Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper combines physical climate hazard (WBGT) with socio-economic vulnerability (GVI) to examine cross-country inequality in heat exposure for outdoor sport and physical activity. The framing is novel and touches on a timely climate justice issue. That said, several points need attention in revision. My detailed comments are below.

 

1.Introduction

 

(1).The introduction spends considerable space on the physiological rationale and on WBGT as an index, but the research gap and the paper‘s specific contributions are not drawn together into a clear, upfront summary. Readers have to extract the three research questions from later paragraphs, which dilutes the opening’s impact.

(2).The distinctiveness of the “sport” lens is not sufficiently justified. Lines 72–81 stress that the analysis is population‑based rather than elite‑athlete focused. This raises an obvious question: if the study uses WBGT and general population exposure, what fundamentally separates it from existing work on occupational heat exposure or heat‑related health risks? If the only difference is rebranding the application context, without a clear argument for why “sport/physical activity” entails a distinct loss of public‑health co‑benefits, the framing‘s academic rationale remains unclear.

(3).The engagement with prior literature is too narrow. The fifth paragraph critiques Sawadogo et al. [22] for focusing on event location, but citing only that one study makes the comparison feel limited. I suggest broadening the discussion to include work on occupational heat stress and on quantitative metrics of climate inequality. Otherwise, readers could easily conclude that the advance here is merely scaling up from regional/event to global analysis.

 

2.Materials and Methods

 

(1).The WBGT reconstruction has limitations that are not acknowledged. Lines 117–127 describe the Stull‑based approximation for afternoon WBGT but say nothing about possible systematic biases in very humid or extremely arid regions. The authors should briefly note this uncertainty and clarify that, because the main findings rely on cross‑country rankings (CI), such biases are less likely to affect the relative conclusions than the absolute numbers.

(2).The GVI dimensions are not specified. Section 2.5 mentions that the GVI covers seven dimensions but does not list them. It is therefore unclear whether the “vulnerability” measured here reflects poor health infrastructure, weak governance, high poverty, or something else. Listing these dimensions briefly would help make the policy discussion more concrete.

 

3.Results

 

(1).The apparent tension between large‑population countries and the concentration result needs clarification. Lines 231–235 note that the United States appears in Table 1 largely because of its population size, despite a low GVI (16.7). This could seem to contradict the concentration finding. I suggest adding a sentence in Section 3.1 to make clear that although absolute burden is driven by population size, the structural inequality remains visible when one looks at per‑capita exposure (e.g., 69 days for India vs. 18 days for the US) alongside the GVI gradient.

(2).The “decoupling” result should be explicitly tied to SSP assumptions. In Section 3.3, the decline (and even partial crossing) of the CI under SSP1‑2.6 in 2085 is attributed to “development” reducing vulnerability in the most exposed countries. The text does not clearly state that this decoupling is driven by the socio‑economic assumptions built into SSP1 (rapid poverty reduction, better education, improved governance), not by physical changes in the climate system itself. This point is touched on in the Discussion, but it should be stated explicitly in the Results to avoid any misleading impression that warming alone will self‑correct inequality.

 

4.Discussion

 

The Discussion interprets the mechanisms and scenario contrasts reasonably well, but it does not engage systematically with the existing quantitative literature. It reads somewhat as a self‑contained account, without clearly positioning the findings relative to earlier work.

(1).There is no quantitative benchmarking against studies on climate inequality. Sections 4.1 and 4.2 stress that the concentration index is positive and increases with heat severity, but the paper never compares its CI values (0.09–0.25) with analogous inequality metrics from previous work (e.g., Gini coefficients or decile ratios for temperature extremes). Without such a comparison, readers have no way of judging whether the degree of inequality found here is moderate or severe by established standards.

(2).The policy recommendations are too broad. The concluding paragraphs (lines 367–383) call for mitigation and development in general terms, but offer little that is sport‑specific or actionable. I would encourage the authors to be more concrete—for example, in vulnerable regions like the Sahel, international sport federations and public‑health agencies could direct climate adaptation funds towards heat‑resilient upgrades to school sports facilities, such as shaded areas, evaporative cooling, and flexible training schedules. This kind of specificity would greatly strengthen the practical takeaway.

 

5.References

The authors should also check the reference list for normative compliance. Reference [34] (Lescure & Defrance, 2026, Research Square Preprint) is a non‑peer‑reviewed preprint, yet it is used in Section 4.5 to support a key contextual statement about broader thermal constraints. I suggest either waiting until this work is formally published before citing it, or replacing it with an already‑published alternative. 

Author Response

Response to Reviewer 2

We sincerely thank the reviewer for the positive assessment of the manuscript and for the constructive comments. The manuscript has been substantially revised, including a clearer statement of the research gap, a stronger justification of the sport and physical-activity framing, expanded engagement with adjacent literatures, more detailed methodological documentation, model-specific uncertainty analyses, and a more cautious interpretation of the scenario contrasts. Our point-by-point responses are provided below.

1. Introduction

Comment 1.1

The introduction spends considerable space on the physiological rationale and on WBGT as an index, but the research gap and the paper’s specific contributions are not drawn together into a clear, upfront summary. Readers have to extract the three research questions from later paragraphs, which dilutes the opening’s impact.

Response: We agree and have substantially revised the final part of the Introduction. The revised text now brings together the relevant research strands, identifies the specific unresolved gap, explains the contribution of the present study, and presents the three research questions in a single explicit sequence. The study is now framed as connecting research on sport-related heat, population exposure and climate inequality, rather than merely extending an event-location analysis to the global scale.

Comment 1.2

The distinctiveness of the “sport” lens is not sufficiently justified. Lines 72–81 stress that the analysis is population-based rather than elite-athlete focused. This raises an obvious question: if the study uses WBGT and general population exposure, what fundamentally separates it from existing work on occupational heat exposure or heat-related health risks? If the only difference is rebranding the application context, without a clear argument for why “sport/physical activity” entails a distinct loss of public-health co-benefits, the framing’s academic rationale remains unclear.

Response: We agree that the sport and physical-activity relevance required a clearer justification. The revised Introduction now explains that the sport lens arises from the use of WBGT thresholds that are operationally linked to outdoor-sport heat policies and from the potential loss of opportunities for school sport, youth sport, community sport and informal physical activity. We also explain that access to protective infrastructure, shaded or indoor facilities, medical supervision and flexible scheduling is unevenly distributed across countries.

In addition, the Methods and Discussion now consistently describe “sport-relevant heat exposure” as a screening-level, population-based proxy. We explicitly state that the analysis does not measure actual sport participation, athlete exposure, activity duration or health outcomes.

Comment 1.3

The engagement with prior literature is too narrow. The fifth paragraph critiques Sawadogo et al. [22] for focusing on event location, but citing only that one study makes the comparison feel limited. I suggest broadening the discussion to include work on occupational heat stress and on quantitative metrics of climate inequality. Otherwise, readers could easily conclude that the advance here is merely scaling up from regional/event to global analysis.

