Improved High Resolution Heat Exposure Assessment With Personal Weather Stations and Spatiotemporal Bayesian Models

Abstract

Most of the United States (US) population resides in cities, where they are subjected to the urban heat island effect. In this study, we develop a method to estimate hourly air temperatures at $0.01°\times 0.01°$ resolution, improving exposure assessment of US population when compared to existing gridded products. We use an extensive network of personal weather stations to capture the intra‐urban variability. The uncertainty associated with this crowdsourced data set is addressed through a spatiotemporal Bayesian model implemented with the Integrated Nested Laplace Approximation‐Stochastic Partial Differential Equation approach. We evaluate the model on Philadelphia (PA), New York City (NY), Phoenix (AZ), and the Triangle area (NC). These case studies span different climatic zones and urban landscapes. They cover several meteorological events including a deadly heatwave in Phoenix and a snowstorm hitting part of the US in winter 2021. We obtain an overall root mean square error of $1.06°\mathrm{C}$, demonstrating the versatility of our model, and its applicability across various regions in the US. The high granularity of our model allows for the precise identification of hotspots that were previously undetected with daymet and gridMET products. Using the data generated by our method, we show that neighborhoods with high population concentration are more likely to experience elevated temperatures and prolonged hot nights, thus encouraging the use of our model for further epidemiological investigations on the impact of heat or cold stress on human health.

Plain Language Summary

Heat exposure is an increasing concern across the United States (US), especially in cities where residents are exposed to the urban heat island effect. In this study, we introduce a novel methodology designed to accurately measure air temperature exposure within all US cities. We demonstrate how this method can enhance the exposure assessment of population compared to existing air‐temperature products. Our approach is applied to four cities with different climate and urban layouts: Philadelphia (PA), New York City (NY), Phoenix (AZ), and the Triangle area (NC). It is validated against several meteorological events including a deadly heatwave in Phoenix and a snowstorm hitting part of the US in winter 2021. Our findings indicate that neighborhoods with high population concentration are more likely to experience high temperatures and prolonged hot nights. This research aims to facilitate further epidemiological investigations on the impact of heat or cold stress on human health.

Key Points

• Novel spatiotemporal Bayesian approach to estimate hourly evolution of air temperatures at high resolution with personal weather stations

• Urban heat island detection allows for the identification of urban hotspots that were previously undetected with daymet and gridMET products

• Neighborhoods with high population concentration are more likely to experience both elevated temperatures and prolonged hot nights

1. Introduction

In recent decades, the United States (US) have witnessed a wide range of devastating natural disasters. As shown in Bell et al. (2024), the number of heatwaves in the US has tripled between the 1960s and 2020s, and their duration moved from an average of 3 days in the 1960s to 4 nowadays. Modeled projections state that temperatures will continue to increase throughout the 21st century (IPCC, 2023), with varying intensity depending on the scenario of greenhouse gas emission.

Extreme temperatures hit human health in multiple ways (Bell et al., 2024), increasing the risk of cardiovascular (Alahmad et al., 2023; Lane et al., 2024; Zafeiratou et al., 2021), respiratory (Konstantinoudis et al., 2023; Zafeiratou et al., 2023) and renal diseases (Lee et al., 2024; Tasian et al., 2014; Zhang et al., 2024). Son et al. (2022) showed evidence that heat exposure during pregnancy increases the odds ratio of preterm births. Extensive literature worldwide on excess mortality summarizes the danger posed by extreme heat events (Vicedo‐Cabrera et al., 2021; Weinberger et al., 2020). Heat strokes primarily affect people with comorbidities and the elderly (S. Chen et al., 2024; de Schrijver et al., 2022), the latter causing a growing public health concern while US population is aging (Bureau, 2023). Intense physical activity can also lead to heat exhaustion, even in young people (Vanos et al., 2023; Vecellio et al., 2023), making outdoor workers particularly vulnerable during heatwaves (Borg et al., 2021; De Sario et al., 2023; Spector et al., 2023).

In the urban environment, temperatures can exceed surrounding rural's by several degrees Celsius. This phenomenon known as the urban heat island (UHI) is mainly caused by a combination of the three‐dimensional layout of the streets and the thermal and radiative properties of the urban infrastructure. It is also exacerbated by anthropogenic heat emissions associated with industries, building thermal regulation, and transportation. Solar radiation stored during the day is released with delay as heat during the night, causing the UHI to vary both intra‐ and inter‐daily. It generally reaches its peak at the end of the night, and is exacerbated under sunny and low‐windy conditions. As a striking example, K. Chen et al. (2022) estimated that the nighttime UHI of Chicago reached more than $2.8°\mathrm{C}$ during 2012 intense heatwave. In summers 2006–2013, Hardin et al. (2018) showed that the average nighttime UHI magnitude in New York City (NYC) was $3.51°\mathrm{C}$. When added to high regional temperatures, urban nocturnal thermal discomfort can turn into a life‐threatening risk (He et al., 2022; Murage et al., 2017; Royé et al., 2021). Neighborhoods affected by high UHI often coincide with those concentrating population with low socioeconomic status (S. Chen et al., 2024; Hsu et al., 2021; Li et al., 2022; Wilson, 2020). Population suffering from poor housing or homelessness are more likely to be exposed to thermal discomfort (Bezgrebelna et al., 2021; du Bray et al., 2023). In urban areas, UHI also acts in combination with other stressors, such as air pollution, noise, and absence of nature (Choi et al., 2022; Piracha & Chaudhary, 2022; Stafoggia et al., 2023; Wang et al., 2023).

