Commonly used indices completely disagree about the relative effect of moisture on heat stress

doi:10.21203/rs.3.rs-2747130/v1

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Commonly used indices completely disagree about the relative effect of moisture on heat stress

https://doi.org/10.21203/rs.3.rs-2747130/v1

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published 05 Jul, 2023

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Irrigation and urban greening can mitigate extreme temperatures and reduce adverse health impacts from heat. However, some recent studies suggest these interventions could actually exacerbate heat stress by increasing humidity. These studies use different heat stress indices (HSIs), hindering intercomparisons of the relative roles of temperature and humidity.

Our novel method compares the sensitivity of HSIs to temperature and humidity, independent of HSI units. Using this method, we explain the properties of different HSIs and identify the conditions under which they agree or disagree. We highlight recent studies where the use of different HSIs could have led to opposite conclusions.

Our findings have significant implications for the evaluation of irrigation and urban greening as adaptive responses to overheating, and climate adaptation measures in general. We urge researchers to be more critical in their choice of HSIs; our method provides a useful tool for making informed comparisons.

Earth and environmental sciences/Climate sciences/Atmospheric science

Earth and environmental sciences/Climate sciences/Climate change/Climate-change impacts/Environmental health

In hot atmospheric conditions and under exertion, the human body must dissipate heat to maintain its internal temperature, which is mainly achieved by perspiration. High atmospheric humidity can limit the rate of evaporation of sweat, and therefore the amount of heat dissipated, so increasing heat stress on the body¹. The concept of moist heat-stress is increasingly used in research into the health effects of urban heat and climate change².

Atmospheric conditions that lead to heat stress are often assessed using heat stress indices (HSIs). Most HSIs combine temperature and humidity in some way (e.g., wet-bulb temperature (WBT), apparent temperature (AT), heat index (HI)), and some incorporate further quantities (thermal radiation and wind speed)³. Choosing the right index is crucial, as it sets the relative importance of temperature, humidity, and any further quantities in determining health outcomes. There is not usually a one-to-one mapping between different HSIs, and they do not operate on a common scale (even if superficially using the same units e.g., °C); this makes it impossible to make direct comparisons between the values of different HSIs.

Many studies have noted that drier conditions lead to higher air temperature, often exacerbating heatwave conditions^4–6; others have modelled or observed the tendency of irrigated agricultural land to reduce air temperature^7–9. Thiery et al¹⁰ found that irrigation expansion has substantially offset the effect of global warming on extreme temperatures in some regions. These relationships point to the conclusion that a drier land surface leads to worsened heat stress. Conversely, some recent studies have argued that droughts generally decrease heat stress because of the effect of reduced humidity¹¹, while irrigation increases heat stress because of the effect of increased humidity ^12–15. This discrepancy has potentially major implications, as some climate adaptation actions intended to reduce heat stress, such as urban greening, rely on conversion of sensible heat to latent heat through evapotranspiration of water. However, we will show that the arguments in these studies are highly subject to the choice of HSI used, so further examination of the correct use of HSIs is imperative.

In this study, we focus on a selection of HSIs commonly used in heat-health studies: WBT, “indoor” wet-bulb globe temperature (WBGT), simplified WBGT (sWBGT), apparent temperature¹⁶, heat index (HI), humidex and universal thermal climate index (UTCI). WBT measures the coldest temperature that can be achieved by evaporative cooling at a given temperature and humidity. Apparent temperature, heat index, and humidex are based on heat balance principles that incorporate temperature and humidity; care must be taken as multiple specifications exist³. Some specifications of AT incorporate wind speed and radiation. UTCI is based on detailed modelling of heat balance¹⁷, incorporating temperature, humidity, wind speed and radiation; it is less commonly used in heat-health studies, which may be due to the requirement for radiant temperature input. WBGT was developed as a field measurement for use by the military in hot-humid environments, and incorporates temperature, humidity (via WBT) and radiation (via black globe temperature)¹⁸. Simplified WBGT is sometimes used in heat-health studies and is intended as an approximation of WBGT at moderately high wind and moderately high radiation levels; WBGT is often calculated without the radiation component leading to a quantity referred to as WBGT-indoor¹⁹. The effects of radiation are often neglected in heat-health studies¹⁹, which may be because radiation data are less widely available, seen as requiring more assumptions, or are seen as less reliable. In this paper we therefore only focus on the relative effects of temperature and humidity. Generally, we will refer to relative humidity in this paper as it will be more familiar to most readers, although the Clausius-Clapeyron relation complicates its comparison at different temperatures; key figures are repeated using specific humidity in the Supplementary Material and the results using either are consistent. We outline the calculations and methods we used to estimate these HSIs in the Methods section.

