Comparing Approximated Heat Stress Measures Across the United States

Abstract

Climate change is escalating the threat of heat stress to global public health, with the majority of humans today facing increasingly severe and prolonged heat waves. Accurate weather data reflecting the complexity of measuring heat stress is crucial for reducing the impact of extreme heat on health worldwide. Previous studies have employed Heat Index (HI) and Wet Bulb Globe Temperature (WBGT) metrics to understand extreme heat exposure, forming the basis for heat stress guidelines. However, systematic comparisons of meteorological and climate data sets used for these metrics and the related parameters, like air temperature, humidity, wind speed, and solar radiation crucial for human thermoregulation, are lacking. We compared three heat measures (HI_max, WBGT_Bernard, and WBGT_Liljegren) approximated from gridded weather data sets (ERA5‐Land, PRISM, Daymet) with ground‐based data, revealing strong agreement from HI and WBGT_Bernard (R ² 0.76–0.95, RMSE 1.69–6.64°C). Discrepancies varied by Köppen‐Geiger climates (e.g., Adjusted R ² HI_max 0.88–0.95, WBGT_Bernard 0.79–0.97, and WBGT_Liljegren 0.80–0.96), and metrological input variables (Adjusted R ² T _max 0.86–0.94, T _min 0.91–0.94, Wind 0.33, Solar_max 0.38, Solar_avg 0.38, relative humidity 0.51–0.74). Gridded data sets can offer reliable heat exposure assessment, but further research and local networks are vital to reduce measurement errors to fully enhance our understanding of how heat stress measures link to health outcomes.

Key Points

• Compared heat stress measures using gridded data sets and in situ data from 17 institutions across 42 states in the contiguous US

• Observed variations in heat measures and weather variables align with Köppen‐Geiger climate classifications

• Installing more Wet Bulb Globe Temperature‐measuring stations in diverse microclimates is key to better heat exposure prevention strategies

1. Introduction

Exposure to extreme heat events is a significant burden on human physiological and mental health and livelihoods in many parts of the world (M. L. Bell et al., 2008; Burke et al., 2018; Heo & Bell, 2019; Parks et al., 2020). According to the Centers for Disease Control and Prevention, an average of 685 people died each year between May and September due to underlying and contributing causes of extreme heat from 1999 to 2009. This death toll is the highest compared to fatalities caused by other extreme weather events, such as tornadoes, in the United States (United States Environmental Protection Agency, 2020). Extreme heat also negatively impacts economic output, from lost labor productivity (Zhang & Shindell, 2021) to damage to infrastructure (J. E. Bell et al., 2018; National Centers for Environmental Information, 2017; Underwood et al., 2017). Understanding extreme heat dynamics will be increasingly important to policymakers as extreme heat events increase in frequency and intensity due to climate change (U.S. Global Change Research Program, 2023).

Epidemiological studies typically have applied dry‐bulb temperature (T _db, e.g., ambient air temperature measured in the shade) as a daily measure of heat exposure (Baldwin et al., 2023; Parks et al., 2023). However, solar radiation, wind speed, pressure, clothing, and metabolic rate also determine heat stress and health impacts (Adams et al., 2022; Bernard & Iheanacho, 2015; Heo et al., 2019). More comprehensive metrics such as Wet Bulb Globe Temperature (WBGT) (Yaglou & Minaed, 1957), which accounts for temperature humidity, solar radiation, and wind speed (Sousa et al., 2022) and Heat Index (HI) (Steadman, 1979), which is a combination of relative humidity (RH) and ambient air temperature, are increasingly used to study heat stress and exposure (Heo & Bell, 2019; Tuholske et al., 2021). These measures better describe factors influencing human thermoregulation and the physiologic impact of heat than air temperature alone.

Moreover, these measures are considered critical information since an increasing number of public health studies and government regulatory bodies use them to measure heat stress. For example, The United States Occupational Safety and Health Administration also developed guidelines for outdoor workers based on HI. National Institute for Occupational Safety and Health guidelines for outdoor workers are based on WBGT and metabolic rate. Moreover, Grundstein and Cooper (2018) also proposed regional WBGT thresholds and guidelines, considering individuals' heat tolerance, which refers to their ability to withstand and adapt to heat stress. However, despite efforts to establish policies and guidelines, heat tolerance varies among individuals and is influenced by various factors such as age, fitness level, acclimatization, hydration status, and overall health (Gardner et al., 2016).

The US National Weather Service (NWS) provides HI information to implement these guidelines according to the weather information. Additionally, in recent years, the NWS began to provide forecast WBGT information which is developed based on the National Digital Forecast Database (National Weather Service Headquarters, 2022a, 2022b). However, only a few weather stations are equipped with a black‐globe thermometer, which is critical to accurately gathering WBGT, and it is thus challenging to provide observed WBGT information for most humans worldwide (Rennie et al., 2021; Uejio et al., 2018).

To overcome the limitations of available in situ station data, researchers have developed various gridded weather data and reanalysis products, as well as several methods to calculate heat stress measures with these products (Bernard & Iheanacho, 2015; Brimicombe et al., 2023; Dimiceli et al., 2011; Liljegren et al., 2008; Spangler & Wellenius, 2021; Stull, 2011; Yaglou & Minaed, 1957). Among the various estimation methods for WBGT, the method proposed by Liliegren (WBGT_Liljegren) has been considered the most robust under outdoor conditions (Bernard & Iheanacho, 2015; Kong & Huber, 2022; Lemke et al., 2019; Patel et al., 2013). HI, calculated with air temperature and RH (Steadman, 1979), is relatively simple to estimate. Therefore, HI is widely applied in epidemiological light winds (Rothfusz, 1990). In other words, HI is limited in utilization for heat exposure guidelines developed based on metabolic rate. Bernard and Iheanacho (2015) suggested a simplified method to estimate WBGT by establishing a quadratic transformation between HI and WBGT_Liljegren that also assumes fixed windspeeds (0.5 m/s) and shade.

