Measurement campaign

A mobile measurement campaign was conducted during the 2024 Dodentocht, which took place on August 09–10, 2024. The Dodentocht is a renowned 100-km endurance hiking event in Belgium, with approximately 12,000 participants annually. The event started at 21:00 local time (UTC+2) and participants had 24 hours to complete the course. The 2024 course, as shown in Fig 1A, consisted of a single clockwise loop which traversed urban, suburban, and rural areas with varying tree cover and no significant changes in elevation (5–30 m above sea level).

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Fig 1. Dodentocht 2024 route and mobile measurement setup.

(A) The 100-km 2024 Dodentocht route (black line) starting and ending in Bornem (Belgium) with red arrows indicating the direction of travel. Measurements where taken along the entire route and in addition along the route segment highlighted in red. (B) The mobile measurement setup with the Davis Vantage Pro2 (left) and black globe thermometer (right). Base map by OpenStreetMap (https://www.openstreetmap.org/) and country borders by Natural Earth (https://www.naturalearthdata.com/downloads/10m-cultural-vectors/10m-admin-0-boundary-lines/).

https://doi.org/10.1371/journal.pclm.0001058.g001

The mobile measurement setup consisted of an ordinary backpack, fitted with a wooden board on which a metal frame was mounted horizontally, as illustrated in Fig 1B. The board housed a battery pack, SD card, GPS shield, and Arduino MKR NB1500 data logger. A Davis Vantage Pro2 unit measured air temperature () and relative humidity (RH), while a Testo black globe thermometer measured the black globe temperature (). Both sensors were mounted on top of the frame. All measurements were logged every 11 seconds. Technical specifications of the measurement instruments, the measured parameters, and their accuracy are listed in Table 1.

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Table 1. Overview of the measurement instruments used in the mobile measurement campaign.

https://doi.org/10.1371/journal.pclm.0001058.t001

Two mobile measurement backpacks were used, each equipped with the same instruments. One participant carried a backpack and covered the full distance (August 09, 20:30 - August 10, 16:30 UTC+2). Between 13:10 and 14:09 UTC+2 on August 10, measurements were lost due to a disconnection between the black globe thermometer and the data logger. A second backpack covered a segment of the route during the hottest part of the day (August 10, 13:29–18:30 UTC+2). The two trajectories are illustrated by the black and red lines in Fig 1A, respectively.

Modelling system

To assess heat stress for the event, a modelling system was developed by chaining AROME-SURFEX CY48t3 [29], a NWP model coupled with the land surface model SURFEX v8 [30], and SOLWEIG [20], a micro-scale radiation model.

AROME is a non-hydrostatic, convection-permitting limited-area model with a horizontal resolution ranging from 2.5 km and higher. It is operationally used by a number of meteorological services in Europe [29,31]. SURFEX is a land surface model which simulates the energy and water fluxes between the atmosphere and the different land surface types, including urban areas [30]. AROME-SURFEX has been thoroughly evaluated [32,33]. In this study, AROME-SURFEX was run at 500 m resolution with 90 vertical levels and a time step of 15 seconds with output saved hourly. The simulation domain was 250 km by 250 km covering Belgium and spanned from August 09, 00:00 to August 11, 00:00, 2024. A NWP setup is used, consisting of 30 hour-cycles, initialized at 00:00 UTC each day, with a 6-hour spin-up time and hourly updated boundary conditions provided by ARPEGE [29]. For each AROME-SURFEX grid box, SOLWEIG was run to downscale radiative fields to 1m resolution, thus capturing local variation in radiation.

SOLWEIG is a 2.5 dimensional radiation model which simulates spatio-temporally varying mean radiant temperature () by modelling shortwave and longwave radiative fluxes in complex urban settings [20]. is defined as the uniform temperature of an idealized container in which the radiative transfer with a human body is equal to the radiative transfer of the human body with the actual non-uniform environment [34,35]. Since its introduction, SOLWEIG has undergone continuous development, incorporating vegetation [36], land-surface interactions [37], anisotropic diffuse shortwave radiation and downwelling longwave radiation [38,39], and most recently, a wall surface temperature scheme [40]. SOLWEIG has been thoroughly evaluated in a wide range of climates in the context of urban environments, for example in Shanghai, China [41], Adelaide, Australia [42], Szeged, Hungary [43,44], and Vancouver, Canada [45]. It is accessible through the Urban Multi-scale Environmental Predictor (UMEP) tool [46]. SOLWEIG uses meteorological input data and pixel-based land cover, building geometry and, optionally, vegetation geometry data to calculate .