Response: Addressed. The Introduction has been broadened to engage with research on occupational heat and work capacity, climate change and physical activity, school-based sport, exercise physiology, population exposure and inequalities in heat-related health and urban environments. The revised text now explains that these research strands provide complementary physiological, operational and distributional foundations for the analysis, but have not previously been combined to quantify the future country-level distribution of a population-based sport-relevant WBGT burden along a projected national vulnerability gradient.

2. Materials and Methods

Comment 2.1

The WBGT reconstruction has limitations that are not acknowledged. Lines 117–127 describe the Stull-based approximation for afternoon WBGT but say nothing about possible systematic biases in very humid or extremely arid regions. The authors should briefly note this uncertainty and clarify that, because the main findings rely on cross-country rankings (CI), such biases are less likely to affect the relative conclusions than the absolute numbers.

Response: Addressed. The revised manuscript now discusses the uncertainty associated with the analytical wet-bulb approximation and empirical black-globe-temperature reconstruction. We specifically acknowledge that errors may be regionally dependent and may be greater in very dry or very humid environments, regions with strong humidity gradients, complex terrain, coastal circulations, and unresolved local radiation or ventilation conditions.

We adopted a more conservative interpretation than assuming that rank-based results are necessarily protected from reconstruction bias. Spatially heterogeneous errors may affect both absolute exceedance frequencies and country rankings, particularly where projected exposure lies close to the nonlinear WBGT thresholds. This limitation is now stated explicitly.

Comment 2.2

The GVI dimensions are not specified. Section 2.5 mentions that the GVI covers seven dimensions but does not list them. It is therefore unclear whether the “vulnerability” measured here reflects poor health infrastructure, weak governance, high poverty, or something else. Listing these dimensions briefly would help make the policy discussion more concrete.

Response: Addressed. Section 2.5 now lists the seven dimensions represented in the GVI: economy, education, gender, health, infrastructure, governance and demography. We have also added information on the underlying indicators, principal-component construction, scale and published external validation of the index.

3. Results

Comment 3.1

The apparent tension between large-population countries and the concentration result needs clarification. Lines 231–235 note that the United States appears in Table 1 largely because of its population size, despite a low GVI (16.7). This could seem to contradict the concentration finding. I suggest adding a sentence in Section 3.1 to make clear that although absolute burden is driven by population size, the structural inequality remains visible when one looks at per-capita exposure (e.g., 69 days for India vs. 18 days for the US) alongside the GVI gradient.

Response: Addressed. We have added an explicit comparison between total burden and per-capita exposure in Section 3.1. The revised text notes that India has a five-model mean population-weighted per-capita exposure of 68.7 days per resident, compared with 17.9 days in the United States, while their projected GVI values are 31.6 and 16.7, respectively.

We now clarify that a highly populated, lower-GVI country may appear among the countries with the largest absolute burdens without contradicting the positive concentration of exposure along the vulnerability gradient. Total burden, per-capita exposure and vulnerability provide complementary rather than interchangeable information.

Comment 3.2

The “decoupling” result should be explicitly tied to SSP assumptions. In Section 3.3, the decline (and even partial crossing) of the CI under SSP1-2.6 in 2085 is attributed to “development” reducing vulnerability in the most exposed countries. The text does not clearly state that this decoupling is driven by the socio-economic assumptions built into SSP1, not by physical changes in the climate system itself. This point is touched on in the Discussion, but it should be stated explicitly in the Results to avoid any misleading impression that warming alone will self-correct inequality.

Response: Addressed. The Results now explicitly state that the comparatively low late-century CI under SSP1-2.6 should not be interpreted as a self-correcting physical effect of warming. It partly reflects the SSP1-specific projected reordering of countries along the GVI gradient.

The revised manuscript also presents a fixed-2020 GVI-ranking sensitivity analysis. This analysis shows that the low SSP1-2.6 late-century CI depends substantially on the projected reordering of countries: when the ranking is held fixed, the CI increases markedly. Section 3.6 further clarifies that SSP1-2.6 and SSP2-4.5 are integrated futures in which climate, population and socio-economic vulnerability evolve jointly, and that their contrast cannot isolate the contribution of any single driver.

4. Discussion

Comment 4.1

There is no quantitative benchmarking against studies on climate inequality. Sections 4.1 and 4.2 stress that the concentration index is positive and increases with heat severity, but the paper never compares its CI values (0.09–0.25) with analogous inequality metrics from previous work, such as Gini coefficients or decile ratios for temperature extremes. Without such a comparison, readers have no way of judging whether the degree of inequality found here is moderate or severe by established standards.

Response: We agree that the magnitude of the reported indices required additional context. However, direct numerical comparison with published Gini coefficients or decile ratios would be potentially misleading because these measures differ in their construction, population weighting, ranking variable and feasible bounds.

The concentration index used here is rank-dependent and preserves the direction of concentration along the projected national vulnerability gradient. A conventional Gini coefficient instead measures unranked dispersion, while decile ratios compare selected parts of a distribution. We have therefore added a paragraph explaining why the observed CI range of 0.09–0.25 cannot be assigned universal categories such as low, moderate or severe inequality through direct comparison with these other metrics.

The revised Discussion interprets the CI comparatively across pathways, horizons and WBGT thresholds, and jointly with the full concentration curves and population-weighted quintile burden shares.

Comment 4.2

The policy recommendations are too broad. The concluding paragraphs call for mitigation and development in general terms, but offer little that is sport-specific or actionable. I would encourage the authors to be more concrete—for example, in vulnerable regions like the Sahel, international sport federations and public-health agencies could direct climate adaptation funds towards heat-resilient upgrades to school sports facilities, such as shaded areas, evaporative cooling, and flexible training schedules. This kind of specificity would greatly strengthen the practical takeaway.

Response: Addressed. We have added more concrete sport- and physical-activity-specific adaptation implications to the Discussion and Conclusion.

The revised text explains that the screening-level results may help identify locations where detailed local assessment and investment should be prioritised. For high-exposure and high-vulnerability regions, including parts of the Sahel, South Asia and sub-Saharan Africa, the manuscript now identifies the following examples:

• shaded or covered school and community activity areas;
• reliable access to drinking water and context-appropriate cooling;
• locally calibrated heat-action protocols;
• flexible training, competition and school-sport schedules.

We also clarify that these measures should be adapted to local climatic conditions, available infrastructure, resources and participation patterns, rather than applied as uniform global prescriptions. The regions identified for prioritisation correspond to the joint high-exposure and high-vulnerability patterns shown in Figure 1.

