as the underlying SST, which means that in principle 35 ° C is the lowest SST that could maintain the value critical of 35 ° C of TW in the air above. In reality, equilibrium will not be reached if the residence times of the air mass above the extreme SSTs are too short, which is more likely if the vertical profile of the atmosphere allows a strong heating of surface to trigger deep convection (ten). Current large-scale SSTs and their trends can therefore provide some indication of the physical plausibility of our projections of extreme TW. It is in this context that we note for the first time average monthly SST exceeding for the first time the threshold of 35 ° C, reaching 35.2 ° C in the Persian Gulf (Fig. 5). Consequently, our GEV projection of large-scale maritime TW ≥ 35 ° C, for warming below 1.5 ° C, seems to be physically consistent with SST observations on the same scale. Analogous corroboration of TW station-based events ≥ 35 ° C is provided by point scale, SST and hourly TW across the Persian Gulf from an independent database of marine observations (see additional documents) (21), in which we find that SSTs have exceeded 35 ° C every year since 1979, with around 33% of observations from July to September 2017 above this threshold. During the summer of 2017, TW reports on Persian Gulf water ≥ 35 ° C also peaked at around 6% of all TW measurements there.

Fig. 5 SST trends and maxima observed.

((A) Annual maximum monthly SST in all cells of the HadISST dataset grid; the orange dotted line is a 30-year moving average and the red line is 35 ° C. (B) Absolute maximum SST around the Persian Gulf and the Arabian Sea. Blue dots mark places where the monthly average OSH exceeded 35 ° C in 2017.


The station approach we adopt here and the model approach adopted in previous studies (1416) represent different methods to gain a valuable perspective on the genesis and characteristics of the TW global extremes. The main strength of station data is its ability to accurately capture local conditions, but even the best available station data have unobserved potential humidity limits, uncertainties and biases (for example, due to observation, type of instrumentation or location), as well as very incomplete spatial coverage (see discussion in additional documents) (32, 33). On the other hand, reanalysis products and high-resolution regional models meet the need for spatio-temporal continuity and consistency and make it possible to analyze additional variables, but often underestimate the extremes (34).

In this study, we demonstrate that efforts to better understand the extreme TW would benefit from closer examination and better standardization and integration of station data to fill the gaps in the model, particularly along the coasts where TW can vary considerably over short distances and where quality is high. humidity data is therefore essential, but station-based and physical modeling approaches are fundamentally complementary. Further research into the origins of extreme TW biases in mesh products and continued progress in data assimilation would also help develop a more unified approach drawing on all available sources of knowledge. For example, it is important to understand the treatment of extreme values ​​in reanalysis, and whether false positive or false negative rejections can occur, especially when the temperature and humidity distributions move towards ever higher values. The main TW processes on several scales requiring closer comparison between observations and models include coastal upwelling, atmospheric convection, earth-atmosphere interactions and atmospheric variability linked to SST (28) —For example, on an hourly scale, from 1 to 10 km. Detailed analyzes of individual events could help shed light on ongoing process interactions and provide additional investigative power, such as tracing and predicting rapid increases in humidity, which tend to accompany TW extremes (fig. S5), and in the assessment of the role of topography and land use / land use in the creation of apparent TW hotspots (fig. S4). Studies comparing the biases and trends of TW and SST among reanalyses, models and regions would be particularly beneficial, as would investigating the sensitivity of projections of extreme TWs to historical variability, to changes in forcing models and statistical methodologies.

The impending severe damp heat is prompting a vast interdisciplinary research initiative to better characterize the health impacts. Increased collection of high-resolution health data, international collaborations with public health and social scientists, and dedicated modeling projects would help answer questions about how vulnerable populations (such as the elderly , outdoor workers and those with pre-existing health conditions) will be negatively affected when the TW peak progresses into the extremes we consider here. It is particularly important to determine how acclimatization to conditions of high heat stress is decreased as the physiological survival limit approaches. These efforts can also help resolve the reasons for the rarity of the reported impacts on mortality and morbidity associated with conditions observed at nearly 35 ° C (11, 14).