Here, we utilized the Flemish Bodembedekkingskaart (BBK) [47] as land cover, Digital Elevation Model (DEM) [48], and Digital Surface Model (DSM) [49], data provided by the Flemish administration at 1 m resolution. The land cover data was reclassified into the SOLWEIG land cover classes, see S1 Table. Additionally, we used the globally available Canopy Digital Surface Model (CDSM) data provided by the World Resources Institute [50] at 1 m resolution. All the input data was re-projected to UTM 31N. For each AROME-SURFEX grid box, SOLWEIG was run in parallel on a high performance computer, thus making the simulations computationally feasible. The total domain was divided in 40x42 sub-domains. This resulted in 1680 SOLWEIG simulations, each covering 500 m by 500 m domains and producing hourly at 1 m resolution, as illustrated in Fig 2.

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Fig 2. Illustration of the modelling system - SOLWEIG nested within AROME-SURFEX.

https://doi.org/10.1371/journal.pclm.0001058.g002

The SOLWEIG simulations were executed on the Flemish Supercomputer Centrum cluster using AMD EPYC 7552 processors, with 4 cores and 4 GB of RAM allocated per simulation. The meteorological input data taken from each AROME-SURFEX grid box included , RH, and downwelling total, diffuse and direct shortwave radiation. The wind speed, required for the WBGT calculation, is obtained from AROME-SURFEX at 500 m horizontal resolution and 10 m height and is transformed to 2 m height using a combination of the log wind profile [51] above the urban canopy layer and an exponential wind profile within the urban canopy layer [52], see S1 Appendix.

Evaluation of modelled heat stress with observations

The WBGT metric is used to assess heat stress and evaluate the modelling system. The outdoor WBGT is defined as the weighted sum of the wet bulb temperature (), black globe temperature (), and air temperature () [8]

(1)

In the standard formulation of the outdoor WBGT, is the natural wet-bulb temperature [9] which is defined as the lowest achievable temperature in ambient wind speed and radiation conditions by evaporative cooling. In contrast, the psychrometric wet-bulb temperature, also known as the thermodynamic wet-bulb temperature, is measured using a wet wick which is ventilated and shielded from radiation. As we did not measure the wind speed in our mobile measurement campaign, we use the psychrometric wet-bulb temperature for both the mobile measurements. This might lead to an underestimation of the WBGT as the psychrometric ignores radiation and assumes forced airflow. This underestimation is mainly driven by low wind speed and in less extent by high solar radiation, such that the natural approaches the psychrometric as wind speed increases [53,54]. As participants are moving there is constant ventilation which should reduce the possible discrepancy between psychometric and natural wet bulb temperatures.

The (psychrometric) wet bulb temperature () is obtained from its empirical relation with air temperature and relative humidity [55]

(2)

This empirical estimation of introduces errors ranging from C to C with a mean absolute error of C for its validity range (C to C for and 5% to 99% for RH) [55].

The modelled is also obtained through the same empirical relation (equation 2), which coincides with the approach taken by Brimicombe et al. [56] designed for numerical weather prediction gridded datasets. This approach is used as it is simple and non-iterative thus computationally efficient. In addition, using the same approach for both the mobile measurements and the modelling system ensures a consistent comparison between the two.

As , , and RH were directly measured, WBGT can be calculated for the mobile measurements using equations 1 and 2. For the modelling system, WBGT is derived through equations 1, using the modelled , obtained through equation 2, and the modelled high-resolution is utilized to determine .

The can be related to by [57,58]

(3)

and can be used to solve for . This is done analytically, using a closed-form, non-iterative method following Guo et al. [57], for the full derivation see S2 Appendix. Here is the wind speed (m/s), the emissivity of the globe (0.95), and D the diameter of the globe (0.15 m). In this study, the Thermofeel python package was used which provides an implementation of these equations [59].

To compare the mobile measurements with the modelling system, modelled data was extracted corresponding to the location and time of each individual measurement. As the temporal resolution of the modelling system was 1 hour, the modelled data was linearly interpolated to the measurement time.