Although scholars have introduced several approximation methods for heat measures from gridded weather data, daily RH, wind speed, solar radiation, WBGT_Bernard, WBGT_Liljegren, and HI approximations have not been quantitatively compared (Spangler et al., 2019). Gridded weather data showed climate‐specific performance differences of approximation due to spatial resolutions and algorithms (Kong & Huber, 2022). Further, numerous studies examined and described thermal comfort with Köppen‐Geiger's climatic classification, which developed based on seasonal precipitation and temperature patterns (Djamila & Yong, 2016; Mishra & Ramgopal, 2015). While previous literature has provided evidence of the potential impact of different climates on certain biases (Liljegren et al., 2008), there remains a significant knowledge gap regarding the accuracy of these approximations in various climate change settings (Kong & Huber, 2022).

We build upon previous efforts to compare and validate heat metrics across gridded weather and climate data sets with in situ observations (Ahn et al., 2022). Our aim is to use three commonly used gridded weather data sets in epidemiological studies to conduct an intercomparison of multiple metrics HI_max, WBGT_Bernard,WBGT_Liljegren) and weather variables according to the Köppen‐Geiger climate (Beck et al., 2018). To achieve our goal, we will address the following questions: (a) To what extent do gridded climate data sets accurately estimate RH, wind speed, solar radiation, WBGT_Bernard, WBGT_Liljegren, and HI. (b) Which climatic zones have the strongest/weakest association with gridded weather data with in situ data in the contiguous United States (CONUS) which has 26 climate categories.

2. Methodology

2.1. In Situ (Station) Weather Data for Observed Heat Measures

We collected hourly air temperature, RH, solar radiation, and wind speed data from April to October 2018 and 2019 from 924 stations operated by 17 institutions (Colorado State University, 2020; Cooperative Agriculture Weather Network, 2020; High Plains Regional Climate Center (HPRCC), 2020; Illinois State, 2019; Kansas Mesonet, 2017; Michigan State University, 2020; Missouri Mesonet, 2020; New Mexico State University, 2020; North Carolina State University, 2020; North Dakota Agriculture Weather Network Center, 2020; South Alabama, 2020; United States Department of Agriculture, 2020; University of Arizona, 2020; University of Florida, 2020; Washington State University, 2020) (Figure A1). Various studies found that the precision of gridded historical weather data differs across various regional climate zones (Ahn et al., 2022; Behnke et al., 2016). Therefore, we stratified analyses of agreement between data sets by Köppen‐Geiger climate categories to understand agreement by climate zone. We regrouped Köppen‐Geiger climate categories into six categories arid desert (BWh, BWk), arid steppe (BSh, BSk), cold dry (Dsa, Dsb, Dwa, Dwb), cold no dry (Dfa, Dfb, Dfc), temperate (Cfa, Cfb, Csa, Csb), and tropical (Af, Am, Aw). The arid desert climate had 103 stations (11%), arid steppe had 197 (21%) stations, cold dry had 34 stations (4%), cold no dry had 311 stations (34), the temperate climate had 262 stations (28), and tropical climate had 17 stations (2%) (Table A1).

We derived auxiliary climatic variables needed for the estimation of HI and WBGT as described in Table A3. Table 1 describes user‐derived variables from the meteorological data sets. Several stations only provided 10‐m wind speed and RH. Therefore, we applied a logarithmic wind profile to approximate 2‐m wind speed profiles (Fleagle & Businger, 1981). Considering most stations were in agricultural fields, 0.1 m, which indicates low crops and occasional obstacles, was applied as the roughness length (Z ₀). We converted dew point temperature (T _d ) from RH and air temperature with the R package “weathermetrics” (Brooke Anderson et al., 2013). Finally, we applied statistical quality control (QC), identifying implausible measurements for the station data (Grassmann et al., 2018; Napoly et al., 2018). This process identified hourly WBGT or HI outliers with z‐scores within the upper or lower 0.5% of all hourly WBGT or HI data across the study period. If a station missed more than 20% of study months, the stations were considered erroneous and eliminated from the study (Napoly et al., 2018).

Table 1.

Overview of the Meteorological Data Sets and User‐Derived Variables

	Station data	ERA5	PRISM	Daymet
Meteorological variables used
Temporal unit	Hourly	Hourly	Daily	Daily
T	O	O
T max			O	O
T min			O	O
T mean			O
RH	O
Solaravg		O		O
Solarmax	O	O
10 m U wind component		O
10 m V wind component		O
Wind speed	O
T d		O
VPDmin			O
Daily level user‐derived variables
Temporal unit	Daily	Daily	Daily	Daily
T mean				O
T d	O
RHmin		O	O	O
2 m windmin	O	O
HImax	O	O	O	O
Maximum WBGTBernard	O	O	O	O
Maximum WBGTLiljegren	O	O	O	O

2.2. Gridded Weather Data for Estimated Heat Measures

2.2.1. European Centre for Medium‐Range Weather Forecasts (ERA5‐Land)

ERA5‐Land data provides hourly data sets from 1950 to the present with a 9 km spatial resolution (European Centre for Medium‐Range Weather Forecasts, 2021). The ECMRWF developed ERA5‐Land based on satellite‐observational data with advanced forecast modeling to produce a global reanalysis of weather data (ECMWF, 2018). ERA5‐Land is an improved spatial version that has finer spatial resolution compared to ERA5 (30 km). This enhancement is achieved by applying the land surface hydrology (HTESSEL) model (version Cy45r1 of the IFS) using high‐resolution atmospheric meteorological data from ERA5. We downloaded hourly ERA5‐Land data for downward solar radiation, air temperature, dew point temperature, and 10‐m U and V wind components via the “cdsapi” package in Python 3.7. We then calculated RH with dewpoint temperature (T _d ) and air temperature with the R package “weathermetrics.” For wind speed, we first computed a 10‐m wind speed from 10‐m U and V components (Table A3). Then we converted the wind from 10‐m to 2‐m with a log wind profile (Table A3), subsequently computing WBGT_Bernard, WBGT_Liljegren, and HI hourly level and selected maximum daily value. Additionally, we calculated daily average T _d , 2‐m wind speed, solar radiation (Solar_avg), daily maximum air temperature, solar radiation (Solar_max), daily minimum RH (RH_min), and air temperature (T _min) for individual variables comparison across data sets (Table 2).

