Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2024 Sep 29;8(10):e2024GH001068.
doi: 10.1029/2024GH001068. eCollection 2024 Oct.

A New, Zero-Iteration Analytic Implementation of Wet-Bulb Globe Temperature: Development, Validation, and Comparison With Other Methods

Qinqin Kong  1 , Matthew Huber  1
Affiliations

A New, Zero-Iteration Analytic Implementation of Wet-Bulb Globe Temperature: Development, Validation, and Comparison With Other Methods

Qinqin Kong et al. Geohealth. .

Abstract

Wet-bulb globe temperature (WBGT)-a standard measure for workplace heat stress regulation-incorporates the complex, nonlinear interaction among temperature, humidity, wind and radiation. This complexity requires WBGT to be calculated iteratively following the recommended approach developed by Liljegren and colleagues. The need for iteration has limited the wide application of Liljegren's approach, and stimulated various simplified WBGT approximations that do not require iteration but are potentially seriously biased. By carefully examining the self-nonlinearities in Liljegren's model, we develop a zero-iteration analytic approximation of WBGT while maintaining sufficient accuracy and the physical basis of the original model. The new approximation slightly deviates from Liljegren's full model-by less than 1°C in 99% cases over 93% of global land area. The annual mean and 75%-99% percentiles of WBGT are also well represented with biases within ± 0.5 °C globally. This approximation is clearly more accurate than other commonly used WBGT approximations. Physical intuition can be developed on the processes controlling WBGT variations from an energy balance perspective. This may provide a basis for applying WBGT to understanding the physical control of heat stress.

Keywords: analytic approximation; energy balance; heat stress; wet‐bulb globe temperature.

PubMed Disclaimer

Conflict of interest statement

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

Figures

Figure 1
Figure 1
(a) hcg, hcw and kx as functions of wind speed. Blue, black, and red curves correspond to surface pressure values of 950, 1,000, and 1,050 hPa respectively with the shading represent spread due to film temperature variations from 20 to 50°C. (b) hcg/hrg (shading), hcw/hrw (solid contour) and hew/hrw (dashed contour) as functions of film temperature and wind speed. Thermal radiative heat transfer coefficients are approximated as hrg≈4σϵgTf3 for the black globe and hrw≈4σϵwTf3 for the wet wick, with ϵg=ϵw=0.95. Surface pressure is fixed at 1,000 hPa in panel (b).
Figure 2
Figure 2
Biases in analytic approximations of (a) Tg, (b) Tnw, and (c) wet‐bulb globe temperature across the parameter space covering selected ranges of temperature Ta (20–50°C), wind speed (0.13–3 m/s), relative humidity (RH) (20%, 60%) and downward solar radiation SRdown (0, 450, 900W/m2). Biases are evaluated against Liljegren's full model. The cosine of the solar zenith angle (cosθ) is set to 0.75. Thermal radiation, and direct and surface reflected solar radiation are approximated from temperature, RH, cosθ, SRdown and an assumed surface albedo following the original formulation of Liljegren et al. (2008). Surface pressure is fixed at 1,000 hPa.
Figure 3
Figure 3
Empirical probability distribution of biases in our analytic approximation WBGTˆ. The y‐axes are designed to represent the percentage of samples showing biases within a 0.2°C interval centered on the corresponding x coordinates. The empirical distribution is derived from land data weighted by grid‐cell area using ERA5 reanalysis for the period 2013–2022 and the ACCESS‐CM2 model for the period 2091–2100 under the SSP585 scenario. Samples with wet‐bulb globe temperature below 15°C are excluded, as they are less relevant to heat stress.
Figure 4
Figure 4
Annual (left) 1% and (middle) 99% percentile of biases, and (right) 99% percentile of the absolute magnitudes of biases in the analytic approximations of (a–c) Tg, (d–f) Tnw and (g–i) wet‐bulb globe temperature. Panels j–l represent the empirical cumulative distribution of these biases across all continental grid cells weighted by area. The 1% percentile of biases in Tgˆ are very close to zero and therefore are omitted in (j). Biases are evaluated by comparing against Liljegren's full model based on hourly ERA5 reanalysis data during 2013–2022.
Figure 5
Figure 5
Empirical probability distribution of (a) biases in our analytic formulation WBGTˆ and several other wet‐bulb globe temperature (WBGT) approximations, and (b) Tnw−Tw and Tg−Ta at both daytime and nighttime. Both (a) and (b) are derived from land data weighted by grid‐cell area using ERA5 reanalysis for the period of 2013–2022. Panel (c) is the same as (a) except for the period 2091–2100 under the SSP585 scenario using the ACCESS‐CM2 model. The y‐axes are designed to represent the percentage of samples showing biases within a 0.2°C interval centered on the corresponding x coordinates. Samples with WBGT below 15°C are excluded, as they are less relevant to heat stress.
Figure 6
Figure 6
Biases in the (a, e, i, m, q) annual mean and (b, f, j, n, r) 75%, (c, g, k, o, s in Figure 6 continued) 90%, and (d, h, l, p, t in Figure 6 continued) 99% percentile values of our analytic approximation WBGTˆ and several other approximations of wet‐bulb globe temperature. Biases are evaluated by comparing against Liljegren's full model based on hourly ERA5 reanalysis data during 2013–2022.
Figure 6
Figure 6
Biases in the (a, e, i, m, q) annual mean and (b, f, j, n, r) 75%, (c, g, k, o, s in Figure 6 continued) 90%, and (d, h, l, p, t in Figure 6 continued) 99% percentile values of our analytic approximation WBGTˆ and several other approximations of wet‐bulb globe temperature. Biases are evaluated by comparing against Liljegren's full model based on hourly ERA5 reanalysis data during 2013–2022.
See this image and copyright information in PMC

Similar articles

See all similar articles

References

    1. ACSM . (1984). Position stand on the prevention of thermal injuries during distance running. (Technical Report). Medicine & Science in Sports & Exercise.
    1. Army, U. (2003). Heat stress control and heat casualty management (Technical Report). Technical Bulletin Medical 507/Air Force Pamphlet.
    1. Australian Bureau of Meteorology . (2010). About the approximation to the WBGT used by the Bureau of Meteorology. Retrieved from http://www.bom.gov.au/info/thermal_stress/#approximation
    1. Bedingfield, C. H. , & Drew, T. B. (1950). Analogy between heat transfer and mass transfer. Industrial & Engineering Chemistry, 42(6), 1164–1173. 10.1021/ie50486a029 - DOI
    1. Brimicombe, C. , Di Napoli, C. , Quintino, T. , Pappenberger, F. , Cornforth, R. , & Cloke, H. (2021). thermofeel [Software]. European Centre for Medium‐Range Weather Forecasts. 10.21957/MP6V-FD16 - DOI

LinkOut - more resources