Due to the response time of the measurement devices, a mobile measurement represents an average over the response time rather than an instantaneous value in equilibrium with the environment [60,61]. On the other hand, the modelled data does represent an instantaneous value at equilibrium with the environment, thus leading to stark contrasts when moving through heterogeneous environments. To account for this, a rolling average of 5 minutes, corresponding to a rough estimate of the black globes 90% response time, was applied to the modelled . The 90% response time is the time required for an instrument to reach 90% of the difference between its initial value and the final equilibrium value after a step change in the environment [62]. Note that there is an inherent assumption that the response is approximately linear during the 90% response time.

The bias and root mean square error (RMSE) between the mobile observations and modelled WBGT are calculated to evaluate the modelling system. In addition to these metrics, we calculate an agreement rate accounting for observational uncertainty, and the Pearson correlation coefficient (r), capturing the spatio-temporal evolution of heat stress along the route.

The agreement rate is the percentage of measurements for which the modelled WBGT falls within the combined observational uncertainty at each measurement, shown as the shaded grey band in Fig 4, which combines instrument accuracy (Table 1) and the approximation error of the empirical estimate (equation 2).

r is calculated between the modelled and observed WBGT time series. As each time step corresponds to a distinct time and location along the route, it reflects how well the modelling system reproduces the spatio-temporal evolution of heat stress, independently of the bias. As correlation over the full trajectory partly reflects the shared diurnal cycle, r is reported for both the full trajectory and the afternoon segment, where the diurnal trend is smaller.

Adaptation scenario analysis

Once the modelling system’s accuracy has been investigated, it can be used as an adaptation tool to evaluate how different event-management scenarios affect participants’ heat-stress exposure. These scenarios include combinations of alternative starting times, different routes, and various walking speeds under the same meteorological conditions. The official Dodentocht route for 2023, 2024, and 2025 are compared to a handmade hypothetical alternative route as shown in Fig 3. The alternative route was designed to include additional shaded segments while keeping the 100 km distance and roughly the same direction in the same region. Walking speed was varied from 4.25 km/h to 6 km/h in 0.25 km/h increments, and the event’s minimum and maximum allowed speeds (4.17 km/h and 10 km/h) were also included. Samples of heat stress along the route were taken at 11 second intervals, matching the measurement frequency. Finally, starting times were varied between 17:00 and 24:00 (UTC+2) in 1 hour increments. For all scenarios, the same meteorological conditions experienced during the 2024 Dodentocht were used to isolate the impact of the adaptation strategies.

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Fig 3. Different Dodentocht routes.

The four different Dodentocht routes considered in the adaptation scenario analysis. The 2023, 2024, and 2025 routes are the official routes while the alternative route is a hypothetical route created for this study. All four routes are 100 km long, have the same start and end location, and should be followed in a clockwise direction. Base maps by OpenStreetMap (https://www.openstreetmap.org/).

https://doi.org/10.1371/journal.pclm.0001058.g003

To quantify and compare the heat stress exposure for these scenarios, the cumulative exposed degree hours (CEDH) above a prescribed WBGT threshold is calculated as

(4)

where WBGT_i is the WBGT at time step i, the time step (hours), and n the number of steps. The CEDH metric is simple, while capturing both the intensity and duration of heat stress exposure [63] throughout the event. Additionally, it is easy to interpret and flexible as the threshold can be adapted to the target population and activity level. In this study, we adopt a threshold of , corresponding to the ISO 7243 [64] critical value at which unacclimatized individuals engaged in very high metabolic activity (520 W) should exercise caution.

Evaluation of modelled heat stress with observations

The modelled WBGT has a bias of C and an RMSE of C along the full 100-km trajectory, as shown in Fig 4A, with an agreement rate of 62.1% and a correlation coefficient r = 0.96. During the full 100-km trajectory, the modelling system captures the diurnal cycle well with lower variability and low heat stress during the night, a period of steady increase in heat stress during the morning, and relatively high heat stress with pronounced variability during the afternoon. The modelled and observed meteorological drivers and components of the WBGT for this trajectory are shown in supplementary material, see S1 Fig.

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Fig 4. Temporal comparison of observed and modelled WBGT.