Table 2.

Linear Regression of Weather Station Observations on Gridded Climate Data Sets Overall and >21°C Average Temperatures

		ERA5				PRISM				Daymet
	Variables (unit)	R 2	Slope	Y‐int	RMSE	R 2	Slope	Y‐int	RMSE	R 2	Slope	Y‐int	RMSE
All	T max (°C)	0.93	0.97	0.81	2.17	0.86	0.89	2.75	3.2	0.94	0.95	1	1.99
	T min (°C)	0.91	0.94	−0.92	2.99	0.92	0.95	1.05	2.24	0.94	0.97	0.67	2.03
	2 m windmin (m/s)	0.33	0.56	0.19	0.93
	Solarmax (W m2)	0.38	0.09	178.64	5,607.49
	Solaravg (W m2)	0.38	0.25	30	1,232.17					0.3	1.14	−11.99	193.6
	RHmin (%)	0.74	0.89	4.45	10.03	0.57	0.77	8.62	13.06	0.51	1.07	−6.26	13.7
	HImax (°C)	0.88	0.69	4.81	5.49	0.85	0.77	4.62	3.89	0.95	0.95	0.61	1.99
	Maximum WBGTBernard (°C)	0.91	0.76	2.67	3.74	0.86	0.79	3.3	3.26	0.95	0.97	0.21	1.68
	Maximum WBGTLiljegren (°C)	0.80	0.8	−0.34	6.64	0.76	0.78	0.77	6.48	0.85	0.96	1.31	2.97
>21	T max (°C)	0.69	0.78	7	1.91	0.48	0.66	10.54	2.27	0.74	0.86	3.94	1.65
	T min (°C)	0.63	0.84	1.82	2.79	0.76	0.8	4.26	1.95	0.75	0.83	3.61	1.95
	2 m windmin (m/s)	0.31	0.45	0.19	0.87
	Solarmax (W m2)	0.19	0.06	359.24	5,948.75
	Solaravg (W m2)	0.33	0.32	−133.01	1,395.57					0.26	1.32	−91.52	197.65
	RHmin (%)	0.78	0.84	6.53	9.79	0.64	0.86	5.32	11.25	0.54	1.28	−16.76	13.87
	HImax (°C)	0.28	0.34	17.7	7.35	0.36	0.4	17.23	4.12	0.7	0.83	4.74	1.79
	Maximum WBGTBernard (°C)	0.26	0.39	12.87	4.27	0.37	0.43	12.72	2.52	0.71	0.84	3.29	1.16
	Maximum WBGTLiljegren (°C)	0.07	0.24	19.26	7.41	0.13	0.41	13.77	6.75	0.22	0.71	8.22	3.48

2.2.2. Parameter‐Elevation Relationships on Independent Slopes Model (PRISM)

The Parameter‐elevation Relationships on Independent Slopes Model (PRISM) data set from Oregon State University provides freely available high‐resolution (4 km) daily spatial gridded weather data from 1981—to the near present (Daly et al., 2015; Oregon State University, 2022). Several sources (Daly et al., 1997, 2008a, 2015) described the PRISM methodology. But in brief, PRISM is produced with a spatial‐weight regression model that utilizes landscape features, such as elevation and aspect, to predict daily meteorological conditions across the CONUS by interpolating data from a dense network of weather stations, thereby generating mean fields. We used daily maximum temperature (T _max), minimum temperature (T _min), mean dew point temperature (T _d ), minimum vapor pressure deficit (VPD_min), and maximum vapor pressure deficit (VPD_max). PRISM does not provide daily solar radiation and wind speed data. We applied the ERA5‐Land data to calculate WBGT_Liljegren. PRISM data does not include RH. Therefore, we approximated the minimum RH (RH_min) to calculate HI_max with the equation in Table A3 with the assumption that RH_min occurs at T _max (Daly et al., 2015).

2.2.3. Daily Surface Weather and Climatological Summaries (Daymet)

Daymet data provides daily weather and climatology variables calculated with ground‐based observations—the Global Historical Climatology Network Daily (GHCN‐Daily) data set—and statistical modeling techniques to produce 1‐km gridded surface data from 1980 over continental North America, Hawaii, and over Puerto Rico from 1950 (Earth NASA, 2022). The data includes daily T _max, T _min, downward solar radiation, precipitation, snow water, and day length. Daymet provides daily Solar_avg, which is an average over the daylight period of the day. To estimate maximum HI (HI_max), we calculated the daily RH_min with an assumption of T _D  = T _min all day (Spangler et al., 2022) (Table A3). We downloaded Daymet data via the R package “daymetr” (Hufkens et al., 2018). We calculated T _mean with the weighted average of minimum and maximum temperatures (Thornton et al., 2020). Since Daymet does not generate wind speed data, we applied ERA5‐Land wind speed data to calculate WBGT_Liljegren.

2.3. Calculating Heat Stress Measures (Heat Index, WBGT_Bernard, and WBGT_Liljegren)

We calculated three commonly used heat stress measures: daily maximum HI (HI_max), maximum WBGT_Bernard, and maximum WBGT_Liljegren from April to October 2018 and 2019 (Table 2). HI was calculated with T _max and RH_min according to the calculations used by the NWS (Rothfusz, 1990; Steadman, 1979). We calculated WBGT_Bernard from HI, according to the quadratic relation established by Bernard and Iheanacho (2015). Because WBGT_Bernard does not account for radiated heat and assumes a fixed wind speed (0.5 m/s), WBGT_Bernard is akin to indoor or shaded WBGT (Bernard & Iheanacho, 2015). Thus, WBGT_Bernard and WBGT_Liljegren cannot be directly compared against each other. HI_max and WBGT_Bernard were calculated with T _max and RH_min from ERA5‐Land, PRISM, and Daymet. Daily HI_max was calculated with hourly air temperature and RH and selected from hourly in situ data and ERA5‐Land. To estimate HI_max with hourly ERA5 data, we first estimated HI at each hour for a given day with hourly air temperature and RH and then selected HI_max from the hourly HI data.

