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

The study investigates how the choice of heat stress index (HSI) influences conclusions about the role of atmospheric humidity in human heat stress, particularly under conditions relevant to climate adaptation measures such as irrigation and urban greening. While high humidity can impede evaporative cooling and increase heat stress, different HSIs weigh temperature and humidity differently and do not share a common scale, complicating comparisons. Prior work shows land-surface dryness can elevate air temperatures and that irrigation can lower temperatures, yet some studies claim drought reduces heat stress due to reduced humidity, or that irrigation increases heat stress because of increased humidity. This discrepancy suggests that conclusions about heat stress impacts of soil moisture changes may hinge on HSI selection. The authors focus on commonly used HSIs (wet-bulb temperature, WBGT and simplified WBGT, apparent temperature, NOAA heat index, humidex, and UTCI) and develop a quantitative method to compare their marginal sensitivities to temperature and humidity to identify conditions where indices agree or disagree.

The paper summarizes evidence that drier conditions can intensify heatwaves by raising air temperatures, while irrigated agriculture tends to reduce air temperatures; irrigation expansion has offset warming of extremes in certain regions. In contrast, some recent studies argue that droughts decrease heat stress and that irrigation increases heat stress due to humidity effects. These conflicting findings often arise from using different HSIs. The authors highlight examples: Wouters et al. argued soil drought reduces heatwave lethality using a specific metric, whereas Thiery et al. found irrigation mitigates temperature extremes. Mishra et al. concluded irrigation increases moist heat stress using WBT, while other indices (e.g., HI) decreased in their results. Prior reviews have noted HSI choice affects the emphasis on humidity, but systematic, quantitative comparison has been lacking, motivating the present analysis.

The authors introduce a calculus-of-variations-based comparison to quantify each HSI’s marginal sensitivity to temperature versus humidity on a common, unit-independent scale. For a given HSI U(T, h) defined over air temperature T and relative humidity h (scaled 0–100%), they define the marginal temperature-equivalent change M as the change in h that produces the same change in U as a 1 °C change in T. Mathematically, for small perturbations, M equals the ratio of partial derivatives (∂U/∂T) / (∂U/∂h). They estimate these partial derivatives numerically using forward finite differences, avoiding analytical differentiation where HSIs are not easily differentiable. This framework can be applied similarly in other variable spaces (e.g., temperature vs wind speed). They compute M fields across a grid of T–h conditions and compare M between indices by differencing. HSIs evaluated: wet-bulb temperature (WBT; Davies-Jones method); apparent temperature (Steadman shaded specification, including wind assumed 0.5 m s−1, no radiation); NOAA heat index (HI; official specification); humidex (Meteorological Service of Canada definition); UTCI (polynomial approximation with wind at 10 m set to 0.5 m s−1, mean radiant temperature assumed equal to air temperature; operational limits per Bröde et al. enforced); WBGT-indoor (calculated per Lemke and Kjellstrom using WBT); and simplified WBGT (sWBGT; standard approximation). Where needed, mean radiant temperature was taken equal to air temperature (more appropriate indoors). Sensitivity tests indicated that assuming higher mean radiant temperature or higher wind generally leaves the M pattern for UTCI similar and increases M overall. To contextualize physical plausibility, they delineate regions of T–h space that did not occur in the 1992–2022 ERA5 reanalysis (hourly 2 m air temperature and dew point used to derive relative humidity; for each humidity, the maximum co-occurring temperature identified). They also analyze case studies from the literature by computing changes in multiple HSIs from reported or modeled temperature and humidity perturbations and by comparing M fields over the relevant T–h ranges.