The observed (blue) and modelled (red) WBGT along the two measurement trajectories during the 2024 Dodentocht. The observed uncertainty is indicated by the shaded grey area and is derived as a combination of instrument accuracy (see Table 1) and the approximation error introduced using an empirical estimation of . (A) The full Dodentocht route from August 09, 20:30 to August 10, 16:30 (UTC+2). (B) The afternoon segment from August 10, 13:29 to 18:30 (UTC+2).

https://doi.org/10.1371/journal.pclm.0001058.g004

From midnight to early morning (August 10, 00:00–04:00 UTC+2), is overestimated resulting in an underestimation of the RH and consequently an overestimation of the WBGT (Bias=C, RMSE=C, agreement rate = 48.6%, r = 0.82). During the morning (August 10, 08:00–11:00 UTC+2), the WBGT is significantly underestimated (Bias=C, RMSE=C, agreement rate = 26.4%), but the spatial-temporal increase in heat stress over this period is captured (r = 0.86). For this period, the and RH are also well captured, but the modelled has a less pronounced increase explaining the underestimation of the WBGT. Finally, during the afternoon section of the full trajectory (August 10, 12:00–16:30 UTC+2), RH is again underestimated despite a good representation of the air temperature, leading to an underestimation of the WBGT (Bias=C, RMSE=C). During this period the observed is high and highly variable due to the strong solar radiation and heterogeneous shading along the route. This variability is also present in the model, with some peaks and troughs exactly matching the observations in scale and timing, while others are missed or misrepresented. Accordingly, r (0.49) and the agreement rate (40.7%) are both markedly lower during the afternoon than during the night and morning, when the diurnal cycle dominates the signal, indicating that reproducing the fine-scale, shade-driven spatio-temporal pattern of heat stress is more challenging than reproducing its broad diurnal evolution.

These findings are further confirmed by the afternoon trajectory, as shown in Fig 4B and S2 Fig. Here, the model has a negative bias of C which is mainly driven by the underestimation of the due to the underestimation of RH. The RMSE for this segment is C, which is comparable to that of the full trajectory, while the agreement rate (42.8%) and r (0.36) are both lower, consistent with this segment covering the afternoon, the period during which the spatio-temporal pattern of heat stress is hardest to capture. Once again, some variability due to spatial heterogeneity is well captured by the model, while other features are missed or misrepresented.

The spatial resolution differs markedly between the two model components: SOLWEIG resolves shading and radiative exchange at metre scale, capturing fine-scale variability in , whereas and RH are taken directly from the 500 m, hourly AROME-SURFEX grid boxes and therefore cannot resolve micro-scale variability. For both trajectories, this difference is most apparent when comparing the modelled and observed (see S1 Fig and S2 Fig), reflecting in part the additional coarseness of AROME-SURFEX’s hourly temporal resolution.

Fig 5 shows a spatial comparison of the observed and modelled WBGT along a shared segment of both measurement trajectories during the 2024 Dodentocht. The observed WBGT is higher in the afternoon trajectory for the whole segment. There is a relative difference between the two observations as the participant of the full trajectory took a break in the shade between 12:30–12:35, while this was not the case for the participant passing the same point at 16:00. For the full trajectory, the simulation does not capture the cooling during the break taken by the participant. The section covered by both trajectories between 12:40–12:45 and 16:05–16:10 respectively, is next to a train track with no shade, resulting in the highest WBGT values for this segment during both trajectories. For both observed trajectories there is a clear cooling for the section covered between 12:45–12:55 and 16:10–16:20 respectively. This section of road is surrounded by large trees providing significant shade.

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Fig 5. Spatial comparison of observed and modelled WBGT.

The observed and modelled WBGT along a segment shared by both measurement trajectories during the 2024 Dodentocht. The first row shows the full 100-km trajectory. The second row shows the afternoon segment. The columns left to right show the modelled WBGT, the observed WBGT, the difference between modelled and observed WBGT, and the time series of the selected section. All times are in local time (UTC+2), base maps by OpenStreetMap (https://www.openstreetmap.org/).

https://doi.org/10.1371/journal.pclm.0001058.g005

For both trajectories, the modelled WBGT has almost identical spatial patterns, showing a similar cooling between 12:45–12:55 and 16:10–16:20 respectively, similar to the observations. In the model, there are several sharp deviations in WBGT up to C over short time periods which are not present in the observations. These sharp changes correspond to transitions between grid boxes in AROME-SURFEX. In the afternoon trajectory, the model captures the higher WBGT values in the built-up areas between 15:50–16:05 as observed but underestimates the WBGT along the exposed section next to the train track between 16:05–16:10. Despite these findings, the model stays within C of the observed WBGT for this section.

Overall, given a good NWP simulation and accurate geospatial input data, the modelling system can be used to produce acceptable WBGT values at meter-scale resolution along a moving trajectory.

