Contrary effects of soil moisture-atmosphere feedback on dry and humid heatwaves

Domain: physics
Published: 2026-03-03
Editorial outcome: major_revision

Abstract
Although soil moisture-atmosphere feedback (SAF) has been widely recognized as a key driver of temperature extremes, its distinct impacts on dry and humid heatwaves remain insufficiently understood, largely due to previous studies focusing predominantly on dry heatwaves alone. In this study, we combine SAF perturbation experiments from CMIP6 with partial differential analysis to construct a global map of SAF’s influence on both humid and dry heatwaves during 1985-2014 and to elucidate the underlying mechanisms. Unlike the homogeneously amplifying effect of SAF on dry heatwaves, SAF reduces the duration and severity of humid heatwaves by 20-40% in low-to-mid latitude regions with strong soil moisture-atmosphere coupling. In contrast, it increases their duration and severity by ≥50% in high latitude regions. These spatially divergent responses are primarily attributed to the competition between SAF-induced thermal warming and moisture depletion, which respectively raise or lower wet-bulb temperatures. Our findings reveal a dual regulatory mechanism by which SAF influences heat extremes through temperature-humidity coupling, providing scientific insights for region-specific adaptation strategies to both dry and humid heatwaves.

Introduction
Heatwaves are among the most devastating natural hazards, frequently causing crop yield reduction, plant mortality, and economic losses, posing severe threats to both ecosystems and socio-economic development1,2. The deadliest heatwave in this century alone resulted in tens of thousands of deaths3. In the context of global warming, extreme weather events have become increasingly frequent and intense, with extreme high-temperature events showing particularly pronounced intensification4. This has spurred growing scientific interest in the mechanisms driving heatwave evolution.

Anthropogenic greenhouse gas emissions are well recognized as the primary global driver of escalating heatwave risks, as the enhanced greenhouse effect raises global temperatures and increases the probability of extreme heat events5. However, one core and significant question is the extent to which land surface moisture and temperature conditions interactively influence the evolution of heat extremes6–9.

While the role of land-atmosphere feedback in modulating heat extremes is being established, research has focused predominantly on dry heatwaves, characterized solely by extreme temperature anomalies. In contrast, humid heatwaves, which involve concurrent anomalies in both temperature and humidity, have received relatively less attention, despite their profound societal impacts10. Crucially, humid heatwaves pose a more severe threat to human health than dry ones, as elevated humidity severely impairs thermoregulation, resulting in substantially higher heat-related mortality rates10–12.

Land-atmosphere feedbacks are increasingly recognized as the local intensifiers of hydrometeorological extremes. As soil moisture declines, reduced evapotranspiration shifts surface energy partitioning toward sensible heat, thereby raising near-surface air temperatures. Concurrently, diminished evapotranspiration reduces atmospheric humidity, which further enhances soil drying by increasing evaporative demand. This positive soil moisture-atmosphere feedback (SAF) loop substantially amplifies both magnitude and duration of heatwaves, accounting for 25% to over 50% of historical increases in dry heatwave occurrence6–9,13–15. Under ongoing global warming, the continued depletion of soil moisture is projected to further intensify SAF, thereby aggravating the frequency, duration, and intensity of dry heatwave events6,16–18.

In contrast, the interaction between soil moisture and humid heatwaves is complicated by shifts in energy partitioning between latent and sensible heat fluxes. While soil drying amplifies extreme temperatures through enhanced sensible heating, the associated reduction in evaporation can simultaneously suppress air humidity—potentially mitigating humid heatwave conditions. For example, a recent study demonstrated a negative correlation between soil moisture and dry heatwaves across nearly the entire contiguous United States, in contrast to a positive correlation for humid heatwaves19. Given these opposing effects—where reduced soil moisture both intensifies temperatures (positive feedback) and lowers relative humidity (negative feedback)—the net influence of SAF on humid heatwaves under climate change is substantially more complex than its influence on dry heatwaves. In addition, emerging evidence reveals divergent responses of humid and dry heatwaves to global warming, with significantly different climate sensitivities10,20. A systematic comparative assessment of SAF’s impacts on these two types of heatwaves is therefore imperative to elucidate their distinct physical mechanisms, ultimately informing effective and targeted climate adaptation strategies.