According to the United Nations (UN, 2018), 83% of North Americans were living in urban areas in 2018, and it is projected to increase to 89% in 2050. In the US, the effect of the UHI on health and mortality might be underestimated: the urban temperature reference is most often derived from weather stations located at airports, which is not representative of dense city centers (WMO, 2018). Environmental epidemiological studies require high resolution and reliable reconstruction of past 2‐m air temperature (T2M). In the US, there are mainly three state‐of‐the‐art daily gridded products available: Daymet (Thornton et al., 2021), gridMET (Abatzoglou, 2013) or PRISM (Daly et al., 1997). Spangler et al. (2019) evaluated and compared these three products for their use in environmental epidemiology, but as they mentioned, weather stations used for the evaluation are not representative of the urban complex territory. Spatial prediction methods differ from one product to the other, but while most of the US population lives in urban areas, as far as we know none of these specifically included urban characteristics in their land use regression. The proper detection of the spatial variation of the UHI has not been demonstrated. Based on this statement, Newman et al. (2024) started to address this issue by creating a new gridded product. They accounted for the land surface heterogeneity, and added observations from local networks available nationwide.

Still, most of US cities remain unmonitored at high resolution, partly due to standards set by the World Meteorological Organization (WMO, 2018). They state that the weather stations should be placed at a height of 2 m, on a flat, low grass surface and at a distance from obstacles like buildings or trees. These criteria are challenging to meet in cities outside of parks, although they have been relaxed for urban environments in T. R. Oke (2004). To address this issue, there is increased global effort to incorporate opportunistic data. In particular, a growing number of meteorological studies incorporates personal weather stations (PWS), also called citizen weather stations when used for the urban environment (Meier et al., 2017). While not rigorously calibrated and controlled, they offer an unrivaled coverage in densely populated areas. After being pre‐processed (Fenner et al., 2021; Napoly et al., 2018), they can be used to capture the intra‐daily variability of T2M. However, despite the efficiency of quality control routines, measurement error and uncertainty remain the main limitation to their use in gridded products.

This paper introduces a new hourly T2M model that properly reconstructs the observed fine‐scale UHI and its intra‐daily evolution. We use PWS data and account for their uncertainty through a spatiotemporal Bayesian approach. We select a set of spatial covariates to have a good representation of terrain and land cover, and reanalysis of hourly meteorological variables at 2 m. The approach is applied and evaluated on four US urban areas with different layouts, population densities, and climatic zones: New York City (NY), Philadelphia (PA), Phoenix (AZ), and the Triangle (NC). Performances are evaluated with independent local state networks and compared to gridMET and daymet state‐of‐the‐art gridded products (Abatzoglou, 2013; Thornton et al., 2021). We run a heat stress exposure analysis as well to emphasize the need to incorporate products that properly detect UHI in health impact studies.

2. Methods

2.1. Study Area Descriptions

Here we describe the four urban areas selected to explore the heterogeneity of the city layout, size, population density, and climatic zones. Figure 1 shows the Local Climate Zones classification that is widely used in urban climatology to characterize the urban land cover types (Demuzere et al., 2020; Stewart & Oke, 2012).

Figure 1.

Local Climate Zones map on Philadelphia—New York City, Phoenix and the Triangle urban areas with personal weather stations (pws) and state reference network (ref) spatial locations.

The first area encompasses both NYC and Philadelphia, two of the most populated areas in the northeast of the US. The inclusion of these two neighbor cities in our analysis aims at demonstrating the capacity of the model to run on reasonably large scale, and simultaneously deals with cities of different characteristics. NYC is a coastal city that encompasses several bays and has dense urban zones. Philadelphia is located 130 km southwest of NYC and approximately 80 km inland from the Atlantic coast. It is mainly covered with a low‐ and mid‐rise built environment while NYC has grown vertically. The two cities are related by the I‐95 corridor, a major highway crossing several urban and suburban areas.

Second, is Phoenix, capital city of the southwestern state of Arizona (US). It is located in the Salt River Valley in the northern part of the Sonoran desert. Defying its extreme hot climate, 5.1 million people were reported in 2023 to live in the metropolitan area, including Phoenix, Mesa and Chandler. Its surroundings are very seldom inhabited and are mainly covered with sparse and low vegetation, with mountainous area to the north east.

The Triangle describes the metropolitan area delimited by the cities of Raleigh, Durham and Chapel Hill (NC). Since the 1950s, the region has attracted many tech companies and environmental health research laboratories, causing the area to grow particularly fast in recent years (U.S. Census Bureau, 2024). The Piedmont region, lying in between the Atlantic coastal plain and the Appalachian mountains, is characterized by a mild topography. The Triangle is located in the Neuse and Cape Fear river basins and accounts for lots of man‐made lakes and reservoirs, notable ones being Falls lake in north Raleigh and Jordan Lake in the south west visible on Figure 1. The urbanization is not very dense, and suburban areas are mixed with hardwood forests with a large variety of trees.

Both NYC, Philadelphia and the Triangle have a humid subtropical climate (Köppen climate classification Cfa, Peel et al., 2007), characterized by hot summers and cold winters. While Philadelphia and the Triangle are further inland, NYC has direct maritime influences, which can help moderate temperature extremes. In Phoenix, hot extremes are usual as the city has a hot desert climate (BWh in Köppen climate classification, Peel et al. (2007)). We specifically pay attention to the summer season, where weather conditions are favorable to extreme heat and high magnitude of UHI. In Philadelphia—NYC, we study July 2024 which was representative of a classical summer month. In Phoenix, we choose July 2023 as it broke records: according to the National Weather Service, it was the hottest month ever recorded at that time in the history of the city, and one of the driest as well. The average monthly temperature reached 38.8$°\mathrm{C}$. According to the 2023 Heat Related Deaths Report of Maricopa County (Batchelor, 2024), 645 people died from heat in Phoenix's county that year. In the Triangle, we study July 2021 when temperature average was around normals. Notably, tropical storm Elsa hit the region on the eighth and brought 50–75 mm of rainfall (Badgett & Danco, 2021). As our method aims at being generalizable, we include the winter month of January 2021 in Philadelphia—NYC as well, when an extreme cold event hit the region.