We demonstrate a novel method that allows estimation of the relative marginal sensitivity of different HSIs to air temperature and humidity on a common scale. We compare the selected HSIs with each other, although we do not carry out an exhaustive review of further HSIs; we restrict the analysis to a few commonly used HSIs for clarity of message. Using this method, we identify the atmospheric conditions under which any HSIs will disagree with each other on the relative importance of temperature versus humidity on heat stress, which fills a major knowledge gap for climate-health studies. We identify specific examples where the choice of HSI reverses the conclusions on the effect of joint changes in temperature and humidity (caused in these examples by changes in soil moisture) on heat stress. We further argue that studies into the effect of joint changes in temperature and humidity on heat stress are nearly guaranteed to find that increased humidity is harmful if WBT is used as the metric.

In our Theory section we present our method of comparison between HSIs using finite differences. Then, in Results, we identify the temperature and humidity ranges under which different commonly used HSIs agree. We present two case studies where opposite conclusions would have been reached if a different HSI were chosen. Finally, we discuss the implications for climate impact science and climate adaptation in general.

We use the example of UTCI and WBT to explain our method of comparison between HSIs but expand to comparison of more HSIs in a later section.

Figure 1 shows isopleths (lines of constant value) for two HSIs plotted on a chart of air temperature and relative humidity (RH). The same is shown using specific humidity in Supplementary Fig. 1. Although both UTCI and WBT are in units of °C, their values are not directly comparable. Firstly, they intersect at multiple points: for example, a WBT value of 20°C could correspond to UTCI values ranging from just over 25°C to over 40°C for different combinations of temperature and RH (Fig. 1). Secondly, they are clearly calibrated to different scales: the 35°C isopleth in WBT approximately corresponds to the 55°C isopleth in UTCI.

Visually comparing the gradients of the isopleths in Fig. 1 gives an intuitive way of comparing these indices. Where the line is steeper, the HSI is more sensitive to temperature; where the line is shallower, the HSI is more sensitive to humidity. At high values (WBT = 35°C and UTCI = 55°C) the WBT and UTCI lines are nearly parallel: this means that the two indices agree on the relative importance of temperature and humidity, but only for these high values. For most of the temperature-humidity space the gradients of the lines are very different between the indices, showing that they disagree about the relative importance of marginal changes to temperature and humidity.

For this example, we use relative humidity because it will be most familiar for most readers, but the same process could be applied to a different measure of humidity. Calculations are made with all else being equal, so there is implicitly a small change in the specific humidity of the air parcel if relative humidity is held constant with changing temperature and vice versa.

We now describe this approach using calculus of variations to generalise the argument. Firstly, consider a point in the temperature-humidity space $(T,h)$ where T is temperature and h is humidity; the HSI calculated at that point is $U(T,h)$. We can imagine increasing the temperature by a small amount $\delta T$, which will change the heat stress to $U(T+\delta T,h)$ assuming humidity remains the same. Then, we can imagine increasing the humidity by a small amount $\delta h$, which will change the heat stress to $U(T,h+\delta h)$.