Here, using simulations from the Land Feedback Model Intercomparison Project with prescribed Land Conditions (LFMIP-pdLC) and the historical experiments from the Coupled Model Intercomparison Project phase 6 (CMIP6), we present a global-scale assessment of SAF’s role in shaping heatwaves during the historical period. We aim to address two key scientific issues: 1) What is the role of SAF in modulating dry and humid heatwaves? 2) What are the differences in the patterns and the physical mechanisms behind?

Results
Historical changes in heatwaves and the reliability of CMIP6 models
Dry and humid heatwave events are defined as periods of three or more consecutive days during which daily mean dry-bulb or wet-bulb temperatures exceed their respective 90th percentile thresholds21,22 (Methods). The ERA5 reanalysis data reveal coherent spatial patterns in the historical (1951–2014) mean annual total duration (TDUR) and total severity (TSEV) of both dry and humid heatwaves (Supplementary Fig. S1). Specifically, TDUR is substantially longer in tropical and subtropical regions, including eastern Africa, northern Australia, and India, while TSEV is more pronounced in high-latitude areas, including northeastern Canada and Siberia. These spatial patterns are well captured by the multi-model ensemble mean of CMIP6 historical simulations, with spatial correlation coefficients ranging from 0.67 to 0.96 and relative absolute errors between 9% and 17% (Supplementary Fig. S1).

Figure 1 illustrates the changes in TDUR and TSEV of heatwaves during 1985–2014 relative to the baseline period of 1951–1980. The reanalysis dataset reveals a global increase in TDUR for humid heatwaves, with the most pronounced trends observed in tropical regions, including northern South America, central Africa, and the Asian Maritime Continent (Fig. 1a). Similarly, TSEV shows a globally increasing trend, but the largest increases are concentrated in high-latitude regions (60-90°N), followed by the tropics (–20°S-20°N) (Fig. 1b). In comparison to humid heatwaves, dry heatwaves exhibit similar spatial patterns of change, but with a smaller increase in TDUR and a more substantial rise in TSEV. The multi-model ensemble mean of CMIP6 historical simulations demonstrates the capability to reasonably simulate the temporal evolution of TDUR for both humid and dry heatwaves (Fig. 1e, g), with spatial correlation coefficients ranging from 0.66 to 0.77. The simulated changes in TSEV show a spatial correlation of approximately 0.5 with ERA5 reanalysis data, and the global mean relative simulation errors remain below 7% (Fig. 1f, h). The CMIP6 models continue to reasonably capture the changing trends and magnitudes of both heatwave types at regional scales (Supplementary Fig. S2), with the spatial correlation coefficients increasing to 0.60-0.89 and mean relative absolute error predominantly below 27%. However, possibly due to the coarse resolution and biases in surface energy partitioning23, relatively larger simulation errors are found in some coastal and high-latitude regions, such as the Caribbean, northeastern Brazil, and northern Europe (Supplementary Fig. S2). Despite some uncertainties at local scales, the ensemble mean of the CMIP6-ALL experiment exhibits strong capability in reproducing the historical increasing trends and spatial variations of both humid and dry heatwaves during 1985–2014.

SAF-induced changes in humid and dry heatwaves
Figure 2 depicts the influence of SAF on humid heatwave changes during 1985–2014, estimated from the differences between the CMIP6-ALL and CMIP6-pdLC experiments (Methods). SAF substantially reduces the annual total duration and severity of humid heatwaves by 10–20 days and 15-20 K, respectively, across low latitudes (–20°S-20°N), southern mid-latitudes (20–60°S), southwestern North America (20°N-40°N, 90°W-125°W) and central and south Europe (20°N–60°N, 10°W-70°E) (Fig. 2a, b). Compared to the combined influence of other factors (e.g., climate warming, as estimated by the CMIP6-pdLC experiment), SAF’s reduction effect alleviates the increasing trends of humid heatwaves by 10-40%, with particularly pronounced values in Europe, Australia, and North Africa (Fig. 2c, d). In contrast, SAF increases the annual total duration and severity by 5–10 days and 15–20 K, respectively, in northern high-latitudes (60–90°N) regions (e.g., Alaska, northern Asia, and northern Europe), therefore amplifying the increasing trends of humid heatwaves by 10-50%. Above results hold consistent at regional scales across both the 26 IPCC SREX regions (Supplementary Fig. S3) and latitudinally defined zones (low-, mid-, and high-latitudes) (Supplementary Fig. S4). The opposing effects of SAF in low-to-mid latitudes and high latitudes also contribute to a smoothing of its global-scale impacts on humid heatwave changes, as the global mean impacts of SAF on TDUR and TSEV are amount to only -0.82 days and -0.26 K, respectively. This indicates that SAF plays a critical role in shaping the spatial distributions of humid heatwave changes, rather than substantially altering the global mean magnitude.