5. References

Comment 5.1

The authors should also check the reference list for normative compliance. Reference [34] (Lescure & Defrance, 2026, Research Square Preprint) is a non-peer-reviewed preprint, yet it is used in Section 4.5 to support a key contextual statement about broader thermal constraints. I suggest either waiting until this work is formally published before citing it, or replacing it with an already-published alternative.

Response: Addressed. The cited study has since been formally published in Theoretical and Applied Climatology. The preprint reference has been replaced with the final peer-reviewed article, including its complete bibliographic information and DOI.

Reviewer 2 Report

Comments and Suggestions for Authors

General Assessment

This manuscript addresses a timely and policy-relevant question: whether future population exposure to sport-relevant heat is disproportionately concentrated in countries with higher socio-economic vulnerability. The study combines reconstructed afternoon Wet-Bulb Globe Temperature (WBGT) exceedance frequencies from a five-model, bias-corrected CMIP6 ensemble, SSP-consistent gridded population projections, and a national Global Vulnerability Index (GVI). It then evaluates the distribution of population-weighted heat exposure along the vulnerability gradient using concentration curves and a Concentration Index (CI).

The manuscript is clearly written, the analytical workflow is generally understandable, and the attempt to introduce an explicit distributional and climate-justice perspective into the sport-climate literature is valuable. The use of coherent SSP-based climate, demographic, and vulnerability projections is also an important strength.

However, the manuscript currently makes several claims that are stronger than the analysis can support. The main concerns relate to: (i) the conceptual characterization of the hazard-exposure-vulnerability framework; (ii) insufficient propagation of climate-model and statistical uncertainty; (iii) the dependence of the CI results on the selected vulnerability ranking; (iv) the attribution of differences between integrated SSP futures; (v) the interpretation of resident-population exposure as sport-related exposure; and (vi) insufficient methodological detail regarding the WBGT reconstruction.

These issues affect the interpretation of the principal findings rather than only their presentation. I therefore recommend major revision before the manuscript can be considered for publication.

Major Comments

1. Conceptual consistency of the hazard-exposure-vulnerability framework

The manuscript repeatedly presents the analysis as an explicit Hazard × Exposure × Vulnerability framework. However, vulnerability is not included in the calculation of the exposure burden. At grid-cell level, the only mathematical product is:

where population is multiplied by WBGT exceedance frequency. Vulnerability is subsequently introduced at the national level as the variable used to rank countries for the concentration analysis.

The authors correctly state in Section 2.1 that vulnerability is “never” used as a third multiplicative grid layer. Nevertheless, retaining the notation A × E × V may remain conceptually misleading because the calculated quantity is not a multiplicative risk metric incorporating vulnerability.

The authors should therefore either:

1. revise the terminology throughout the manuscript; or
2. provide a stronger conceptual justification for retaining the A × E × V notation.

A more accurate formulation would be:

“a hazard-population exposure assessment evaluated along a national socio-economic vulnerability gradient”

or:

“a hazard-exposure analysis stratified by socio-economic vulnerability.”

This distinction is important because the study measures the distribution of a climate-exposure burden according to vulnerability; it does not estimate vulnerability-weighted risk, health impact, or loss of adaptive capacity.

The manuscript should also consistently distinguish among:

• hazard frequency;
• population exposure;
• person-days of exposure;
• population-weighted per-capita exposure;
• socio-economic vulnerability;
• risk or impact.

At present, these concepts are occasionally discussed as though they were interchangeable.

2. Climate-model uncertainty is not sufficiently propagated through the analysis

The analysis uses five CMIP6 models, but the main results appear to be calculated from ensemble-mean WBGT exceedance fields. This is a major limitation because threshold-exceedance metrics are nonlinear. Calculating exceedance frequency from an ensemble-mean field is not necessarily equivalent to calculating exceedance frequency separately for each model and subsequently averaging the resulting metrics.

The manuscript should clearly specify the order of operations:

• Was WBGT reconstructed separately for each climate model?
• Were threshold exceedance days computed for each model before ensemble averaging?
• Or was an ensemble-mean WBGT field produced before applying the thresholds?
• Were country burdens and CIs calculated separately by model?

The current Data Availability Statement reports ensemble minimum, maximum, and mean products, but the uncertainty represented by these products is not propagated into the country burden, ranking, concentration curves, or CI estimates.

At minimum, the authors should:

• calculate country-level burden and CI separately for each climate model;
• report the median or mean CI across models;
• provide inter-model ranges, interquartile ranges, or other appropriate uncertainty intervals;
• show whether the sign of the CI remains positive for all individual models;
• assess whether the increase in CI with WBGT severity is consistent across models;
• evaluate the stability of the highest-burden country rankings.

This is particularly important for the claim that increasing heat severity systematically concentrates exposure on more vulnerable countries. Such a conclusion should not be based solely on a five-model ensemble mean.

3. Statistical uncertainty and inference for the Concentration Index

The manuscript reports CI values to three decimal places but provides no confidence intervals, uncertainty bounds, or statistical tests. This creates an impression of precision that is not supported by the analysis.

Several reported differences are very small. For example:

• SSP1-2.6 in 2085: CI decreases from 0.102 to 0.091;
• SSP2-4.5 in 2085: CI changes from 0.161 to 0.163;
• SSP2-4.5 in 2055: CI changes from 0.173 to 0.169 before increasing to 0.198.

Without uncertainty estimates, it is not possible to determine whether these differences represent robust changes, sensitivity to model selection, country aggregation effects, or negligible numerical variation.

The authors should provide uncertainty intervals for the CI. Depending on the intended inferential framework, these could be derived through:

• resampling countries;
• population-weighted bootstrap procedures;
• resampling climate models;
• a hierarchical bootstrap incorporating both country and climate-model variability;
• analytical standard errors appropriate for grouped concentration indices.

The manuscript should also distinguish between:

• a positive point estimate;
• evidence that the CI is statistically distinguishable from zero;
• evidence that two CI values differ from one another;
• evidence of a monotonic relationship between WBGT severity and concentration.

Claims such as “severity concentrates the burden further” require more than visually increasing point estimates in one or two scenario-horizon combinations.

4. The concentration results are not independent of the vulnerability index

The manuscript repeatedly argues that the severity gradient is independent of the vulnerability metric because WBGT is calculated independently of the GVI. This reasoning is incomplete.

Although the physical hazard is calculated independently of vulnerability, the CI depends explicitly on:

• the selected vulnerability indicator;
• its constituent dimensions;
• the weighting of those dimensions;
• its projected SSP-specific trajectories;
• its national spatial resolution;
• the ranking of countries generated by the indicator.

Therefore, the measured concentration and its variation across WBGT thresholds remain conditional on the chosen vulnerability ranking. A different vulnerability metric could reorder countries and alter both the concentration curves and the CI.

The statements in Sections 2.7, 3.3, 4.2, Figure 3, and the conclusions should be revised. The analysis may suggest that the geographical distribution of increasingly severe heat contributes to stronger concentration under a particular GVI ranking. It does not demonstrate independence from vulnerability measurement.