We also approximated WBGT_Liljegren with the R package “HeatStress” (Casanueva et al., 2019). Liljegren's method to calculate WBGT includes air temperature, dew point temperature, wind speed, solar radiation, and surface pressure as input. This study calculated HI and WBGT and selected the maximum hourly value from the in situ data for each day. We applied maximum solar radiation (Solar_max), T _max, minimum dew point temperature, and minimum wind speed to calculate maximum WBGT_Liljegren from PRISM, and Daymet (Weatherly & Rosenbaum, 2017).

2.4. Comparison Analysis

We conducted a linear regression of daily T _max, T _min, RH_min, Solar_max, mean wind speed, HI_max, maximum WBGT_Bernard, and maximum WBGT_Liljegren. To analyze the direct and linear concordance between PRISM, ERA5‐ Land, and Daymet estimates and ground‐based meteorological observations at the same point in space, the meteorological observations from stations against the coincident, single‐pixel PRISM, ERA5‐Land, and Daymet grid cell estimates. To evaluate the alignment between the variables and measures in hot conditions, we additionally performed a linear regression analysis for each variable and measure under conditions where the average temperature exceeds 21°C considering the focus on exposure assessment within the framework of heat‐related health impacts (Spangler et al., 2019).

For the comparison analysis, we calculated the goodness of fit (adjusted R ²), slope, and intercept of the lines of best fit, as well as mean square errors (RMSE). Higher R ² values, lower RMAEs, and slopes closer to one and y‐intercepts closer to zero were considered more accurate estimations of the observed data. To suggest the best gridded and HI product for each Köppen‐Geiger climate, this study conducted the comparison analysis nationally and according to Köppen‐Geiger climate groups (Beck et al., 2018).

3. Results

After the statistical QC process, we included information 916 from the initial 924 stations in our analysis (Figure A1 and Table A2).

3.1. Individual Variables Comparison

We found that in situ data and T _max showed a strong relationship (adjusted R ² 0.86 < m < 0.94) across the data sets. T _min from the estimated data sets also showed a strong relationship with in situ (adjusted R ² 0.91–0.94). Among the data sets, Daymet showed the smallest RMSE from both T _max and T _min (T _max 1.99°C, T _min 2.03°C) and the highest R ² (T _max 0.94, T _min 0.94). ERA5‐Land's wind speed showed a relatively weak correlation (adjusted R ²: 0.33, RMSE 0.93 7%. Solar_max from ERA5‐Land data showed a low correlation with in situ data adjusted R ² was 0.38 and RMSE was 5,607.49 W m² Solar_avg from ERA5‐Land also showed a weak relationship with in situ data adjusted R ² was 0.38 and RMSE was 1,232.17 W m². Solar_avg from Daymet data showed even weaker, which showed adjusted R ² 0.30 and 193.6 W m². ERA5‐Land's RH_min showed a significant relationship with station data adjusted R ² was 0.74 and RMSE was 10.03%. PRISM's RH_min adjusted R ² was 0.57, and RMSE was 13.06. Daymet's RH_min showed the weakest relationship with the station data, which adjusted R ² was 0.51 RMSE 13.

Regression analysis between station data and estimated data sets showed a significant relationship for ${\text{HI}}_{\min }$, ${\text{WBGT}}_{\text{Bernard}}$, and ${\text{WBGT}}_{\text{Liljegren}}$. The adjusted R ² of ERA5‐Land's ${\text{HI}}_{\max }$ was 0.80 and RMSE was 6.64°C. PRISM's adjusted R ² was 0.85, and RMSE was 3.89°C. Daymet showed the strongest correlation with station data (0.95 and RMSE 1.99°C). The relationship between ERA5‐Land, PRISM, and Daymet and station data's ${\text{WBGT}}_{\text{Bernard}}$ also showed a strong relationship (adjusted R ²: 0.91, RMSE: 3.74°C, adjusted R ²: 0.86, RMSE: 3.26°C, adjusted R ²: 0.95, RMSE: 1.99°C), ${\text{WBGT}}_{\text{Liljegren}}$ (adjusted R ²: 0.80, RMSE: 6.64°C, adjusted R ²: 0.76, RMSE: 6.48°C, adjusted R ²: 0.85, RMSE: 2.97°C) respectively (Table 2).

In the category of temperatures exceeding 21°C, T _max and T _min exhibited varied degrees of correlation across the data sets. For instance, T _max showed a moderate to high correlation with ERA5‐Land (R ²: 0.7, RMSE: 1.91°C) and Daymet (R ²: 0.74, RMSE: T _min correlates strongly with PRISM (R ²: 0.76, RMSE: 1.95°C) and Daymet (R ²: 0.75, RMSE: 1.95°C). Wind_min, Solar_max, Solar_avg, and RH_min revealed mixed results with some data sets not providing sufficient data for comparison. For example, ERA5‐Land's Solar_avg showed an R ² of 0.38 and a high RMSE of 1,232.17 W m², indicating a less strong relationship.

Furthermore, the HI_max and WBGT indices, such as Bernard and Liljegren, displayed significant correlations. For instance, HI_max with ERA5‐Land shows an R ² of 0.88 and an RMSE of 5.49°C, while PRISM shows an R ² of 0.85 and an RMSE of 3.89°C. The WBGT Bernard model also presents strong relationships across the data sets, with Daymet showing an R ² of 0.95 and the lowest RMSE of 1.99°C.