In contrast, SAF generally enhances the duration and severity of dry heatwaves (Supplementary Fig. S5a, b). The impact of SAF exceeds 1.5 times of the combined influence of other factors over subtropical regions, suggesting that SAF is the dominant driver of dry heatwave changes (Supplementary Fig. S5c, d). Previous studies have also shown that SAF increases the risk of global warming and extreme temperatures globally and they attributed SAF’s strong influence in subtropical regions to the strong coupling strength between soil moisture and the atmosphere6,8,9.

Here we defined the SAF coupling index as the correlation between monthly soil moisture and surface specific humidity multiplied by the standard deviation of surface specific humidity (Methods)24. Therefore, a higher coupling index suggests a stronger change in surface specific humidity induced by a unit change in soil moisture. Hotspots of strong SAF coupling are identified in South Asia, Southeast Asia, central North America, eastern South America, northern and southern Africa, and Australia (Fig. 3a). These patterns are consistent across seasons with those in ERA5 reanalysis when using the same coupling index (Supplementary Figs. S6, S7), and align with previous studies using other coupling indices25,26. The spatial variation in SAF’s effects on humid and dry heatwaves across 26 IPCC SREX regions is found to be significantly correlated with the coupling index. Specifically, SAF tends to increase the annual total duration and severity of humid heatwaves in regions where the coupling index is low (<0.2), but decrease them as the index increase beyond 0.4. In contrast, the stronger the coupling index, the greater the SAF-induced increase in total duration and severity of dry heatwaves.

A reduction in soil moisture, often initiated by precipitation deficits, can efficiently suppress evaporative cooling, leading to higher surface temperatures and enhanced atmospheric heating8,9. This initiates a positive feedback loop, in which drier soils further intensify heatwave conditions by increasing sensible heat flux and reducing latent heat flux. Additionally, reduced soil moisture inhibits cloud formation and precipitation, thereby exacerbating the persistence and intensity of dry heatwaves6. These mechanisms collectively explain why soil moisture-atmosphere coupling tends to increase both the duration and severity of dry heatwaves, particularly in regions where evaporation is sensitive to soil moisture deficits. However, they fail to explain the effect of SAF on the humid heatwave changes, potentially because the wet-bulb temperature reflects both thermal and moisture conditions.

Mechanisms for the impact of SAF on humid and dry heatwave changes
We calculated the duration and severity of heatwaves in the CMIP6-ALL simulations after removing SAF-induced mean-state changes in daily wet-bulb temperature (Methods), in order to quantify the influences of SAF-driven shifts in mean wet-bulb temperature against changes in wet-bulb temperature variability. Figure 4a, b demonstrate that heatwave changes attributable to adjustments in mean wet-bulb temperature closely resemble the patterns observed in Fig. 2a, b. In contrast, changes in wet-bulb temperature variability generally increase the duration or severity of humid heatwaves across the tropical and subtropical regions (Fig. 4c, d). The SAF-driven shifts in mean daily wet-bulb temperature during 1985-2014 also closely aligns with SAF-induced changes in TDUR and TSEV of humid heatwaves with spatial correlation coefficients ranging from 0.6 to 0.75. These findings suggest that, SAF spatial varying effect on humid heatwaves is primarily attributed to alterations in the mean state of wet-bulb temperature, rather than by altering its variability. Similarly, for dry heatwaves, SAF influences primarily through shifts in the mean state of dry-bulb temperature, though both mean-state and variability changes act in concert to increase heatwave duration and intensity globally (Supplementary Fig. S8), resulting in a net positive influence of SAF observed in Supplementary Fig. S5.

We further evaluated the role of the mean state by comparing daily temperature distributions between the ALL and LFMIP-pdLC experiments (Supplementary Note 1). The spatial structure of SAF-induced changes in the probability of hot humid days and hot dry days closely consistent with SAF’s impacts changes in actual heatwaves (spatial correlation coefficients = 0.78–0.87; Figs. S9a, b, 2a, b, and S5a, b). A statistical attribution shows that shifts in the location parameter (mean) explain >70% of this change in most regions, robust across models (Supplementary Figs. S9c, d, g, h), while the scale parameter (variability) plays a minor role (Supplementary Figs. S9e, f). These results independently corroborate that SAF exerts distinct influences on dry and humid heatwaves primarily via its modification of the mean states of dry-bulb and wet-bulb temperature, respectively.

