Introduction

On May 22, 2021, a hailstorm with extreme cold temperature and heavy rain struck Baiyin City, Northwest China, and 21 ultramarathon runners died from it during an ultramarathon event (a 100 km long-distance footrace), including Liang **g, one of the world’s top ultramarathon runners1. Similar catastrophic extreme weather events, including devastating droughts and raging heatwaves, are claiming lives, and these events are anticipated to occur more intensely and frequently under a warming climate2,3,4. Marathon, a 42.195 km long-distance footrace, has been a central part of the modern Olympics since 1896. It also takes places in numerous cities around the world every year. Nearly 18 million people registered for marathon and other long-distance race events in the US in 2019 (https://www.runninginsight.com/running-usa-releases-u-s-running-trends-report). Resembling other outdoor activities, performances of marathon running are susceptible to environmental factors, including weather conditions5. Warmer temperature tends to slow both elite and non-elite marathon runners6,7,8,9,10,11 although some discrepancies in the weather-performance relationship exist among the athletes of different levels12,13,14,15. No consensus has been reached on the influence of rise in altitude (equivalent to reduction in air pressure)6,7,8,9,10,11. The roles of other weather parameters, including solar radiation, relative humidity, wind speed and rainfall, have also been explored previously7,16,17.

Commonly, elite marathon runners’ competition results were obtained at different marathon races with different meteorological conditions, which are characterized by variables such as ambient temperature, atmospheric pressure, relative humidity and solar radiation6,7,8,9,10,11,15,16,17,18. Approaches used in existing studies conventionally focus on the results and weather conditions of the marathon events at certain locations (analogous to Eulerian representation of fluid dynamics), yet runners participated in these events that held at the same places usually differ greatly across time9,17,18, leading to substantially uncertain conclusions. Moreover, only general associations of marathon performance with meteorological conditions were previously reported, while studies involving underlying mechanisms remain limited9,11. A theoretical analyses19 emphasized the role of atmospheric oxygen loss associated with rise in altitude and the resultant reduction in pressure in degraded marathon performance. Dehydration and body-skin temperature increase were also regarded as the reason for worse performance under higher temperature conditions20.

Global warming is anticipated to continue in coming decades, and the associated increase in occurrences of extreme weather may thus pose greater influences on performances of marathon running21,22. Projections suggested that number of cities with appropriate weather conditions for hosting Olympic marathon would decline significantly by the end of this century under RCP8.5 emission scenario21. The marathon race at 2019 Doha World Athletics Championships was held when air temperature was above 30 °C23,24. Given these circumstances, we believe that Olympic marathon events are very likely to be held still under a warming climate. Here we aim to understand how weather conditions affect the performances of elite marathon runners through a systematic investigation based on the global datasets of marathon performance and weather observations. In the investigation we track the performances of each runner across different events (analogous to Lagrangian representation of fluid dynamics) to eliminate the large uncertainties caused by the different runners participating the events held at the same place in different time in existing studies. We will further investigate the underlying mechanism from the perspective of the thermodynamic processes in the atmosphere, which will be revealed to be essential for the effects. This mechanism has not been emphasized previously. We hypothesize that the rise in temperature, altitude or humidity can worsen the marathon performance since they can reduce the oxygen partial density (Eq. (3)). We also hypothesize that the future progression of marathon performance is likely to be substantially slowed or even halted by the changed climate without powerful greenhouse gas mitigation, which will be investigated with model projections of future climate.

The rest of the paper is organized as follows. Section “Effects of weather conditions on marathon-running performance” quantitatively analyzes the effects of the ambient weather conditions on the marathon performance of elite athletes via tracking the performances of each runner across different events. Section “Essential role of atmospheric thermodynamic processes in the effects” explores for the underlying mechanism for the effects focusing on the thermodynamic processes in the atmosphere. Section “Projected changes in future marathon-running performances of top athletes” projects the long-term changes in the elite marathon athletes’ performance in the past and in the future under the different emission scenarios, followed by a brief conclusion and further discussion in Section “Discussion”. Section “Methods” brief the data and methods used in the present study

