1. Introduction
Historic heat waves across Eurasia and North America in summer 2022 led to thousands of deaths. With global temperatures rising, similar levels of extreme heat will become more common with more frequent and intense heat waves expected in future climates (e.g., Meehl and Tebaldi 2004; Teng et al. 2016; Perkins-Kirkpatrick and Gibson 2017; Lopez et al. 2019). Extreme heat leads to cascading effects such as strain on water supplies due to increased human and agricultural consumption, stress on electrical systems, and heat-related illnesses occupying emergency medical resources (e.g., Lesk et al. 2022). Heat waves are defined by air temperature (e.g., Meehl and Tebaldi 2004; Anderson and Bell 2011; Peng et al. 2011) or indices based on temperature and humidity (e.g., Steadman 1979, 1984; Tan et al. 2007) and require some minimum temporal extent (Smith et al. 2013). While using a definition solely based on temperature is convenient, and often necessitated by data limitations, air temperature does not fully capture what can make extreme heat deadly. For example, as humidity increases, the human body is not able to effectively cool itself through sweat (Parsons 2006; Mora et al. 2017). Theoretically, if wet-bulb temperature increases above 35°C (95°F), the human body is unable to cool to a safe level (Sherwood and Huber 2010), but for many, this threshold may be much lower (Vecellio et al. 2022; Vanos et al. 2023).
However, even humid heat measures such as wet-bulb temperature or heat index do not fully capture the physiological response to extreme heat as they do not account for the wind or solar radiation, both of which can contribute to personal heat stress. In some cases, the effects of these factors can be significant and result in an incorrect estimation of heat stress if they are omitted. Several indices have been created to measure heat stress that consider a broader range of conditions with fewer assumptions (Epstein and Moran 2006; Liljegren et al. 2008; Buzan et al. 2015), and organizations such as the Occupational Safety and Health Administration (OSHA) and the U.S. Army use wet-bulb globe temperature (WBGT) (Departments of Army and Air Force 2003; OSHA 2017). WBGT is an index that factors in temperature, humidity, wind speed, and solar radiation by taking a weighted average of dry-bulb temperature, natural wet-bulb temperature, and black globe temperature. By accounting for more factors, WBGT is able to better represent heat stress in humans than other metrics that just use air temperature and humidity (e.g., Ioannou et al. 2022). However, none of these metrics account for what a person is wearing and doing.
Research on WBGT has generally focused on how well it discriminates human mortality and its trend on climate scales. This research has shown that WBGT is better at differentiating high mortality events from lower mortality events than temperature-only metrics (Hyatt et al. 2010). Further, WBGT is increasing in much of the world as global temperatures increase (Hyatt et al. 2010; Knutson and Ploshay 2016; Li et al. 2020). The number of people annually exposed to extreme WBGT above 33°C (91.4°F) has already tripled compared to preindustrial numbers (Li et al. 2020). Climate projections show that WBGT will continue to increase in the future over most regions of the globe, with average WBGTs over land exceeding 1970s record maxima by the 2030s under the RCP 8.5 scenario (Li et al. 2017).
Extreme heat often occurs over several days as heat waves. Studies such as Anderson and Bell (2011) suggest that longer, more intense heat waves, as well as the first heat wave of the year, typically have the largest effects on human mortality, as no opportunity to acclimate to such conditions has occurred. Further, mean and minimum temperature are shown to be just as important to predicting human mortality as maximum temperature (Robinson 2001; Hajat et al. 2002; Nissan et al. 2017). In some locations, such as Florida, mean and minimum air temperature, heat index, and WBGT are increasing at faster rates than the maximum of the same metrics (McAllister et al. 2022). As atmospheric variability could increase in the future (Teng et al. 2016), the frequency and/or intensity of heat waves could increase. However, as WBGT is a function of more environmental variables, the behavior could differ from the temperature-based definitions, motivating a need to understand the behavior of heat waves defined by WBGT.
In the U.S. Great Plains (USGP), a region with large gradients in environmental quantities such as temperature and humidity, our understanding of heat waves has focused on temperature-based definitions (e.g., Anderson and Bell 2011; Peng et al. 2011; Smith et al. 2013; Perkins-Kirkpatrick and Gibson 2017). Heat waves in the USGP typically occur with high pressure and clear skies with at least one heat wave on average each summer (e.g., Anderson and Bell 2011; Smith et al. 2013; Teng et al. 2013). Heat waves are often preceded 15–20 days by anomalous midlatitude planetary waves with wavenumber 5 (Teng et al. 2013). Additionally, heat waves in the USGP and midlatitudes have also been shown to be driven by latent heat release by the Southeast Asian monsoon (Lopez et al. 2019) and La Niña (Hoerling et al. 2014; Seager et al. 2014; Lopez et al. 2019).
As WBGT is better than air temperature and other common humid heat metrics in predicting human mortality, and the increased urgency in discriminating between heat mortality events, it is important to understand extreme heat events under the WBGT paradigm. This study creates a gridded climatology of WBGT from reanalysis data in the USGP calibrated by observations from the Oklahoma Mesonet and uses this climatology to define heat waves in the USGP in order to provide a basis for future work evaluating extreme heat in the USGP.
