https://orcid.org/0000-0003-0150-529X
Figures
Abstract
Climate change and ongoing urbanization are increasing human exposure to heat stress in cities, where strong spatial contrasts in shading and imperviousness generate large variations at the scale of streets and public spaces. Urban adaptation planning therefore requires high-resolution information on outdoor heat stress. Microscale climate models provide such information, but their reliability must be demonstrated at meter-scale spatial resolution. This study presents a validation approach for such models through a detailed evaluation of the coupled UrbClim-HiREx modeling framework. UrbClim is a fast urban boundary layer model operating at 100 m resolution, while HiREx is a radiation-based model that simulates wet-bulb globe temperature (WBGT) at 1 m resolution. Model performance is assessed against a dense observational dataset collected during 7 consecutive heat wave days in June 2023 in Ghent, Belgium, spanning multiple urban microenvironments within a 300 m × 300 m area. UrbClim reproduces air temperature and humidity with high accuracy and provides realistic pedestrian-level wind speeds after in-canopy extrapolation, yielding a reliable forcing for HiREx. HiREx reproduces the diurnal evolution of WBGT with root mean squared errors of 0.95 °C at an open site and 0.51 °C beneath tree canopy. It resolves transient shading effects and meter-scale spatial variability, with hourly daytime root mean squared errors across the microenvironments remaining below 1.59 °C. The model reproduces the observed reductions in peak daytime heat stress under tree shade of approximately 4 °C WBGT. These findings provide the most detailed validation of the UrbClim-HiREx modeling framework to date and establish a transferable approach for evaluating microscale heat stress models. The results confirm the framework’s suitability for identifying urban heat stress hotspots and assessing adaptation strategies at meter-scale resolution.
Citation: Hellebosch I, Souverijns N, Top S, Lauwaet D, Caluwaerts S, De Ridder K (2026) Modeling outdoor heat stress at meter-scale resolution: Validation of the UrbClim-HiREx framework. PLOS Clim 5(8): e0000973. https://doi.org/10.1371/journal.pclm.0000973
Editor: Thomas Thaler, University of Natural Resources and Life Sciences, AUSTRIA
Received: March 3, 2026; Accepted: July 31, 2026; Published: August 20, 2026
Copyright: © 2026 Hellebosch et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The observational dataset used for model validation is publicly available on Zenodo (https://doi.org/10.5281/zenodo.13785282) (Hellebosch et al. 2024, 2025). The UrbClim and HiREx simulation outputs underlying the findings of this study are publicly available on Zenodo (https://doi.org/10.5281/zenodo.18668445). The UrbClim and HiREx model source codes are proprietary to VITO and cannot be made publicly available or redistributed. UrbClim-based simulations can be requested through VITO’s Urban Climate Simulator service (https://urban-climate.eu/), and custom applications, including high-resolution heat stress assessments through HiREx simulations, can be requested via urbclim@vito.be.
Funding: This work was done with the support of the University Foundation of Belgium. I. H. was supported by VITO Grant VITO_UG_PHD_22022. S. T. received funding from FWO via fellowship 1270723N and BELSPO under research project grant B2/223/P1/CORDEX.be II. The contribution of D. L. was supported by the BELSPO research project grant B2/223/P1/CORDEX.be II. S. C. was supported by the BELSPO project FED-tWIN 2020-018\_AURA. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Anthropogenic climate change is leading to more frequent and more severe extreme heat events across the globe [1,2]. Urban areas are particularly vulnerable due to the urban heat island (UHI) effect, which amplifies nighttime air temperatures through the combined influence of dense built environments, anthropogenic heat emissions, and limited vegetation [3,4]. At the same time, ongoing urbanization concentrates a large and growing share of the global population in urban areas, intensifying heat stress exposure in cities worldwide [5,6]. Therefore, cities increasingly require actionable information to guide adaptation strategies that reduce outdoor heat stress and protect public health [7–10].
Human heat stress describes the thermal strain experienced by the human body. Heat stress depends not only on air temperature, but is also strongly influenced by humidity, wind speed, and radiation, all of which can exacerbate adverse physical and mental health outcomes [11–17]. Such stress is commonly quantified using integrated heat stress indicators, such as the physiological equivalent temperature (PET) [18], the universal thermal climate index (UTCI) [19], and the wet-bulb globe temperature (WBGT) [20]. WBGT is widely used within the health and climate change sector [21–31] and is used in this study because it is standardized by ISO [20] and depends exclusively on meteorological variables, without requiring assumptions about clothing, activity level, or individual physiological characteristics. During daytime conditions, radiative forcing is the dominant driver of outdoor heat stress, making adaptation strategies that reduce direct solar exposure, such as tree shading, the most effective measures for lowering peak daytime heat stress [10,26,29,30,32–35]. Because radiative conditions vary strongly at meter scale, heat stress exhibits pronounced spatial variability across urban microenvironments [26]. The largest variability and highest heat stress levels typically occur during daytime peak conditions and therefore warrant particular attention [10,26]. However, nighttime heat stress is also relevant, as sufficient nighttime cooling is essential for recovery from daytime heat exposure [36,37]. To support effective heat adaptation planning, high-resolution knowledge of both daytime and nighttime heat stress patterns across diverse urban microenvironments is required.
Detailed information on urban heat stress patterns can be obtained through urban observational networks and dedicated measurement campaigns [10,25,26,29,30,32,38–43]. Such observations are essential for capturing microenvironmental variability associated with shading, urban morphology, and surface characteristics. However, establishing and maintaining these observations is labor- and cost-intensive, particularly for long-term monitoring or for spatially extensive coverage across large urban areas [26,30,44,45]. Moreover, while observations provide critical insights into present-day conditions, they cannot address the urgent need for projections of future heat stress under climate change or urban development scenarios. Numerical climate models therefore provide an effective complement, offering high-resolution simulations of heat stress across diverse geographic and climatic contexts for past, present, and future conditions. In addition, heat stress models enable the systematic evaluation of adaptation scenarios and thus offer a powerful framework for assessing the effectiveness of heat-resilient urban design strategies. Robust observational datasets remain essential for validating such models and ensuring their reliability at the spatial scales relevant for urban planning [29,30,32,46–48].