If $\delta T$ were fixed and $\delta h$ were solved to give the same change in the HSI $U$, i.e., solving

$$U(T+\delta T,h)-U(T,h)=U(T,h+\delta h)-U(T,h)$$

for $\delta h$ at fixed $\delta T$, then the quantity $\frac{\delta h}{\delta T}$ would tell us what change in humidity would produce a change in $U$ equivalent to a ${1}^{o}C$ change in temperature. This is illustrated in Fig. 2. If $\delta T$ and $\delta h$ are small, then this is equivalent to

$$\frac{\delta h}{\delta T}=\frac{dU}{dT} / \frac{dU}{dh}$$

It is more practical numerically to estimate $\frac{dU}{dT}$ and $\frac{dU}{dh}$ directly using a finite differences method, rather than solving the equation. If $\delta T$ and $\delta h$ are small, then we can estimate the one-dimensional gradients of the function $U(T,h)$ using the forward difference approximation:

$$\left(U\right(T,h)-U(T+\delta T,h\left)\right)/\delta T\approx \frac{dU}{dT}(T,h)$$

and

$$\left(U\right(T,h)-U(T,h+\delta h\left)\right)/\delta h\approx \frac{dU}{dh}(T,h).$$

We choose to do this numerically because not all the HSIs are analytically differentiable, and we choose this approximation because it is easiest to explain.

We will call the gradient of the isopleth of a heat stress function $U$ in temperature-humidity space the point $(T,h)$ the marginal temperature-equivalent change (MTEC)

$$MTEC=\frac{dU}{dT}/\frac{dU}{dh}.$$

MTEC can be interpreted as how much of a change in humidity produces a change in the HSI that is equivalent to a unit change in temperature. The smaller the value of MTEC the more sensitive the HSI is to changes in humidity compared to changes in temperature.

MTEC can be compared freely between different HSIs under the same conditions $(T,h)$ as the HSI is not one of the dimensions of MTEC. This procedure is valid whether humidity is represented as relative humidity, specific humidity, vapour pressure or even WBT; we will use relative humidity in this paper as it is most intuitive. This procedure is not restricted to the temperature-humidity space, and could be equivalently performed for other variables, for example, in the temperature wind speed space.

To make the comparison between different HSIs more explicit, we can take the difference in MTEC between them. Figure 3c shows the difference in MTEC ($\varDelta$MTEC) between UTCI and WBT, subtracting Fig. 3b from Fig. 3a. In this case a positive value of $\varDelta$MTEC means that WBT is more sensitive to a change in relative humidity, while a negative value means that UTCI is more sensitive to a change in relative humidity. A value close to zero indicates that the HSIs agree. Generally, humidity is much more important for WBT than UTCI for low-temperature low-humidity conditions, and the two HSIs agree under high-temperature high-humidity conditions. UTCI and WBT are closest in MTEC at around 35°C WBT or 55°C UTCI: $\varDelta$MTEC is generally below 7.5% for a WBT of > 30°C, below 5.0% for a WBT of 32°C or above, and closest to zero around a WBT of 35°C, that is, the difference in the change in relative humidity required to produce a change in the two HSIs equivalent to a 1°C change in temperature is least in this range. For context, in the present climate WBT rarely exceeds 31°C, but WBT > 35°C occurs in some locations for a few hours at a time and could begin to occur at a large scale with global warming of around 7°C^20,21.

Examples of heat stress index selection reversing the conclusion

In this section, we examine two illustrative examples of recent studies where the conclusions were strongly determined by the choice of HSI.