2. Data and methods
a. Oklahoma Mesonet
The Oklahoma Mesonet records 5-min observations of meteorological variables at 120 sites (https://www.mesonet.org/about/mesonet-sites) across the state of Oklahoma (Brock et al. 1995; McPherson et al. 2007). This study uses 1.5-m air temperature, 2- and 10-m wind speeds, 1.5-m dewpoint temperature, surface pressure (measured at 0.75 m), and incoming solar radiation (measured at 1.5 m) from 1998 to 2020 to calculate WBGT using the instantaneous observations at the top of every hour. The Oklahoma Mesonet data are used to validate reanalysis data as described in section 2b and verify the resulting WBGT calculations as described in section 2c.
b. ERA5
The fifth major global reanalysis produced by ECMWF (ERA5) hourly data on single levels from 1960 to 2020 are used for this study (Hersbach et al. 2018). Several recent studies have used hourly ERA5 reanalysis for calculating WBGT using various formulations (Li et al. 2020; Spangler et al. 2022; Kong and Huber 2022). To calculate WBGT, the following ERA5 variables are used: 2-m temperature, 2-m dewpoint temperature, downward shortwave solar radiation flux (solar radiation), 10-m wind speed, and surface pressure. The 2-m wind speed is extrapolated from 10-m wind speed as described in section 2c. All variables are interpolated to a 0.5° × 0.5° grid via an option in the ERA5 Application Programming Interface (API) at the time of download due to storage limitations. As the climatological analyses conducted in this study investigate large-scale patterns or are shown for a single point, the coarser spatial resolution has minimal impact on the results. While the Oklahoma Mesonet solar radiation is instantaneous, the downward shortwave solar radiation flux from ERA5 is a time average over the 1-h duration leading up to the analysis time. Due to the time averaging, the ERA5 downward shortwave solar radiation flux is valid at HH:30. To account for the timing differences, the ERA5 downward shortwave solar radiation flux is linearly interpolated to HH:00 to match the valid time of all remaining data.
c. WBGT calculation
WBGT can be measured using specialized equipment that measures wet-bulb temperature, dry-bulb temperature, and black globe temperature at 2 m above ground level. However, this equipment is expensive and not commonly placed at meteorological observing stations. As a result, several studies have derived formulations of WBGT based on standard meteorological variables (Hunter and Minyard 1999; Matthew et al. 2001; Liljegren et al. 2008; Dimiceli et al. 2011). These formulations are often able to recreate WBGT to within 1°C (1.8°F) of the instrumentation.
This study calculates WBGT from the Oklahoma Mesonet observations (section 2a) and ERA5 reanalysis (section 2b). Oklahoma Mesonet data are regridded to a 0.5° × 0.5° grid to match the ERA5 grid prior to calculating WBGT. Missing data and data that failed the Oklahoma Mesonet quality control procedure are removed prior to interpolation.
The second method used in this study to calculate WBGT, Liljegren WBGT, follows Liljegren et al. (2008) for both Tbg and Tnwb, which is calculated using Cython code obtained from Kong and Huber (2022). Unlike the Tbg of Dimiceli et al. (2011), the Tbg of Liljegren et al. (2008) is not linearized and is more computationally expensive. A full description of this method can be found in Liljegren et al. (2008) and Kong and Huber (2022). Notable differences between the results from the two methods are discussed where appropriate.
d. WBGT risk categories
WBGT is often divided into risk categories based on the human impacts and necessary precautions needed to avoid heat stress. The National Weather Service (NWS) and the Oklahoma Mesonet use the categories in Table 1, which we refer to throughout as “uniform categories.” WBGT is shown in Table 1 in °F and throughout the paper for consistency with operational users such as the NWS, the Oklahoma Mesonet, the OSHA, and the U.S. Army. As acclimation varies based on local climatology, the risks associated with a given WBGT range may vary regionally. Grundstein et al. (2015) proposed regional adjustments to these risk categories based on an extended summer [May–September (MJJAS)] 90th percentile of daily maximum WBGT, which were calculated from airport surface observation using the Liljegren et al. (2008) model for WBGT. Areas with 90th percentile of mean MJJAS < 86°F are classified as region 1, areas between 86° and 90°F are classified as region 2, and >90°F are classified as region 3, and the risk category ranges per region have been adjusted as shown in Table 2. This study considers these adjustments using regions shown in Fig. 1 which approximates the regions in Grundstein et al. (2015) while considering differences between the datasets and the WBGT calculation method used. Specifically, this study follows the methods of Grundstein et al. (2015) except that the 90th percentile of daily maximum WBGT ranges that classify each region is shifted to 4.0°F cooler for Dimiceli WBGT and 2.0°F cooler for Liljegren WBGT. These offsets are determined by finding the value that best aligns the boundaries of the regions calculated from our WBGT datasets (Fig. 1) with those presented in Grundstein et al. (2015). The risk thresholds for the Grudstein regions are shown in Table 2 and are referred to throughout the paper as “regional categories.” Note that the same risk levels are used for all WBGT datasets and thus will not offset any differences between the two datasets.
WBGT heat risk categories as defined by the Oklahoma Mesonet and the NWS and work/rest recommendations for unacclimated individuals (Oklahoma Mesonet 2016).
Map of regional categories based on Grundstein et al. (2015) as used throughout the paper, with boxes representing the northern, central, and southern USGP subdomains and locations used for point analysis from the northern, central, and southern USGP indicated by stars. (a) Dimiceli WBGT. (b) Liljegren WBGT.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
e. Heat wave definition
Three definitions for heat waves are used in this study due to the importance of maximum daytime temperatures and warm overnight minimum temperatures to human heat stress. The first definition uses daily maximum WBGT, the second uses daily minimum WBGT, and the third uses daily mean WBGT. The daily maximum, minimum, and mean WBGT are defined as the maximum, minimum, and mean of the hourly WBGT values from 0000 through 2300 UTC each day, respectively. A WBGT daily threshold is established by taking a centered 31-day period and calculating the 90th percentile over the 61-year period of record. For each definition, a heat wave is declared when the metric is at or above the threshold for two consecutive days. A heat wave is terminated when the metric is below the threshold for two consecutive days. The 2 days at the end which fail to meet the threshold are not considered part of the heat wave. However, once a heat wave begins, a single day below the threshold will not terminate the heat wave. This is done to prevent a single prolonged period of extreme heat from being counted as separate heat waves because a single day may have been just below the threshold.
f. Statistical significance
The statistical significance of trends throughout this study is calculated using two-tailed Monte Carlo resampling. The analysis is repeated 5000 times while randomly shuffling the order of the years without resampling each iteration. A trend is considered statistically significant at the 95% confidence level (α = 0.05) if it is below the 2.5th percentile or above the 97.5th percentile (α/2) of the trends calculated from the randomly sampled data.