2.2. Weather Station Data

The main objective of our methodology is to provide a tool applicable anywhere in the US at high spatial resolution. To this end, our model is trained on PWS from Weather Underground and validated against local or regional monitoring networks. PWS from the Weather Underground platform are widely spread out across the world, especially in western countries and in the US (see https://www.wunderground.com/wundermap for real‐time map of worldwide Weather Underground stations). The selected regions are covered by state networks visible on the map and depicted in Table 1. As opposed to PWS, these stations have been installed by meteorologists and are expected to comply with the World Meteorological Organization standards (WMO, 2018). We use them as reference stations, both to estimate the PWS measurement error in a preliminary analysis and to evaluate our model results.

Table 1.

State Reference Networks Used to Estimate Personal Weather Stations Measurement Error and Evaluate the Bayesian Hierarchical Model Approach

Name	State	Reference	# Stations used for evaluation
MESONET	New York	Brotzge et al. (2020)	5
MESONET	New Jersey	Office of the NJ State Climatologist (2024)	30
AZMET	Arizona	Arizona Meteorological Network (2023)	5
ECONET	North Carolina	North Carolina State Climate Office (2025)	9

PWS are abundant in Phoenix and in the Triangle, and slightly sparser in the north east region of Philadelphia—NYC (Figure 1). As mentioned in Brousse et al. (2024), Calhoun et al. (2024), spatial coverage disparity also occurs at the intra‐urban level. It is partly explained by sociodemographic indicators but also by housing type. Few PWS are available in Manhattan, likely due to high‐rise buildings not suitable for outdoor PWS deployment. In Phoenix, while the urbanized area is densely covered, PWS in the desert are very scarce. A similar pattern is observed in the Triangle, even though the area surrounding the city is not as extreme.

There are many personal or low‐cost monitor calibration methods (Beele et al., 2022; Cornes et al., 2020; Fenner et al., 2021). Here we apply a statistical cleaning technique outlined in Fenner et al. (2021) using the CrowdQCplus R package. We eliminate observations failing at main routines checking for invalid metadata or unlikely measurements when compared to their neighbors. Isolated PWS are kept to improve rural coverage. We are unable to get rid of PWS located on high floors since the height of the Weather Underground stations is not provided.

Statistical quality control is efficient for detecting part of the erroneous observations, but some uncertainty remains in the data. In a preliminary analysis, we estimate the measurement error with the help of stations coming from independent state networks. Only PWS located less than 5 km from reference stations are kept for the estimate. A smaller radius would not provide a sufficient number of pairs for a robust error estimation. We take the precaution to remove reference stations when their surrounding PWS are not classified with similar land cover: the differential between measurements would likely be caused by the difference between their respective environments, and not by the sensors' quality itself.

Figure 2 shows the distribution of the estimated measurement error throughout the course of the day on the different territories and seasons. While this error is quite low and centered in NYC—Philadelphia in winter, PWS tend to overestimate in summer. In particular, T2M is underestimated in the Triangle mornings and overestimated in the Phoenix afternoons. For practical reason, we deduce beforehand the hourly average error in each region. The dispersion of the error is directly accounted for in the model itself (see Section 2.4).

Figure 2.

Empirical distribution of the estimated measurement error of personal weather stations after CrowdQC + quality control and calculated against independent state networks. Each plot corresponds to a case study and the distributions are vertically displayed for each hour of the day.

2.3. Covariates

PWS observation sparsity is partly accommodated by the inclusion of relevant geographic covariates. All covariates are listed in Table 2.

Table 2.

Spatial and Spatiotemporal Covariates Included in the Bayesian Hierarchical Model of 2 m‐Air Temperature

	Full description	Resolution
elev	Terrain elevation (m) (Danielson & Gesch, 2011)	7.5 arc‐s
fch	Forest canopy height (m) (Potapov et al., 2021)	30 m
imp	Imperviousness (%) (Dewitz, 2024)	30 m
t2m	ERA5 reanalysis of 2 m‐air temperature $(°\mathrm{C})$ (Hersbach et al., 2020)	0.25$°\times$ 0.25$°$ hourly
rh	Relative humidity derived from ERA5 reanalysis of 2 m‐air temperature and 2 m‐dew point temperature (%)	0.25$°\times$ 0.25$°$ hourly
tp	ERA5 reanalysis of total precipitation (m) (Hersbach et al., 2020)	0.25$°\times$ 0.25$°$ hourly
u10	ERA5 reanalysis of 10 m U wind component (m) (Hersbach et al., 2020)	0.25$°\times$ 0.25$°$ hourly
v10	ERA5 reanalysis of 10 m V wind component (m) (Hersbach et al., 2020)	0.25$°\times$ 0.25$°$ hourly
tcc	ERA5 reanalysis of total cloud cover (%) (Hersbach et al., 2020)	0.25$°\times$ 0.25$°$ hourly

To model terrain and land cover variations, we add altitude from the Global multi‐resolution terrain elevation data 2010 (Danielson & Gesch, 2011), the forest canopy height from the Global Land Analysis and Discovery laboratory (Potapov et al., 2021), and the imperviousness from the National Land Cover Database (Dewitz, 2024). The latter is essential to represent the level of urbanization. Atmospheric variables from reanalysis are included to account for the temporal evolution of T2M. The use of meteorological products often requires to arbitrate between high spatial and high temporal resolution. We prioritize the hourly availability of the Copernicus ERA5 reanalysis on single level (Hersbach et al., 2020) and select six relevant covariates listed in Table 2. Relative humidity is not directly provided in the ERA5 data set and has been derived from 2 m‐air temperature and 2 m‐dewpoint air temperature (Kraus, 2007).

We initially included tree canopy cover, building footprint (Heris et al., 2020) and solar radiation variables. After several experimental trials, we removed them to avoid colinearity in the additive model (see Section 2.4) and help interpret covariate contribution to the output (Section 3.2).