Urban climate models exist across a wide range of spatial scales [9]. Mesoscale models with resolutions of several hundred meters, such as WRF [49] and UrbClim [50], can simulate city-wide meteorological conditions, but cannot resolve the fine spatial variability in heat stress driven by local shading and urban morphology. At the microscale, computational fluid dynamics (CFD)-based models, such as PALM [51–55] and ENVI-met [47,56], explicitly resolve flow and energy exchange processes at meter-scale resolution but are typically limited to small spatial domains or short simulation periods due to their high computational cost. In addition, radiation-based microscale models, such as SOLWEIG [34,57,58] and the High-Resolution heat Exposure (HiREx) model [29,30], efficiently capture meter-scale shading and radiative effects on outdoor thermal comfort without relying on computationally intensive CFD calculations. The existing UrbClim-HiREx modeling framework [29,30] bridges the gap between city-scale climate simulations and meter-scale heat stress variability. UrbClim is a fast urban boundary layer climate model providing meteorological information for an entire urban domain at 100 m spatial resolution [50]. HiREx uses UrbClim output as meteorological forcing and resolves shading and radiative effects to compute WBGT at 1 m spatial resolution [29,30].
This study provides an extensive high-resolution validation of the coupled UrbClim-HiREx modeling framework under heat wave conditions and assesses its performance in reproducing meter-scale heat stress patterns in various urban microenvironments. Therefore, we validate the HiREx model against a high-resolution observational dataset collected during a dedicated urban heat stress measurement campaign [26]. The dataset includes all meteorological variables required to compute WBGT and is characterized by a dense monitoring network of 15 measurement devices covering multiple microenvironments within a compact area of less than 300 m × 300 m. The validation encompasses full diurnal cycles at an hourly time step over 7 consecutive heat wave days, enabling assessment of both daytime and nighttime heat stress and its components. As such, this study provides the most detailed validation of the HiREx model to date, at unprecedented spatial and temporal resolution. At the same time, it offers a transferable approach for high-resolution validation of similar microscale climate models.
The “Materials and methods” section describes the study area, observational dataset, and the UrbClim-HiREx modeling framework. The “Results and discussion” section first presents a detailed validation of UrbClim during the heat wave, followed by the HiREx validation of WBGT and all its individual components at both an open site and a tree-shaded location. Subsequently, HiREx’s ability to capture fine-scale spatial variability in outdoor heat stress across a full diurnal cycle is assessed for multiple closely situated urban microenvironments. Additionally, the model’s capability to quantify the cooling effect of urban green vegetation on heat stress is evaluated. Finally, the study discusses the advantages and limitations of the UrbClim-HiREx framework and outlines directions for future research.
Materials and methods
Study area and observations
The observational dataset used in this validation study [59] was collected during a dedicated outdoor heat stress measurement campaign described in detail by Hellebosch et al. [26]. The campaign was conducted in the urban fringe of Ghent, Belgium, during a 10-day heat wave. Specifically, measurements were collected at an hourly temporal resolution for 7 full diurnal cycles from 9 June to 15 June 2023. The campaign involved 2 research-grade Campbell Scientific weather stations and 13 consumer-grade portable AT-HTS01 devices (Fig 1). The research-grade Campbell stations accurately measured air temperature, relative humidity, globe temperature, wind speed, and downwelling shortwave radiation (SWR). The consumer-grade portable AT-HTS01 devices registered air temperature, relative humidity, and globe temperature. A device intercomparison demonstrated that the accuracy of the AT-HTS01 devices to obtain WBGT is comparable to that of the Campbell stations [26].
(Upper panel) Map of Ghent and its surroundings covering the UrbClim model domain, based on the WorldCover dataset (https://doi.org/10.5281/zenodo.5571936) [60]. The study area is indicated by a square. (Lower left) Map of the study area at campus Sterre, Ghent University, covering the HiREx model domain, based on Bodembedekkingskaart 2018 (https://www.vlaanderen.be/datavindplaats/catalogus/bodembedekkingskaart-bbk-1m-resolutie-opname-2018) [61] and Groenkaart Vlaanderen 2021 (https://www.vlaanderen.be/datavindplaats/catalogus/groenkaart-vlaanderen-2021) [62]. The locations of the research-grade Campbell stations and the 13 portable AT-HTS01 measurement devices are indicated by white and orange dots, respectively. (Lower right) Photographs of the Campbell stations at an open paved location and beneath tree canopy in a small forest patch [26].
Measurements were collected across a medium-dense suburban area containing a variety of microenvironments and exposure conditions, including locations influenced by building and tree canopy shade, a small urban forest patch, open paved and unpaved surfaces, and an urban canyon with a solitary tree. All measurement locations were situated within a compact area of less than 300 m × 300 m (Fig 1), enabling a high-density analysis of meter-scale heat stress variability. The research-grade Campbell stations were located within and next to a small urban forest patch: one station was continuously shaded from direct solar radiation by the tree canopy, while the other was fully exposed to solar radiation at an open paved location (Fig 1). The consumer-grade portable AT-HTS01 devices were deployed at multiple nearby locations representing various microenvironments. For example, several devices were placed on an open grass field that was shaded by an 18-m-high building during the morning and by trees in the evening.