3. Verification of WBGT
a. Verification of ERA5’s ability to recreate observations
Before the ERA5 can be used to investigate WBGT, it must first be verified that it is capable of accurately representing WBGT. Here, WBGT is calculated from the ERA5 using Dimiceli’s WBGT formulation, and the mean and standard deviation are compared to those from WBGT calculated from Oklahoma Mesonet observations, and the root-mean-square difference (RMSD) between the two WBGT datasets is calculated (shown in Figs. 2a,b for July). Values are area-averaged for all points in Oklahoma west of 97°W. The difference in the mean is between 0.5° and 1.0°F (0.3° and 0.6°C), and the absolute difference in standard deviation is typically under 0.2°F (0.1°C), which is less than 5% error. The difference in the mean is mostly explained by a difference in the temperature overnight (60% via Tnwb) and a difference in dewpoint temperature (100% via Tnwb) during the day. Note that overnight Tbg reduces to Tdb, and thus, the remaining 40% of the overnight sensitivity is split between Tbg and Tdb in proportion to their weights in Eq. (1). Finally, the RMSD is typically ≤1.8°F (1°C). As this error is smaller than the categorical ranges (Tables 1 and 2), this is sufficiently small to be certain of the results within the ±1 risk category. Further, the largest errors in the mean are overnight when temperatures are the coolest. The combination of these results suggests that WBGT has been well recreated by the ERA5 reanalysis. Other comparisons, such as that of Liljegren et al. (2008), have concluded that similar errors compared to a reference are acceptable. Other months (not shown) show similar results.
Verification of July (a),(b) ERA5 Dimiceli WBGT against Oklahoma Mesonet Dimiceli WBGT by hour showing area-averaged values and differences for the state of Oklahoma west of 97°W and (c),(d) ERA5 Dimiceli WBGT against ERA5 Liljegren WBGT by hour showing area-averaged values and differences for the state of Oklahoma. (a),(c) Mean, difference, and RMSD of WBGT and (b),(d) standard deviation of WBGT.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
b. Comparison of Dimiceli and Liljegren WBGT
As with the comparison between the ERA5 and Oklahoma Mesonet WBGT, the Dimiceli and Liljegren WBGT formulas are compared. Notably, the Liljegren formula results in lower WBGT overnight but higher WBGT during daytime hours throughout the year (as shown in Figs. 2c,d for July). Sensitivity analysis of Tnwb and Tbg shows that for near-normal temperature and dewpoint temperature at the southern USGP location, both Liljegren Tnwb and Tbg are lower overnight (when solar radiation is 0 W m−2) than Dimiceli with Tnwb accounting for about 80% of the difference. However, for near-normal conditions representing the July daytime maximum WBGT, Liljegren Tbg can be around 7°F higher than Dimiceli Tbg with a larger difference for higher solar radiation. Liljegren Tnwb is similar to Dimiceli Tnwb during the daytime. Thus, the increased diurnal range in Liljegren is due to Liljegren Tnwb being consistently lower than Dimiceli Tnwb overnight, while Liljegren Tbg is consistently much warmer than Dimiceli Tbg during periods with high solar radiation. The larger diurnal range in Liljegren WBGT explains the necessity of using different values of WBGT for the Dimiceli and Liljegren WBGT datasets compared to Grundstein et al. (2015) when defining the three heat risk regions, which are defined using MJJAS 90th percentile of daily maximum WBGT. Further, this suggests that the Oklahoma Mesonet may report lower WBGT risk during the hottest part of the day than what the Liljegren WBGT formula would suggest. The standard deviations of the two formulations are in good agreement (Fig. 2d). The RMSD between Liljegren WBGT and Dimiceli WBGT is largest during the winter (not shown) and overnight (Fig. 2c). During the summer daytime hours, the RMSD is around 1.8°F (1.0°C), while during winter months, it may be as high as 3.2°F (1.8°C). Nighttime RMSD is consistently near 1.8°F (1.0°C) year-round. As the forthcoming results (other than category-based analysis) use thresholds based on percentiles, the results shown for the remainder of the paper are using Dimiceli WBGT from the ERA5 except where notable differences exist between Dimiceli WBGT and Liljegren WBGT.
4. Climatology of WBGT and risk categories
a. Trends in WBGT
To evaluate how the frequency of each category is changing over time, the trend in the number of days with a daily maximum Dimiceli WBGT in each category during the extended summer (MJJAS) is shown (Fig. 3). These trends are calculated by taking the mean of the number of days per year at each grid point with a daily maximum WBGT category across each subdomain (Fig. 1) and calculating the trend using linear ordinary least squares regression. The extended summer is chosen for this analysis to capture the annual trend without including a large period of time that is overwhelmingly in the no-risk category (around 135–140 of the MJJAS days with uniform categories and around 120–130 days per year for regional categories). In general, the northern USGP shows weak, nonsignificant trends (Figs. 3a,d) with almost all risk days in the low-risk category at ∼10–20 days per year for uniform categories and ∼20–30 days per year for the regional categories. With regional categories, the number of moderate-risk days is ∼5–10 yr−1. In the central USGP, the total number of low- and moderate-risk days increases from ∼25 to ∼35 days per year for low risk and from ∼5 to ∼10 days per year for moderate risk with uniform categories and from ∼30 to ∼40 days per year for low risk and from ∼5 to ∼10 days per year for moderate risk with regional categories (Figs. 3b,e). Correspondingly, the number of no-risk days decreases from ∼125 to ∼110 days per year from 1960 to 2020. The number of high- and extreme-risk days is small but with slight positive significant trends.