The authors should conduct sensitivity analyses using alternative rankings, where data permit. Possible alternatives include:

• Human Development Index;
• income per capita;
• ND-GAIN vulnerability or readiness indicators;
• adaptive-capacity indicators;
• individual components of the GVI;
• a fixed baseline vulnerability ranking rather than SSP-varying rankings.

At minimum, the authors should repeat the CI calculations using several GVI subcomponents or plausible alternative weighting schemes.

A more defensible interpretation would be:

“The geographical distribution of severe WBGT exceedance contributes to the observed increase in concentration, although the magnitude of the CI remains conditional on the vulnerability metric and country ranking used.”

5. The analysis does not isolate mitigation, demographic, and development effects

The comparison between SSP1-2.6 and SSP2-4.5 changes several drivers simultaneously:

• radiative forcing and climate hazard;
• population size and spatial distribution;
• socio-economic development;
• projected vulnerability;
• country rankings along the vulnerability gradient.

Consequently, the observed difference between the two scenarios cannot be attributed separately to “mitigation,” “development,” or a “double dividend” without additional analysis.

The manuscript should present SSP1-2.6 and SSP2-4.5 primarily as alternative integrated futures, rather than treating their differences as causal estimates of individual policy levers.

To separate the contributions, the authors could perform a factorial or counterfactual decomposition, for example:

• SSP1 climate + SSP1 population + SSP1 vulnerability;
• SSP2 climate + SSP1 population + SSP1 vulnerability;
• SSP1 climate + SSP2 population + SSP1 vulnerability;
• SSP1 climate + SSP1 population + SSP2 vulnerability.

Such combinations would help quantify the contributions of hazard, demography, and vulnerability trajectories, while acknowledging that some combinations are intentionally counterfactual.

If no decomposition is performed, the discussion and conclusions should avoid language implying that the study has independently quantified mitigation and development effects.

6. Temporal mismatch between climatological exposure and central-year population

The climate hazard represents an average over 30-year periods, 2041-2070 and 2071-2100, whereas population and vulnerability are represented by single central-year values, 2055 and 2085.

This is a simplifying assumption rather than a fully temporally integrated exposure assessment. It may be consequential in countries undergoing rapid population growth, decline, urbanization, migration, or socio-economic change.

The authors should:

• justify the use of central-year population and vulnerability values;
• clarify whether 2055 and 2085 are exact mathematical midpoints or representative labels;
• evaluate sensitivity to alternative population years;
• preferably calculate time-averaged population exposure using population data across each climatological window, if the required data are available.

At minimum, a sensitivity analysis using population at the beginning, midpoint, and end of each period would indicate whether the country burden and CI rankings are materially affected.

7. “Unsafe regime” is too categorical for the metric used

The manuscript defines an “unsafe regime” as residence in a grid cell experiencing at least a specified number of annual days above WBGT 32 °C. This terminology implies a direct and universal determination of safety.

However, the authors themselves acknowledge that:

• WBGT thresholds differ across sports;
• physiological tolerance depends on age, acclimatization, clothing, health status, intensity, and duration;
• the WBGT reconstruction is a screening-level approximation;
• actual activity schedules and adaptation measures are unknown.

Accordingly, “unsafe regime” is stronger than the evidence supports.

More appropriate terminology would include:

• “high-frequency severe-WBGT exceedance regime”;
• “potentially unsafe heat regime”;
• “screening-level high-risk heat regime”;
• “persistent severe heat-exceedance regime.”

The revised terminology should be used consistently in the abstract, methods, results, figures, discussion, and conclusions.

8. The relationship between resident-population exposure and sport exposure needs stricter interpretation

The study does not quantify the exposure of athletes, schoolchildren participating in sport, outdoor workers, recreational exercisers, or any other activity-defined population. It estimates the number of residents living in places where afternoon WBGT thresholds are exceeded.

No data are included on:

• sport participation rates;
• timing or duration of physical activity;
• age structure;
• type or intensity of sport;
• indoor versus outdoor participation;
• school schedules;
• access to shade or cooling;
• heat-action plans;
• behavioural adaptation;
• local WBGT policies.

The manuscript acknowledges this limitation but then extends the interpretation to school sport, youth sport, community sport, and everyday physical activity. These are plausible implications, not directly measured outcomes.

The authors should more rigorously separate:

1. Directly measured: population living in grid cells with specified WBGT exceedance frequencies.
2. Inferred implication: potential constraints on opportunities for outdoor sport and physical activity.
3. Not measured: realized exposure, participation loss, health outcomes, cancellation days, or adaptation failure.

The title, abstract, and conclusions should avoid giving the impression that actual sport participation or athletic exposure was quantified. The term “sport-relevant heat exposure” may be retained only if it is repeatedly defined as a screening-level, population-based proxy.

9. Insufficient methodological detail for the WBGT reconstruction

The WBGT reconstruction is the core hazard component, yet Section 2.2 refers readers to a companion study for most technical details.

A research article should remain sufficiently self-contained for readers to evaluate the appropriateness and reproducibility of its primary exposure metric. The manuscript should therefore provide, in the main text or supplementary material:

• the full WBGT equation;
• the method used to estimate wet-bulb temperature;
• how relative humidity was made consistent with daily maximum temperature;
• the globe-temperature or radiation formulation;
• assumptions regarding solar radiation and wind speed;
• whether shaded or outdoor-sun WBGT was estimated;
• treatment of missing values;
• temporal aggregation procedures;
• threshold application procedures;
• the exact order of model-level and ensemble-level processing;
• a concise summary of validation performance;
• geographical variation in reconstruction error;
• known limitations in arid, humid, coastal, mountainous, or high-latitude environments.

The use of daily maximum temperature to approximate afternoon WBGT also deserves further discussion because the timing of maximum temperature, humidity minima, radiation maxima, and wind conditions may not coincide.

10. Spatial aggregation and country assignment require sensitivity assessment

The population data are aggregated from approximately 1-km resolution to a 0.25° climate grid, after which grid cells are assigned to countries through rasterized national boundaries.

This may introduce substantial uncertainties for:

• small island developing states;
• narrow coastal countries;
• fragmented archipelagos;
• countries with irregular borders;
• transboundary metropolitan regions;
• coastal cells containing both land and ocean;
• countries represented by very few 0.25° cells.

The authors should specify:

• whether cell centroids, majority-area assignment, or fractional coverage were used;
• how coastal and border cells were treated;
• whether population was clipped by national boundaries before aggregation;
• whether grid cells could contribute fractionally to several countries;
• how countries with no valid 0.25° land-cell centroid were retained;
• whether overseas territories were included;
• which countries or territories were excluded.

A sensitivity analysis using fractional area or population-weighted country allocation would be valuable. The number of countries included in each scenario-horizon calculation should also be reported.