Outdoor human heat stress in the observational dataset is quantified using WBGT (°C), which is defined as a weighted sum of the natural wet-bulb temperature (, °C), globe temperature (
, °C), and dry-bulb air temperature (
, °C):
In the observational analysis, air temperature and globe temperature are directly measured, while the natural wet-bulb temperature is estimated using the iterative ISO method [20], which is based on observed air temperature, globe temperature, wind speed, and humidity. This method is particularly suitable when measurements of SWR are unavailable, as is the case for the portable AT-HTS01 devices. Importantly, all input variables required to compute WBGT were obtained through direct in situ measurements, without reliance on auxiliary model data, enabling an unbiased comparison between observations and model output.
UrbClim model
The UrbClim urban boundary layer climate model is specifically developed to produce fast and accurate long-term (decades) meteorological output such as air temperature, humidity, wind speed, heat fluxes, and soil parameters at a high spatial resolution of 100 m for complete urban agglomerations. UrbClim consists of a detailed land surface scheme, coupled to a 3-D atmospheric boundary layer module. Synoptic‑scale meteorological fields from a global climate model (GCM), regional climate model (RCM), or reanalysis are imposed at the lateral and upper boundaries of the atmospheric module. The land surface scheme is based on the soil-vegetation-atmosphere transfer scheme of De Ridder and Schayes [63], which is extended to account for urban surface physics. This is accomplished by representing the urban surface as a rough impermeable slab, with appropriate values for the albedo, emissivity, thermal conductivity, and volumetric heat capacity. The main feature of the urban scheme is the inclusion of a parameterization of the inverse Stanton number, which is known to be much higher in urban areas [64,65]. A full technical description of the UrbClim model is provided by De Ridder et al. [50]. UrbClim’s performance is comparable to more sophisticated mesoscale climate models, yet it operates two orders of magnitude faster [50,66]. Moreover, the model has been successfully validated across a wide range of cities and climatic contexts [29,30,33,44,50,67–72]. This model is therefore ideally suited to generate accurate climatological information for the full spatial extent of urban agglomerations for past, present, and future decades in a computationally cheap way.
For this study, UrbClim was run over the city of Ghent and its surroundings, covering a domain of 25 km × 25 km (Fig 1) at a spatial resolution of 100 m, for 20 vertical levels. The simulation produced hourly output for the period 1 May to 30 June 2023. This period includes more than one month of spin-up prior to the analyzed heat wave to ensure model equilibrium [67]. This UrbClim simulation was performed on 4 CPU cores and required approximately 73 wall-clock hours.
Running UrbClim over the study domain requires a range of meteorological and land surface datasets. Large-scale atmospheric boundary conditions are provided by the ERA5 reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF), which offers hourly meteorological data at a spatial resolution of 31 km [73]. Land cover classification, including but not limited to urban, suburban, forest, and cropland classes, is derived from the WorldCover dataset at 10 m resolution [60] (Fig 1). Building, sealed, and vegetation fractions are further specified using additional input datasets. The building fraction per grid cell is obtained from the Global Human Settlement Layer, which provides built-up information based on Sentinel-2 data at 10 m resolution [74]. Soil sealing fractions are based on a 30 m resolution global impervious surface map constructed using remote sensing data and machine learning methods [75]. Soil texture variability is taken from Hengl and MacMillan [76]. Monthly mean values of normalized difference vegetation index (NDVI) are obtained from Landsat 8 imagery at 30 m resolution using Google Earth Engine [77] and subsequently converted to vegetation cover fractions using the linear relationship proposed by Gutman and Ignatov [78]. Terrain elevation is taken from the Copernicus GLO-30 Digital Elevation Model (DEM), providing terrain height at 30 m spatial resolution [79]. Finally, anthropogenic heat fluxes are incorporated using the 1 km resolution dataset from Jin et al. [80], based on energy demand and population density, which is interpolated to the 100 m UrbClim grid.
UrbClim uses a bulk approach [81] and provides meteorological information at urban canopy height. However, the outdoor heat stress experienced by people is especially relevant at pedestrian level, which also corresponds to the height of the observational measurements. This needs to be considered when comparing the model with the observations. As described by De Ridder et al. [50] the air temperature is assumed to be homogeneously mixed throughout the urban canopy layer [82–85]. In contrast, wind speed varies vertically within the canopy due to microscale urban obstacles. Consequently, a post-processing step is applied to the UrbClim wind speed output to derive representative pedestrian-level wind speeds prior to its use in the heat stress calculations. Above canopy height, wind speed follows a logarithmic profile, which is also described by De Ridder et al. [50] for the UrbClim model, while below canopy height it is described by an exponential profile [86,87]. The latter is described by Macdonald [88]:
Here, is the wind speed at height
,
is the wind speed at urban canopy height
, and
with
and
the frontal area index. This formulation is valid for
. Previous studies [87,88] indicate that the exponential profile tends to deviate from observed wind speeds near the surface; therefore, pedestrian-level wind speed is best approximated at
. The frontal area index is defined as the total area of the building facades projected onto the plane normal to the incoming wind direction, divided by the total site area [89]. This value was calculated for the study area taking into account building heights and footprints at meter-scale resolution [90] using the Urban Morphology: Morphometric Calculator (Grid) tool implemented in the Urban Multi-scale Environmental Predictor (UMEP) plugin for QGIS [91]. Specifically, calculations were averaged over every 5° wind direction throughout the UrbClim grid cell that contained the location of the Campbell 2 scientific station, the station outside of a forest that measured wind speeds, yielding a value of
.