Therefore, the divergent responses can be mechanistically understood and are directly linked to SAF’s modulation of these mean conditions.

SAF-induced dry-bulb warming is typically attributed to the “warmer climate-drier soil” feedback whereby climate warming exacerbates the precipitation-evapotranspiration deficit, leading to soil drying that further amplifies warming via increased sensible heat (and consequently reduced evapotranspiration) and surface solar radiation6,9,27,28. However, this climatological-scale feedback alone cannot fully account for the widespread increasing of dry heatwave, as pronounced soil moisture declines are largely confined to subtropical regions during 1985-2014 (Supplementary Fig. S10). Crucially, at sub-seasonal to interannual scales, soil moisture variability in response to positive temperature anomalies can also trigger a “warmer-drier” feedback29. This feedback exacerbates negative anomalies in soil moisture and latent heat flux while concurrently amplifying the positive anomalies in sensible heat flux (Fig. 5a, c, e), thereby explaining the stronger temperature anomaly observed when SAF is accounted for (Fig. 5g). Similar patterns are observed for dry spells (Supplementary Fig. S11). In contrast, during cold days, although soil moisture variability tends to produce positive soil moisture anomalies, its impact on surface energy fluxes is negligible (Fig. 5b, d, f, h), likely because evapotranspiration is energy-limited during these periods. This asymmetric impact of soil moisture variability between warm and cold periods results in a net positive effect on dry-bulb temperature. Moreover, the amplitude of soil moisture anomalies driven by variability generally exceeds that associated with the long-term trend (Fig. 5a and Supplementary Fig. S10). Consequently, even in regions where soil moisture exhibits a wetting trend over time, the warming effect induced by soil moisture variability can dominate over any cooling tendency arising from the trend itself, thereby still contributing to net warming of dry-bulb temperature.

The influence of SAF on wet-bulb temperature shifts is a combined effect of SAF-induced changes in dry-bulb temperature and relative humidity. We used the SAF-induced changes in dry-bulb temperature and relative humidity at climatological scales (Fig. 6b, c) to estimate mean SAF-induced changes in daily wet-bulb temperature based on a partial difference function (Methods). Although some uncertainties remain due to the nonlinear relationship between wet-bulb temperature and dry-bulb temperature (and relative humidity), the estimation method demonstrates robust skill in reproducing the sign of SAF-induced wet-bulb temperature changes, capturing spatial agreement with reference values across 85% of global land areas for the multi-model ensemble mean (Fig. 6a vs. 6d). Importantly, this capability extends to individual CMIP6 models, with 88–95% of global land grids showing consistent sign agreement between estimated and simulated anomalies (Supplementary Fig. S12). The estimation process is visually illustrated in the isopleths diagram of wet-bulb temperature (Fig. 6e). For example, in the regions such as western Australia and Central Europe, the positive effect of SAF-induced dry-bulb temperature warming on wet-bulb temperature is weaker than the negative effect of SAF-induced drying in relative humidity, resulting in a decrease in wet-bulb temperature (from the red circle to the yellow triangle in Fig. 6e). In high latitude regions, like northern Asia, SAF does not cause strong drying in relative humidity, therefore, the dry-bulb temperature warming dominates SAF’s influence on wet-bulb temperature.

The SAF-driven warming will reduce relative humidity under constant water-vapor pressure according to the Clausius-Clapeyron relation (Supplementary Fig. S13a). Across mid- to low-latitude regions, the pronounced SAF-induced suppression of evapotranspiration depletes near-surface moisture supply (Supplementary Fig. S14a), causing declining trends in specific humidity (Supplementary Fig. S14b) and amplifying thermodynamic drying (Supplementary Fig. S13b). The combined effect of elevated temperature and reduced moisture drives a marked decline in relative humidity (Fig. 6c). Critically, in these regions the drying influence of SAF outweighs its warming effect, leading to lower wet-bulb temperatures and a corresponding decrease in humid heatwaves. By contrast, in high-latitude regions where evapotranspiration is energy-limited, atmospheric warming can stimulate additional evapotranspiration that partly counteracts the thermodynamic drying from higher temperatures (Supplementary Fig. S13b). Here, the warming effect of SAF dominates, producing a net increase in wet-bulb temperature and contributing to more frequent humid heatwaves.