Results

Effects of weather conditions on marathon-running performance

Multiple linear regression analysis of marathon finishing time upon the possible influencing variables is conducted and the regression coefficients are shown in Table 1. Here the increase in marathon finishing time denotes the worsening in performance. For the top-96 athletes, the marathon performance tends to worsen significantly with the rise in ambient temperature by 0.31 min °C−1. The performance tends to significantly improve by 0.025 min hPa−1 as the ambient pressure rises, which is equivalent to the reduction in the altitude based on Eq. (1). The increase in relative humidity tends to worsen the marathon performance. Among the four influencing variables related to athlete individuals, the age significantly and positively affects athlete’s performance, while home advantage does not have significant relationship with the marathon performance. The athlete’s sex also has no significant relationship with the marathon performance since most of its effects have been included in the effects of the athlete’s average performance. In fact, if not including the average performance in the model, the regression coefficient of marathon performance upon the sex is 19.1 min, which is significant at 0.999 confidence level.

Table 1 Regression model results
Full size table

Similar analysis is also conducted for athletes in the six areas of the world, respectively. The marathon performance tends to significantly worsen with the rise in ambient temperature in all the six areas except the North America, where the worsening is not statistically significant. The relationships with atmospheric pressure and relative humidity for 5 of the 6 areas have the same sign with those for the world, but are statistically significant for only 1 of the 6 areas. The lower statistical significance and the differences among areas may be associated with both ethnic difference as well as small sample sizes for each area (Table 2). In fact, the sample size is the smallest in the North America, the Asia and the Oceania among the 6 areas. In the Asia (Oceania), the relationship of marathon performance with air pressure (relative humidity) has the opposite sign to that for the world. In the North America, the relationship with ambient temperature is not significant.

Table 2 Marathon participants and the years of their competitions
Full size table

The relationship between influencing variables and the performances is also further investigated with GLM for the results obtained by the world top-96 marathon athletes. Among the four influencing variables related to athlete individuals, here only athlete’s average performance and age are used in the model since the relationship of the other two variables with marathon performance is weak as revealed in Table 2. In fact, adding the home advantage and sex to the model only increases the confidence interval of the relationship (Supplementary Fig. 1a–c vs. Supplementary Fig. 1d–f) and thus reduces the statistical significance and increases the uncertainty. When analyzing the relationship between ambient temperature and marathon performance, the performance is predicted using only ambient temperature and other influencing variables are used as covariates, and so on for other meteorological variables.

As the ambient temperature rises, marathon finishing time (MFT) slightly decreases (Fig. 1a) when the ambient temperature is extremely low (<12 °C), indicating the slight improving of the runners’ performance. When the ambient temperature is above 12 °C, MFT increases monotonously with ambient temperature, indicating the marathon performance worsening. The MFT increases by 0.56 min/°C in average as the ambient temperature rises when it is above 15 °C. Since men and women athletes may have different responses to heat stress and other weather condition changes25,26, analysis is also conducted for men and women athletes, respectively. Similar shapes of curves are also found for men and women athletes, separately (Fig. 2a, b). The MFT of both men and women athletes slightly decreases and monotonously increases with ambient temperature when it is below and above 12 °C, respectively. When it rises beyond 15 °C, MFT sharply increases by 0.39 and 0.71 min °C−1 in average with ambient temperature for men and women athletes, respectively. Such a nonlinear relationship is different from those reported previously using Eulerian representation6,20, which show that the MFT increases monotonously as ambient temperature rises for all temperatures and for both men and women athletes. Moreover, these previous reports show that the MFT increases by ~0.2 and 0.3 min °C−1 in average when ambient temperature rises from 15 to 25 °C for men and women6,20, respectively, substantially smaller than the current 0.38 and 0.70 min °C−1.

Fig. 1: Relationship between ambient weather conditions and marathon-running performance.
figure 1

Relationship of MFT with ambient air temperature (a), atmosphere pressure (b) and relative humidity (c) obtained with GLM. d Relationship between ambient temperature and vapor pressure obtained with GLM. The shadings denote the 95% confidence intervals for the relationships and the solid curve denotes the fitting line. a, c and d are obtained based on the competition results of top 96 athletes over the world, and b is based on those of top-160 athletes.