HiREx model
The HiREx model [29,30] is an add-on module to UrbClim that simulates outdoor heat stress using the WBGT indicator (Eq 1) at a spatial resolution of 1 m. Unlike the observational approach, which relies on the ISO method [20], HiREx applies the formulation of Liljegren et al. [92] to compute both wet-bulb and globe temperatures. The ISO method estimates wet-bulb temperature from air temperature, relative humidity, wind speed, and globe temperature, without explicitly requiring shortwave radiation as input. The more physically explicit and input-demanding Liljegren formulation additionally requires surface pressure and shortwave radiation, while it does not use globe temperature to estimate wet-bulb temperature. Despite these methodological differences, Hellebosch et al. [26] showed that both methods yield very similar WBGT values. A detailed discussion and comparison of the ISO method and the more complex Liljegren formulation used in the HiREx model are provided by Hellebosch et al. [26].
HiREx uses 100 m resolution UrbClim output, including air temperature, humidity, and wind speed, together with surface pressure and shortwave and longwave radiation from the ERA5 reanalysis as meteorological forcing [30]. These inputs are used to perform meter-scale radiation calculations and to derive WBGT at 1 m spatial resolution. To enable these fine-scale calculations, the model requires a detailed land cover map of the study area, including paved, unpaved, and water surfaces, as well as building and tree canopy footprints and heights. Building and tree heights, in combination with solar zenith and azimuth angles, provide the necessary information to calculate hourly shade patterns and allow to determine direct and diffuse solar radiation, explicitly accounting for radiation transfer through tree canopies [29]. Additionally, sky view factors based on buildings determine longwave radiation (LWR) contributions from the sky and surrounding buildings. The impact of paved and unpaved surfaces is incorporated into the HiREx calculations through the land surface temperature (LST) values provided by UrbClim for each surface category.
The HiREx simulation is performed for the study area of 300 m × 300 m at a spatial resolution of 1 m and an hourly temporal resolution, covering the locations and time period of the measurement campaign (Fig 1). For this domain size and resolution, the HiREx calculation was computationally inexpensive, requiring only a few seconds per simulated day using a single CPU core. However, memory requirements increase substantially for larger domains.
Terrain input data are obtained from datasets made available by the Flemish administration and are further processed in QGIS. The land cover map with the paved and unpaved surfaces and building footprints is retrieved from the Bodembedekkingskaart (BBK) acquired in 2018 [61]. Tree canopy footprints are retrieved from Groenkaart Vlaanderen acquired in the summer of 2021 using orthophotos [62]. The height of the buildings and trees is retrieved from a Digital Surface Model (DSM) obtained from LiDAR height data acquired in the period 2013–2015 in the framework of Digitaal Hoogtemodel Vlaanderen II (DHMV II) [93], from which the height of the surface above sea level (a constant 10 m for the whole study area) has to be subtracted. These data are provided at a spatial resolution of 1 m providing an unprecedented detail of building and tree height input compared to previous inputs the HiREx model was driven with (e.g., the study of Souverijns et al. [30]). The resulting terrain maps are further refined using local terrain knowledge by improving paved-unpaved boundaries and adding some trees that were not yet present at the time of terrain data acquisition. These manual refinements are applied to enable a highly detailed spatial validation of the HiREx model. The final land cover map is shown in the lower panel of Fig 1.
An important parameter controlling the cooling and shading effect of trees in the HiREx model is the leaf area index (LAI). LAI is defined as the ratio of one-sided leaf area to ground area and is commonly used to characterize vegetation canopy density, it varies with tree species, age, canopy density, spatial arrangement, and seasonality in the case of deciduous vegetation. In many HiREx applications, a relatively high LAI value (typically around 4) is assumed, representing dense foliage to estimate the upper bound of tree-induced heat stress reduction [29,30]. In the present validation study, however, model output is compared directly with in situ observations. Therefore, LAI is determined specifically for the study area based on hemispherical (fisheye) photography. The images are processed using the hemispheR R package [94], yielding an LAI of approximately 2 during the investigated period in June 2023.
The combination of the computationally efficient UrbClim model and the radiation-based HiREx model enables high-resolution WBGT simulations at limited computational cost. Although memory requirements increase substantially for larger HiREx domains, the calculations can be parallelized in both space and time because individual spatial tiles and time steps can be processed independently for HiREx. This makes city-scale applications technically feasible. Such parallelized larger-domain HiREx applications have already been performed for Berlin [95] and for the region of Flanders, Belgium [96].
Model performance is evaluated by comparing UrbClim and HiREx outputs with in situ observations at corresponding locations and time steps, and quantified using the mean bias and root mean squared error (RMSE). Additionally, to place the absolute RMSE values in context, the normalized RMSE (nRMSE) values expressed as percentages are calculated. The normalized values are defined as the RMSE divided by the mean observed diurnal range of the evaluated variable over the analyzed period.
Results and discussion
UrbClim validation
Fig 2 shows the UrbClim 2-meter air temperature () output for the city of Ghent and its surroundings during the night after the clear-sky heat wave day of 13 June 2023. The higher nighttime air temperatures in the urban area compared to its rural surroundings, known as the UHI effect, are resolved by UrbClim [50]. From Fig 2 it is clear that the study area is located in the UHI zone of Ghent.
UrbClim 2-meter air temperature at 100 m spatial resolution for the city of Ghent and its rural surroundings, nighttime average from 13 June 23:00 to 14 June 05:00 local time (UTC + 2).
Since HiREx uses UrbClim simulation output as meteorological forcing, the UrbClim model is first validated over the study area for the 7-day measurement period of the June 2023 heat wave. Fig 3 presents a comparison between UrbClim output and in situ observations at a representative open paved location within the study area. An open site is selected because local effects of small forest patches influence meteorological variables at spatial scales that are not resolved by UrbClim’s 100 m resolution. Consequently, observations are taken from the research-grade Campbell 2 station, which accurately measures all required meteorological variables at an open location. Modeled values correspond to the 100 m × 100 m grid cell encompassing the station.