Trend in subdomain mean number of MJJAS days with each daily maximum Dimiceli WBGT category for (a)–(c) uniform and (d)–(f) regional categories for the (a),(d) northern, (b),(e) central, and (c),(f) southern USGP. Dashed lines indicate the trend, with trends that are statistically significant at the 95% confidence level in bold.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
In the southern USGP when using uniform categories, both the high- and extreme-risk categories increase significantly over the 1960–2020 period (Fig. 3c). For high risk, the annual number of days increases from ∼5 yr−1 in 1960 to ∼10 in 2020. During the same period, extreme risk increases from ∼1 to ∼3 days per year. Correspondingly, there is a significant decrease in no-risk days, dropping from around 100 days per year to ∼80 days. Low (∼40–50 days per year) and moderate (∼20–25 days per year) risks show statistically significant positive trends as well with uniform categories. For the southern USGP using regional categories, the total number of high- and extreme-risk days is smaller than with uniform categories but still shows statistically significant positive trends. There is a statistically significant increase in the number of moderate-risk days, with the number of days per year increasing from ∼10 in 1960 to ∼20 by 2020. The number of no-risk days decreases from ∼95 to ∼80 days per year over the same period.
Liljegren (Fig. S1 in the online supplemental material) categories exhibit similar trends to Dimiceli. However, because Liljegren tends to have warmer maximum WBGT, there are fewer no-risk days and more days in the other risk categories. No-risk days are typically reduced by ∼10–15 yr−1 with those days distributed proportionally to the risk days frequency in the northern USGP, primarily to the low- and moderate-risk days in the central USGP, and primarily to the high- and extreme-risk days in the southern USGP. Additionally, the analysis is repeated at the three points from Fig. 1 which suggests that the southern point, which is near Oklahoma City and within region 3, has substantially more moderate- and high-risk days than shown by the regional means (Figs. S2 and S3).
Trends in WBGT by day of the year are shown using WBGT at 2000 UTC, as this is typically the warmest part of the day across most of the domain. The trends presented in Fig. 4 represent the trend in the mean of the 2000 UTC WBGT across the entirety of each subdomain calculated via linear ordinary least squares regression. Trends in Dimiceli WBGT are generally positive except during transitional seasons. In fact, during October, all three subdomains experienced negative trends during the study period. Across the domain, the largest trends are during the extended cold season of December–March, with trends of up to 1°F decade−1. Warm season trends are typically between 0.2° and 0.4°F decade−1. The positive cold season WBGT trends tend to be the largest in the northern USGP during January and the central USGP in March. Differences in trends between Dimiceli WBGT and Liljegren WBGT are minimal (Fig. S4).
Trend in 2000 UTC Dimiceli WBGT averaged across each subdomain.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
b. Seasonality of WBGT risk
Figures 5a–c show the distribution of the daily maximum Dimiceli WBGT uniform category per day for three representative locations shown in Fig. 1. As mentioned previously, the category never exceeds low risk outside of April–October (extended warm season), with the southern location having the longest period where the low risk or higher regularly occur. The north only exceeds no risk on about 35% of days during the peak in July, with the June–August period generally exceeding no risk by >20% of days. Typically at the northern USGP location, when there is a heat risk, it is a low risk, as moderate and high risk only exceed 5% combined for a brief period at the end of July. However, most of the year does not see any days with any heat risk during the study period when using uniform categories. Due to infrequently exceeding the no-risk level, individuals in the northern USGP may not be well acclimated to low-risk or upper-no-risk conditions. At the central location, the low risk is the most common daily maximum category during the peak warm season, and as many as 20% of all days reach moderate risk. At the south location for the peak of the warm season in July and August, the most frequent category is moderate, peaking at about 50% of all days, with both high risk and low risk being more frequent than no risk. In fact, no risk is only the maximum category for around 10% of all days in July and August, while high-risk peaks at just under 20% of days. For the remainder of the extended warm season outside of July and August, low risk is the most frequent category at around 45%–60% of days.
Daily maximum Dimiceli WBGT category by relative frequency using (a)–(c) uniform categories and (d)–(f) regional categories, for the (a),(d) north, (b),(e) central, and (c),(f) southern USGP.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
Repeating this analysis using the mean over each subdomain results in fewer low-risk days in the central USGP regardless of which categorization scheme is used (Fig. S5). In the southern USGP, there are more no-risk and low-risk days and fewer moderate-risk days during the warm season, with low not having a reduced frequency in July and thus remaining more frequent than moderate risk throughout the warm season.
Using Liljegren WBGT (Fig. 6) increases the number of days in high and extreme risk while decreasing the frequency of no-risk days in all regions. This is consistent with the higher daytime WBGT found (shown in section 3b). The clearest example is in the south location where extreme risk occurs >20% of all days at the peak in late July and early August (Fig. 6c), increasing from under 10% when using Dimiceli WBGT (Fig. 5c). A corresponding decrease in low-risk days results in each of the moderate and extreme categories becoming more frequent than the low-risk category. At the north location, the Liljegren WBGT results in a decrease in no-risk days that corresponds with increases in all other categories; however, no risk remains the most frequent category for all days. These results show that southern portions of the domain face significant heat risk for much of the summer months. In these conditions, many outdoor activities should be moved to the morning or evening, especially if they cannot be moved indoors or delayed until conditions improve (Table 2).