Methods
Data
The fifth-generation ECMWF reanalysis (ERA5) is used as the reference dataset due to its good performance and assimilation of extensive station and satellite observations worldwide47. The original spatial resolution of the ERA5 dataset is 0.25°×0.25°, and it was remapped to 1°×1° by bilinear interpolation. Hourly relative humidity in ERA5 was calculated from the hourly near-surface temperature, surface pressure, and specific humidity48. Daily mean temperature and relative humidity were computed from the hourly values.

Daily mean temperature and relative humidity from the CMIP6 historical (ALL) experiment during 1951-2014 and the LFMIP-pdLC experiment during 1980-2014 were collected. The CMIP6 ALL experiment includes all external forcings and simulates the real-world climate system, making it suitable for comparison with observations49. The LFMIP-pdLC experiment begins in 1980 with the initial conditions from the ALL experiment in the same year50. In addition, LFMIP-pdLC experiments share the same settings with ALL experiment except that the soil moisture was prescribed to a climatological mean state during 1980-2014. Five CMIP6 models, including CNRM-CM6-1, EC-Earth3, IPSL-CM6A-LR, MIROC6, and MPI-ESM1-2-LR, were selected because they provide daily outputs for both experiments. We used the r1i1p1f1 realization consistently across all CMIP6 models, except for CNRM-CM6-1, for which r1i1p1f2 was used due to the unavailability of r1i1p1f1.

Wet-bulb temperature and the partial differential equation for estimating its changes
The daily wet-bulb temperature (Twet, °C) was derived from daily dry-bulb temperature or daily mean temperature (T, °C) and relative humidity (RH, %) using the following formula51:

Twet = T * tan^-1(0.152(RH+8.314)^1/2) + tan^-1(T+RH) - tan^-1(RH-1.676) + 0.004RH^3/2 * tan^-1(0.023RH) - 4.686 (1)

where the tan^-1 denotes the arctangent function.

Considering that the changes in temperature (ΔT_pdLC->ALL) and relative humidity (ΔRH_pdLC->ALL) from the LFMIP-pdLC to ALL experiments are smaller relative to the mean temperature (T_pdLC) and relative humidity (RH_pdLC) in the LFMIP-pdLC experiments, the SAF-induced wet-bulb temperature change (ΔTwet) can be estimated using the first-order Taylor expansion of Eq. (1):

ΔTwet = (∂Twet/∂T) * ΔT + (∂Twet/∂RH) * ΔRH (2)

∂Twet/∂T = tan^-1(0.152(RH_pdLC + 8.314)^1/2) + 1 / (1 + (T_pdLC + RH_pdLC)^2) (3)

∂Twet/∂RH = T * [0.076(RH_pdLC + 8.314)^-1/2] + 1 / (1 + (T_pdLC + RH_pdLC)^2) - 1 / (1 + (RH_pdLC - 1.676)^2) + 0.006RH_pdLC^1/2 * tan^-1(0.023RH_pdLC) + 0.004RH_pdLC^3/2 * [0.023 / (1 + (0.023RH_pdLC)^2)] (4)

Definition of SAF coupling index
The SAF coupling index is calculated based on the monthly soil moisture (w) and monthly near surface specific humidity (ϕ) during 1985-2014 as:

I(wm, ϕm) = Σ(w', ϕ') / sqrt(Σ(w')^2 * Σ(ϕ')^2) = r(wm, ϕm) * σ(ϕm) (5)

where primes denote anomalies from the mean annual cycle over the total n years, and m and y represent the month and year, respectively. The term r(wm, ϕm) denotes the correlation between soil moisture and the humidity, while σ(ϕm) is the standard deviation of humidity. This SAF coupling index follows the formulation of prior terrestrial indices24,52, but specifically focuses on humidity rather than surface energy fluxes. The coupling index was calculated for each month separately, and then averaged annually.