The observations (full line) and the UrbClim model results (dotted line) of (first panel) air temperature (), (second panel) specific humidity (
), and (third panel) in-canopy extrapolated wind speed (
) for Campbell 2 at the open paved location during the heat wave in June 2023 agree well. The bias and the root mean squared error (RMSE) between the model and the observations are displayed in the upper right corner. The shaded areas correspond to nighttime between sunset and sunrise.
The two gaps in the observational air temperature record correspond to periods of power outage during which active ventilation of the temperature sensor was temporarily disrupted. The modeled air temperature reproduces the observed diurnal cycle well. However, the simulation shows a slight delay within the sub-hourly range, consistent with previous UrbClim validation studies [33,70]. This delay is likely related to the temporal representation of the ERA5 radiative forcing. The shortwave and longwave radiation from ERA5 are used as hourly mean radiative forcing, whereas the observations represent more instantaneous conditions. This temporal aggregation may slightly shift rapid changes in radiative forcing and can contribute to a small delay in the UrbClim-simulated air temperature. Nighttime temperatures are slightly overestimated by about 0.7 °C, in agreement with findings reported by De Ridder et al. [50], Souverijns et al. [29], and Lauwaet et al. [69]. This overestimation under stable conditions is a common limitation of many boundary layer models, where weak turbulence is difficult to represent and schemes tend to apply relatively strong vertical mixing, leading to insufficient near-surface nocturnal cooling [50,97]. In addition, local nighttime cooling induced by nearby urban green space may not be fully resolved at the model’s 100 m spatial resolution [29]. During the night of 11–12 June, observed air temperatures decreased more rapidly compared to the other nights due to a localized rain shower. This rain was not resolved by the ERA5 reanalysis causing the modeling results to significantly deviate from the observations. Accordingly, this rainy period is excluded from subsequent UrbClim and HiREx statistical evaluation. Overall, the model performance is good, with a mean bias of -0.13 °C and an RMSE of 0.98 °C, corresponding to an nRMSE of 9% relative to the mean observed diurnal temperature range. These values are in line with those reported in earlier UrbClim validation studies [33,50,66,68,69,72] and are in the same range as more sophisticated mesoscale climate models such as WRF [66]. The modeled specific humidity (second panel of Fig 3) also closely matches the observations, with error statistics comparable to those reported by Souverijns et al. [29]. A sharp increase in observed humidity during the night of 11–12 June is not captured by the model and is again attributable to the unresolved local rain event.
The third panel of Fig 3 shows the observed wind speed alongside the modeled wind speed after in-canopy profile extrapolation [88], obtained by dividing the modeled values by 1.447 (Eq 2) (S1 Fig). The modeled wind speed reproduces the observed diurnal pattern well, with a near zero bias and an RMSE of 0.36 m s-1, indicating that the in-canopy extrapolation is essential to avoid a positive bias. However, nighttime minimum wind speeds remain overestimated, reflecting the same stable boundary layer mixing limitations discussed above [50,97]. Day-to-day variability in the performance of the in-canopy wind correction may be attributed to the heterogeneous building distribution within the study area. The frontal area index used in this study represents a mean value over all wind directions, whereas the heterogeneous building pattern causes the actual frontal area index to vary with wind direction [89].
Overall, the UrbClim simulations show strong agreement with local observations of air temperature, humidity, and wind speed during the June 2023 heat wave. The obtained error statistics are in line with, or better than, those reported in previous UrbClim validation studies [29,30,33,50,66,68–70,72]. These results confirm that UrbClim provides sufficiently accurate meteorological forcing for the HiREx heat stress model in the present study.
HiREx validation
Components of WBGT.
Fig 4 compares HiREx output with in situ observations at a location beneath the tree canopy in a small urban forest patch and at an open paved location exposed to direct solar radiation during the June 2023 heat wave. These in situ observations were obtained from research-grade Campbell stations (Campbell 1 in the forest patch and Campbell 2 at the open site, Fig 1) [26]. Modeled values correspond to the 1 m × 1 m grid cell at the station’s location.
The observations (full line) and the HiREx model results (dotted line) of (first panel) globe temperature (), (second panel) wet-bulb temperature (
), and (third panel) WBGT for the open paved location exposed to direct solar radiation (Campbell 2) and the location under tree canopy in the small forest patch (Campbell 1) during the heat wave in June 2023 agree well. The bias and the root mean squared error (RMSE) between the model and the observations are displayed in the upper right corner. The shaded areas correspond to nighttime between sunset and sunrise.
The first panel of Fig 4 presents the modeled and observed globe temperature. HiREx reproduces the diurnal cycle well and clearly distinguishes between the solar-exposed and tree-shaded environments, with particularly good agreement during the morning and evening periods. The deviation during the night of 11–12 June due to the local rain shower remains present in the HiREx results and is again excluded from the statistical analysis. The recurring afternoon dip around 19:00 UTC + 2 in the modeled and observed globe temperature at the open location is caused by temporary shading from nearby trees. During these dips, the observed globe temperature decreases more slowly than the modeled values, which can be attributed to the equilibrium time of the black globe device in the Campbell stations [98]. For the period 12–15 June, maximum globe temperatures are overestimated at both the open and shaded locations, which was also found by Souverijns et al. [29]. The positive daytime globe temperature bias is partly consistent with the underestimated modeled wind speeds during several daytime periods in the last days of the heat wave (Fig 3, S1 Fig). Lower wind speeds lead to higher globe temperatures, especially under high radiative forcing. During the first heat wave days, the overestimation is partly compensated by underestimated SWR in the ERA5 forcing data (S2 Fig). Differences between observed and ERA5 SWR are likely related to the spatial and temporal representation of clouds in ERA5. ERA5 has a much coarser spatial resolution than the point observations and is used here as hourly mean radiative forcing. As a result, small or shallow clouds affecting the measurement site may not be represented at the correct location, timing, or intensity in ERA5, and may therefore be missed or smoothed in the forcing data. Conversely, ERA5 may represent clouds that reduce SWR at its grid-cell scale while the local observation site remains under clearer conditions, leading to underestimated SWR. These differences in radiative forcing also contribute to the smoother modeled globe temperature, wet-bulb temperature, and WBGT time series compared to the observations. During nighttime, defined as the period between sunset and sunrise, SWR is absent, making LWR effects relatively more pronounced. Under these conditions, the modeled globe temperature is similar for the open site and the forest and agrees with the observed globe temperature at the open site. In contrast, the observed nighttime globe temperature is higher under the tree canopy compared to the open location, due to enhanced LWR originating from the surrounding vegetation [26]. This LWR from trees is currently not represented in HiREx, which accounts only for LWR from the sky (ERA5) and from surrounding buildings.