11. Properties and comparability of the Concentration Index need fuller discussion

The CI is applied to grouped national data while individuals inherit the GVI value of their country. This creates a large number of tied ranks and ignores within-country inequality.

The manuscript should clarify:

• how fractional ranks were assigned when countries had tied or nearly tied GVI values;
• whether the CI estimator was corrected for grouped data;
• whether countries with missing population, hazard, or GVI values were excluded;
• whether the set of included countries was identical across scenarios and horizons;
• how zero-exposure countries were treated;
• whether the standard CI bounds remain appropriate for the distribution used.

The authors state that the CI lies between −1 and 1. However, the feasible bounds of concentration indices can depend on the nature and distribution of the outcome variable and on grouped rankings. This issue should be verified and, if necessary, clarified.

The manuscript should also explain why a population-weighted CI of country-level per-capita exposure was selected instead of alternative inequality measures, such as:

• slope index of inequality;
• relative index of inequality;
• Gini-type exposure indices;
• quantile contrasts;
• regression-based associations between GVI and exposure.

Complementary measures would make the distributional interpretation more robust, particularly where concentration curves cross the equality line.

12. Concentration-curve crossings limit the interpretation of a single CI

For SSP1-2.6 in 2085, the concentration curves cross the equality line. In such cases, a single summary CI can conceal offsetting inequalities across different parts of the vulnerability distribution.

Although the manuscript acknowledges this issue, the analysis should go further. The authors should consider reporting:

• cumulative burden shares by vulnerability quintile or decile;
• partial concentration indices;
• dominance tests between curves;
• separate results for the least, middle, and most vulnerable population groups;
• absolute and relative inequality measures.

The manuscript should avoid summarizing crossing curves as simply representing a “lower concentration.” The same CI can arise from substantially different distributional structures.

13. Country-level vulnerability may not support some adaptation claims

The manuscript interprets national GVI as reflecting the ability to provide indoor facilities, medical supervision, cooling, scheduling flexibility, and formal heat policies. However, these specific sport-sector capacities are not directly measured by the GVI.

The authors should avoid assuming that the composite national GVI is a validated proxy for sport-specific adaptive capacity. Such implications should be presented as hypotheses or plausible mechanisms.

A stronger analysis could compare the results with sport-relevant indicators, where available, such as:

• access to electricity;
• urban green space;
• school infrastructure;
• health-system capacity;
• air-conditioning access;
• public expenditure on sport;
• prevalence of formal heat-action plans.

Without such data, the discussion should refer to general socio-economic vulnerability rather than specific sport-adaptation capacity.

14. Novelty claims should be moderated and more comprehensively supported

The manuscript states that this is the first global, country-resolved demonstration of inequity in outdoor sport and physical activity heat exposure.

“First” claims require a comprehensive and reproducible literature search, especially given the rapidly expanding literature on climate, sport, occupational heat, physical activity, and environmental inequality.

The authors should either provide stronger support for the claim or use more cautious wording, such as:

“To our knowledge, this study is among the first global country-level assessments of the distribution of sport-relevant heat exposure along a socio-economic vulnerability gradient.”

The literature review should also more clearly distinguish this study from existing global work on:

• physical activity and climate change;
• climate suitability for sporting events;
• heat exposure and work capacity;
• school and community sport under extreme heat;
• international inequalities in climate-related heat exposure.

15. Conclusions should be aligned more closely with the evidence

The conclusion that the erosion of safe outdoor activity is “structurally inequitable” is plausible, but the current analysis establishes a between-country statistical concentration of modeled population exposure along one national vulnerability index. It does not directly quantify structural mechanisms, participation losses, health effects, or adaptation capacity.

The conclusions should therefore be reframed to emphasize that:

• the study identifies a projected between-country distributional inequality;
• the inequality is conditional on the selected GVI and SSP assumptions;
• the outcome is potential resident-population exposure;
• within-country inequality is not resolved;
• causal mechanisms are not directly evaluated;
• scenario contrasts represent integrated futures rather than isolated policy effects.

Minor Comments

1. Clearly define and consistently distinguish “total exposure burden,” “per-capita exposure,” “exceedance frequency,” and “population in a persistent exceedance regime.”
2. In the abstract, avoid presenting the SSP1-2.6 versus SSP2-4.5 contrast as direct evidence of separate mitigation and development effects.
3. Remind readers in all relevant table and figure captions that 2055 and 2085 refer to central-year labels for the 2041-2070 and 2071-2100 climatological windows.
4. Report the exact number of countries included in each analysis and identify countries excluded because of missing data or spatial-resolution constraints.
5. Table 1 should include inter-model uncertainty for country burden and per-capita exposure.
6. Consider reporting the contribution of each country as a percentage of the global person-day burden.
7. Explain whether country rankings in Table 1 are stable across individual climate models.
8. Improve the readability of the bivariate legend in Figure 1. The class boundaries and directions of increasing exposure and vulnerability should be explicit.
9. State whether Figure 1 uses scenario-specific terciles or common class thresholds across all panels. Common thresholds are preferable for comparison.
10. Figure 2 would benefit from confidence bands or model-specific concentration curves.
11. Explain the substantive meaning of the curve crossings in Figure 2 rather than attributing them only to the socio-economic trajectory.
12. Figure 3 should display uncertainty intervals and avoid implying monotonicity when the reported point estimates are nearly flat.
13. The Figure 3 caption should remove the claim that the pattern is “independent of the vulnerability index.”
14. Consider labeling major countries in Figure 4 or providing a supplementary table containing country values.
15. Figure 4 compares differences between two fully integrated SSP futures. The axes should not be interpreted as isolated “hazard relief” and “vulnerability relief” effects without qualification.
16. Specify whether the population used to size the points in Figure 4 is taken from SSP1, SSP2, or another reference population.
17. Clarify whether Figure 5 is based on ensemble-mean exceedance, model-level estimates, or an average of model-level population counts.
18. Replace “unsafe regime” throughout the manuscript with less categorical terminology.
19. Avoid reporting CI values to three decimal places unless the uncertainty justifies that precision.
20. Harmonize the terminology used for SSP1-2.6, including “sustainable pathway,” “low-emission pathway,” and “low-forcing pathway.”
21. Verify that the wording “physiologically hazardous regimes” is adequately supported and consistent with the screening-level nature of the WBGT estimates.
22. The claim that rank-based results are less sensitive to systematic WBGT reconstruction bias should be demonstrated rather than assumed. Spatially heterogeneous biases could materially alter country rankings.
23. Discuss whether population-weighting causes a small number of highly populated countries to dominate the CI.
24. Consider presenting results with and without the largest-population countries, such as India, China, Nigeria, and Pakistan, as a leverage or influence analysis.
25. The manuscript should clarify how countries with zero or near-zero WBGT exceedance were handled in covariance and concentration calculations.
26. Provide supplementary country-level tables for all scenarios, horizons, and thresholds.
27. Include a workflow diagram showing the processing sequence from model-specific climate data to WBGT reconstruction, population overlay, national aggregation, vulnerability ranking, and CI calculation.
28. Verify the consistency of capitalization, journal titles, DOI formatting, equations, symbols, and reference style throughout the manuscript.