Daily maximum Liljegren WBGT category by relative frequency using (a)–(c) uniform categories and (d)–(f) regional categories, for the (a),(d) north, (b),(e) central, and (c),(f) southern USGP.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
If regional acclimation is accounted for in the category definitions (i.e., using regional categories), then the differences in the distributions across regions are reduced by design (Figs. 5d–f and 6d–f). The northern location is in region 1, the central location is in region 2, and the southern location is in region 3 (Fig. 1). In the north, no risk is still the most common maximum category, but it is nearly matched by low risk at between 40% and 50%, while moderate risk is nearly 20% at peak frequency in July (Fig. 5d). The central region is unchanged from the uniform category distribution (Figs. 5b,e are identical). The south has a reduced frequency of moderate category days during the warm season, leading to the low-risk days being the majority of all days during the duration of the warm season. Moderate risk is still more frequent than no risk during July and August, reaching between 20% and 40%. The regional categories suggest that southern regions still see higher heat-risk categories than northern climates after accounting for regional acclimation, but the difference is less pronounced than for uniform categories. Differences between Liljegren and Dimiceli WBGT using regional categories are consistent with those for uniform categories (Figs. 5d–f and 6d–f). As with Dimiceli WBGT, analyzing the subdomain mean daily maximum heat-risk frequencies fewer low risk and more no-risk days in the central USGP, while the southern USGP has more no-risk and low-risk days and fewer moderate, high, and extreme days (Fig. S6). As the peak of the WBGT warm season is July throughout the domain, the remainder of the climatology in this paper will focus on July.
c. Diurnal cycle of WBGT
As WBGT undergoes a significant diurnal cycle (Fig. 2) and nighttime heat can prevent heat stress recovery, here, we examine the diurnal cycle in more detail. Figure 7 shows that the lowest values of Dimiceli WBGT occur in the northern USGP and the highest values occur in the southern USGP, as expected. The southern location peaks at approximately 82°F with the central and northern USGP at around 78° and 74°F, respectively. The maximum WBGT occurs at approximately 2000 UTC in all locations, with the minimum at approximately 1000 UTC. Nighttime low WBGTs follow the same relative pattern with WBGTs around 67°, 63°, and 60°F for the southern, central, and northern points. Liljegren WBGT does not show any notable differences from Dimiceli WBGT (Fig. S7) aside from the previously shown increase in the diurnal range.
July hourly mean of Dimiceli WBGT representing the northern (green), central (red), and southern (blue) USGP subdomains.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
One limitation of using either of the risk categories is that WBGT is always in the no-risk category overnight in our domain, which is problematic if one wishes to use low temperature as part of a heat wave definition. This is not a problem when using uncategorized WBGT, but many users of WBGT, including the public, may not be familiar with these values and their context, which is an advantage of the category system.
d. Distribution of WBGT
To examine the WBGT distribution, the mean and standard deviation of the daily maximum, minimum, and mean WBGT for July are shown (Fig. 8). For each, the mean WBGT increases to the south and east, while the standard deviation increases to the north and east, with standard deviations in the northern portions of the USGP twice those in the southern USGP. The mean daily maximum WBGT is around 70°F in the northern portions of the USGP, while the southeastern portions of the USGP are around 85°–90°F. Minimum WBGTs are around 15°F below the maximum, and mean WBGTs are typically around the midpoint of the maximum and minimum WBGT. Liljegren WBGT results in a similar pattern but with a larger diurnal range and noisier standard deviations (Fig. S8).
Mean (filled contours) and standard deviation (contours) of July daily (a) maximum, (b) minimum, and (c) mean Dimiceli WBGT.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
Further, histograms of July daily maximum, minimum, and mean Dimiceli WBGT are shown for one location in each subdomain (Fig. 9). Along with the lower peak in the northern USGP, the distribution of daily maximum WBGT is wider than in the southern locations. In all regions, the distribution is skewed to the left. This suggests that exceptionally cool daily maximum WBGT values are more common than exceptionally hot daily maximum WBGT values. The Liljegren maximum WBGT distributions are skewed slightly warmer, typically with longer warm tails but the same mode (Fig. S9).
Distribution of July daily (a)–(c) maximum, (d)–(f) minimum, and (g)–(i) mean Dimiceli WBGT for the (a),(d),(g) northern, (b),(e),(h) central, and (c),(f),(i) southern USGP. The cumulative distribution function is in orange with the 90th percentile indicated by the blue horizontal line.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
Histograms of daily minimum Dimiceli WBGT are shown in Figs. 9d–f. Dimiceli WBGT has a peak in the 55°–65°F range in the northern USGP, with the central peak at 65°–70°F and the southern USGP peaking at the 70–75°F bin. As with the maximum Dimiceli WBGT, the distribution is wider with lower frequency at the peak (<40%) in the northern USGP and a narrower distribution and higher frequency at the peak of the distribution (∼70%) in the southern USGP. The distributions tend to be left skewed in the central and southern USGP but near normal in the northern USGP. This suggests that while most days are near the higher part of the distribution, it is more common to have an exceptionally cool low than an exceptionally warm low. The Liljegren WBGT (not shown) is typically shifted to the left of Dimiceli WBGT (Figs. 9d–f), consistent with the observation that Liljegren WBGT is cooler at night than Dimiceli WBGT (Fig. 2c).
Histograms of daily mean Dimiceli WBGT are shown in Figs. 9g–i. In the northern USGP, the peak is in the 65°–70°F bin with a frequency near 40%, the central USGP peaks in the 70°–75°F bin at around 50% of all days, and the southern USGP peaks at the 75°–80°F bin peaking around 70%. Correspondingly, the distribution in the northern USGP tends to be wider than those in the southern USGP. The Liljegren WBGT formulation produces nearly identical results and is not shown.