The second panel of Fig 4 shows the modeled and observed wet-bulb temperature. As for globe temperature, HiREx captures the diurnal cycle well and reproduces the contrast between solar-exposed and tree-shaded conditions, with particularly good agreement during the morning and evening periods. Maximum wet-bulb temperatures for 12–15 June are accurately simulated. The underestimation of wet-bulb temperature during 9–11 June can be attributed to underestimated SWR in the ERA5 forcing during these days (S2 Fig). No distinction is present in the modeled nighttime wet-bulb temperature between the open and forested locations, as the Liljegren method used in HiREx to calculate wet-bulb temperatures does not account for LWR or LST.
The resulting WBGT values (third panel of Fig 4), which integrate air temperature, globe temperature, and wet-bulb temperature (Eq 1), are well reproduced at both locations. HiREx accurately captures the diurnal evolution of WBGT in terms of both timing and magnitude and clearly distinguishes between open and tree-covered environments during daytime conditions. A small positive bias remains, consistent with the globe temperature bias. During nighttime, modeled WBGT values align with the observations, although the small observed heat stress difference between the open location and the forest is not reproduced, consistent with the globe and wet-bulb temperature results. Nevertheless, model performance is good, with RMSE values of 0.95 °C at the open location and 0.51 °C under the tree canopy, corresponding to nRMSE values of 9% and 8%, respectively, relative to the mean observed diurnal WBGT range. These error statistics are comparable to those reported by Souverijns et al. [29,30] in broader HiREx WBGT applications. They are also within the range reported by Vandelanotte et al. [58], who validated SOLWEIG-derived WBGT values. Overall, HiREx demonstrates robust skill in simulating WBGT and its individual components under both exposed and shaded conditions.
Heat stress across different microenvironments.
Fig 5 presents the hourly HiREx-simulated WBGT fields for 13 June 2023, overlaid with corresponding point observations from the portable AT-HTS01 devices. 13 June was chosen since it is the clearest day of the heat wave without any clouds, as confirmed by both the observations and the ERA5 forcing data (S2 Fig). This visualization of one clear-sky day enables a detailed evaluation of HiREx’s ability to reproduce both the diurnal evolution and the fine-scale radiatively driven spatial variability of outdoor heat stress across the study area (Fig 1). The general model performance on the other heat wave days is assessed through the full-period analysis in Fig 4. At a small number of forested locations, the simulations exhibit spatially fixed patches of anomalously low WBGT values that persist throughout the day and are not reflected in the observations. These localized artifacts are related to the strong spatial variability introduced using meter-scale tree height input data. Accordingly, station coordinates were slightly adjusted for Campbell 1 and devices A12 and A14 to ensure comparison with physically representative model grid cells.
Hourly WBGT point observations and HiREx model results (in local time UTC + 2) of 13 June 2023. The bias and the root mean squared error (RMSE) between the model and the observations are displayed in the lower right corner.
During nighttime hours, WBGT values are low and modeled values are spatially homogeneous except for the anomalously low WBGT values for particular forest patches. A positive bias is present between nighttime modeled and observed values. This bias partly originates from a systematic error in the AT-HTS01 devices, which underestimate nighttime WBGT [26]. An additional contribution comes from a slight overestimation of nighttime wet-bulb temperature during the night of 13 June (Fig 4). The small observed nighttime WBGT difference between paved and unpaved surfaces is not fully reproduced by the HiREx model at this high spatial resolution. After sunrise, increasing solar radiation leads to pronounced spatial heterogeneity in WBGT, which is well captured by the model. During daytime, biases remain small (ranging from -0.60 °C to 1.12 °C) and hourly RMSE values are consistently below 1.59 °C, indicating robust model performance under highly variable radiative conditions.
A key strength of HiREx is its ability to resolve dynamic shading effects at meter-scale resolution. This can be seen in several of the shading transitions in Fig 5. An example that clearly illustrates this can be found for the cluster of stations (A1, A2, A3, A4, and A6) located on a grass field in the southwest of the domain. These stations transition through different shading conditions throughout the day: they are shaded by a nearby building during the morning, exposed to direct solar radiation around midday, and shaded by trees in the late afternoon and evening. Such transitions provide a stringent test of the model’s capacity to represent time-dependent shading processes. The progression from building shade to sun exposure is evident during hours 09:00 – 11:00, while the transition into tree shade occurs during hours 17:00 – 20:00. These shading transitions are consistently reflected in both the observations and the HiREx simulations, and the resulting spatial WBGT gradients induced by buildings and trees are well reproduced throughout the day. To the authors’ knowledge, this study provides one of the most comprehensive validations of dynamic shading transitions in meter-scale heat stress simulations, supported by an exceptionally dense observational network of closely spaced measurement devices.