Strengths

The manuscript has several important strengths:

• it addresses a timely and socially relevant research question;
• it introduces a useful distributional perspective into the sport-climate literature;
• it combines climate, population, and vulnerability projections under broadly coherent SSP narratives;
• it clearly distinguishes potential resident-population exposure from athlete-specific exposure in parts of the manuscript;
• it uses concentration curves rather than relying exclusively on a single summary statistic;
• it provides code and derived-data availability statements;
• it acknowledges several important limitations;
• it offers a potentially valuable basis for future research incorporating participation, infrastructure, adaptation, and within-country inequality.

Recommendation

The manuscript has clear potential, but substantial methodological clarification, uncertainty analysis, sensitivity testing, and moderation of the causal and sport-specific interpretations are required. I therefore recommend major revision.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The manuscript is well written in clear and fluent academic English. The terminology is appropriate, and the text is generally easy to follow. I did not identify any major language issues requiring revision. However, careful English-language editing is still recommended to improve grammatical accuracy, sentence structure, concision, and terminological consistency. Several sentences are overly long or contain multiple claims that would be clearer if divided. The authors should also revise occasional categorical or ambiguous expressions, ensure consistent use of technical terms throughout the manuscript, and correct formatting and capitalization inconsistencies in the reference list.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all of my comments and made substantial revisions to the manuscript, which have significantly improved its quality. The manuscript can be accepted for publication in its current form

Author Response

Comments 1: The authors have addressed all of my comments and made substantial revisions to the manuscript, which have significantly improved its quality. The manuscript can be accepted for publication in its current form

Thank you Reviewer 1 for this comments. We have nothing to done.

Reviewer 2 Report

Comments and Suggestions for Authors

Manuscript: Sport-relevant heat exposure and socio-economic vulnerability: a country-level assessment under coherent Shared Socioeconomic Pathways Author: D. Defrance Journal: Sustainability (MDPI) Version under review: Revised manuscript submitted 22 July 2026 (compared against the original submission of 30 June 2026)

Recommendation: Minor revision

Summary

This revision responds constructively to concerns about statistical support and causal framing in the original submission. The core data pipeline (WBGT reconstruction, GVI matching, concentration-index calculation) is unchanged, but the author has added a paired hierarchical bootstrap, a fixed-baseline-ranking sensitivity analysis, and a population-temporal-averaging sensitivity analysis, and has substantially softened language that previously implied statistical significance and causal mechanism where the original analysis supported only a descriptive, rank-dependent association. The result is a more defensible and more transparent paper. I have a small number of remaining points, mostly requesting clarification or minor additional robustness checks rather than new analysis.

Major Comments

1. Bootstrap resampling unit and spatial dependence (Section 2.11, Section 4.6). The hierarchical bootstrap resamples countries independently with replacement, which does not represent spatial/regional dependence among neighbouring countries (e.g., correlated climate anomalies or correlated GVI trajectories within the Sahel or South Asia). This is acknowledged in the Limitations (paragraph beginning "The bootstrap analysis also relies on assumptions..."), which is appropriate, but given that the headline claim of the paper rests on whether the 95% interval excludes zero, I would ask the author to at least discuss - even qualitatively - the likely direction of bias this induces. Clustered/correlated resampling units typically widen effective uncertainty relative to i.i.d. resampling, which would argue that the reported intervals may be, if anything, optimistic. If this reasoning is correct, it would be worth stating explicitly, since it strengthens (rather than undermines) the paper's already-cautious interpretation of the SSP1-2.6/2085 null result. If a block-bootstrap by region is feasible within a reasonable timeframe, I would welcome it as a robustness check in the Supplementary Material, but I do not consider it a condition for acceptance.
2. Framing of the severity-gradient result in the Abstract and Conclusions. Section 3.3 and Section 4.2 are appropriately cautious - the text now correctly states that the 28→32 °C contrast is a "descriptive tendency" not distinguishable from zero at the 95% level in any scenario-horizon combination. However, the Abstract still states the point estimate ("the five-model mean CI showed a descriptive increase from 0.17... to 0.25...") without any qualifier that this increase is not statistically supported by the paper's own bootstrap analysis. A reader skimming only the Abstract would come away with a stronger impression of the severity gradient than the Results support. I recommend adding a short clause to the Abstract, e.g., "...although paired bootstrap intervals for this contrast include zero," to keep the Abstract consistent with the more careful framing achieved in the body text.
3. Interpretation of the fixed-2020-ranking sensitivity analysis (Section 3.4, Section 4.4). This is a valuable addition and I think it is one of the strongest parts of the revision - it correctly identifies that the low, bootstrap-null CI under SSP1-2.6 at 2085 depends materially on the projected reordering of countries along the GVI gradient, not solely on a change in the physical hazard. I would ask the author to state more directly, in one sentence in the Discussion, what this implies for the paper's central claim: namely, that under a fixed (2020) notion of "who counts as vulnerable," the SSP1-2.6 late-century concentration would in fact be statistically distinguishable from zero in most cases (per Table S6 / the 0.155-0.184 range quoted in §3.4), and it is specifically the use of a time-varying, SSP-consistent vulnerability ranking that produces the null result. This is already implicit in the text but stating it explicitly would help readers correctly attribute the null result to a modelling choice (which vulnerability ranking to use) rather than to the underlying phenomenon being weak.
4. GVI as the sole vulnerability construct. The manuscript is transparent that results are conditional on the selected GVI ranking (Sections 2.7, 2.8, 4.6) and defends the GVI's use via its published external validation correlations with ND-GAIN, INFORM, and the World Risk Index (Section 2.5). This is a reasonable defense, but correlation with other indices at the contemporary, cross-sectional level (Smits & Huisman's 2020 validation) does not guarantee that the projected, SSP-specific trajectories of GVI used here would agree with projected trajectories of an alternative index - and it is precisely the projected reordering that the paper shows to be consequential (point 3, above). I do not think the author needs to add a second vulnerability index to this paper, but I would ask that the Limitations paragraph on this point (Section 4.6, second limitation) be sharpened to note that the external validation cited applies to the base-year index, not to its projected trajectory, which is the component actually driving the SSP1-2.6/2085 sensitivity.
5. Country-level GVI as an ecological measure - quantify, if possible, the likely direction of within-country bias. This is well-flagged as a limitation (Section 4.6, first limitation), but purely as a caveat. Given the paper's framing around equity in sport and physical activity specifically, it would strengthen the Discussion to note explicitly (even briefly) that within-country heat exposure inequality (e.g., urban heat islands falling disproportionately on lower-income neighbourhoods, per refs [15-17] already cited) would be expected to add to, not subtract from, the reported between-country concentration - i.e., the reported CI values should be read as a lower bound on total inequity, not merely an incomplete measure. A sentence to this effect (partially present already, e.g., "the concentration we report is therefore a between-country lower bound," carried over from v1 §4.6) should be retained/reinforced in this version, as I could not find it clearly restated in the v2 Limitations section.