Our results indicate that reported occurrences of extreme TW have increased rapidly at weather stations and in reanalysis data over the past four decades and that parts of the subtropics are very close to the 35 ° C survival limit, which has probably already been reached on both seas. and the earth. These trends highlight the magnitude of the changes that have occurred as a result of global warming to date. On the spatial scale of the reanalysis, we predict that TW will regularly exceed 35 ° C at points on the Earth’s network with less than 2.5 ° C of warming since the pre-industrial period, a level which could be reached in the coming decades (35). According to our analysis of weather stations, the emphasis on points on the Earth’s grid minimizes the real risks of extreme TW along the coasts, which tend to occur when sea air masses are advected even slightly ashore (14). The coastline of the southern Persian Gulf and northern South Asia are home to millions of people, placing them on the front line of exposure to TW extremes at the edge and outside the range of natural variability in which our physiology has evolved. ((36). The deadly heat episodes already known in recent decades indicate the continuing trend of increasingly extreme humid heat, and our results highlight that their diverse, consequent and increasing impacts represent a major societal challenge for the decades to come.


Weather station observations

We use HadISD, version, which is produced by the Met Office Hadley Center as a more rigorous quality version of the National Climatic Data Center’s integrated surface database (ISD) (17, 18). HadISD results from the implementation of additional data availability and quality control procedures for ISD, including both temperature and Td checks, the two variables needed to calculate TW. Due to a lack of good quality data in the tropics, our conclusions are most reliable in the subtropics and mid-latitudes, especially when several neighboring stations agree. TW uncertainties vary from ~ 0.5 ° C for the most recent data from North America and Europe to ~ 1.2 ° C for the oldest data and those from South Asia, Africa and Latin America. Data validation is discussed in detail in the additional documents.

We are using a MATLAB implementation (37) of the formula (38) to calculate TW. We calculate daily maximum TWs independently of the time resolutions of the stations, which vary from 1 to 6 hours. The TW values ​​are for 2 m above ground level, the surface pressure of the station being calculated from its elevation using a standard atmosphere and a presumed pressure at sea level of 1013 mb. A sensitivity analysis reveals that the TW error due to this assumption is on the order of 0.1 ° C.

We are also eliminating data from HadISD stations that fail one of the following weather and climate tests. The tests are listed in the order implemented, the fraction of HadISD 31 + ° C readings being deleted at each successive step indicated in parentheses:

1. An extreme TW occurs in conjunction with a dew point depression of ≤0.5 ° C (65/10 492).

2. The Td associated with an extreme TW is different by more than 10 ° C from the value adjusted according to the altitude at the nearest grid cell and at the time step in the ERA-Interim reanalysis (289/10 427).

3. An extreme TW occurring in 1979–1993 is higher than the maximum for 2003–2017 (67 / 10,138).

4. An extreme TW is followed at all times by at least 1,000 consecutive days of missing Td data (365/10,071).

5. An extreme TW occurs on a day when the daily maximum and the daily minimum T or Td are identical (53/9706).

6. An extreme TW is more than 7.5 ° C higher than any other TW value co-produced in a 7.5 ° × 7.5 ° box centered on the station (405/9653).

7. An extreme TW is associated with a change in Td of more than 8 ° C in 1 hour or 12 ° C in 3 hours (77/9248).

8. An extreme TW is associated with a Td higher than the world maximum value of 35 ° C reported previously, although not official, recorded in Dhahran (Saudi Arabia) on July 8, 2003 (18/9171).

9. An extreme TW occurs during a period with at least two identical maximum daily values ​​identical TW and Td (289/9153).