Fig 6 provides a more detailed time-series comparison of two representative stations from this grass field, further substantiating the spatial patterns shown in Fig 5. The model accurately captures the full diurnal WBGT evolution at both locations, including the timing of transitions out of building shade in the morning and into tree shade in the evening. Similar to Fig 5, the positive nighttime bias is visible, which mainly originates from the underestimation of nighttime WBGT by the AT-HTS01 observations. Peak WBGT values are closely matched, demonstrating HiREx’s ability to reproduce maximum daytime heat stress levels. Together, Fig 5 and Fig 6 confirm that HiREx successfully captures both the spatial heterogeneity and temporal dynamics of WBGT in complex urban microenvironments.
The observations (full line) and the HiREx model results (dotted line) of WBGT on 13 June 2023 on a grass field in the shade of a building in the morning and in the shade of trees in the evening. The bias and the root mean squared error (RMSE) between the model and the observations are displayed at the bottom.
Accurate validation at this spatial scale critically depends on precise station coordinates and high-resolution terrain data, including detailed representations of building and tree heights. Even a positional offset of a single model grid cell (1 m) can result in substantially different shading conditions and, consequently, markedly different heat stress estimates. The strong agreement observed here therefore highlights not only the skill of the HiREx model, but also the importance of high-quality geospatial input data for meter-scale heat stress modeling and validation. A notable exception occurs at location A11 for certain hours in the afternoon, where HiREx underestimates WBGT relative to the observations. This location is situated within the small forest patch, but in reality it is located under a small canopy opening where direct solar radiation can reach the sensor during part of the day, as described in detail by Hellebosch et al. [26]. In the land cover input used by HiREx, this small opening is not resolved, and the corresponding grid cells are classified as tree canopy. As a result, the model overestimates shading at this location and consequently underestimates WBGT.
Urban green effect on heat stress.
Tree shade is one of the most effective adaptation measures for reducing high daytime heat stress in urban environments [10,29,30,32–34]. Accurately representing this effect is therefore essential for numerical heat stress models. Fig 7 presents observed and modeled WBGT values during the June 2023 heat wave for the hours associated with the highest heat stress conditions. A distinction is made between locations exposed to direct solar radiation throughout the analyzed period and locations situated in the shade of tree canopy.
Boxplots of the observed and HiREx modeled WBGT values for non-shaded locations (A1, A3, A4, A6) and for tree-shaded locations (A12, A14) during the strongest daily heat stress (12:00 – 16:00 local time, UTC + 2) for 9 June – 15 June 2023. The black diamonds indicate the mean WBGT value. The mean WBGT difference between the non-shaded locations and the tree-shaded locations for the observed values and the modeled values are displayed in the upper right corner.
Overall, the HiREx model agrees well with the observations, showing a small positive bias for both non-shaded and tree-shaded environments. The spread on non-shaded modeled values is considerably smaller compared to the observations. This reduced modeled spread is mainly related to the smoothing of the ERA5 radiative forcing, as discussed earlier. For non-shaded locations, WBGT is strongly controlled by incoming shortwave radiation. Therefore, short-term variability in SWR, for example caused by small or shallow clouds, directly increases the observed WBGT spread. Such cloud effects may not be represented at the correct location, timing, or intensity in ERA5, which is used here as hourly radiative forcing. As a result, the modeled WBGT values at non-shaded locations are smoother and show a smaller spread than the observations. The mean modeled WBGT reduction between non-shaded and tree-shaded conditions amounts to 3.76 °C, which closely matches the observed mean reduction of 4.23 °C. The slightly weaker modeled difference is partly attributable to an underestimation of SWR in the ERA5 forcing on certain days, resulting in lower modeled WBGT values especially at the open locations and thus lower contrasts between shaded and non-shaded locations. It should be noted that, despite generally clear-sky conditions during the heat wave, the shallow clouds that occasionally developed in the afternoon reduce incoming solar radiation and thus diminish the contrast between shaded and non-shaded conditions. Under fully cloud-free conditions, the WBGT difference between non-shaded and tree-shaded locations would likely be even larger, for both observations and model results.
Figs 5–7 demonstrate that both the observations and the HiREx simulations confirm the predominantly local, yet substantial, reduction of daytime heat stress provided by tree canopy shading. These findings indicate that urban tree planting is a highly effective measure to lower peak daytime WBGT. Because the strongest reductions occur where direct solar radiation is blocked, tree placement should prioritize shading of the most heat-exposed pedestrian areas [26,99].
Model limitations and future directions
The results presented in this study confirm that meter-scale variability in outdoor heat stress is predominantly driven by radiative processes, particularly the spatial and temporal variability of direct solar exposure induced by buildings and vegetation. As a radiation-based heat stress model, HiREx is specifically designed to resolve these effects at very high spatial resolution, which explains its strong performance in reproducing observed daytime heat stress patterns and shading transitions across diverse urban microenvironments. However, HiREx currently does not include LWR contributions from vegetation, and the wet-bulb temperature formulation in HiREx does not account for LWR or LST effects. These simplifications likely contribute to the underrepresentation of observed nighttime differences between open and tree-covered environments. Extending the radiation scheme to include vegetation-emitted LWR and exploring approaches to incorporate LWR and LST influences in the wet-bulb component could further improve nighttime WBGT performance.
At the same time, wind speed variability also influences outdoor heat stress in urban environments [10,100]. In the present modeling framework, a wind speed correction is represented through a vertical extrapolation from urban canopy height to pedestrian level using an in-canopy wind profile. While this correction substantially improves agreement with observations at pedestrian level (S1 Fig), HiREx does not explicitly resolve horizontal meter-scale wind speed heterogeneity, as is done in CFD models.