3.2. Comparing Heat Measures According to the Köppen‐Geiger Climate Category

Figures 1a–1f illustrate the relationship between in situ data and derived values from the gridded data according to the Köppen‐Geiger climate. Figures 1a, 1d, and 1g show the regression results of HI. Adjusted R ² ranged from 0.46 to 0.95. Similar results were shown with ERA5‐Land, PRISM, and Daymet data. From all data sets, tropical climate showed the lowest adjusted R ². Meanwhile, cold and no dry climate in ERA5‐Land (0.90), Arid Desert climate (0.91) in PRISM, and cold dry climate (0.95) in Daymet data showed the highest R ².

Figure 1.

Correlation between heat matrices according to Köppen‐Geiger climate.

Figures 1b, 1e, and 1h exhibit the regression results of WBGT_Bernard. The results show that R ² was from 0.56 to 0.93 with ERA5‐Land data, 0.56–0.93 with PRISM data, 0.46–0.91 with Daymet data. From all estimated data, the tropical climate showed the lowest RMSE. The cold and not dry climate in ERA5‐Land (0.92), arid desert climate (0.91) in PRISM, cold dry climate (0.95 in both climates) in Daymet data showed the highest R ².

Figures 1c, 1f, and 1i describe the regression results of WBGT_Liljegren. ERA5‐Land data also showed was 0.34 (ERA 5) in the tropical climate. A week to strong relationship in most climates (0.37–0.87), and cold‐dry climates showed the highest R ² (0.94). PRISM data showed a moderate relationship from all climates. R ² ranged from 0.37 to 0.87. Cold and dry, and arid desert climates (0.87) showed the strongest relationship. Daymet R ² showed strong relationships from most of the Köppen‐Geiger climates, which ranged from 0.44 to 0.95. Cold‐dry climates showed the highest R ² (0.96). On the other hand, R ².

RMSE of HI varied from 1.42 to 9.54°C. The arid desert climate exhibited the lowest RMSE in ERA5‐Land (2.80°C), while the highest RMSE was observed in the tropical climate (9.54°C). PRISM data revealed that the lowest RMSE (1.27°C) was discovered in the arid tropical climate, while the highest RMSE (2.8°C) was observed in the arid steppe climate. Daymet data also indicated that the tropical climate had the lowest RMSE (1.75°C), whereas the arid desert climate had the highest RMSE (2.41°C). Overall, Daymet showed the smallest variance in RMSE compared to the other data sets (Figures 2a, 2d, and 2g).

Figure 2.

RMSE of heat matrices according to Köppen‐Geiger climate.

The RMSE of WBGT_Bernard ranged from 1.19 to 5.35°C. The arid desert climates exhibited the lowest RMSE (2.08°C) in ERA5‐Land, while the tropical climate had the highest RMSE (5.35°C) in ERA5‐Land data. Similarly, PRISM data showed that arid desert climates had the lowest RMSE of 1.19°C, while tropical climates had the highest RMSE of 3.04°C. However, Daymet data provided somewhat contradictory results compared to ERA5‐Land. The lowest RMSE was found in the tropical climate (1.20°C), while the highest was observed in the arid steppe climate (2.02°C) (Figures 2b, 2e, and 2h).

WBGT_Liljegren exhibited a range of RMSE from 1.63 to 8.18°C across the data sets. In ERA5‐Land data, the lowest RMSE (5.13°C) was observed in cold no dry climate, while the highest RMSE (8.18°C) was found in arid desert climates. From the PRISM data, the cold no dry climate had the lowest RMSE (4.62°C), and the arid steppe climate had the highest RMSE (6.84°C). Daymet data showed the lowest RMSE (1.63°C) in the cold dry climate and the highest RMSE (2.98°C) in the cold no dry (Figures 2c, 2f, and 2i). Overall, Daymet data demonstrated the smallest variance in RMSE compared to the other data sets. Additionally, most heat indices showed the highest RMSE in the Tropical climate based on ERA5‐Land and PRISM data. Daymet data exhibited similar results across the Köppen‐Geiger climate (Figures A2 and A3).

4. Discussion

We compared three heat stress measures (HI_max, WBGT_Bernard, and WBGT_Liljegren) from PRISM, Daymet, and ERA5‐Land data with in situ observations for the CONUS. All heat stress measures were highly correlated with observation data (overall temperature R ² ranged from 0.85 to 0.95) across the three gridded weather data—however, we found that the strength of correlation varied considerably by climate zone in the CONUS and the correlation with ground observations diminish slightly in scenarios where temperatures exceed 21°C across the three gridded weather data.

The correlations (R ² values) for both T _max and T _min are generally higher for overall temperatures compared to when temperatures exceed 21°C across all three data sets (ERA5‐Land, PRISM, Daymet). For all variables under study, R ² and RMSE values are generally lower than temperatures of >21°C. Among the gridded data sets, Daymet consistently shows the strongest correlation and the lowest RMSE in both overall and >21°C temperatures, indicating its higher accuracy and reliability in capturing temperature variations compared to ERA5‐Land and PRISM. Our analysis indicates that the approach of using T _max, RH_min, Solar_max, and Wind_min to estimate daily maximum WBGT_Liljegren may be less effective at higher temperatures. In other words, relying on these variables could oversimplify the capture of detailed and comprehensive heat stress metrics, potentially reducing accuracy. However, it's noteworthy that the WBGT_Bernard and HI measures in the Daymet data set maintained high accuracy for temperatures exceeding 21°C, outperforming other data sets in this regard.

The complex interaction between the input variables used to calculate HI and WBGT may offer an explanation for the observed discrepancies. ERA5‐Land and PRISM data showed the lowest RMESs and higher R ² in tropical climates among the estimated data from all heat measurements. Another possible source of the differences could be the model's algorithms considering cloudiness, sea breeze dynamics, and coastal approximation (Y. Chen et al., 2018; Colle, 2003; Daly et al., 2008b; Perry & Hollis, 2005).

We found estimations of solar radiation were overall poor. According to previous studies, ERA5 solar radiation data showed a better estimation in desert areas due to a higher proportion of days with clear sky conditions in the desert (Andrews et al., 2012; Yang & Bright, 2020). On the other hand, Daymet estimation showed better performance in tropical climates than in other climates. Slater (2016) applied hourly solar radiation data gathered from non‐profit organizations in North America and found that Daymet solar radiation tended to have bigger differences in arid deserts, arid steppe, and temperate climates (e.g., California, Florida, Texas, Colorado, New Mexico, and Wyoming State).