Adaptation scenario analysis

The decreases significantly with increasing walking speed, as shown in Fig 6A. The fastest participants, moving at 10 km/h for 10 hours, incur no cumulative heat stress (), whereas the slowest group, moving at 4.17 km/h for 24 hours, experience the highest exposure, with degree hours during the official 2024 Dodentocht route starting at 21:00 (UTC+2). The faster one walks, the less time is spent exposed to heat stress, as the hottest part of the day is avoided, leading to a lower .

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Fig 6. CEDH for adaption scenarios.

The cumulative exposed degree hours () for different walking speeds, starting times (UTC+2), and routes. For all scenarios, the meteorological conditions experienced during the 2024 Dodentocht were used. (A) as a function of walking speed and starting times. (B) Weighted average as a function of starting times for different routes. The average is weighted according to the binned distribution of walking speeds observed during the 2024 Dodentocht, see S3 Fig.

https://doi.org/10.1371/journal.pclm.0001058.g006

For the official 2024 Dodentocht, the optimal starting time to minimize is 18:00 (UTC+2) for most walking speeds, as shown in Fig 6A. The earlier starting time reduces the time spent walking during the hottest part of the following day. Starting earlier than 18:00 (UTC+2) is suboptimal because additionally avoided heat stress during the following day is offset by the heat stress experienced at the start of the event. The group with the slowest walking speed (4.17 km/h) are on the move for 24 hours and thus can not avoid walking during the hottest part of the day. Starting earlier for this group only reduces if the meteorological conditions are cooler for the starting day compared to the following day or if the route is more exposed at the start compared to the finish. The latter plays a role for the official 2023 Dodentocht route, where starting earlier does not reduce for the slowest group under the same meteorological conditions as experienced in 2024 (see S4 Fig).

To compare the different routes, a weighted average is calculated for each route and starting time. The weights are based on the distribution of walking speeds observed during the 2024 Dodentocht, thus giving more weight to the slower walking speeds which are more affected by heat stress, see S3 Fig. The weighted average for the official 2024 Dodentocht route starting at 21:00 (UTC+2) is 6.44 degree hours as shown in Fig 6B. The alternative route, designed to include additional shaded segments while following the same general direction as the official routes, surprisingly results in an average of 7.01 degree hours. The 2024 route is the least heat prone of the routes considered, with the 2023 route having the highest average of 7.72 degree hours. On average choosing the 2024 route over the 2023 route reduces by 16.5%. The difference in between the routes is smaller than the reduction achieved by optimizing the starting time which is between 26% and 35% for all routes.

Measurement campaign

Our mobile measurement setup consists of a basic but robust backpack with standard high-quality instruments, resulting in reliable and accurate measurements, yet it is relatively costly, heavy, and bulky. It provides a unique dataset of the meteorological conditions experienced by a participant along their route during an ultra-endurance event. Other measurement campaigns use smaller, lighter and cheaper devices, making them easier to carry and deploy in larger numbers [14,65,66]. The use of such devices might enhance user comfort but they often lack location tracking. An exception is the Kestrel 5400 device that can simultaneously track GPS coordinates when using it in combination with a smartphone equipped with the Kestrel LiNK app. It is however a known issue that the Kestrel device overestimates WBGT under sunny conditions [16]. On the other side of the spectrum, fully equipped mobile weather stations often mounted on vehicles or bicycles include a wider range of high-quality instruments, for example [21,67–69]. These setups typically measure directional radiation directly, avoiding the need for a black globe thermometer, and thus more directly capturing which would simplify the comparison with the modelling system. The downsides of such setups are that they are more expensive and less portable, making them less suitable for mass sporting events with many participants in a compact space. Overall, our measurement setup strikes a balance between high-quality measurement devices and portability, however, developing a lighter and more compact wearable device would increase the comfort during the data collection [70]. We would recommend exploring the use of smaller black globes, which have faster response times or, alternatively, directly measuring directional radiation to capture .

In this study, we utilized a 5-min (90%) response time for the black globe thermometer while other studies report response times of 15–25 minutes for similar devices [62,71,72]. This is partly due to the fact that we use the 90% response time, while in other studies the equilibration or 99% response time is typically reported. Hellon and Crockford [73] found that the equilibrium response time of a 150 mm black globes is significantly reduced (6 min instead of 18 min) when using a thermocouple thermometer instead of a mercury thermometer and when the black globe is vigorously stirred, both of which are the case in our study. For a detailed overview and discussion of existing studies on the black globe thermometer response time and the attempt to reduce it we refer to Oliveira et al. [74]. In their study of the response time, which included a Testo 150 mm black globe thermometer, they found 99% response times between 11.4 and 55.7 minutes for 150 mm black globes and varying wind speeds. This corresponds 90% response times of 5.3 to 20 minutes using the conversion described in the ISO 7726 [62] standard.