Spatial variability in wind speed could be introduced by applying location-specific wind speed corrections based on locally varying frontal area indices, and by explicitly accounting for vegetation-induced drag in addition to building-induced effects. However, such extensions would increase computational complexity and runtime, thereby reducing the key advantage of the UrbClim-HiREx framework: its ability to efficiently simulate heat stress at meter-scale resolution over spatially extensive urban domains. Moreover, the exponential in-canopy wind profile applied here is formally valid only for frontal area indices below 0.30 [88], whereas values in densely built neighborhoods typical for city centers often exceed this threshold [87], limiting the applicability of the exponential profile in highly compact urban settings.
The observational dataset used in this study was specifically designed to resolve radiative variability at high spatial resolution and includes only limited information on wind speed variability. However, future research on wind speed parameterizations of the UrbClim-HiREx framework, or comparable urban climate models, would benefit from measurements at similar spatial resolution that specifically target wind speed variability and extend to multiple heights above the surface.
The study area is a medium-dense suburban environment that includes several closely spaced urbanized and green microenvironments, making it well suited for validating the microscale radiative effects represented by HiREx. The validation focuses on heat wave conditions, when outdoor heat stress is most relevant for adaptation planning and when direct solar radiation and shading exert strong control on daytime WBGT. The ability of HiREx to reproduce shading-induced heat stress variability is therefore expected to be transferable to other urban environments where radiative contrasts between shaded and non-shaded locations dominate daytime heat stress patterns. However, this transferability was not directly tested in the present study. Additional validation in other urban settings, including strongly urbanized city centers and regular urban street canyons, would therefore be valuable future work.
Applying the UrbClim-HiREx framework to other cities requires appropriate meteorological forcing and high-resolution geospatial input data. The availability and accuracy of these input data determine the transferability of the framework, especially at meter-scale resolution where small positional errors can lead to different shading conditions. UrbClim itself has already been validated across a wide range of cities and climatic contexts [29,30,33,44,50,67–72] and is applied for places all around the globe [101]. Previous HiREx applications have been performed in other climates and urban settings, namely Johannesburg and Ekurhuleni [29] and Niamey [30]. However, these studies did not provide the same level of spatially dense, meter-scale validation or detailed evaluation of the diurnal evolution as the present work.
Conclusions
Climate change and urbanization are increasing human heat stress exposure in cities, creating a need for high-resolution information on microenvironmental urban heat stress patterns to guide adaptation and protect public health. Such information can be derived from observations or urban climate models; the latter must be validated against the observations.
This study presented a high-resolution evaluation of the UrbClim-HiREx modeling framework, which simulates heat stress using the WBGT indicator. Validation was conducted using a unique observational dataset collected during 7 full diurnal cycles of a June 2023 heat wave in the urban fringe of Ghent, Belgium, characterized by a dense network of measurement locations across urban microenvironments, including paved and unpaved surfaces, building and tree shade, a small urban forest patch, and an urban canyon with a tree.
The results show that UrbClim provides reliable meteorological forcings for the microscale HiREx model. HiREx reproduces WBGT during the heat wave with RMSE values of 0.95 °C at an open, solar-exposed site and 0.51 °C under tree canopy. Across the dense sensor network, hourly daytime RMSE values remain below 1.59 °C, demonstrating the model’s ability to capture meter-scale spatial and temporal variability in WBGT across diverse urban microenvironments. HiREx accurately represents strong daytime heat stress contrasts induced by building and tree shading. Under peak heat stress conditions, the modeled WBGT reduction of 3.76 °C in tree shade closely matches the observed reduction of 4.23 °C. The magnitude of this reduction depends on meteorological conditions, such as cloud cover, and on canopy LAI. Nighttime heat stress is generally well represented, although limitations remain in the treatment of LWR from vegetation and in the wet-bulb temperature formulation, which does not account for LWR and LST effects. Improved representation of LWR and LST in HiREx would likely enhance nighttime performance.
These findings confirm that meter-scale heat stress variability is primarily governed by radiative processes, which are efficiently resolved within the radiation-based HiREx model. However, wind speed also influences heat stress. In-canopy wind speed extrapolation improves pedestrian-level estimates, but horizontal wind heterogeneity is not explicitly resolved in the HiREx model. Furthermore, the applicability of the exponential wind profile in densely built areas exceeding a frontal area index of 0.30, typical for city centers, is limited. Future research would benefit from dedicated high-resolution wind measurements.
Overall, this study demonstrates the strength of coupling UrbClim’s computationally efficient urban climate modeling with HiREx’s high-resolution radiation calculations. The UrbClim-HiREx modeling framework supports accurate assessment of shading-based urban heat stress adaptation strategies, especially those involving trees. Additionally, the study provides a robust approach for validating microscale urban heat stress models using high-resolution observational datasets. Such validation is essential for increasing confidence in high-resolution modeling tools that inform climate-resilient urban planning.
Supporting information
S1 Fig. Wind speed comparison between observations and UrbClim model results.
The observations (full line), the original UrbClim model results at urban canopy height (dashed line), and the UrbClim model results after in-canopy profile extrapolation (dotted line) of the wind speed (V) for Campbell 2 at the open paved location during the heat wave in June 2023. The bias and the root mean squared error (RMSE) for the model at urban canopy height and after in-canopy extrapolation are displayed in the upper right corner. The shaded areas correspond to nighttime between sunset and sunrise.
https://doi.org/10.1371/journal.pclm.0000973.s001
(TIF)
S2 Fig. Shortwave radiation comparison between observations and ERA5 reanalysis.
The observations (full line) and the ERA5 reanalysis results (dotted line) of the shortwave radiation (SWR) for Campbell 2 at the open paved location during the heat wave in June 2023. The shaded areas correspond to nighttime between sunset and sunrise.
https://doi.org/10.1371/journal.pclm.0000973.s002
(TIF)
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