Definition of dry and humid heatwaves
There is no universal definition of a heatwave, but most operational definitions characterize it as a period of abnormally high temperatures relative to the local climate and time of year, often based on percentile thresholds (e.g., exceeding the 90th percentile)53. Such a relative threshold-based method is more generalizable to large regional scales or different climate divisions, compared to the absolute threshold approach54,55. A dry hot day was defined when the daily mean dry-bulb temperature exceeds its corresponding 90th percentile, while a dry heatwave event was identified when at least three consecutive dry hot days occurred. The 90th percentile thresholds were calculated using a 15-day moving window centered on each calendar day across the 1951–1980 baseline period, yielding 450 reference values (15 days × 30 years) for each temperature metric. Heatwave duration refers to the total days in an event, while severity is calculated as the accumulated temperature exceedance above daily thresholds during the event period. Mean annual total duration and total severity represent the accumulated duration and severity of all the heatwave events within a given year.

The definition of humid heatwave events follows that of dry heatwaves, except that wet-bulb temperature, a key indicator of humid heat stress, is used in place of air temperature10,20,56.

Quantifying the SAF’s impact on historical heatwave changes
For a given heatwave metric M (e.g. annual total duration), let Mbl and Mhist_ALL denote its mean values in the ALL experiment during the baseline (1951-1980) and historical (1985-2014) periods, respectively, and let Mhist_pdLC represent the corresponding mean in the LFMIP-pdLC experiment during 1985-2014. The total observed change in the historical period is therefore ΔM_total = Mhist_ALL - Mbl, which includes the combined influence of all factors (e.g., external forcing, internal variability, and SAF). The change in the absence of SAF is ΔM_noSAF = Mhist_pdLC - Mbl. Hence, the effect of SAF is defined as ΔM_SAF = ΔM_total - ΔM_noSAF, and its relative contribution is calculated as (ΔM_SAF / ΔM_noSAF) × 100%.

Because both the sign and magnitude of changes vary across models, ΔM_SAF and its relative contribution are first computed for each individual model, and the multi-model ensemble mean is then derived from those individual estimates. A signal is considered statistically significant when at least four of the five models agree on the sign of the ensemble-mean result6,31,45.

SAF impacts on heatwaves: mean state vs. variability effects
The distinct heatwave characteristics between the ALL and LFMIP-pdLC experiments (1980-2014) stem from SAF-induced modifications in both temperature the mean state (warming or cooling) and its variability. Following previous research5, we fitted separate second-order polynomials to the monthly mean temperature series (1981–2014) from the ALL and LFMIP-pdLC experiments at each grid cell to capture the warming/cooling signal. Their difference, which varies by year and month, is considered as the SAF-induced component of warming/cooling and was subtracted from the daily temperature record of the ALL experiment. The different heatwave metrics between this adjusted ALL series and the original LFMIP-pdLC experiment, reflects SAF-induced variability effects, encompassing interannual, seasonal, intraseasonal, and diurnal components. Consequently, the residual component of SAF-induced heatwave changes represent the effect of mean temperature shifts. Similar methods have been widely used to examine the relative roles of mean shifts versus variability changes climate extremes36–38,57,58, although approaches to estimating the mean shifts vary (e.g., using polynomial fittings of different orders).

Contribution of temperature and humidity to relative humidity changes
According to the Clausius-Clapeyron equation, the influence of temperature (T) on the saturated water vapor pressure (es) is expressed as:
dln(es) / dT = L / (Rv * T^2) (6)
where the L is latent heat of vaporization and Rv is specific gas constant for water vapor. The effect of temperature change on relative humidity (RH) under a fixed water vapor content can be derived as:
d(RH) / dT = d(e / es) / dT = -(e / es^2) * (des / dT) = -(RH * L) / (Rv * T^2) (7)

We therefore calculated the relative humidity change (ΔRHT) induced by the SAF-related temperature change (ΔT) using the following approximation:
ΔRHT ≈ -(RH_pdLC * L) / (Rv * T_pdLC^2) * ΔT (8)
where RH_pdLC and T_pdLC represent the mean daily relative humidity and daily temperature in the LFMIP-pdLC experiment during 1985-2014, respectively.