2.4. Spatiotemporal Bayesian Hierarchical Model Definition

We develop a spatiotemporal geostatistical model using a Bayesian Hierarchical Model (BHM) designed to leverage both information contained in the data and additional knowledge brought by covariates and prior definitions, while being interpretable and providing complete uncertainty quantification (Wikle et al., 1998). Let $\mathit{z}$, $\mathit{y}$ and $\mathit{\theta }$ be random vectors representing the latent field of T2M, PWS observations, and model parameters, respectively. The BHM utilizes Bayes's theorem to estimate the most likely outcome distribution given the observations plus prior information on the data and parameter space through the following structure:

$$p(\mathit{z},\mathit{\theta }\mid \mathit{y})\propto p(\mathit{y}\mid \mathit{z},\mathit{\theta })\times p(\mathit{z}\mid \mathit{\theta })\times p(\mathit{\theta }).$$ (1)

The latent field $\mathit{z}$ is observed at $S$ spatial locations and $T$ hourly timestamps:

$$y(\mathbf{s},t)=z(\mathbf{s},t)+ϵ(\mathbf{s},t),\mathbf{s}=1,\text{…},S,t=1,\text{…},T.$$ (2)

where $ϵ(\mathbf{s},t)$ represents the measurement error, with $\mathit{ϵ}\sim \mathcal{N}\left({\mathit{\mu }}_{\mathit{y}},{\sigma }_y^2\mathcal{I}\right)$. The prior on the precision ${\left({\sigma }_y^2\right)}^{-1}$ is a log‐Gamma distribution with hyperparameters derived from the measurement error estimation (Section 2.2). Each observation follows a Gaussian distribution $y\sim \mathcal{N}\left(\eta +{\mu }_y,{\sigma }_y^2\right)$, with

$$\eta (\mathbf{s},t)={\beta }_0+\sum _{i=1}^3\sum _{h=1}^{24}{\mathbb{1}}_{t\in {\mathcal{D}}_h}{\alpha }_{i,h}{x}_i(\mathbf{s})+\sum _{j=1}^6{\beta }_j{x}_j(\mathbf{s},t)+f(\mathbf{s},t).$$ (3)

${\beta }_0$ is a Gaussian intercept with prior mean 0 and a high precision of 10. ${\left\{{\mathit{x}}_{\mathit{i}}\right\}}_{i\in \{1\text{…}3\}}$ is the set of spatial covariates encompassing elevation, imperviousness and forest canopy height. ${\mathcal{D}}_h$ is the set of timestamps with local time hour $h$ (e.g., on July 2024 case study, ${\mathcal{D}}_8=\{2024/07/01:0800,2024/07/02:0800,\text{…},2024/07/31:0800\}$). The term ${\mathbb{1}}_{t\in {\mathcal{D}}_h}{\alpha }_{i,h}$ means that we have different coefficients for the spatial covariates for each hour of the day. This choice has been made based on the assumption that the influence of topography and land cover on T2M varies throughout the course of the day. For example, T2M at time $t$ partly results from the energy balance of the surrounding surfaces integrated through the past hours. Physically, a coefficient for each hour of the day makes more sense where a single linear relationship would miss part of the mechanism. Some atmospheric circulation processes induced by topography also change with diurnal—nocturnal cycle. We choose low informative priors but make sure to keep coefficients within physically‐likely ranges. For the elevation, we set a Gaussian prior with mean $-0.006°\mathrm{C}.{\mathrm{m}}^{-1}$ and a high precision as it is commonly admitted that T2M in the troposphere is linearly decreasing by 5.5–6.5$°C$ every 1,000 m. This allows sparse high‐elevation mountain observations to inform the BHM.

${\left\{{\mathit{x}}^{(j)}\right\}}_{j\in \{1\text{…}6\}}$ is the set of meteorological factors coming or derived from ERA5 reanalysis. They help the model to adapt with meteorological conditions and seasonality. As for spatial covariates, we set low informative priors for $\mathit{\beta }$. For ERA5 T2M, despite its low spatial resolution, we consider that it should be very close to the outcome field of T2M. We set a Gaussian prior with mean 1 and a precision of 10.

$f(\mathbf{s},t)$ can be seen as the remaining part of the spatiotemporal field that has not been modeled through the first additive terms. It is a non‐linear effect modeled through a centered Gaussian field $\mathit{f}=MVN\left(\mathbf{0},{\mathbf{\Sigma }}_{\mathcal{S}\mathcal{T}}\right)$, with a separable spatiotemporal covariance matrix:

$${\mathbf{\Sigma }}_{\mathcal{S}\mathcal{T}}={\mathbf{\Sigma }}_{\mathcal{S}}\otimes {\mathbf{\Sigma }}_{\mathcal{T}}$$ (4)

where ${\mathbf{\Sigma }}_{\mathcal{S}}$ is the spatial covariance of a Matérn field (Gneiting et al., 2010). With Integrated Nested Laplace Approximation (INLA), priors on its range $r$ and variance ${\sigma }_s$ can be set with penalized complexity priors (Fuglstad et al., 2019): here $p(r<0.1)=0.99$, and $p\left({\sigma }_{\mathcal{S}}>4\right)=0.01$. The smoothness parameter $\nu =\alpha -1$ is fixed and is equal to 1, as we keep the default parametrization for $\alpha =2$. ${\mathbf{\Sigma }}_{\mathcal{T}}$ is the covariance of an autoregressive process of order 1 on time $t$ (Blangiardo & Cameletti, 2015):

$$y_t=\rho y_{t-1}+{\omega }_t,t=2,\text{…},T$$ (5)

with $\mid \rho \mid <1$ and ${\omega }_t$ a white noise. The bigger $\mid \rho \mid$ is, the stronger the correlation from one timestamp to the next will be. To force the model to provide coherent sequences of T2M map, we set the following penalized complexity hyperprior on $\rho$:

$$p(\rho >0.6)=0.9.$$ (6)