5. Heat wave climatology
As discussed in section 2e, three heat wave definitions are presented here (Fig. 11). The definitions are based on 1) daily maximum WBGT, 2) daily minimum WBGT, and 3) daily mean WBGT. These three definitions are chosen as each has been shown to be important for heat stress and recovery (Robinson 2001; Hajat et al. 2002; Anderson and Bell 2011; Smith et al. 2013; Nissan et al. 2017). Heat wave thresholds are based on the 90th percentile of the 31-day running mean of the appropriate metric across the 61-yr period of the dataset. The threshold must be met for two consecutive days to be classified as a heat wave and must fail to be met for two consecutive days to terminate a heat wave.
Heat wave definitions based on categories were investigated but are not included here for several reasons. First, the number of WBGT categories is small, so categories containing the 90th percentile often contain significantly more than 10% of the data and thus lead to varying effective thresholds across the domain, even with regionally varying categories. Second, minimum WBGT is universally in the no-risk category, making heat waves using this definition nonexistent. Third, it is challenging, and not very meaningful, to define the mean WBGT category. Even when doing so, as overnight is in the no-risk category, it only provides information about daytime conditions, thus negating much of the reason for using mean WBGT. Additionally, only definitions based on local percentiles are presented as thresholds that do not vary spatially and have the additional problem of failing to account for acclimation.
a. Heat wave thresholds
The 90th percentile thresholds are shown for Dimiceli and Liljegren maximum WBGT (Figs. 10a,b), minimum Dimiceli WBGT (Fig. 10c), and mean Dimiceli WBGT (Fig. 10d). Minimum Liljegren WBGT is shown in Fig. S10a. These values consider the period of 1–31 July, which is the threshold applied to the 16 July WBGT. The 90th percentile of maximum, minimum, and mean WBGT all exhibit both a north–south and west–east (dominant) gradient for both Dimiceli and Liljegren WBGTs. This is due to both the north–south gradient in temperature, as well as the east-to-west slope in elevation and west-to-east moisture gradients. Maximum (minimum) Liljegren WBGT has slightly higher (lower) values of WBGT due to the larger diurnal variation as shown in section 3b. Mean WBGT is similar for both Liljegren and Dimiceli WBGTs (Fig. S10b).
The 16 Jul 31-day centered 90th percentile (a) maximum Dimiceli WBGT, (b) maximum Liljegren WBGT, (c) minimum Dimiceli WBGT, and (d) mean Dimiceli WBGT.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
b. Heat wave characteristics
To see the behavior of heat waves in the USGP, several heat wave characteristics are presented. The first characteristic is the annual number of heat wave days. When using the maximum WBGT heat wave definition, there is a local minimum of heat wave days centered over eastern Colorado and western Kansas (∼20–24 days) with higher numbers (∼26–30 days) occurring in northern and eastern parts of the domain (Figs. 11a–c). For the definition using minimum WBGT, the gradient is from northwest to southeast. A local maximum associated with a strong gradient occurs in northeast Texas decreasing across Oklahoma and western Texas before decreasing in magnitude over the rest of the domain. Overall, much of the north and western portions of the domain see ∼22–26 heat wave days each year, while much of Oklahoma and North Texas see greater than 28 days per year. For the mean WBGT definition, the number of heat wave days is largest in the south decreasing gradually to the north. As a result, most regions see the most heat wave days (∼25–30) under the mean WBGT definition.
Mean (a)–(c) heat wave days per year, (d)–(f) number of heat waves per year, and (g)–(i) number of days per heat wave using a heat wave definition based on (a),(d),(g) maximum WBGT, (b),(e),(h) minimum WBGT, and (c),(f),(i) mean WBGT.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
The second characteristic is the average number of heat waves per year (Figs. 11d–f). For all three definitions, there is a local maximum in northeast Texas. Because this is coupled with a local maximum in heat wave days and heat wave duration (Figs. 11g,h), this suggests that this local maximum is driven by a persistent phenomenon. Some possible explanations may be moisture from evapotranspiration from the local forests, relative ease of moisture transport from the Gulf of Mexico due to proximity, or fewer cold fronts to break up heat. For maximum WBGT, the local maximum extends into much of eastern Oklahoma and eastern Kansas, with another local maximum in western North Dakota. Each of these local maxima is around 10 heat waves per year. The minimum frequency is in eastern Colorado, in western Kansas, and into the Texas and Oklahoma Panhandles, at around 7–8 heat waves per year. For the minimum WBGT heat waves, there is a stronger north-to-south gradient with around 8 heat waves per year in the north increasing to around 11 in the south. However, as with the maximum WBGT heat waves, there is a higher amount in Oklahoma and eastern Kansas than in regions to the west. The mean WBGT heat wave definition leads to a similar north-to-south gradient, but it is more gradual than with minimum WBGT.
The third characteristic presented is heat wave duration or the average number of days in a heat wave. Heat wave duration (Figs. 11g–i) based on maximum WBGT is typically slightly shorter than other definitions, with a broad area in the west-central USGP between 3 and 3.25 days with much of the rest of the region being 3.25–3.5 days. While the duration is similar using minimum WBGT, the region of 3–3.25 days is confined largely to southwest South Dakota and western Nebraska, with much of the rest of the domain being in the 2.35–3.5 range. Parts of the southeastern and far eastern domains exceed 3.5 days. When using mean WBGT, most of the domain is around 3.25–3.5 days per heat wave, with the southern USGP exceeding 3.5 days per heat wave.
Liljegren WBGT produces fewer maximum WBGT heat waves than Dimiceli WBGT across the USGP region, generally reducing the number of heat wave days (Fig. 12a vs Fig. 11a). Correspondingly, the number of heat waves per year is reduced by about 2 days per year when using maximum Liljegren WBGT (Fig. 12b). For minimum and mean WBGT, there are no notable differences between Liljegren and Dimiceli WBGT heat waves (Figs. S11 and S12).