The contribution of SAF-induced changes in water vapor content (ΔRHq) was estimated as:
ΔRHq = RH_ALL - RH_pdLC - ΔRHT (9)
where RH_ALL denotes the mean daily relative humidity in the ALL experiment during 1985-2014.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The study by Chen et al. investigates the impacts of soil moisture-atmosphere feedback (SAF) on dry and humid heatwaves using a set of CMIP6 simulations. The derived heatwave characteristics from CMIP6 are evaluated using ERA5 reanalysis, and SAF impacts are identified by comparing all-forcing and prescribed soil moisture simulations. They find that soil moisture feedback could amplify the dry heatwaves, but reduce humid heatwaves in the tropics and midlatitudes due to SAF-induced drying in relative humidity. Overall, this is an interesting study; the methodology is straightforward, and the results are well structured. However, I have a couple of major concerns regarding the methodology and physical mechanism of the soil moisture feedback that need to be addressed before publication.\nFirst, many studies suggest that the characteristics of humid heatwaves, and their sensitivity to soil moisture or humidity, strongly depend on the temperature metrics used. Besides wet-bulb temperature, other common heat metrics include wet-bulb globe temperature, heat index, Universal Thermal Climate Index, and equivalent temperature. This study, however, relies solely on wet-bulb temperature.. I suggest the authors consider other metrics to explore and discuss the uncertainty of the identified humid heatwaves.\nSecond, while the study attempts to explain how SAF affects the two types of heatwaves, the underlying reason for the feedback remains unclear. The authors argue that “SAF causes a declining trend in soil moisture under global warming.” This is a critical argument, as declining soil moisture would subsequently influence surface fluxes, temperature, and humidity, ultimately affecting heatwave severity and duration. However, no results are presented to support this statement. If I understand the CMIP experiments correctly, the LFMIP-pdLC experiment uses the climatological soil moisture in 1980–2014 derived from the ALL experiment. In that case, there should be no difference in the long-term mean soil moisture between the two experiments; only soil moisture variability differs. Moreover, even if there is a declining trend, the processes causing soil drying remain unexplored. The authors need to further investigate the mechanisms behind soil moisture variability and its impacts.\nSpecific comments:\nL131: All the figures are about the changes in heatwaves. I am a little surprised that there is no negative change in any case. Can the author confirm?\nL163: How does SAF increase the risks of global warming?\nL273: Canada would be located in a similar climate regime. Any explanation for why SAF does not increase dry-bulb there?", "reviewer_2": "This study extends the understanding of the impacts and underlying mechanisms of soil moisture–atmosphere feedbacks on humid heatwaves. This paper is been well-written, and the research presents significant scientific interest. However, I still have some suggestions regarding the methods and conclusions for your reference.\n1. In the parts of results and conclusion, the paper attributes the observed differences to distinct phenomena occurring at high and low latitudes. However, the study does not clearly define or specify which regions are classified as high-latitude or low-latitude areas. As a result, the conclusions remain largely qualitative. It is recommended that the author avoid generalizing results based on latitude bands and instead provide descriptions grounded in specific geographic regions.\n2. Lines 174-176, the calculation of SAF coupling index is defined as the correlation between monthly soil moisture and surface specific humidity multiplied by the standard deviation of surface specific humidity. However, in the listed references, the standard deviation of soil moisture was used. Please check the results and the calculation process.\n3. This paper applied LFMIP data to analyze the impact of soil moisture- atmosphere feedbacks on humid heatwaves. However, when discussing the soil moisture–atmosphere feedback effect, its underlying drivers—such as vegetation changes, climate change, and other contributing factors—should be explicitly addressed. A comprehensive analysis of these factors is necessary at the global scale to provide context for the feedback mechanism.", "reviewer_3": "This study examines the global scale effects of soil moisture-atmosphere feedback (SAF) on dry and humid heatwaves. Global climate model simulations, both idealised (LFMIP-pdLC) and realistic (CMIP6-all), are used to explain the contributions of SAF to historical changes in dry and humid heatwaves across the globe, and to disentangle the mechanisms. CMIP6 models’ ability to reproduce historical properties and changes in dry and humid heatwaves is first evaluated with respect to ERA5. The SAF-induced changes are then quantified by comparing LFMIP-pdLC and CMIP6-all simulations, and the SAF effects are decomposed into contributions from dry-bulb and relative humidity effects. The main outcome of this study are the opposite effects of SAF on humid heatwaves in regions of strong and weak land-atmosphere coupling.