10. An extreme TW before 2001 is higher than any value recorded since 2001 (270/8864).

11. The five most important TW extremes of a station all occur within 365 days (60/8594).

12. The Td associated with an extreme TW is greater than the 99.5th percentile of the first 5000 days, only at stations where this value is more than 1 ° C higher than the 99.9th percentile of the last 5000 days (55/8534).

13. The Td associated with an extreme TW is greater than the 99.5th percentile for the last 5000 days, only at stations where this value is more than 6 ° C higher than the 99.9th percentile for the first 5000 days (362/8479).

14. Extreme TW is associated with relative humidity ≥95% (29/8117).

15. Un TW extrême se produit un jour où le TW maximum quotidien a lieu avant 11 h 00 ou après 20 h 00. heure locale (26/8088).

16. Un TW extrême est le maximum absolu à une station et est supérieur de plus de 2 ° C à la valeur immédiatement supérieure (6/8062).

17. Il est établi manuellement qu’un extrême TW ≥33 ° C restant est associé à un point de changement significatif ou n’est pas entièrement pris en charge par les données d’humidité et de température maillées (508/8056).

Les lectures TW = 35 ° C restantes sont également examinées de près tous les jours afin d’en garantir la validité dans la mesure du possible. Nous jugeons valides toutes les autres valeurs qui passent les mesures de contrôle de qualité supplémentaires ci-dessus, au-delà du contrôle de qualité et de l’homogénéisation d’origine (17, 18). Les résumés des valeurs TW = 33 ° C et 35 ° C dans l’ensemble de données final sont donnés dans les tableaux S1 et S2.

Les tendances interannuelles sont calculées à l’aide d’une régression des moindres carrés ordinaires, la signification étant évaluée à l’aide d’un t test sur le coefficient de pente. Notre évaluation de la fréquence TW extrême considère les dépassements de seuil par incréments de 2 ° C de 35 ° à 27 ° C, afin de trouver un équilibre entre des valeurs suffisamment distinctes les unes des autres tout en étant suffisamment élevées pour rester pertinentes du point de vue de l’impact.

Observations marines

Nous utilisons des SST mensuels du jeu de données 1 ° HadISST version 1.1 (20) pour évaluer le réalisme physique de nos extrapolations GEV et utiliser des observations ponctuelles in situ de SST et TW tirées de l’International Comprehensive Ocean-Atmosphere Data Set (ICOADS) (21) en tant que contrôle indépendant (versus HadISD) des valeurs extrêmes de TW signalées dans les stations météorologiques terrestres à proximité. Les détails de ces comparaisons sont fournis dans les documents supplémentaires.

Données de profil marin et vertical

L’ensemble de données intégré ICOADS (21) est utilisé comme validation des conditions de surface près de l’eau. Les radiosondes proviennent des archives des radiosondes globales intégrées (22, 39).

Modélisation GEV des extrêmes TW dans les données de réanalyse

Nous ajustons une distribution GEV à la série chronologique de TW maximum annuel à partir de cellules de grille sélectionnées dans ERA-Interim, un ensemble de données de réanalyse qui mélange de manière optimale les observations avec une rétrodiffusion numérique et, ainsi, fournit une estimation de l’état atmosphérique moins sensible aux erreurs d’observation et variabilité microclimatique (19). Bien que bien adapté à l’identification et à l’extrapolation des tendances mondiales, il est inévitable dans une telle approche que les tendances des températures décennales et d’autres variabilités à grande échelle peuvent affecter modestement nos résultats.

La fonction de distribution cumulative du GEV est donnée par



Le quantile TW pour un notpériode de retour de 5 ans peut être évaluée en inversant Eq. 1

F1((p)=ζ+βк{[[[[ln ((p)]к1}

(2)où les paramètres d’emplacement, d’échelle et de forme sont notés ζ, β et к, respectivement. Notez que, dans notre analyse, nous utilisons not = 30 (et donc P = 0,967), bien que nous nous attendions à des choix not n’affecterait pas qualitativement les résultats. Nous estimons ces paramètres à l’aide de la méthode du maximum de vraisemblance, en ajustant uniquement les distributions aux séries à partir de cellules de grille dont la valeur maximale entre 1979 et 2017 était dans le plus haut 0,1% au monde (119 cellules de grille supérieures), correspondant à un seuil TW de 30,6 ° C.