Full size image
Fig. 2: Relationship between ambient weather conditi ons and marathon-running performance for men and women.
figure 2

Same as Fig. 1a–c but for men athletes (a, c, e) and women athletes (b, d, f), respectively.

Full size image

For both men and women athletes and for mixed-sex athletes, MFT increases approximately linearly as ambient atmospheric pressure decreases (Figs. 1b and 2c, d), indicating the worsening of marathon performance. A 100 hPa decrease in ambient atmospheric pressure (equivalent to an increase of ~1000 m in altitude) is associated with an increase of 1.8, 4.5 and 3.6 min in MFT for men, women and mixed-sexed competitors, respectively. The difference in MFT change rate with ambient atmospheric pressure between men and women athletes might be due to the physiological differences in adapting to environmental changes. These results are overall similar to those by Peronnet et al.19 obtained through theoretical analyses, which shows that MFT monotonously increases with altitude by 4.1 min per 1000 m for men and 4.5 min/1000 m for women. However, the changing rates revealed here are substantially smaller than those concluded by Lara et al.18 (10.8–12.3%, ~15 min per 1000 m) based on conventionally-used Eulerian method. The consistence with the previous theoretical results and difference from the conventionally-used Eulerian-representation-based results confirm the robustness of the previous theoretical results as well as the advantage of the present methods based on Lagrangian representation.

When relative humidity is below 80%, marathon performance worsens as relative humidity rises (Fig. 1c). While relative humidity rises beyond 80%, marathon performance exhibits an improving trend. Similar shapes of curves are also obtained for men and women athletes, separately (Fig. 2e, f). Overall, MFT changes associated with relative humidity (max ~2 min, Figs. 1c and 2e, f) are much smaller than those associated with ambient temperature (max ~10 min, Figs. 1a and 2a, b) and atmospheric pressure (max ~7 min, Figs. 1b and 2c, d).

The scatter plots of marathon finishing time versus meteorological variables are shown in Supplementary Fig. 2. It shows obvious performance worsening with ambient temperature, especially when the ambient temperature is above 15 °C (Supplementary Fig. 2a). Correlation between ambient temperature and the marathon finishing time for the 678 results is 0.17, significant at 0.95 confidence level. The scatter plot also shows obvious performance worsening with the reduction of the ambient pressure (~altitude rise) and the correlation between ambient pressure and the marathon finishing time is −0.17 (P < 0.05) (Supplementary Fig. 2b). The marathon finishing time change with relative humidity is positive but weak (Supplementary Fig. 2c) and the correlation is 0.03 (P > 0.05). These results are overall consistent with those based on GLM and multiple linear regression analysis (Fig. 1a–c, Table 2), confirming the robustness of the results based on these two methods.

We repeat these analyses using the competition results obtained by the 100 best athletes throughout the world (Supplementary Fig. 3). The results are overall similar to those based on the top-96 and top-160 athletes (Figs. 1 and 2), confirming the robustness of the above results. Some differences are found in the magnitude of athletes’ performance changes with weather conditions. For example, the performance worsens with ambient temperature by 0.20 min °C−1 based on the top-100 athletes (Supplementary Fig. 3a), which is smaller than that based on the top-96 athletes (0.37 min °C−1, Fig. 1a). This discrepancy may be associated with the many more athletes from Africa than from other areas of the world. In fact, there are only 12 athletes (5 men and 7 women) from areas outside Africa among the top 100 athletes. The performance improvement with ambient temperature for athletes in Africa is only 0.23 min °C−1, which is among the smallest over the six areas of the world (Table 2). The dataset of competition results for top-100 athletes is too biased toward the African athletes, while the top-96 athletes are equally distributed over the six areas of the world. Therefore, we conduct the analysis primarily based on the top-96 athletes in the present study.

Wet-bulb globe temperature index (WBGT) is a widely used index to describe the effect of heat stress on the human beings22. We repeat the above analysis with WBGT and found that the performance improves with the rise of WBGT if WBGT is not very low (Fig. 3). These results are similar to those with ambient temperature (Figs. 1a and 2a, b).