In Wouters et al.¹¹, a combination of observations and atmospheric modelling is used to argue that soil droughts lead to a reduction in heatwave lethality. For selected heatwave events, they use atmospheric modelling to estimate what the effect would be if at the start of the heatwave the soil moisture had been at the mean climatological level for that location rather than its actual value. They found that higher soil moisture leads to lower temperature and higher specific humidity. Based on Mora et al.²² they introduce a new heat stress metric

$${T}_{s}={T}_{w}+4.5(1-{\frac{RH}{100}}^{2}).$$

The counterfactual used meant that some cases had soil moisture increased while others had soil moisture reduced; those which had soil moisture increased had increased air humidity and vice versa. They found that lower soil moisture leads to lower values of ${T}_{s}$, which they argued means soil drought reduces heatwave lethality. However, using their Table 1 we calculated changes in a variety of HSIs (our Table 1) which highlights that some other HSIs have the opposite correlation with specific humidity, indicating that increased soil moisture would decrease heat stress.

The reason for this can be understood by comparing MTEC for the various HSIs in temperature-humidity space for the temperature and relative humidity range of interest for their study. Figure 4 shows the difference in MTEC between ${T}_{s}$ and UTCI (shading), as well as the changes in temperature and humidity given by Wouters et al¹¹ Table 1. In the heatwaves conditions from Wouters et al, UTCI is much more sensitive to temperature (as opposed to relative humidity) compared to ${T}_{s}$ in the same range of conditions. This does not necessarily mean that the choice of HSI in Wouters et al is wrong, but it is clearly problematic that different HSIs give such opposing conclusions.

Table 1

Rank correlation (Kendall’s tau and Spearman’s R) between the changes in specific humidity and the changes in heat stress indices (HSIs) calculated from the temperature and humidity changes induced by soil moisture changes modelled by Wouters et al. A positive number means that increasing humidity (and decreasing temperature as a result) led to an increase in that HSI, and vice versa. While the changes in the HSI used in Wouters et al are positively correlated with the corresponding changes in humidity, other commonly used heat stress indices have weaker or the opposite correlations.
	Kendall	Spearman
${T}_{s}$	0.66	0.83
WBT	0.85	0.94
UTCI	-0.85	-0.95
WBGT-indoor	0.18	0.24
Humidex	0.33	0.50
Heat index	-0.30	-0.37
sWBGT	0.64	0.75
Apparent temperature	-0.50	-0.61

As another example, we examined Mishra et al.¹², in which the effect of irrigation was modelled using the Weather Research and Forecasting regional climate model at ${0.25}^{o}$ horizontal resolution driven by ERA5 reanalysis and covering the 2000–2018 period. Two scenarios were modelled: with and without irrigation. Mishra et al. find that irrigation decreases dry-bulb temperature but increases WBT, and therefore conclude that increased irrigation area can be detrimental to human heat stress. The accuracy of the assumptions Mishra et al. made about when and how much irrigation occurs have been discussed elsewhere²³. The conclusion of Mishra et al. is in contrast with the interpretation provided by other studies e.g., Thiery et al¹⁰ which found that expansion of irrigation had a large enough effect to cancel out the effect of global warming on temperature extremes in some regions. However, the results in Mishra et al. show that while 95th percentile WBT increased, 95th percentile temperature and HI decreased (their Fig. 4). The increase in WBT was emphasised rather than the decrease in HI, which is not mentioned in the text.

When do commonly used indices agree?

Figure 5 shows MTEC for several commonly used HSIs. MTEC differences between each of the variables are shown in the Supplementary Fig. 4. We have chosen these HSIs to show a range of different outcomes and this is not intended to be exhaustive. MTEC enables comparisons between different conditions (e.g., between hot-humid and hot dry conditions) as well as between different heat stress indices even if calibrated to completely different scales. Patterns of agreement and disagreement between these HSIs can be summarised by examining MTEC in three regimes: lower temperature regime (LTR), hot-humid regime (HHR), and the hot-dry regime (HDR). We define representative values of temperature and humidity for these regimes, but these are only intended to be illustrative. The LTR is the left-hand side of the plot, which we characterise as 20°C temperature and under. The HHR is the top right-hand side of the plot, which we characterise at 35°C temperature and 80% relative humidity (this is extremely hot and humid but occurs in the present-day climate). The HDR is the bottom right-hand side of the plot, which we characterise as 40°C with 20% relative humidity.