During the measurement campaign, maximum observed WBGT during the 2024 Dodentocht was 24.48°C, with a significant portion of the afternoon spent above 20°C. Havenga et al. [24] found similar conditions using stationary measurements during the 2022 Comrades ultra-marathon, a 90-km event in South Africa, with a maximum WBGT of approximately 22°C and a 4 hour period of sustained “low risk” WBGT heat stress (18.4-22.2°C) according to the American College of Sports Medicine guidelines [75]. The long duration of both events warrants extra caution despite only moderate to low maximum heat stress values.

Comparing mobile and fixed measurements is challenging due to differences in spatial representativeness, sampling frequency, and instrument response times, so a limited number of studies exist. The most common method is the “stop-and-go” approach [76,77], where the mobile measurements pause at fixed stations to enable direct comparisons. Other types of mobile measurements have also been evaluated against fixed stations [78]. The main advantage of mobile measurements is that they capture the micro-scale spatial heterogeneity in heat stress, which more closely resembles the felt experience of participants. The spatial resolution captured by the mobile measurements is response time dependent, thus in this study, spatial patterns of the order of 500m (6 minutes at 5 km/h) and coarser are well captured, while finer variations are only partially captured.

Heat stress metric

WBGT is used as the meteorological heat stress metric due to its simplicity to calculate, widespread adoption in sports and occupational health (ISO 7243 standard [64]), and ability to account for the complex interaction between meteorological drivers of heat stress, making it ideal for real-time applications and practical implementation. The wet bulb temperature () component of WBGT is seldom measured directly, thus multiple empirical approximations exist both for the natural wet-bulb temperature and the psychometric wet-bulb temperature. The method proposed by Liljegren et al. [79] is often considered the most accurate but is computationally expensive as it requires iterative calculations. Previous research suggests Davies-Jones’ [80] approximation of the (psychometric) is more accurate than that of Stull [81] although the former requires complex iterative convergence methods. However, due to the available variables in both the mobile measurements and the modelling system, and the need for a non-iterative computationally efficient method for the modelling system, we opted for the simple non-iterative approximation proposed by Stull [55]. Combined with Eq 3, this provides a computationally efficient and accurate method to calculate WBGT. Brimicombe et al. [56] report a mean absolute error (MAE) of 0.76–1.13°C for this method relative to Liljegren’s method across three heatwave case studies.

Note that WBGT does not directly account for heat stress modifiers such as clothing, metabolic rate, or heat-acclimatization - a significant modifier of the heat stress response [82]. In particular for non-elite endurance events, the metabolic rate and heat-acclimatization of participants can vary widely. To deal with this, modifier dependent WBGT thresholds are proposed in the ISO 7243 standard [64] and by Liljegren et al. [79]. Alternative heat stress indicators that directly account for some of these modifiers exist, for example the Universal Thermal Climate Index [83] and the Physiological Equivalent Temperature [84]. These were not considered in this study as WBGT is relatively simple to calculate and interpret while still capturing the complex interaction between the meteorological drivers of heat stress making it ideal for NWP forecasting and real-time warning systems. Additionally, WBGT’s widespread adoption in sports and occupational health with established guidelines ease the communication of results and the implementation of adaptation strategies.

Most Dodentocht participants are likely unacclimatized to heat, given Belgium’s temperate climate and the fact that most are not elite athletes, so we apply the corresponding 20°C WBGT threshold from the ISO 7243 standard, as the event’s long duration also imposes a higher metabolic demand. In general, sporting bodies prescribe specific WBGT thresholds, of which the actual physiological risk, evaluated using physiological models, is often underestimated [85]. In this framework, the WBGT threshold for CEDH can be adapted for the specific use case.

Modelling system

Other heat stress modelling studies typically focus on smaller domains, for example, a single urban square, or use coarser resolution numerical models. For the purpose of estimating the heat stress experienced by participants along an endurance event route, restricted domains or coarse resolutions are insufficient to capture the required variability along the full trajectory. To the best of the authors’ knowledge, this is the first study to combine a NWP model run at hectometric-resolution (AROME-SURFEX) with SOLWEIG and evaluate the resulting meter-scale heat stress over such a large domain. Here, AROME-SURFEX provides forecasts of large-scale meteorological conditions, while SOLWEIG accounts for local-scale modifications of radiation due to surface geometry, including shading and sky-view effects.