Among the gridded weather data, Daymet showed the smallest variance of R ² and RMSE in different Köppen‐Geiger climates. ERA5‐Land showed higher correlations and smaller RMSE from RH than Daymet. However, Daymet showed a stronger correlation of temperature than PRISM and ERA5‐Land, which likely caused higher R ² and RMSE of HI and WBGT. This finding contradicts previous studies, which have suggested that PRISM performed better than Daymet (Daly et al., 2015; Spangler et al., 2019). A possible explanation might be that the recent update of Daymet data reduced inconsistencies and bias and improved accuracy and precision (Thornton et al., 2021). Additionally, different data processing techniques applied to this study compared to the previous studies might have resulted in different outcomes. Moreover, it is challenging to explain heat measures' relationship with the specific variable analysis outcomes directly since the effect of RH on HI is nonlinear according to Ta increase, and WBGT is the weighted sum of natural wet bulb temperature, black globe temperature, and air temperature (Chakraborty et al., 2022).

Overall RMSE ranged from 1.42 to 9.54°C, 1.19 to 5.35°C, and 1.63 to 9.79°C respectively for HI, WBGT_Bernard, and WBGT_Liljegren across the data sets. The tropical climate, characterized by high air temperature and humidity, which necessitates more complex heat stress measures, exhibited the smallest R ² and largest RMSE. For instance, ERA5‐Land overall showed robust results except for the tropical climate. Since many occupational heat exposure guidelines are formulated according to the HI or WBGT, heat measures are critical information for activity/work and rest decisions (National Institute for Occupational Safety and Health [NIOSH], 2016; The National Oceanic and Atmospheric Administration, 2023). A difference as small as 2–3°C in WBGT and HI can have a significant impact on recommended activity modifications, potentially leading to drastically different health outcomes. This is particularly crucial when strict thresholds are applied in work/rest schedule guidelines. Similarly, a 5–10°C variation in HI can also mislead the application of these guidelines, with similar risks to health. Further work is required to establish fine‐scale data that considers local variability caused by complex topography, land use, and building heterogeneity to understand local microclimates further (S. Carter et al., 2018; H. Chen et al., 2010; Klinges et al., 2022; Oke, 1982; Tripp et al., 2020). Some studies suggested a fine spatial scale (10–25 m) is necessary to capture mountain terrain and ocean effects (Dadic et al., 2010; Du Vivier & Cassano, 2013; Gultepe, 2015; Liston, 2004; Mott et al., 2008).

Of the individual weather variables (T _max, T _min, RH_min, wind speed, and solar radiation), T _max and T _min showed the highest R ² and lowest RMSE. Wind speed, solar radiation, and RH showed relatively lower R ² and higher RMSE. Lower correlations of solar radiation, wind speed, and RH between gridded weather data and station data are consistent with other research which compared station data with gridded weather data (Bonshoms et al., 2022; A. W. Carter et al., 2020; Jared Rennie et al., 2021; Rupp et al., 2022; Slater, 2016; Spangler et al., 2022).

Spangler et al. (2019) compared Daymet data with US Climate Reference Network (USCRN) data and showed that RH_min showed a relatively low R ² (0.52). Another study that compared Automated Surface Observing Systems and USCRAN data showed lower correlation coefficients in wind speed (coefficient 0.4) (Rennie et al., 2021). The mean of the absolute error was eight percent different from the comparison analysis with hourly solar radiation data from the National Renewable Energy Laboratory database and several gridded weather data sets, including Daymet and PRISM (Rupp et al., 2022). Bonshoms et al. (2022) validated ERA5‐Land RH data with Automatic Weather Stations data from eight stations in four study areas on a glacier and discovered that the R ² ranged from 0.3 to 0.6.

The discrepancies between station data and gridded weather data have been discussed in the broader literature. Comparison of the findings with those of other studies confirms that one of the major causes was geographical features such as elevation, topography, proximation to coastlines, cloud cover, and land use (Barry, 2008; Daly et al., 2008b; Du Vivier & Cassano, 2013; Gultepe, 2015; Gultepe et al., 2014; Karger et al., 2021; Kilpelainen et al., 2011; Monson & Baldocchi, 2014; Reeve & Kolstad, 2011; Thornton et al., 1997). Previous studies found complex terrain creates local climates that alter solar radiation reflection and wind flows (Hilliker et al., 2010; Slater, 2016; Yang & Bright, 2020; Zardi & Whiteman, 2013). Tscholl et al. (2022) applied cloud cover correction and included solar radiation to estimate 100m spatial resolution air temperature, and the cloud correction model reduced the mean absolute error of estimated air temperature by 23% compared with the clear‐sky model.

Moreover, land use and land cover were suggested as other factors causing the differences. Land use and land cover create different interactions between the biosphere and atmosphere via heat, water, and energy fluxes. Due to these phenomena, adjacent land can have different local climates, and it has been challenging to consider in the model (Albergel et al., 2018; Page et al., 2018; Zardi & Whiteman, 2013). Chakraborty et al. (2022) examined urban‐rural differences in HI and found that urban form alters RH and heat stress in Europe. Vegetation cover in urban areas is often recommended to reduce air temperature and heat exposure. However, vegetation cover does not necessarily correspond to a decrease in air temperature, and vegetation evaporation would increase RH, leading to an increase in HI (Chakraborty et al., 2022). Additionally, the differences might be caused by user‐derived variables such as RH, T _mean, and T _d . This study derived RH with air, dew point temperatures, and vapor‐pressure deficits from the three gridded weather data sets this study applied in this study. For example, this study assumed that T _d is equal to T _min throughout the day to calculate RH_min from PRISM, and RH_min occurs at T _max from Daymet to calculate RH_min (Thornton et al., 1997).