Figure 5 shows that AT, HI, and UTCI are mainly sensitive to temperature in the LTR. In fact, HI is defined as equal to temperature when below 26.7°C (80°F). In comparison, WBT has very low MTEC even in the LTR. Humidex, WBGT-indoor, and sWBGT are slightly higher MTEC in the LTR compared to WBT, but clearly have lower MTEC compared to AT, HI, UTCI. Physiologically, we would not expect the effect of humidity to be important in the LTR: changes in the air temperature will dominate changes in heat balance as the sweat evaporation rate required to maintain heat balance is low²⁴.

In the HDR of Fig. 5, we see a different pattern of disagreement between the HSIs. MTEC is relatively low in AT, WBT, humidex, WBGT-indoor, and sWBGT. In contrast, HI and UTCI have an area of relatively high MTEC extending into the HDR, more extensive in UTCI. In the HDR, the sweat evaporation rate required to maintain a stable body temperature is high but sweat evaporation efficiency is also high as the vapour pressure is low²⁵. Therefore, it makes sense that MTEC is low. However, if one assumes that there is a limit to the sweat secretion rate, the HDR is the region where that limit is most likely to be reached. If the sweat secretion rate is reached, then increasing the relative humidity (and therefore the vapour pressure) will not necessarily decrease the sweat evaporation rate as there is no more sweat to evaporate^25,26. Sweat secretion rate limits in the underlying model may explain the higher MTEC values seen in the HDR for UTCI; this can be reproduced in a heat balance model (e.g. ISO standard 7933:2004) by reducing the sweating rate limit.

In the HHR, we would expect changes in relative humidity to be at their most important, as it is the regime where vapour pressure is likely to be the limiting factor in sweat evaporation rate²⁵. AT, HI, UTCI, WBT, humidex, WBGT-indoor, and sWBGT all have low MTEC in the HHR; so are roughly in agreement.

UTCI displays some unexpected properties at very high temperature and humidity and at very low humidity. This is an artefact of the UTCI being calculated as a polynomial beyond the range for which is it well conditioned and is related to Runge’s phenomenon wherein high-degree polynomial interpolations show large oscillations at the edges of the domain. We prevented this behaviour in this study by limiting the UTCI calculating to vapour pressure values below 7 kPa, which is approximately the saturation vapour pressure at 40°C. The values at which this occurs are so extreme that it is not a problem for general use of the UTCI but could limit its applicability in future extreme conditions. We have made assumptions about the mean radiant temperature and wind to calculate the UTCI, but our general qualitative description is still valid under different assumptions, see the Supplementary Fig. 3.

Use of different HSIs leads to different conclusions

We have highlighted two recent examples of papers which argued that an increase in soil moisture is generally harmful for heat stress due to an increase in humidity^11,12. Taken at face value, these studies foreclose climate adaptations that would reduce temperature extremes while increasing humidity. But in both cases, using a different HSI would have reversed the conclusion, which demonstrates the importance of choosing the appropriate HSI. This is concerning from the perspective of climate change adaptation action: if we cannot identify what metrics are meaningful then how are we to evaluate potential interventions?

In both Mishra et al¹² and Wouters et al¹¹, the choice of HSI was justified by regression of some measure of mortality against atmospheric conditions; however, in both cases the solution chosen is not demonstrated to be better than other alternatives, and uncertainty is not considered. While the association between mortality and temperature is well established by epidemiological studies, research into the effect of humidity on mortality has yielded conflicting results: variously finding a protective effect from humidity²⁷, a U-shaped relationship between humidity and mortality²⁸, or that no HSI is consistently better than others²⁹. This may be resolved in future as more multi-country epidemiological studies are performed.

Certain HSIs aim to be rationally based on more detailed assumptions about the human body (especially UTCI, HI, humidex). However, the complexity of these HSIs means it may be difficult to understand the differences between them. Documentation of the modelling assumptions used to derive different HSIs, for example, the body mass and metabolic rate assumed, is sparse. Our MTEC method allows the properties of HSIs to be compared without the need to closely examine the process used to derive the HSI.