Fig. 3: Relationship between WBGT and marathon-running performance.
figure 3

Panel a–c: Same as Figs. 1a and 2a, b, respectively, but for WBGT. Here the WBGT is calculated using the method introduced in ref. 36,37. These effect and mechanism may also exist when living in the tropics since the high temperature can also cause hypoxia through expanding air parcels, which merits further study. Besides, this study suggests that the harm of climate warming may reach the area of sports (especially endurance sports) and efficient greenhouse gas mitigation may substantially reduce the harm in the future (scenario SSP245 v.s SSP585). This supports the urgency of more efficient measures to mitigate greenhouse gas emission.

Methods

Selection of marathon athletes and their race results

Top 8 marathon athletes from each of the 6 major regions of the world, namely Africa, Asia, North & Central America, South America, Europe and Oceania, are selected as potential medal-winning athletes for marathon race at Olympics. Eventually, top 96 athletes, including 48 men and 48 women, are considered, and their marathon results obtained after 2013 are used in this study. The list of these athletes and their information (name, world rankings, birth year and area) are shown in Table 2. The list of these athletes and their marathon results are obtained from the official website of world athletes (https://worldathletics.org/world-rankings/marathon/men) and the rankings in July 2021 are used here38. Here we focus on the full marathon (i.e., 42.195 km long distance race). To explore the effects of ambient atmospheric pressure and altitude on performances, we extend the list to include 160 elite marathon athletes to cover enough events held at high-altitude cities (top 160 athletes). This list contains 10 men and 10 women from each of the above 6 major regions, additional 20 men and 20 women from Africa. Additional athletes in Africa are considered given the fact that there are more elite marathon runners in Africa than in other regions (8 of 10 world top marathon athletes are from Africa38). In order to confirm the robustness of the results based on the above athletes, we also select the 100 best athletes (i.e., top-100 athletes for short) from the official website of world athletes, which include 50 men ranking 1–50th and 50 women ranking 1–50th over the world.

Observations, reanalysis, climate model outputs and data processing

Hourly observations of meteorological variables, including air temperature, sea level pressure and dew point, are obtained from the Integrated Surface Data dataset (ISD, https://www.ncei.noaa.gov/data/global-hourly/archive/isd/)39. This dataset is supplied at stations and contains observation records at time interval ranging in different stations from several minutes to several hours. As of 2020, observations from ~13,000 stations have been included in this dataset. Weather data at the station nearest to route of each marathon race is extracted and daily mean of all the records of meteorological observations on the day of the marathon race is calculated to represent the weather conditions of the race. When less than two valid records exist at the nearest station on the day of an event, records at the second nearest station are used. If this criterion fails again at the second nearest station, the associated event will be ignored in the analysis.

We derive altitudes of route of each event using the high Terrain Elevation Above Sea Level (ELE) Data (at 30 × 30 arc-sec) developed by Solargis and provided by the Global Solar Atlas (GSA) (https://datacatalog.worldbank.org/search/dataset/0037910)40. We also use the monthly-mean near surface air temperature, pressure and relative humidity derived from the NCEP/NCAR Reanalysis 1 dataset that are offered on 2.5° × 2.5° grids and over 1948–202041.

As the ISD dataset does not provide land surface atmospheric pressure, we use the equation below to infer it:

$${p}_{{\rm{ls}}}={p}_{{\rm{sl}}}{\left(1+\frac{\gamma H}{T+273.15}\right)}^{-\frac{g}{{{\gamma }}R}}$$
(1)

where psl denotes sea level pressure (hPa), g represents the gravitational acceleration (9.8 m s−2), R is the gas constant for dry air (287.053 J K–1 kg–1), \(\gamma\) stands for the environmental lapse rate, H denotes the altitude of the marathon route and T is near surface air temperature. This formula is deduced based on ideal atmosphere that is in hydrostatic balance and has constant \(\gamma\) (6.5 °C km−1). As observed psl values are commonly missing in the ISD, we set psl as a constant of 1013 hPa here. According to scale analysis42, the order of the variation of psl is ~101 hPa, while the altitudes of the marathon events range from 0 to 2300 m, leading to pressure changes greater than 200 hPa. Thus, the errors of setting psl as a constant are acceptable here.