Nous incorporons l’effet du réchauffement climatique sur la période de retour en paramétrant ζ en fonction de l’anomalie annuelle moyenne de la température de l’air


(3)où α2 et α3 sont les coefficients d’interception et de pente d’une régression linéaire.

L’ampleur de l’amélioration de ce modèle non stationnaire pour chaque cellule de la grille est évaluée à l’aide d’un test de rapport de vraisemblance, avec une statistique de test lambda


(4)or L est la log-vraisemblance du non stationnaire (indice A) et stationnaires (indice 0). Dans l’hypothèse nulle (que le modèle non stationnaire n’est pas supérieur), lambda a une distribution chi carré avec un degré de liberté. Sur les 119 cellules de grille équipées d’une distribution GEV, pour ~ 83% d’entre elles (99 cellules de grille), paramétrant zêta en fonction de 〈T〉 Se traduit par une amélioration statistiquement significative P = Niveau 0,05.

Nous utilisons le modèle non stationnaire pour déduire la quantité de réchauffement climatique requise pour qu’un TW annuel maximum = 35 ° C soit au maximum un événement sur 30 ans. Ceci est calculé en substituant Eq. 3 en Eq. 2 et résoudre pour 〈T



Appliquer Eq. 5 à 99 grilles avec des modèles non stationnaires permettent des évaluations spatialement explicites de la quantité de réchauffement climatique requise jusqu’à TW = 35 ° C devraient être attendues, en moyenne, une fois par période de 30 ans dans chaque cellule. Ici, nous avons utilisé l’ensemble de données HadCRUT4 (version pour caractériser le réchauffement observé (40).

Température d’émergence TW = 35 ° C et estimation de son incertitude

Les estimations de 〈résolues spatialementT〉 De l’Eq. 5 fournissent les moyens d’identifier la ToE, que nous définissons comme la plus faible des 99 valeurs de 〈T〉 Retourné par Eq. 5 et que nous mettons en évidence avec des lignes pointillées verticales sur la figure 4. L’incertitude dans la ToE est évaluée avec une simulation bootstrap de 10 000 membres. Nous sélectionnons au hasard avec remplacement de 30 ans de données TW et SST au cours de la période 1979-2017, les paramètres d’ajustement (pente, intersection, forme et échelle pour l’équation 5) pour chaque sous-ensemble. Pour chaque itération bootstrap, nous répétons le calcul de la ToE. These 10,000 estimates are then sorted to identify the 5th, 50th, and 95th percentiles; the most likely estimate; and the 90% confidence intervals.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is do not for commercial advantage and provided the original work is properly cited.


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  3. G. J. Van Oldenborgh, M. Collins, J. Arblaster, J. H. Christensen, J. Marotzke, S. B. Power, M. Rummukainen, T. Zhou, Annex I: Atlas of global and regional climate projections. in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, T. F. Stocker, D. Qin, G.-k. Plattner, M. Tignor, S. K. Allen, Eds. (Cambridge Univ. Press, Cambridge, U.K, 2013).

Acknowledgments: Code for computing TW using the Davies-Jones formulae was provided by R. Kopp at Rutgers University. Part of this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Funding: Funding for R.M.H. and C.R. was provided by the National Oceanic and Atmospheric Administration’s Regional Integrated Sciences and Assessments program, grant NA15OAR4310147. Author contributions: C.R. and T.M. produced the datasets and conducted the analyses. C.R., T.M., and R.M.H. collectively developed ideas and wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: Datasets are described in the Supplementary Materials. Data and code used in the analysis are publicly available in a Github repository at All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.


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