The validity of WBT as a heat stress metric

While WBT was originally designed as a reliable field measurement of humidity, it is often presented as a model of human heat stress, especially in climate change scenarios where the survivability limit of 35°C is often emphasised¹⁹. In the present climate such extreme conditions are rare, occurring in certain locations for a few hours, but will become more common with climate change²¹. However, heat-related mortality is observed to occur in much less extreme conditions in the present climate. Sherwood³⁰ noted that WBT is not well calibrated as a generally applicable HSI: while it may be useful for describing future extreme weather it is not suitable for describing heat stress under normal conditions, but argued that WBT is still a useful metric when considering human tolerance of future extreme scenarios, mainly as WBT approaches human skin temperature. However, some studies use WBT as a HSI at relatively low values (25–30°C), which is misleading. A study exposing healthy volunteers to varied atmospheric conditions in experimental chambers has shown that the body temperature response to WBT is not consistent between high humidity and low humidity environments, demonstrating its unsuitability as a globally applicable indicator of human heat stress³¹; comparison of MTEC between WBT and UTCI provides a simple explanation of this observation in terms of sweat rate limitation.

WBT is defined as the lowest temperature that can be achieved by adiabatic evaporation, i.e., adding water mass to an air mass with no other heat exchange. Therefore, by definition, adiabatic evaporation occurs at constant thermodynamic WBT³². It is impossible to reduce WBT by adding water vapour (i.e., increasing specific humidity) to an air parcel. Therefore, evaporative cooling in the environment will only decrease the WBT if a meteorological feedback occurs, for example, if it leads to changes in air circulation. Any study where a change in specific humidity leads to a change in temperature is almost guaranteed to find that increasing specific humidity increases heat stress if they use WBT as the sole heat stress metric, regardless of whether the environment is humid or dry to begin with.

Limitations

In this study, we have only compared the effect of temperature and humidity for a non-exhaustive selection of commonly used HSIs. Radiation and wind are important components of heat stress but are beyond the scope of this paper. The effect of different calculation assumptions on the estimated effect of radiation could be an important avenue for future investigation which is also amenable to the MTEC approach.

Recommendations

HSIs do not have to be based on physiological assumptions if there is strong empirical justification for their use. For example, work to identify the most appropriate HSIs for use in occupational settings identified the indoor and outdoor WBGT and the UTCI as the best, based on 17 criteria derived from an expert consultation process (e.g., correlation coefficient between the HSI and body core temperature) evaluated against field data from multiple countries and occupational environments³³. However, if physiological justifications are used for a particular HSI, then the HSI used must correctly reflect physiology. For example, it is inappropriate to use WBT as an HSI except in extremely hot-humid conditions (which we estimate starts above a WBT of 32°C, Fig. 3c), as outside these conditions, it simply does not reflect physiological dynamics. It is generally preferable to use UTCI with simplified assumptions (that mean radiative temperature is equal to air temperature and wind is fixed) rather than using WBT, as this better reflects physiology.

Our MTEC method provides a straightforward and rational basis for comparisons between HSIs. Researchers can identify the range of temperature and relative humidity most relevant to their study, then examine Fig. 5 to identify whether there is likely to be disagreement between different HSIs in that range. We expect that in many cases it will be sufficient to compare results using HI, UTCI, and WBT as these cover most of the variation shown in Fig. 5. Calculating and reporting multiple HSIs can be useful, especially if disagreement is identified as a result.

In all cases, it is best practice to report component measurements as well as composite indices. For example, if reporting the 95th percentile HI, one should also report the temperature and humidity corresponding to that value (which will not necessarily be the 95th percentile of temperature and humidity separately) as this allows the reader to make conversions to other HSIs. If a change in (for example) WBT is reported, at a minimum the baseline value of WBT, as well as the corresponding baseline and change values of dry-bulb temperature need to be reported for it to be meaningful.