Minor Comments

6. Table 1 vs. Table in-text numbers. Please double-check consistency between the exposure/CI figures cited in the Abstract (4.1 billion / 2.1 billion) and those in Section 3.6 and Figure 5 (4.11 billion / 2.14 billion at τ = 30 days yr⁻¹). These are consistent to rounding, but a reader comparing Abstract to Results may benefit from matching precision (e.g., both to one decimal place).
7. Section 2.2, WBGT formula. Please confirm that the coefficients in "WBGT = 0.7 Tw + 0.2 Tg + 0.1 Ta" are correctly attributed and consistent with the Sawadogo et al. [22] methodology cited immediately before the equation; a brief parenthetical noting this is the standard outdoor WBGT formulation (as opposed to the indoor/shade formulation) would help readers unfamiliar with the index.
8. Section 2.7, tie-handling in fractional ranks. The description of population-weighted mid-ranks for tied GVI values (Equation 7) is clear, but it would help to state explicitly, once, how many countries (if any) in the working sample of 174 actually share identical GVI values within a given scenario-horizon combination, since this affects how much the tie-handling procedure matters in practice versus how much it is a theoretical safeguard.
9. Section 3.1, Table 1 caption. The caption states "Global burden share is the country contribution to the sum of the five-model mean burdens across all country-assigned grid cells," which is helpful, but the table only reports this for the top 12 countries; consider adding the cumulative share of these 12 countries in the caption or text, to give readers a quick sense of how concentrated the absolute burden is (as distinct from the relative-to-vulnerability concentration measured by the CI).
10. Section 4.5, distinction from Defrance & Lescure [42]. The relationship between this paper and the author's own companion paper is now clearly described as building on the hazard mapping in [42] "by adding a population-based and distributional dimension." Given the overlap in climate data and methodology between the two papers, I would ask the author to state explicitly (perhaps in a footnote or one sentence) whether any hazard/exposure data products are shared/reused between the two papers' archived datasets, for the benefit of readers attempting to reproduce or extend either study.
11. Data/code availability. The Zenodo DOIs and GitHub repository are provided and appear complete. Please confirm at proof stage that the Zenodo DOIs are activated/resolvable (they read as placeholder-style DOIs at present), and that the archived code corresponds to the exact model version used to generate the bootstrap results reported in Table 2 and Section 3.3, since these are new relative to the previous submission.
12. Language/typography. Minor: in the abstract, "days yr1" is missing a superscript minus sign ("days yr⁻¹"); please check this throughout for consistent superscript rendering in the typeset version. Also check consistent use of "5000 replications" vs. "5,000" for numeral formatting per journal style.

Assessment of Response to Presumed Prior Review

Assuming this revision responds to a prior round of review requesting (a) proper uncertainty quantification beyond inter-model spread, and (b) removal of causal ("hazard-driven mechanism") language unsupported by the study design, the author has responded thoroughly and in good faith. The addition of the paired hierarchical bootstrap, the fixed-ranking sensitivity analysis, and the systematic distinction drawn throughout between "climatic hazard," "population exposure burden," "population-weighted per-capita exposure," and "projected vulnerability" (Section 2.1) represent substantial improvements in rigor and clarity. The paper is now considerably more careful about distinguishing directionally consistent point estimates from statistically supported differences, which is the correct standard for a study of this design.

I recommend acceptance following minor revisions addressing points 2-5 above (framing/clarification only; no new analysis required) and the small clarifications requested in points 6-12.

Comments on the Quality of English Language

The English throughout the manuscript is clear, fluent, and grammatically correct, consistent with the acknowledgment that professional language-editing assistance was used during preparation. I have no major concerns about readability or clarity. Only minor typographical issues remain (e.g., missing superscript minus signs in unit notation such as "days yr1" instead of "days yr⁻¹" in the Abstract), which should be corrected at the copy-editing/proof stage but do not require substantive revision.

Author Response

1. Bootstrap resampling unit and spatial dependence (Section 2.11, Section 4.6): 

   We thank the reviewer for this important clarification. We agree that independently resampling countries does not represent the spatial and regional dependence that may exist among neighbouring countries sharing correlated climatic anomalies or socio-economic trajectories.

   We have expanded the corresponding paragraph in Section 4.6 to discuss the likely direction of this limitation. Specifically, the revised text now states that treating spatially correlated countries as independently resampled units may overstate the effective amount of independent information and may therefore produce uncertainty intervals that are somewhat too narrow, or optimistic, relative to those obtained using an explicitly spatial or regional block-resampling design.

   Because the magnitude of this effect cannot be established without selecting and implementing a specific regional blocking structure, we do not attempt to quantify it in the present revision. We now clarify that this limitation reinforces the cautious interpretation of combinations whose intervals already include zero, particularly SSP1-2.6 in 2085. As suggested by the reviewer, we retain the current hierarchical bootstrap and identify spatially structured resampling as a potential extension rather than as an additional condition for the present analysis.

2. Framing of the severity-gradient result in the Abstract and Conclusions: 

   We thank the reviewer for identifying this inconsistency between the Abstract and the more cautious interpretation provided in the Results, Discussion and Conclusions. We agree that reporting only the change in the point estimate could give readers an overly strong impression of statistical support for the severity gradient.

   We have therefore revised the Results section of the Abstract to state explicitly that, although the five-model mean CI increased descriptively from 0.17 at WBGT ≥ 28 °C to 0.25 at WBGT ≥ 32 °C under SSP1-2.6 at mid-century, the 95% paired hierarchical-bootstrap interval for the corresponding 32-minus-28 °C contrast included zero.

   We also verified the wording of the Conclusions. This section already states that the threshold contrasts include zero, that no combination provides evidence of a strictly monotonic increase across all three thresholds, and that the severity gradient should be regarded as a descriptive and, in some cases, model-consistent tendency rather than a statistically established effect. No further modification of the Conclusions was therefore required.

3. Interpretation of the fixed-2020-ranking sensitivity analysis (Section 3.4, Section 4.4). : 

   We thank the reviewer for highlighting the central interpretative implication of the fixed-ranking sensitivity analysis. We agree that the Discussion should state more directly that the comparatively weak late-century concentration obtained under SSP1-2.6 is materially associated with the SSP-specific projected reordering of countries along the GVI gradient.