2.5. Inference and Prediction With INLA

We have defined each term of Equation 1. The likelihood is known thanks to Equation 2: conditional on the latent process $\mathit{z}$ and on a set of likelihood parameters $\left({\mathit{\mu }}_{\mathit{y}},{\sigma }_y^2\right)$, observations are i.i.d with Gaussian distribution $y_{mt}\mid \mathit{z},{\mathit{\mu }}_{\mathit{y}},{\sigma }_y^2\sim \mathcal{N}\left({\mu }_{y,mt},{\sigma }_y^2\right)$. Based on Equation 2 as well, $\mathit{z}\mid \mathit{\theta }\sim MVN\left(\mathit{\eta },{\mathbf{\Sigma }}_{\mathcal{S}\mathcal{T}}\right)$. All priors on parameters and hyperparameters are independent and are multiplied to get $p(\mathit{\theta })$. The posterior distribution of T2M is derived through the hierarchical structure enounced in Equation 1, and this process is known as the inference of the BHM.

The inference is commonly done through Markov Chain Monte Carlo (MCMC) methods which sample the joint posterior distribution of model parameters. These algorithms are often impractical on large‐scale and high‐resolution spatiotemporal fields due to the computational complexity of inverting and storing the large covariance matrix. The INLA approach employs a sequence of approximation and optimization techniques to provide accurate deterministic approximations to the posterior marginals of latent Gaussian processes (Rue et al., 2009). For this specific class of models, extensively employed in practice, this alternative to MCMC significantly accelerates the inference. Additionally, the Spatial Partial Differential Equation (SPDE) method (Krainski et al., 2018; Lindgren et al., 2011) complements INLA to approximate spatial fields with Matérn covariance. Another big advantage of the INLA‐SPDE approach is that its complex algorithms have been synthesized in functions available in INLA R library (Lindgren & Rue, 2015).

2.6. Evaluation Method

INLA‐SPDE provides inference and access to the full posterior distribution of the T2M spatiotemporal field. For conciseness, we will focus on the mean of that distribution, subsequently referred to as ${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$. The mean is the most likely value, and the most relevant as well to assess heat exposure. As a quantitative evaluation (Section 3.1), we compare reference measurements to predicted values. We define residuals as the difference between measurement and ${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$ at the same location. These will be used to calculate the root mean square error (RMSE) for each case study.

We detail in Section 3.2 how materials provided through the INLA‐SPDE approach can be analyzed to better understand both the model itself and physical processes at stake. The standard deviation ${\sigma }_{\text{BHM}}(\mathbf{s},t)$ is an indicator of the uncertainty of the BHM at each point in the spatiotemporal domain. We also have access to posterior marginals for all model parameters. These distributions, compared to prior settings, help to understand covariate contributions to T2M for each case study and at different times of the day.

In Section 3.3, we compare ${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$ to daymet and gridMET. Daymet applies a spatial and temporal interpolation of the preprocessed Global Historical Climatology Network—daily (Menne et al., 2012). GridMET merges PRISM, a land‐use regression on US observational networks (Daly et al., 2008), with North American Land Data Assimilation System (Mitchell et al., 2004). As opposed to our BHM, developed with specific attention to densely populated areas, these products were not developed for human health applications. Still, they are often used in epidemiological studies as they have a better spatial coverage than observational networks (e.g., Castro et al., 2023; Healy et al., 2023; Thomas et al., 2021). We compare the two products to daily minima ${\mathrm{T}2\mathrm{M}}_{\text{min}}$ and maxima ${\mathrm{T}2\mathrm{M}}_{\text{max}}$ derived from our BHM hourly predictions at each spatial location. In accordance with the two products, extrema are calculated from midnight to midnight (local standard time), for each day.

The last phase of our model evaluation focuses on its capacity to provide an accurate heat exposure assessment (Section 3.4). We first analyze the exposure spatial disparities by mapping the UHI, calculated by removing the spatial domain mean of ${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$. We also compare ${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$ at two locations, one rural and the other urban, to have an insight on its intra‐daily evolution. Additionally, we take advantage of the hourly resolution to calculate exposure duration to nighttime extreme heat. For each night $n$, the hot night duration ${\tau }_n$ is defined as follows:

$${\tau }_n=\sum _{h=10\text{pm}}^{6\text{am}}{\mathbb{1}}_{{\mathrm{T}2\mathrm{M}}_h\ge \delta },{\tau }_n\in 1\text{…}9,$$ (7)

with $\delta$ the average of the 0.9‐quantile of the minimum temperature recorded in July on the reference period 1991–2020:

$$\delta =\frac{1}{31}\sum _{d=07/01}^{07/31}{q}_{0.9}\left(\text{min}{\left({\mathrm{T}2\mathrm{M}}_d\right)}_{\mathit{1991-2020}}\right).$$ (8)

T2M on the reference period are measured by a reference station from the neighboring, daily Global Historical Climatology Network (Menne et al., 2012). High percentile of T2M generally comes with public health concerns (Royé et al., 2021), therefore we fix the threshold to $q_{0.9}$. We then cross both the UHI and the hot night duration with population density data (Warszawski et al., 2017). A linear relationship between the UHI amplitude and the logarithm of the total population of cities has long been established (T. Oke, 1973). With our approach, we can investigate if the positive correlation remains valid at the intra‐city level, and look at the relationship with the duration of extreme exposure as well.

3. Results

3.1. Model Performances

The overall RMSE is of $1.06°\mathrm{C}$, with slight variations between case studies: $0.93°\mathrm{C}$ and $1.08°\mathrm{C}$ for January 2021 and July 2024 respectively in Philadelphia‐NYC, $1.33°\mathrm{C}$ for July 2023 in Phoenix and $1.23°\mathrm{C}$ January 2021 in the Triangle. RMSE on the 81 reference weather stations used for the evaluation ranges between 0.44 and $1.69°\mathrm{C}$, with an outlier of $2.76°\mathrm{C}$ for a coastal station located near the beach.