Vanos et al¹⁹ observed that only simple HSIs have been used for future projections, and that there may be a lack of communication between health scientists and climate scientists on this topic. While our method can address the problem of inappropriate or contradictory use of HSIs, HSIs in general cannot easily account for individual differences between people which are crucial to understanding the relationship between heat and health¹⁹. Use of heat balance models such as those demonstrated by Guzman-Echavarria, Middel and Vanos³⁴ may be a promising compromise between complexity and physiological accuracy.

In this study we presented a new method of comparing the sensitivity of different HSIs to temperature and humidity. From this we found that commonly used HSIs completely disagree about the effect of humidity under most atmospheric conditions. We presented examples where choice of heat stress metric reversed the conclusions of studies into the effect of soil moisture on heat stress. This is especially important in cases where a joint change in temperature and humidity is considered, for example as a result of expanding irrigation or increasing urban greening.

We argue that the choice of HSI needs to be specifically justified by the domain of the study, and that WBT should not be used as a sole indicator of heat stress. We encourage researchers to report component measurements (temperature and humidity) alongside their heat stress indices, as this allows conversion between different heat stress indices.

We present a more accessible numerical comparison of HSIs than previous studies and encourage researchers to critically assess how their findings may be dependent upon their choice of HSIs.

UTCI was calculated using the UTCI polynomial, which is described in Bröde et al and available on the web from www.utci.org. Wind Speed at 10m was assumed to be 0.5 m/s, which is the minimum value for which reference conditions were included³⁵. In this study, when an estimate of mean radiative temperature was required the air temperature was used; this is thought to be reasonably accurate for indoor conditions²⁴. When calculating the UTCI we limited the range of vapour pressure to 0-7kPa, as above this the polynomial is poorly conditioned and this is far beyond the range of normal vapour pressures. In Supplementary Fig. 4 we show that if, instead, the mean radiative temperature is assumed to be higher than air temperature by a constant increment, or if the wind speed is assumed to be higher, then the MTEC pattern of UTCI remains similar and MTEC generally increases.

WBT was calculated using the Davies-Jones method³⁶. Heat index was calculated using the National Oceanic and Atmospheric Administration specification from https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml. Apparent temperature was calculated based on Steadman’s shaded specification¹⁶ which we found in Ioannou et al³. Humidex is defined by the Meteorological Service of Canada; we used the equation listed in Ioannou et al. WBGT-indoor was calculated in line with Eq. 2 in Lemke and Kjellstrom¹⁸, where WBT was again calculated using the Davies-Jones method. sWBGT was calculated using the equation listed in Ioannou et al.

Data availability

The full Python code used in this analysis is archived and available for download from https://doi.org/10.5281/zenodo.7777647. No other data was generated by this study.

Competing interests

The Authors declare no Competing Financial or Non-Financial Interests.

Author contributions

CS: Conceptualization, Methodology, Software, Writing - Original draft. OB: Conceptualization, Writing - Review and Editing. KE: Writing - Review and Editing. CH: Conceptualization, Writing - Review and editing, Supervision, Funding acquisition.

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Commonly used indices completely disagree about the relative effect of moisture on heat stress

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Abstract

Figures

Introduction

Theory

Examples of heat stress index selection reversing the conclusion

When do commonly used indices agree?

Discussion

Use of different HSIs leads to different conclusions

The validity of WBT as a heat stress metric

Limitations

Recommendations

Conclusion

Methods

Declarations

Data availability

Competing interests

Author contributions

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

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	Kendall	Spearman
\({T}_{s}\)	0.66	0.83
WBT	0.85	0.94
UTCI	-0.85	-0.95
WBGT-indoor	0.18	0.24
Humidex	0.33	0.50
Heat index	-0.30	-0.37
sWBGT	0.64	0.75
Apparent temperature	-0.50	-0.61