Mean (a) heat wave days per year, (b) number of heat waves per year, and (c) number of days per heat wave and trend in (d) heat wave days per year, (e) number of heat waves per year, and (f) number of days per heat wave. All panels use a heat wave definition based on daily maximum Lijegren WBGT. Black dots indicate trends that are not statistically significant at the 95% confidence level.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
c. Heat wave characteristics trends
Trends in the number of heat wave days, annual number of heat waves, and number of days per heat wave are calculated using linear ordinary least squares regression over the period 1960–2020. Generally, the number of WBGT heat waves and heat wave days have increased throughout the domain (Figs. 13a–f), consistent with the broad increases observed in WBGT shown previously. The strongest trends in heat wave days are in minimum and mean, with the strongest trends in the south and the total number of heat wave days increasing by more than 15% of the mean value each decade on average over the study period. Trends in heat waves show much of the same pattern as a number of heat wave days. The largest increases in heat waves occur in the southern portions of the domain. Further, minimum and mean WBGT heat waves are increasing at rates faster than those when defined by maximum WBGT. Peak rates of increase exceed 1.5 additional heat waves per decade or nearly 20% of the mean per decade in some locations.
Trend in mean (a)–(c) heat wave days per year, (d)–(f) number of heat waves per year, (g)–(i) number of days per heat wave using a heat wave definition based on (a),(d),(g) maximum WBGT, (b),(e),(h) minimum WBGT, and (c),(f),(i) mean WBGT. Black dots indicate trends that are not statistically significant at the 95% confidence level.
Citation: Journal of Applied Meteorology and Climatology 63, 8; 10.1175/JAMC-D-23-0213.1
Heat wave duration trends are generally small, with trends in the maximum and minimum WBGT heat waves mostly insignificant and near 0. However, in regions of eastern Kansas, Nebraska, and the Dakotas, the length of heat waves is increasing by >0.05 days per heat wave per decade in the maximum WBGT definition. In southeastern portions of the domain, heat wave duration for the mean WBGT heat waves is increasing between 0.05 and 0.1 additional days per heat wave per decade. Further, southern Manitoba experiences >0.1 additional day per heat wave per decade across all definitions.
Trends in heatwaves using Liljegren WBGT (Figs. 12d–f) are similar to those when using Dimiceli WBGT but with a lower magnitude, reflecting the reduction in the number of heat waves and heat wave days each year.
Generally, heat wave days are increasing regardless of the heat wave definition used. However, the number of heat waves is increasing fastest in the minimum and mean WBGT definitions. For most regions, the increase in heat wave days is primarily due to an increase in the total number of heat waves. However, using the mean WBGT definition, the duration of heat waves is also increasing in some regions, compounding with the number of heat waves to lead to a large increase in the number of heat wave days.
6. Discussion
WBGT is typically calculated from standard meteorological observations, and several methods exist to estimate it. Here, we show notable differences in USGP WBGT characteristics depending on which of two commonly used methods of calculating WBGT are used–Dimiceli (Dimiceli et al. 2011) and Liljegren (Liljegren et al. 2008). The mean WBGT does not change significantly depending on which method is used. Liljegren WBGT is shown to have a larger diurnal cycle than Dimiceli WBGT with Liljegren WBGT about 1°F higher for the daily maximum WBGT and 2°F lower for the daily minimum WBGT. As a result, Liljegren WBGT reaches higher-risk categories more frequently during the warm season compared to Dimiceli WBGT throughout the USGP. Conversely, as Liljegren WBGT has lower WBGT overnight, this suggests better opportunities for heat stress recovery than those suggested by Dimiceli WBGT. Patel et al. (2013) found that Liljegren WBGT performed better at calculating the daily maximum WBGT than WBGT calculated from other methods (e.g., Matthew et al. 2001) but with a larger RMSD at higher WBGT values. However, Rennie et al. (2021) found that Dimiceli WBGT performs comparably to Liljegren WBGT on average, with regional variability in which method correlates better with observed WBGT.
In this study, we found that during the daytime, Dimiceli WBGT was around +1°F warmer and Liljegren WBGT was around +2°F warmer when using the ERA5 compared to the Oklahoma Mesonet (Fig. 2), which uses Dimiceli WBGT calculated from standard meteorological observations. The Dimiceli WBGT from the ERA5 reproduces the Oklahoma Mesonet WBGT distribution more closely during the warmest part of the day. However, this is likely the result of using the same model for both. Ahn et al. (2022) show that Liljegren WBGT has a slight positive bias across the USGP at a majority of stations in Nebraska and Kansas (our central USGP subdomain) compared to in situ observations. Additionally, Ahn et al. (2024) show that in climate regions common to the USGP, Liljegren WBGT calculated from the ERA5 tends to overestimate WBGT more than with other input sources and more than some other models with the ERA5 input. However, because Ahn et al. (2024) do not examine Dimiceli WBGT, it is uncertain if the ERA5 input is the source of the differences in Liljegren WBGT and Dimiceli WBGT in our study. Each of these studies is limited by the small number of in situ WBGT observations available, which can bias results toward those found in certain environmental conditions. We do not assess the accuracy of either method compared to directly observed WBGT, and from this work and prior studies mentioned, it is unclear which of Liljegren WBGT and Dimiceli WBGT perform better in the USGP. Users of modeled WBGT are cautioned to understand which methodology is used and to use caution when making comparisons between WBGT from different datasets or methodologies.