Figure 3 helps to evaluate the consistency of the BHM in space and time for July 2024 case study in Philadelphia—NYC. On panel a, the residual distribution for each hour of the day consistently spreads around zero, showing that the performances barely vary with the time of day. The circles in plot B correspond to reference stations and are filled with their RMSE. The model performs better on average in some areas than others. In Durham and Phoenix, urban reference stations score better than rural ones (see Supporting Information S1). Even if the BHM is built to extrapolate to unobserved zones, its performances might still be downgraded in those areas because of the lower amount of information available. These critical areas can at least be detected through the additional material supplied by our Bayesian inference approach.

Figure 3.

Bayesian Hierarchical Model (BHM) diagnostic plots for the output in Philadelphia—New York City urban area on July 2023. (a) Overall residuals per local time hour. (b) Average standard deviation of the BHM and root mean square error at each MESONET weather station, with black dots corresponding to each personal weather stations.

3.2. BHM Output Interpretation

The background of the map in Figure 3b shows the average ${\sigma }_{\text{BHM}}(t)$ at each location extracted from the posterior distribution. Areas with high standard deviation generally correspond to neighborhoods with few PWS or to areas where neighboring PWS do not agree. Phoenix for example, is surrounded by a desert and mountainous areas where PWS coverage is very low (Figure 1). The T2M field is inferred in those areas as well thanks to covariates, but it has a higher uncertainty than in the extensively covered urban area (see Supporting Information S1). Similarly to all statistical models, performances of the BHM both vary in space and time because of sampling, but this uncertainty aspect is monitored through the BHM standard deviation.

On Figure 4a, marginal posterior mean and 95% confidence intervals are displayed for elevation, forest canopy height and imperviousness coefficients. As mentioned in Equation 3, these change for each hour of the day. Priors for these coefficients are plotted on the left with same scale, to show how the precision and mean evolved through the inference process. The coefficient for the height of the forest canopy is not included in Phoenix, as the covariate barely varies throughout that region. Although we set a prior based on the known relationship between elevation and T2M in the troposphere, the posterior coefficient does not necessarily stay around the prior mean. It suggests that other meteorological effects related to terrain are at stake. The imperviousness mostly has a positive contribution, but as opposed to what we expect with our knowledge on UHI, it is not peaking at the end of the night. In our model, the forest canopy height seems to play a decisive role at this moment of the day. In the Triangle, imperviousness coefficient can even be negative, especially at night. For this specific region, the urbanized area slightly overlooks three basins located in the rural surroundings. This particular topography might partly explain why the nocturnal UHI is mild (see Supporting Information S1). Two lakes located in these reservoirs are particularly hot: the eye of an expert would help to determine if the storage and release of heat makes physically sense, or if it is an artifact of our probabilistic model. This specific case illustrates that even if they are informative, it is always delicate to draw definitive physics conclusions from the marginal posteriors.

Figure 4.

(a) Spatial covariate coefficient marginal priors (left) and posterior marginal's mean and 95% confidence interval evolution throughout the day. (b) ERA5 coefficients posterior marginals. Color corresponds to each case study (nps = Philadelphia—New York City (NYC) July 2024, npw = Philadelphia—NYC January 2021, phoe = Phoenix July 2023, tri = Triangle July 2021).

In Figure 4b, we plot the whole posterior marginals for each hourly meteorological variable ($\mathit{\beta }$ in Equation 3). Its prior mean being set to 1 (Section 2.4), we notice that the BHM relies less than expected on the reanalysis of temperature, especially in Phoenix where the coefficient has been offset to less than 0.75. Total precipitation has a negative contribution on the Triangle and a positive one on summer 2024 in Philadelphia—NYC. Marginals are centered around zero for the other cases, suggesting no significant effect.

The analysis of the marginal posterior reveals that the contribution of covariates changes with the region and the season. With the Bayesian approach, the model is fit to each case study through the inference process. The effect of covariates should not be generalized, but rather interpreted conditional on the layout of the city, its geography and the meteorological event under consideration. Covariates are also incorporated through a relatively simple linear additive function: interpretation must be made accordingly.

We also analyze the parametrization of the non‐linear spatiotemporal term $f(\mathbf{s},t)$ (Equation 3). For every case study, the posterior mean of $\rho$, the coefficient of the AR1 process, is between 0.86 and 0.95, with very high precision. It means that the field at time $t-1$ strongly contributes to the next time step $t$. Thanks to this property, ${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$ field is a coherent sequence that can be observed like a movie, partly revealing atmospheric processes like horizontal advection (movies of the case studies are shared in Supporting Information S1). The spatial range of the Gaussian field varies greatly from one case study to the next. It is larger for Philadelphia—NYC area. The variance of the field is between 1 and $1.8°\mathrm{C}$: the spatial field can be seen as a mold for the non‐negligible information contained in the data that the additive linear terms missed.

3.3. Comparison to Daily Gridded Products

Figure 5 shows one example of ${\mathrm{T}2\mathrm{M}}_{\text{min}}$ maps obtained with GridMET, daymet and our BHM approach on January 2021, where the overall RMSE is of 0.93$°\mathrm{C}$. It is representative of all the maps obtained on each of our case studies: the BHM brings a higher granularity and detects some hot spots that do not appear on other products. It has a higher spatial resolution than gridMET, and even though daymet has a similar grid cell size, their T2M field looks smoothed across the region. In that example, the UHI of Philadelphia is shifted to the south west with gridMET, and it is simply not detected with daymet. In NYC, the BHM shows a ${\mathrm{T}2\mathrm{M}}_{\text{min}}$ up to 3 to 4$°\mathrm{C}$ in some neighborhoods of the city when it does not exceed 1$°\mathrm{C}$ for daymet and 3$°\mathrm{C}$ for gridMET.