Relative humidity is calculated using observed dew point, air temperature and derived actual and saturated vapor pressure. Actual and saturated vapor pressure are calculated from observed dew point and air temperature, respectively, with the Magnus formula43 as follows:

$${\rm{E}}=6.1094{e\,}^{\frac{17.625t}{t+243.04}}$$
(2)

where E denotes saturated vapor pressure (hPa), and t stands for air temperature (°C).

In this study we consider the influence of atmospheric oxygen on elite marathon runners’ performance, and use the following equation44 to calculate oxygen partial density (ρO2):

$${\rm{\rho }}{{\rm{O}}}_{2}=\frac{0.232(p-e)}{{R}_{{\rm{d}}}T}$$
(3)

where p represents air pressure (hPa), e is vapor pressure (hPa), Rd denotes the gas constant for dry air (287.053 J K–1 kg–1), and T is air temperature (K).

After these processes, 678 competition results with valid weather data (including air temperature, dew point, altitude and the derived atmospheric pressure, ρO2 and relative humidity) are selected. The years of these competition results for each athlete are shown in Table 1. The geographical position, altitude and historical average temperature of the races for these results are shown in Fig. 8 and Supplementary Table 1.

Fig. 8: Location, altitude and historical average temperature for each of the 676 races.
figure 8

Each point in a and b shows the position where each marathon race was held. The color of point denotes altitude and the climatology of air temperature over 1979–2014 at the holding position of each race in a and b, respectively. The temperature is derived from GHCN CAMS monthly 2-m land surface air temperature dataset. The altitude is derived from the high Terrain Elevation Above Sea Level (ELE) Data (at 30 × 30 arc-sec) developed by Solargis. Since many marathon races are held at the same city, 148 different points are shown in the map.

Full size image

The country of the competition venue and the nationalities of each athlete are also obtained from the official website of world athletes to analyze the effect of home advantage on the competition performance. If an athlete finishes a marathon in his/her country, we think that home advantage exists for the competition result, and otherwise does not exist. If an athlete has home advantage in a competition, the variable characterizing the home advantage is set as 10, and otherwise set as 0. The variable sex is set as 0 and 10 for men and women, respectively. The average marathon finishing time of all the competition results obtained by an athlete after 2013 is used to characterize his/her competition level.

Generalized linear model (GLM) is used to analyze the relationships between marathon results and influencing factors45,46. In the model, three meteorological variables (ambient temperature, relative humidity and ambient pressure) and four variables related to the athletes (average finishing time, gender, age and the home advantage) are considered as the possible influencing factors. Restricted cubic spline function with four knots is applied to each influencing variable in the GLM47 to analyze the possible nonlinear relationship (if any) of the marathon performance with the influencing factors except for average finishing time. The four knots are set at the quantiles of 5%, 35th, 65% and 95%. The confidence intervals are obtained along with the fitting lines using R language, which calculates confidence interval by making an interval on the scale of the linear predictor, then applying the inverse link function from the model fit to transform the linear level confidence intervals to the response level (https://search.r-project.org/CRAN/refmans/ciTools/html/add_ci.glm.html). Besides, multiple linear regression analysis is also used to analyze the relationships between marathon results and influencing factors.

To explore the impacts of climate change on the marathon-running performance, we use the bias-corrected global dataset based on 18 models of the Coupled Model Intercomparison Project Phase 6 (CMIP6) and the European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5)48. This dataset covers the period of 1979–2100 and data is provided at a horizontal resolution of 1.25° × 1.25°. We used the monthly-mean near surface temperature, relative humidity and air pressure for historical period (1979–2014), and two future shared socio-economic pathway scenarios (SSP585 and SSP245) over 2015–2100. The monthly-mean near surface temperature is directly derived from the datasets. The relative humidity and air pressure are averaged over each month from the daily data reported on pressure levels and then interloped onto land surface. The SSP245 is called the “middle of the road” scenario with an approximately 4.5 W m−2 radiative forcing level by 2100, while SSP585 is a high fossil fuel development scenario.