Our study does have limitations. First is the geographic distribution of weather stations. Only 17 stations (2%) are in the tropical climate, and no stations were from cold, dry summer and cold summer climates. Moreover, higher discrepancies in tropical climate might be caused by the methodology used to calculate daily maximum heat measures. While observation and ERA5‐Land RH_min, T _min, and T _max from Daymet and PRISM. Consequently, we advise readers to interpret these results with caution. Further investigation should be conducted to consider various climates more accurately. This study also applied wind speed and solar radiation data from ERA5‐Land for estimating heat measures from PRISM and Daymet. We acknowledge that employing data with varying spatial resolutions could lead to certain implications in our results.

Additionally, we approximated several variables and heat measures with several assumptions. Installing additional stations that directly measure WBGT at diverse microclimates (rural, suburban, and urban regions) to enhance field data collection in diverse microclimates will be essential to preventive measures against heat exposure. This will also enable us to investigate further the relationship between estimating heat measures across microclimates within different climate zones. More specifically, in our calculations of the HI_max, we used the RH_min and T _max. This approach assumes that RH tends to decrease as temperature increases. It's important to note that the validity of the HI calculation is applicable primarily in shaded conditions.

Finally, it is important to note that at any location, T _a , RH, radiation, and wind speed might not align in their diurnal patterns, potentially impacting our estimates of HI_max and WBGT. For instance, Justine et al. (2023) observed that the peak wet bulb temperature often occurs several hours after the peak dry bulb temperature. In tropical areas near coasts or rivers, where temperature (T) variation throughout the day is minimal, the afternoon influence of the water body can result in higher daily HI or WBGT_max compared to when the T _max happens. The complexity of these factors underscores the need for more research to accurately assess how the diurnal cycle influences the peak hour of heat stress (Justine et al., 2023; Rusticucci & Vargas, 1995). Given the complexity of the inputs, assessing the impacts of the diurnal cycle on estimating the hour of maximum heat stress will require further research.

5. Conclusion

We examined three heat measures with Daymet, PRISM, and ERA5‐Land. The heat measures, which were calculated from Daymet, PRISM, and ERA5‐Land and station data, showed strong relationships (R ² 0.82–0.96, RMSE 1.69–5.37°C). However, the discrepancies varied according to Köppen‐Geiger climates and warmer conditions (average temperature >21°C). We need to conduct further work to gather more accurate and higher‐resolution weather information over space and time, which will help reduce bias and uncertainties. We suggested installing more stations to gather WBGT information and develop gridded weather data, including solar radiation and wind speed. Ultimately, this will lead to a more robust understanding between the links between humid heat and health outcomes.

Conflict of Interest

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

Appendix A.

Figure A1 describes the location of stations and grouped Köppen‐Geiger climate categories used for this study. Each color on the map corresponds to a different Köppen‐Geiger climate classification, while the gray dots indicate the locations of stations where we collected observational data.

Figure A1.

Köppen‐Geiger and station locations.

Figure A2 illustrates the correlation between the observed data and the data products (ERA5, Daymet, and PRISM) for the variables utilized in this study, categorized according to the Köppen‐Geiger climate classification.

Figure A2.

Linear regression of weather station observations on gridded climate data sets according to Köppen‐Geiger climates categories.

Table A1 represents the number of stations according to Köppen‐Geiger climate categories.

Table A1.

Number of Stations According to Köppen‐Geiger Climate Categories

Köppen‐Geiger climate groups	Köppen‐Geiger climate categories	Number of stations (%)	Köppen‐Geiger climate groups summary
Arid desert	BWh	20 (2)	103 (11)
Arid desert	BWk	83 (9)
Arid steppe	BSh	3 (0)	197 (21)
Arid steppe	BSk	194 (21)
Cold dry	Dsa	1 (0)	34 (4)
Cold dry	Dsb	14 (2)
Cold dry	Dwa	4 (0)
Cold dry	Dwb	15 (2)
Cold no dry	Dfa	157 (17)	311 (34)
Cold no dry	Dfb	145 (16)
Cold no dry	Dfc	9 (1)
Temperate	Cfa	233 (25)	262 (28)
Temperate	Cfb	6 (1)
Temperate	Csa	1 (0)
Temperate	Csb	22 (2)
Tropical	Af	4 (0)	17 (2)
Tropical	Am	8 (1)
Tropical	Aw	5 (1)

Table A2 shows the number of stations included during the study period (April to October 2018–2019) after the quality control process.

Table A2.

Number of Stations Included for the Analysis After Quality

Year	Month	Number of stations
2018	4	696
2018	5	712
2018	6	559
2018	7	559
2018	8	558
2018	9	562
2018	10	479
2019	4	761
2019	5	554
2019	6	558
2019	7	561
2019	8	547
2019	9	524
2019	10	459

Table A3 details the formulas employed for estimating heat stress metrics. The WBGT_Liljegren calculation was performed using the “HeatStress” package in R which was developed based on Liljegren et al. (2008) study. The package includes the “esat” function which computes vapor pressure using air temperature and relative humidity, applying the coefficient recommended by (Sonntag, 1990). Additionally, the package includes an algorithm for estimating solar irradiation, taking into account solar radiation, the Earth‐Sun distance, and the zenith angle. This algorithm was developed by analyzing a full year of direct and diffuse solar irradiance data, gathered by the Atmospheric Radiation Measurement Program at their facility in north‐central Oklahoma (Ackerman & Stokes, 2003). For accurate WBGT_Liljegren calculations using the HeatStress package, users must input variables such as time, latitude, and longitude to determine the zenith angle.

Table A3.