At 500 m resolution, AROME-SURFEX represents the current state-of-the-art in NWP modelling, reflecting the broader shift of operational meteorological services toward such high-resolution forecasting [86]. The AROME-SURFEX simulations used in this study were themselves part of ongoing operational tests at this resolution. The added value of hectometric-resolution NWP lies in its improved representation of topography, higher resolution physiography, and key physical processes [86], including convection, fog, and urban effects. As these processes influence heat stress, the resulting forcing for SOLWEIG, as well as the variables directly used in the heat stress calculations, could, under certain conditions, yield a more accurate representation of local-scale heat stress.

However, this added value is not expected to materialize for the case studied here, as the conditions under which it can be demonstrated are largely absent. The Dodentocht domain is flat and includes no significant urban centres, and the evaluation covers a single, largely clear-sky day. In this modelling setup, alternative lower-resolution meteorological forcing datasets such as ERA5 or ARPEGE (typically 5–30 km resolution) could therefore also be used. In particular in this study, replacing AROME-SURFEX with ERA5 or ARPEGE would likely not significantly change the resulting heat stress estimates nor the conclusions drawn from the adaptation scenario analysis.

SOLWEIG was run and forced with hourly AROME-SURFEX output, although sub-hourly coupling is technically possible. Sub-hourly forcing would likely improve heat-stress estimates by including more temporal variability in the AROME-SURFEX meteorological conditions and shade in SOLWEIG. In particular, the modelled temporal variability of RH, , and consequently along the route is smaller than observed, partly due to the linear interpolation in time, which could be improved through sub-hourly coupling. However, hourly forcing was selected because current NWP forecast products are commonly available at hourly to 3-hourly intervals, particularly for medium-range forecasts, and because sub-hourly SOLWEIG simulations substantially increase, the already significant, computational costs. Nevertheless, this study demonstrates that hourly forcing and SOLWEIG simulations already provide useful heat-stress estimates.

Running SOLWEIG at 1 m resolution represents a high spatial resolution, and land-surface data at such fine resolution are not always available. Although SOLWEIG can be run at coarser resolutions, when coarser than 10m, surface geometry becomes increasingly distorted, and the position of a moving participant is no longer accurately represented within the larger grid boxes. In this context, SOLWEIG is essential for heat-stress estimation along endurance event routes, as it resolves the fine-scale radiative environment that strongly influences human exposure.

For operational applications, the trade-off between computational efficiency and the added value of high-resolution simulations, in time and space, of both AROME-SURFEX and SOLWEIG require further investigation. With the current computational capabilities, meter-scale SOLWEIG simulations over large domains are only feasible when the domain is divided into smaller sub-domains, typically 500 m 500 m grid cells. Lindberg et al. [87] and Ding et al. [88] used this approach to simulate city-wide at 2 m resolution over three major Swedish cities and at 10 m resolution over Guangzhou, China respectively. This approach remains computationally demanding: our SOLWEIG simulations required several hours on a high-performance computing (HPC) system. While SOLWEIG can in principle be run on a laptop, the size of this domain means the sub-domains would largely need to run in series requiring computation times in the order of days to two weeks.

Alternatively, machine learning (ML) based emulators are used to overcome the computational burden. They learn the mapping between meteorological inputs and from a limited set of SOLWEIG simulations, and can subsequently generate more efficiently. Briegel et al. [89] demonstrated this approach over Freiburg (Germany) at 1 m resolution. Their emulator, trained on 56 (500 x 500 m) SOLWEIG simulated domains, is an order of magnitude faster than running SOLWEIG which enables the exploration of long-term (30-year period) thermal comfort conditions. Yi et al. [90] used a similar ML-based approach to train an emulator in Philadelphia (USA) at 1 m resolution. The SOLWEIG simulations used to train their emulator utilized a GPU-optimized implementation of the sky-view factor calculations in SOLWEIG [91] speeding up the simulation but still requiring the large domain to be split into smaller sub-domains.