Figure 5.

From left to right: minimal 2 m‐air temperature estimation in Philadelphia—New York City on 2021 14 January with gridMET, daymet, and the Bayesian Hierarchical Model approach.

When averaged on all the four urban areas explored in this study, it appears that the ${\mathrm{T}2\mathrm{M}}_{\text{max}}$ is almost systematically 0.5 to 3$°\mathrm{C}$ higher for existing products than for our BHM. For the ${\mathrm{T}2\mathrm{M}}_{\text{min}}$, the three products globally agree, except on the winter case study where the BHM estimates hotter ${\mathrm{T}2\mathrm{M}}_{\text{min}}$ in rural areas. Further investigation on other cities is necessary to see if these patterns are the same in every climatic region and for all seasons. Daymet and gridMET have known and documented uncertainties in mountainous areas. Even though this analysis is not sufficient to draw conclusions about their performances in the urban environment, it encourages the user to be cautious when using these products for epidemiological studies. In contrast, the BHM approach is designed to optimize urban exposure assessment and shows better accuracy in densely populated areas.

3.4. Intra‐Daily Thermal Exposure Assessment

Figure 6a is a map of the UHI on Philadelphia—NYC averaged over July 2024, as defined in Section 2.6 (see Supporting Information S1 for other summer case studies). Philadelphia and NYC urban areas are up to $4°\mathrm{C}$ hotter than the average of the region. The UHI is milder in the Triangle, where the urban area is mainly composed of open low‐rise local climate zone with a lot of vegetation patches (Figure 1). On Philadelphia and NYC, the UHI amplitude is smaller in winter than in summertime. The T2M gradient between the Atlantic ocean coastal area and the inland territories appears to be stronger in July 2024 than in January 2021, suggesting seasonal oceanic influences on T2M. Even if it is a good tool to target hot spots, the map of the average UHI smooths the intra‐daily variation. In Figure 6c, the intra‐daily variation on July 2024 can be read with a sweep from left to right. The UHI is stronger at night in Philadelphia, NYC, and Phoenix, as opposed to Durham and Raleigh where it reaches its maximum during the day. We observe a cool island in the afternoon in NYC and in the very late night and morning in Phoenix, where the rural point is located at the southwest of the city. The results on Philadelphia—NYC are coherent with those obtained in Hardin et al. (2018) in terms of UHI shape, intra‐daily amplitude and seasonal variation.

Figure 6.

Heat exposure analysis in July 2024 on Philadelphia—New York City with (a) average differential to regional hourly mean (urban heat island, UHI), (b) hot night average duration, (c) UHI evolution in the two city throughout the month, and (d) empirical density of the UHI and hot night duration per population density ranges. Legend is common to every plot. Points represent urban and rural locations used to create plot (c).

In Figure 6b, we map the median duration of hot nights in July 2024 in Philadelphia—NYC. For all of the four cities, we observe that hot nights in July were much longer within intensively urbanized areas. By crossing heat exposure data with population density (Figure 6d), we show that neighborhoods where a lot of people are living are more likely exposed to both higher amplitude and longer heat exposure.

4. Discussion

4.1. Urban Heat Island Detection

The BHM is designed to be applicable to any territory in the US, with a specific focus on urban areas. Our BHM properly detects the UHI thanks to three components: it uses a dense observational network of PWS, it has a high $0.01°\times 0.01°\mathrm{C}$ spatial resolution and it incorporates urban land cover covariates. With this high spatial resolution, we detect for instance the cooling effect of Central Park in NYC and other urban parks. Both in Philadelphia and in the Triangle, our model detects hot spots in zones near Delaware River and other water bodies. Some urban neighborhoods are hotter than others.

While being densely inhabited, cities are often misrepresented in observed T2M reconstruction. In that respect, our approach fills a gap when compared to existing gridded products. Further work is needed on that topic to explore the added value of BHM in comparison to concurrent approaches to assess adverse health outcomes.

4.2. Intra‐Daily Evolution

The use of a spatiotemporal covariance allows to keep a certain amount of information from one time step to the next. It provides a temporal coherence that can be exploited to study the path of storms and other atmospheric events. Movies of the UHI hourly evolution on all case studies are shared in Supporting Information S1. Some physical processes however might be missed by the current BHM. The latter would gain to have non‐separable spatiotemporal structure. Covariances designed for advection and/or diffusion representation have already been implemented for the INLA‐SPDE approach (Clarotto et al., 2024; Lindgren et al., 2023). They are highly promising as they tend to hybrid the physics properties to the probabilistic approach, and deserve to be investigated in future versions of our BHM.

4.3. Model Performances and Crowdsourced Data

Our model is fitted with PWS data because of their dense urban coverage. Despite this advantage, PWS are not always reliable and their measurement error is not fully understood. The quality control routines applied before the BHM are not always sufficient, but they are also challenging to improve. Unlike institutional networks, Weather Underground data do not come with precise metadata such as weather station model or location environment. It is not possible to know if they are installed in gardens, balconies, or against obstacles. One of the strengths of our approach is the incorporation of the estimated measurement uncertainty in the BHM. Despite several modeling tricks, the BHM standard deviation is larger in the desert, in the mountains, and in rural areas where sensors are sparse. At the intra‐city level, some types of neighborhood might have fewer sensors than others (Brousse et al., 2024; Calhoun et al., 2024), and the consequences of that coverage inequity on exposure assessment would deserve more exploration. PWS are also a relatively recent source of data. Their availability does not cover the entire climatological period 1991–2020. The number of available stations increases with time. The accuracy of the products derived from PWS might increase as well in future years in covered areas.