• Common HSIs disagree widely on the relative importance of temperature versus humidity except under very hot and humid conditions. Even indices in °C (e.g., WBT vs UTCI) are not directly comparable: identical WBT values map to a wide range of UTCI values, and their scales are offset (e.g., WBT 35 °C roughly aligns with UTCI 55 °C).
• The marginal temperature-equivalent change M provides a unified comparison: high M means the index is more sensitive to temperature (a large RH change is needed to match a 1 °C change), and low M means greater sensitivity to humidity.
• Agreement regimes:
  • Low-temperature regime (≤20 °C): AT, HI, and UTCI predominantly respond to temperature (high M), whereas WBT has very low M; humidex, WBGT-indoor, and sWBGT are in between but closer to WBT. Physiologically, humidity effects are expected to be minor here.
  • Hot-dry regime (≈40 °C, 20% RH): AT, WBT, humidex, WBGT-indoor, and sWBGT have relatively low M (humidity changes meaningfully affect the HSI), while HI and UTCI exhibit zones of high M (temperature dominates). Higher M in UTCI here is attributable to sweat secretion limits in its underlying thermophysiological model.
  • Hot-humid regime (e.g., ≈35 °C, 80% RH): all assessed HSIs have low M, indicating broad agreement that humidity changes are highly consequential.
• Direct comparison of UTCI vs WBT: ΔM (UTCI minus WBT) is generally positive at low T and low RH (humidity is much more important for WBT than UTCI), and approaches zero at very hot-humid conditions. They are most similar around WBT ≈ 35 °C (UTCI ≈ 55 °C). In the present climate, WBT rarely exceeds 31 °C, though brief exceedances of 35 °C occur in limited locations and could expand with large global warming (~7 °C).
• Case-study reanalyses demonstrate conclusion reversals with different HSIs:
  • Wouters et al. (2022): Using their metric Ts = WBT + 4.5(1 − h²), increases in soil moisture (raising specific humidity, lowering temperature) were associated with higher Ts (implying worse heat stress). However, rank correlations between modeled specific humidity changes and HSI changes computed here show strong positive correlations for WBT (Kendall 0.85; Spearman 0.94) and Ts (0.66; 0.83) but strong negative for UTCI (−0.85; −0.95), HI (−0.30; −0.37), and AT (−0.50; −0.61). Thus, different HSIs yield opposite conclusions about soil moisture impacts.
  • Mishra et al. (2020): Irrigation increased WBT’s 95th percentile but decreased 95th percentile temperature and HI; emphasizing WBT led to the conclusion that irrigation worsens heat stress, whereas HI suggested improvement.
• Physiological coherence: Patterns of M align with known thermoregulation: at hot-dry, high required sweat rates but efficient evaporation imply humidity increases can strongly worsen stress (low M), while model-imposed sweat limits can mute humidity sensitivity (higher M in UTCI/HI).

The findings show that widely used HSIs encode different relative sensitivities to temperature and humidity, such that conclusions about interventions that jointly alter both (e.g., irrigation, urban greening) can be index-dependent and even reversed. The proposed marginal temperature-equivalent change framework enables objective, unit-independent comparisons across indices and atmospheric regimes, allowing researchers to anticipate disagreement from baseline T–h conditions before running complex models. The case studies illustrate practical stakes: using WBT or a WBT-augmented metric can imply that added moisture (from higher soil moisture or irrigation) worsens heat stress, while HI, AT, or UTCI may indicate the opposite due to stronger weighting of temperature reductions. The work underscores the need to align HSI choice with physiological realism and the target population or outcome, to recognize applicability limits of each index (e.g., UTCI undefined at very high vapor pressure; NOAA HI poorly extrapolated at extreme heat and humidity), and to report component variables alongside composite HSIs for transparent cross-index interpretation. These insights have direct implications for evaluating and communicating climate adaptation strategies intended to mitigate heat exposure.

The study introduces a simple, quantitative method (M) to compare HSIs’ marginal sensitivity to temperature versus humidity, overcoming unit and scale incompatibilities. Applying this method reveals substantial disagreement among commonly used HSIs outside very hot-humid conditions and demonstrates that index choice can reverse conclusions about the heat-stress impacts of soil moisture changes, irrigation, and greening. The authors recommend: selecting HSIs grounded in the intended application and population; where possible, using physiologically consistent indices (e.g., UTCI with clear assumptions) instead of relying solely on WBT; calculating and reporting multiple HSIs when disagreement is likely; and always reporting the underlying temperature and humidity alongside composite indices. The approach offers a practical tool for researchers and practitioners to make informed HSI choices and to enhance robustness in heat-health assessments and adaptation evaluations. Future work should extend the framework to include wind and radiation effects and broaden evaluation across more HSIs and populations.

• The analysis focuses on temperature and humidity, omitting explicit treatment of radiation and wind in the main comparisons; assumptions such as mean radiant temperature equal to air temperature and fixed wind (0.5 m s−1) may not reflect many outdoor settings.
• UTCI calculations are constrained by operational limits (e.g., vapor pressure >5 kPa, air temperature >50 °C), and NOAA HI extrapolates poorly at extreme heat-humidity combinations; these constraints limit global and extreme-condition applicability.
• The set of HSIs examined is non-exhaustive; simplified indices (e.g., sWBGT) are known to be poor approximations of more detailed measures.
• Numerical estimation of partial derivatives uses forward finite differences, introducing approximation error, especially where HSIs are not smooth.
• Relative humidity was the primary humidity metric; although key results are consistent when using specific humidity, comparisons across temperatures can be complicated by Clausius–Clapeyron effects.
• ERA5-based delineation of plausible present-day T–h space may differ from local microclimates or observational records; conclusions about rarity of conditions depend on reanalysis fidelity.
• Many HSIs embed fixed physiological and activity assumptions (e.g., UTCI’s 74 kg person walking at 1.1 m s−1), limiting representativeness for diverse or vulnerable populations.