Equations for User‐Derived Meteorological Variables

Variable	Data set	Expression	Unit	Note
T d	In situ	$T_d=T-(\frac{100-\text{RH}}{5}$)	T, T d in °C RH in %
		• T d  = Dew point temperature
		• T = air temperature
		• RH = relative humidity
2 m wind speed	ERA5, in situ	V ≈ V ref *$\ln \frac{Z\ast Z_0}{Z_{\text{ref}}\ast Z_0}$	m/s
		• V = velocity to be calculated at height z
		• Z = height above ground level for velocity v
		• V ref = known velocity at height z ref
		• Z ref = reference height where v ref is known
		• Z 0 = roughness length in the current wind direction
Hourly solar radiation (W m2)	ERA5	$\frac{\text{Hourly}\text{solar}\text{radiation}}{3600\left[\mathrm{s}\right]}$	Hourly solar. Radiation in J m2, s represents second
RHmin (%)	ERA	$100·\frac{e^{\left(\frac{17.625·T_D}{243.04˚C+T_D}\right)}}{e^{\left(\frac{17.625·T}{243.04˚C+T}\right)}}$	T, T d in °C	Minimum based on hourly values
		• T d  = Dew point temperature
		• T = air temperature
	PRISM	$100·\frac{\left[610.94\text{Pa}·e^{\left(\frac{17.625·T_{\max }}{243.04˚C+T_{\max }}\right)}\right]-\text{VP}{\mathrm{D}}_{\max }}{610.94\text{Pa}·e^{\left(\frac{17.625·T_{\max }}{243.04˚C+T_{\max }}\right)}}$	T max in °C VPDmax in Pa	Assumes RHmin occurs at T max
		• VPDmax = maximum vapor‐pressure deficits (VPD)
	Daymet	$100·\frac{e^{\left(\frac{17.269·T_{\min }}{237.3˚C+T_{\min }}\right)}}{e^{\left(\frac{17.269·T_{\max }}{237.3˚C+T_{\max }}\right)}}$	T min, T max in °C	Assumes T D  = T min all day
T mean	PRISM	0.606 ⋅ T max+0.394 ⋅ T min	T max in °C
HImax	ERA5, PRISM, Daymet, in situ	0.5 * {Ta + 61.0 + [(Ta − 68.0)*1.2] + (RH *0.094)}	T a in °FRH in %, T max and RHmin were applied instead for Ta and RH for ERA5, PRISM, and Daymet
		If this heat index value is 80°F or higher, the full equation with adjustments should be applied.
		−42.379 + 2.04901523* Ta + 10.14333127* RH − 0.22475541*Ta* RH − 0.00683783* Ta2 − 0.05481717*RH2 + 0.00122874*Ta2* RH + 0.00085282* Ta *RH2 − 0.00000199*Ta2 *RH2 − ADJ
		*Condition 1: RH < 13% and T a is between 80 and 112°F
		• ADJ1 = −[(13 − RH)/4]∗ $\sqrt{((17-T_a-95)/17)}$
		* Condition 2: RH > 85% and T a is between 80 and 87°F
		ADJ2 = ((RH − 85)/10)*((87 − T a )/5)
		T a  = Ambient Dry Bulb Temperature
		• RH = relative humidity
WBGTBernard	ERA5, PRISM, Daymet, in situ	−0.0034*HI*2 + 0.96*HI − 34	HI in °F
		• HI = Heat Index
WBGTLiljegren	ERA5, PRISM, Daymet, in situ	0.7∗Tw + 0.2∗Tg + 0.1*Ta
		• T w : Wet‐Bulb Temperature
		• T g : Globe Temperature
		• T a : Dry Bulb Temperature
		WS = $\sqrt{\left(uw{d}^2+vw{d}^2\right)}$
		• WS: wind speed
		• uwd: 10 m U wind component
		• vwd: 10 m V wind component
		Vapor pressure = a*exp ($\frac{\left(\frac{b\ast T_{\text{air}}}{c+T_{\text{air}}}\right)}{100}$)
		a = 611.2, b = 17.62, and c = 243.12
		$F_{\text{dir}}=\left\{\begin{array}{c}\exp \left(3-1.34S^{\ast }-\frac{1.65}{S^{\ast }}\right)\\ 0,\theta >89.5°\end{array}\right.\theta \le 89.5°$
		F dir = solar irradiation
		$S^{\ast }=\frac{S}{S_{\max }}$
		$S_{\max }=\frac{S_0\cos \theta }{d^2}\left(\theta \le 89.5°\right)$
		S 0 = solar constant (=1,367 W/m2)
		θ = Zenithangle and d = earth‐sun direction

Figure A3.

Linear regression of weather station observations on gridded climate data sets according to Köppen‐Geiger climates categories (relative humidity without zeros).

Figure A4.

Gridded weather data and station locations across Washington areas (Daymet and PRISM data sets represent daily maximum temperatures, while the ERA5 data set illustrates the air temperature at 2 p.m. on 1 August 2018).

Figure A4 illustrates the daily maximum temperature from Daymet, PRISM, and air temperature at 2 p.m. ERA5‐Land on 1 August 2018, alongside the locations of the stations from which we collected observational data.

Ahn, Y. , Tuholske, C. , & Parks, R. M. (2024). Comparing approximated heat stress measures across the United States. GeoHealth, 8, e2023GH000923. 10.1029/2023GH000923

Data Availability Statement

ERA5‐Land (European Centre for Medium‐Range Weather Forecasts, 2021), PRISM (Oregon State University, 2022), Daymet (Earth NASA, 2022), were used for calculating estimated WBGT. The in station WBGT was calculated from the data sets that were gathered from 17 institutes (Colorado State University, 2020; Cooperative Agriculture Weather Network, 2020; Illinois State, 2019; Kansas Mesonet, 2017; Michigan State University, 2020; Missouri Mesonet, 2020; North Carolina State University, 2020; North Dakota Agriculture Weather Network Center, 2020; South Alabama, 2020; STEM, 2020; University of Arizona, 2020; University of Florida, 2020). The quality control method (Napoly et al., 2018) was applied for the in station WBGT data. Köppen‐Geiger climate classification at a 1‐km resolution for a contemporary climatology period (1980–2016) from Beck et al. (2018). Figures were made with the package “ggplot2” in R (version 4.1.0). The code for calculating HI (Tuholske, 2021) and downloading ERA5 (Parks, 2022) is available on GitHub. The storage of the data set is licensed under Harvard Dataverse (Ahn, 2022).