4.4. Scalability Problem

Environmental health studies have better precision and can detect smaller effect sizes within noisy data when applied to large cohorts and domains. Weather Underground data is extensively available across the whole contiguous US, and the covariates cover the entire territory. From this perspective, and as shown with the different case studies, we can apply the BHM anywhere. Through Phoenix's heatwave and cold winter in Philadelphia——NYC case studies, we also illustrate the ability to properly capture extreme temperature events. Our approach, which can be applied on any US city, offers a new tool for urban planning and public health actors.

Scaling the BHM to the entire contiguous US on long periods is not trivial, even though INLA‐SPDE approach is one of the fastest to estimate Bayesian spatiotemporal Gaussian fields. We ran our experiments on a high computing platform, with 10 CPUs with 6 Gb memory each. PWS cleaning, covariates extraction, and data formatting before running the model take a lot of time, but these steps are algorithmically simple and can easily be parallelized. The call to INLA function in itself takes 41 min total on Phoenix $\left(\sim 11,000{\text{km}}^2\right)$, 17 min in the Triangle $\left(\sim \mathrm{4,500}{\text{km}}^2\right)$ and around 1h10 on the largest area encompassing NYC and Philadelphia $\left(\sim 22,000{\text{km}}^2\right)$. On larger scales, promising work showed that running time can significantly be reduced by using the PARDISO library for sparse linear algebra (Gaedke‐Merzhäuser et al., 2023) or a novel block tridiagonal arrowhead solver to leverage the power of GPUs Gaedke‐Merzhäuser et al. (2024). These solutions could be considered to accelerate future versions of our model.

Additional scientific challenges also arise with the creation of a country‐wide and hourly model: how to optimize the SPDE mesh with PWS coverage inequities across the whole US territory? How to generalize the coefficients of static covariates with the different seasons, timezones and geographies? Such a model would probably require to be complexified with additional covariates like solar angles, or to be stratified by climatic region and season. The current version of our model has the advantage to be fitted to a specific region and season each time, as shown in Figure 4. For the time being, the code of our approach is available in three open‐source R libraries (see Section 5). It makes it easier to use in a parallel framework to quickly generate large data sets of US cities for climatic events of interest. This strategy implies having zones and periods remaining uncovered. It still has the advantage of creating a decent learning set to potentially train a downscaling model for ERA5 or MERRA2 hourly reanalysis products. For example, a deep learning approach would ideally make profit of parallel computing on GPUs and CPUs to generate hourly data at $0.01°\times 0.01°$ resolution for several years on the contiguous US $\left(\sim 7,700,000{\text{km}}^2\right)$.

5. Conclusion

Heat exposure is a major public health concern in the US and the epidemiological literature on this topic is very active. In urban areas, people are exposed to the UHI effect, whose full amplitude is sometimes missed in state‐of‐the‐art gridded products. The UHI phenomenon varies by several degrees Celsius throughout the day, typically peaking at the end of the night. The impact of hot night exposure on human health is not fully understood in the US, partly because accurate 2 m‐air temperature (T2M) data for populated areas is difficult to obtain.

The Bayesian spatiotemporal model we propose in this article addresses several of these concerns. First, it leverages PWS data to achieve a spatial resolution of $0.01°\times 0.01°\mathrm{C}$ and successfully detects the UHI amplitude. Our approach also provides coherent hourly estimations of the T2M, allowing us to examine intra‐daily exposure evolution. It is applicable anywhere in the contiguous US and can be adapted with equivalent data sets to other countries.

We have applied the BHM to four urban areas with very different climates and geographies. It has been tested under normal weather conditions, as well as extreme hot and cold events. Its performance has been evaluated against independent reference networks, with a consistent RMSE ranging from 0.93 to 1.33$°\mathrm{C}$ depending on the case study. As most of studies using PWS do, we run a quality control before the model inference. We go further with our approach by incorporating the remaining measurement uncertainty in the Bayesian framework itself. The inference provides the entire distribution of the field, making the model's uncertainty accessible through its dispersion measures.

We provide an overview of the implications that our model could have on heat exposure assessment. In comparison to gridMET and daymet, our approach offers a significantly better granularity, allowing to target local hotspots that were not detected before. Both exposure duration and amplitude can be calculated at high spatial resolution. Notably, we show that neighborhoods with high population concentration are more likely to experience high temperatures and longer hot nights. These preliminary findings raise the question of the accuracy of extreme heat risk assessment regarding urban environments. The model we propose will contribute to the ongoing effort to tailor heatwave alerts to each territory, thereby reducing the number of victims. It will offer an accurate gridded product to feed heat stress research and assist public health initiatives to help vulnerable populations.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Supporting information

Supporting Information S1

Marquès, E. , & Messier, K. P. (2025). Improved high resolution heat exposure assessment with personal weather stations and spatiotemporal Bayesian models. GeoHealth, 9, e2025GH001451. 10.1029/2025GH001451

Data Availability Statement

${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$ rasters on Philadelphia—NYC (July 2024 and January 2021), Phoenix (July 2023) and the Triangle (July 2023) are archived on the Chemical Effects in Biological Systems database (Marques & Messier, 2025a). Additional data generated with our approach is available on the top largest US Urban Census areas, covering different climatic events (heatwave, blizzard, typical weather) and seasons. The ${\mathrm{T}2\mathrm{M}}_{\text{BHM}}$ rasters are stored in an open‐access versioned repository in the CAFE Climate and Health Research Coordinating Center Collection of the Harvard Dataverse (Marques & Messier, 2025b).

Software: R codes used to prepare Weather Underground data in the preliminary analysis are available in https://github.com/NIEHS/brassens/ (Marques & Messier, 2025c). R codes for the Bayesian Hierarchical Model and 2‐m air temperature rasters generated on the four urban areas can be found in https://github.com/NIEHS/samba/ (Marques & Messier, 2025e). R codes for the gridded products comparison are shared in https://github.com/NIEHS/mercury/ (Marques & Messier, 2025d).