A relative threshold at the 90th percentile is used for each of the daily minimum, daily maximum, and daily mean WBGT to define heat waves to account for local acclimation, which is in the typical range of other heat wave studies (Smith et al. 2013). The mean and minimum WBGT heat wave definitions tend to have more heat waves and heat wave days than the maximum WBGT heat wave definition. Further, the mean WBGT heat wave definition produces heat waves of longer duration, particularly in the southern USGP than the other definitions. Because mean WBGT is an average of 24 observations throughout the day compared to a single extreme value in minimum or maximum WBGT, which may reduce the day-to-day variability and prevent this variability from being the factor that ends a heat wave early or delays the start of a heat wave or even prevent the onset of a heat wave altogether.
Over the 61-yr study period, the total number of heat waves and heat wave days increased. Using the maximum WBGT heat wave definition, the increase is mostly occurring in the southern and central portions of the USGP. Perkins (2015) notes in their review of heat wave literature that there is a “warming hole” over portions of North America in the second half of the twentieth century. While the exact location changes based on methodology and choice of dataset, the warming hole often extends into the USGP and may be driven by the interdecadal Pacific oscillation (Meehl et al. 2012). As such, these regions could see stronger increases in the future.
The mean and minimum WBGT heat wave definitions result in larger increases in heat waves and heat wave days over the entire domain compared to the maximum WBGT heat wave definition. Studies have shown that minimum temperature and heat waves based on minimum temperature are increasing faster than their maximum temperature equivalents (Perkins 2015; Oswald 2018). As WBGT is strongly correlated with air temperature, this rapid increase in minimum air temperatures is likely the culprit for the similar behavior in minimum WBGT heat waves. Additionally, since the mean WBGT incorporates the minimum WBGT into its calculation, it explains why the mean WBGT heat waves see similar trends to the minimum WBGT heat waves. This is particularly concerning given the evidence that overnight low temperatures are critical for recovery from heat stress (Robinson 2001; Hajat et al. 2002; Nissan et al. 2017). Seasonally, WBGT is increasing faster during the winter and early spring months, with the largest trends in the northern USGP. Studies have shown that northern latitudes are warming faster than the midlatitudes and even faster in the winter than in the summer (Bekryaev et al. 2010; Collins et al. 2013). While winter heat risks are currently zero, if these trends continue, it could lead to more days in which outdoor activities are disrupted outside of the current warm season.
7. Conclusions
This study calculates a climatology of WBGT and the associated heat waves for the USGP using the ERA5 reanalysis using the WBGT formulation from Dimiceli et al. (2011), which is used in several operational settings. WBGT calculated from the ERA5 is shown to be able to accurately represent WBGT calculated from standard Oklahoma Mesonet meteorological observations to within 1.5°C and well represents the overall statistical distribution of WBGT. Further, Dimiceli WBGT is compared to the Liljegren et al. (2008) formulation of WBGT. The Liljegren WBGT is found to have a larger diurnal cycle than the Dimiceli WBGT, leading to higher WBGT during peak heating (∼+1°F) but lower WBGT overnight than Dimiceli WBGT (∼−2°F). As a result, Liljegren WBGT has slightly more frequent occurrences of the high- and extreme-heat-risk categories than Dimiceli WBGT in the southern USGP and of the low- and moderate-heat-risk categories in the northern and central USGP. Otherwise, the differences are small. In the southern USGP, the most frequent categories during the warm season are moderate; however, high and extreme categories occur more frequently than in other parts of the plains, where it is uncommon to experience a risk higher than moderate.
WBGT trends are strongest in the winter. However, as these WBGT values are below the low-risk threshold, the cold season category trends are universally 0. During the warm season, the southern regions of the domain are both warmer and WBGT and risk category is increasing faster than in the northern portions of the region. During the warm season, the no-risk category is decreasing in frequency in the central and southern USGP as the low and moderate regions increase in frequency in the central USGP, while the high and extreme categories become as much as three times more frequent over the 61-yr study period in the southern USGP.
Overall, there tend to be more heat waves in the southern part of the domain than in the northern part; however, the maximum WBGT heat wave definition tends to produce a more west-to-east gradient than north-to-south gradient. The most heat wave days and longest heat waves tend to occur when using a mean WBGT heat wave definition. While using minimum and mean Liljegren WBGT to define heat waves produces similar results to using Dimiceli WBGT, the maximum WBGT heat wave definition does have some notable differences. Specifically, the Liljegren WBGT definition produces fewer heat waves than Dimiceli WBGT, with a shorter average duration as well. This suggests that there could be some additional variability in Liljegren WBGT that may be breaking up longer strings of extreme heat that may be damped in Dimiceli WBGT. The trends in heat waves and heat wave days are generally positive, with the strongest occurring in the southern USGP and with definitions based on the minimum and mean WBGT. However, the heat wavelength does not show statistically significant trends using the minimum WBGT definition, and only some localized positive trends appear in maximum and mean WBGT-based heat waves.
The information presented in this study may be useful to those planning outdoor work to schedule the work more efficiently. Further, the trends presented suggest that the risk of heat stress has been increasing, making it more important than ever to understand the risks and their timing.
Acknowledgments.
The authors thank the anonymous reviewers and editor for comments and guidance that improved the work presented in this manuscript. This project was supported by the National Science Foundation EPSCoR program, Grant OIA-1946093. Hersbach et al. (2018) was downloaded from the Copernicus Climate Change Service (C3S) Climate Data Store. The results contain modified Copernicus Climate Change Service information 2022. Neither the European Commission nor ECMWF is responsible for any use that may be made of the Copernicus information or data it contains.
Data availability statement.
Oklahoma Mesonet data are available to download by request through the Oklahoma Mesonet at https://mesonet.org. ERA5 data are available to download through the Copernicus Climate Data Store at https://cds.climate.copernicus.eu/cdsapp#!/home. Scripts used to process the data are available through the authors’ GitHub at https://github.com/BJDavis4/WBGT_Climatology_USGP.
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