   We have therefore revised Section 4.4 to state explicitly that, when the country ranking is fixed at its 2020 baseline, the late-century SSP1-2.6 concentration-index estimates remain positive across all five climate models and increase substantially, from 0.088–0.101 under the projected rankings to 0.155–0.184 under the fixed ranking. This demonstrates that the low concentration estimates obtained with the projected GVI ranking are specifically associated with changes in the relative ordering of countries, rather than solely with a weakening of the underlying climatic exposure pattern.

   We have not, however, stated that the fixed-ranking estimates are statistically distinguishable from zero. Supplementary Table S6 reports model-specific point estimates for the fixed-ranking sensitivity analysis, but the hierarchical bootstrap was not repeated under that alternative ranking. Consequently, statistical separation from zero cannot be inferred directly from the magnitude or consistency of these point estimates. We have added this qualification to avoid making an inferential claim that is not supported by the analysis.

4. GVI as the sole vulnerability construct.: 

   We thank the reviewer for this important distinction. We agree that the published external validation of the GVI supports the contemporary cross-sectional vulnerability construct, but does not independently validate its SSP-specific projected trajectories or the resulting future reordering of countries.

   We have sharpened the second limitation in Section 4.6 accordingly. The revised text now clarifies that alternative vulnerability indices could be strongly correlated with the GVI at the contemporary baseline while nevertheless producing different projected trajectories and future country rankings. This issue is particularly relevant because the fixed-2020-ranking sensitivity analysis demonstrates that projected changes in country ordering materially influence the late-century SSP1-2.6 concentration estimates.

   As suggested by the reviewer, we have not added a second vulnerability index or presented the existing sensitivity analysis as a complete assessment of vulnerability-model uncertainty. Instead, we now state explicitly that the fixed-ranking analysis evaluates temporal reordering within the selected GVI framework, but does not validate the projected GVI trajectories against alternative future vulnerability constructs.

5. Country-level GVI as an ecological measure - quantify, if possible, the likely direction of within-country bias.: 

   We thank the reviewer for encouraging us to discuss the likely direction of the unresolved within-country component. We agree that treating every resident of a country as having the same projected GVI value omits potentially important socio-economic gradients in both heat exposure and access to protective resources.

   We have expanded the first limitation in Section 4.6 to note that evidence from urban-heat and environmental-justice studies, including references already cited in the manuscript, frequently shows greater heat exposure among lower-income and otherwise disadvantaged communities. Such subnational gradients may reinforce the between-country concentration identified in the present study, and the national analysis is therefore likely to capture only part of the broader inequality in heat exposure and adaptive conditions.

   We have, however, avoided defining the reported CI as a formal numerical lower bound on total individual-level inequality. The present study does not observe subnational exposure or vulnerability, and within-country gradients may differ in magnitude and direction among countries. Moreover, a national concentration index and an individual- or community-level index would not necessarily be directly comparable under the same ranking structure. We therefore describe the reported CI as the between-country component of a broader multiscale distributional pattern, while acknowledging that unresolved subnational inequalities may plausibly reinforce it.

6. Table 1 vs. Table in-text numbers.: Thank you for your remark. We correct the abstract and we put 4.11 billion / 2.14 billion in the abstract to be consistent with the results part. 
7. Section 2.2, WBGT formula.: 

   We thank the reviewer for requesting this clarification. We confirmed that the coefficients 0.70.70.7, 0.20.20.2 and 0.10.10.1 correspond to the standard outdoor-sun WBGT formulation and are consistent with the methodological approach applied by Sawadogo et al. [22].

   We have revised the introductory sentence immediately preceding the equation in Section 2.2 to distinguish the standard formulation itself from its application in Sawadogo et al. The revised text now states that outdoor WBGT was calculated using the “standard outdoor-sun formulation,” following the methodological approach applied by Sawadogo et al. [22]. This also makes explicit that the equation differs from the indoor or shaded WBGT formulation.

8. Section 2.7, tie-handling in fractional ranks:

   We thank the reviewer for requesting this useful descriptive information. We agree that reporting the prevalence of identical GVI values helps distinguish whether the tie-handling procedure is primarily theoretical or materially relevant to the working dataset.

   We examined the projected GVI values in the common complete-case sample of 174 countries. Under SSP1-2.6, 82 countries formed 36 tied groups in 2055 and 99 countries formed 43 tied groups in 2085. Under SSP2-4.5, 63 countries formed 29 tied groups in 2055 and 84 countries formed 39 tied groups in 2085. The largest tied group contained four countries under SSP1-2.6 and three countries under SSP2-4.5.

   We have added these counts to Section 2.7 immediately after the description of exact-value tie identification. These results confirm that explicit tie handling is practically relevant rather than merely a theoretical safeguard. As already described in the Methods, only exactly identical reported GVI values were grouped; no numerical tolerance was applied to values that were close but distinct

9. Section 3.1, Table 1 caption.:  

   We thank the reviewer for this helpful suggestion. We calculated the cumulative contribution of the 12 countries reported in Table 1. Together, they account for 75.6% of the global five-model mean population exposure burden under SSP2-4.5 in 2085 for afternoon WBGT ≥ 32 °C.

   We have added this cumulative percentage to the caption of Table 1. This provides a direct indication of the concentration of the absolute person-day burden among the highest-burden countries, while retaining the distinction between this descriptive concentration of total burden and the relative distribution along the vulnerability gradient measured by the concentration index.

10. Section 4.5, distinction from Defrance & Lescure [42]: 

    We thank the reviewer for requesting this clarification. The two studies use the same underlying NASA NEX-GDDP-CMIP6 archive, the same five-model selection and a broadly related daily WBGT-processing framework. However, no population-exposure or distributional data product is shared between the two studies.

    The archived climate-hazard products are also distinct. Defrance and Lescure [42] provide seasonally aggregated ensemble-mean WBGT indicators for morning, afternoon and evening conditions over 1991–2020, 2031–2060 and 2071–2100. The present study generated model-specific annual afternoon WBGT exceedance climatologies at thresholds of 28, 30 and 32 °C for 2041–2070 and 2071–2100, before calculating ensemble summaries.

    All SSP-consistent population overlays, country-level exposure burdens, projected GVI matching, concentration curves and indices, hierarchical-bootstrap results, ranking-stability estimates and sensitivity analyses were produced specifically for the present study and are provided in a separate data and software archive. We have added a sentence to Section 4.5 to make this relationship explicit.

11. Data/code availability.: We thank the reviewer for this reminder. We verified that both Zenodo DOI links are active and resolve to the corresponding public records. We also confirmed that the archived software corresponds to the exact version used for the revised analysis, including the hierarchical-bootstrap calculations and paired threshold contrasts reported in Table 2, Section 3.3 and the Supplementary Information. The associated derived-data archive contains the corresponding model-specific and bootstrap outputs required to reproduce these results. No further modification of the manuscript was required.
12. Language/typography:  All "days yr⁻¹" have verified and that is corrected in the abstract. Thank you.