Of the aforementioned studies, only Ding et al. [88] used a spatially varying meteorological forcing by coupling a NWP model with SOLWEIG, as done in this study. The other studies used spatially invariant meteorological forcing per city. Briegel et al. [92] also emulated urban‑climate and LES models alongside SOLWEIG, enabling spatially varying meteorological forcing for SOLWEIG. By using a spatially varying forcing, local differences in meteorological conditions can be represented. This could be further amplified by hectometric-resolution NWP forcing in settings with more complex topography or urban structure than considered here, where fine-scale processes are unresolved by coarser forcing datasets.

Evaluation of modelled heat stress with observations

Evaluating high-resolution simulations is difficult because observations are sparse [93], and this is particularly true for heat-stress assessments, as is not commonly measured [94]. Dense and diverse measurement networks help assess spatial patterns, but scale mismatches between point observations and grid averages complicate separating model errors from representativeness errors [95]. In Figs 4 and 5, the sharp deviations in the modelled WBGT correspond to the transitions between the AROME-SURFEX grid boxes (500 m). This impact on WBGT is direct through , RH and wind speed, and indirect through the meteorological forcing of SOLWEIG. To deal with this, higher resolution NWP models or other downscaling methods for , RH and wind speed could be explored in future work. Briegel et al. [92] reported a similar grid-box transition phenomenon despite also simulating meter-scale wind speed.

For mobile measurements, the response time of the instruments must be accounted for to make a fair comparison with instantaneous model output. To achieve this, one can correct the measurements to represent instantaneous values [60], adapt the mobile measurement campaign, for example use the “stop-and-go” approach [61] or transform the model output to represent the observed response. The latter was chosen, since the delayed response in the observations better reflects the experience of the participants, namely a delayed response in skin temperature and thermal sensation to changing environmental conditions [96,97].

In Fig 4A the modelled WBGT increases less rapidly during the morning. As and RH are well captured, this is mainly driven by the modelled . This may be caused by an overestimation of shading in the morning by SOLWEIG and/or an overestimation of the 2 m wind speed. More specifically, the hourly temporal resolution of the meteorological forcing may be insufficient to capture the rapid changes in shading during the morning. During this period, the route travelled along a road lined with houses, but the corresponding 500m grid boxes mainly consisted of open fields and crops surrounding the road. Therefore, the 2 m wind speed could arguably be overestimated due to a lack of roughness elements in these grid boxes, despite local presence of buildings. A limitation of the current approach is that the impact of the participants’ movement on the experienced wind speed is not accounted for by the model, while it is implicitly included in the observed .

One of the main limitations of the evaluation is that it is based on a single meteorological case study. Despite this, the evaluation demonstrates the feasibility of modelling accurate heat stress estimates at meter-scale resolution along a moving trajectory.

Adaptation scenario analysis

The scenarios explored in this study demonstrate the use of the modelling system to evaluate the effectiveness of various event-management adaptation options. For the meteorological conditions experienced during the 2024 Dodentocht, optimizing the starting time was more effective in reducing heat stress exposure compared to optimizing the route. We acknowledge that implementing these adaptation strategies is constrained by other practical considerations such as logistics and safety. Optimizing the route for shade is often in conflict with the need for wide accessible roads, which are typically more heat exposed. Altering the start time may be the most practically feasible adaptation strategy.

Remarkably, the alternative route, designed to have more shade, did not have the lowest . This is due to the timing of heat exposure along the route for this particular meteorological case, as the majority of heat stress exposure occurred in the last quarter of the event. In Fig 3, it is clear that the alternative route does not have significantly more shade in the last quarter compared to the other routes. In addition, these shaded sections are often forests where increased humidity and reduced wind speeds partially counteract the benefits of shade. This highlights the complexity of optimizing routes for heat stress mitigation and this should be investigated under a wider range of meteorological conditions.

Future work

Development of a lighter and more compact wearable measurement device, having a similar accuracy as the used equipment, would improve comfort during the data collection. An extension of this work would be to explore a wider range of meteorological conditions, including the warmest historical conditions encountered during past editions of the event, as well as potential future heat wave conditions. The modelling system could be used to expose sections of the route which are particularly heat prone, to further inform route optimization or targeted cooling strategies such as shading or misting stations. Evaluating forecast predictability by using NWP ensemble forecast systems would quantify the usefulness of the modelling system as an early warning system to activate event heat plans several days in advance, as illustrated by Klöwer et al. [98]. Finally, testing hectometric-resolution NWP forcing against coarser, readily available, and computationally cheaper alternatives such as ERA5 or ARPEGE would help identify when such forcing can provide similar results. In particular, identifying meteorological and terrain conditions where hectometric resolution is expected to matter more than in the studied case.