\nAlthough SAF has been extensively studied from the perspective of dry heatwaves, much less is known about SAF effects on humid heatwaves, as is clearly introduced in the paper. In this respect, the contribution of this study is original and of interest for the land-atmosphere/climate community as well as the heat stress/impact community. However, the methods used in this paper suffer from several approximations and misuses that need to be addressed before the paper may be considered further for publication.\nMajor comments\nMy main comment relates to the first scientific issue raised by the authors: “How has SAF modulated historical changes in both dry and humid heatwaves?”\nComparing models’ capacity to capture heatwave statistics (duration and severity) with respect to ERA5 over the 1951-2014 period is meaningful, as it indicates the extent to which each model’s background climate is realistic. However, comparing the changes between 1980-2014 and 1951-1980 as is done in the paper is less so, because the multi-model mean would filter out the part of the change that is due to internal variability, which is large at the grid cell scale. This is illustrated by comparing, for instance, Fig.1a with Fig.1e: in the former, the pattern of change in Tw_TDUR is more speckled than in the latter. The same conclusion holds when comparing each pair of ERA5vsCMIP6-MME panel, and the coefficients of spatial correlation between these pairs of maps are rather low, indicating that the forced signal, as estimated by the CMIP6 MME explains only a limited part of the observed spatial pattern of change. As expected, this analysis is more convincing when looking at regionally or zonally averaged values. I think it would make more sense to consider these spatial scales in subsequent analyses, in conjunction to aggregating locations according to land-atmosphere coupling regimes, as evaluated with e.g., the coupling index.\nIn the following sections, multi-model means from the LFMIP-pbLC and ALL experiments are compared, which allows to quantify the forced effect of SAF on dry and wet heatwaves. Although interesting on its own, this approach doesn’t allow to quantify the contribution of SAF to the observed changes in heatwave duration and severity. Indeed, authors do not link these forced changes to those quantified with ERA5. It should also be noted that considering an ensemble of 5 single-member model runs may not be sufficient to isolate the forced SAF signal robustly, which should be discussed.\nI am also not convinced by the decomposition of changes in wet-bulb temperature into mean and variability signals. First, because adding the SAF-induced annual mean temperature change to daily temperature time series doesn’t seem appropriate; authors refer to ref #5, but I couldn’t see a similar approach described there. A second source of concern is the resort to the GEV distribution, which is designed for the statistical modelling of block maxima; however, in this paper, GEV distributions are fitted to “daily temperature data” (L422), without further details about the sampling procedure (but again using ref #5). In addition, it is not quite clear to me what the expected outcome of this procedure is, as hot days in this paper are defined based on a percentile calculated on the whole distribution of daily values, not on the tail of the distribution. In addition, explaining this result in just one sentence (L228-231) is not sufficient. So, I would encourage authors to clarify their objective and procedure.\nIn sum, this article has merit in dealing with an important knowledge gap but, in my opinion, it falls short of providing robust answers to the first key scientific question raised – mainly because it is not formulated correctly. The second issue, which is about how SAF controls heatwaves properties across the globe, is more consistently addressed but may suffer from methodological caveats that should be addressed. It would also be interesting to see whether the two mechanistic approaches (the statistical one and the physical one) can be linked.\nMinor comments\ni) Authors refer to refs. #21 and 22, where heatwaves’ definitions are based on daily maximum values, but it is unclear how a heatwave is defined here. My guess is that daily mean values are used, in which case the citations are not relevant. In addition, authors may consider removing the seasonal cycle of T and Tw before calculating the 90th percentile on 15-day moving window, as recommend by Brunner and Voigt (2024).\nii) It is not clear how the statistical significance of changes between ALL and LFMIP experiments is assessed (see stippling in Figures).\niii) The coupling index in ref #24 is defined as the linear regression (or coefficient of correlation) between a flux (e.g., latent heat) and soil moisture, multiplied by the standard deviation of soil moisture; so, the description in L174 may be incorrect. In addition, it is not clear whether the calculation is based on daily values and done monthly, or if it is based on monthly values?\niv) Authors indicate in L324-326 that “The strong performance of CMIP6 models to capture SAF across most regions —as indicated by previous studies28,30 and confirmed by our evaluation (Fig. 1 and Supplementary Fig. S1-S2)— further strengthens the credibility of our findings.” This statement may be wrong, as the evaluation performed here and shown in Figs. 1, S1, S2 does not relate to the SAF. Evaluating the ability of the five GCMs used here to capture coupling regimes across the globe would indeed be a useful addition to this paper.\nv) The resolution of the figures is low, authors are encouraged to generate higher-resolution figures when possible."}, "author_response": "Responses to thecomments fromReviewer#1\n1. The study by Chen et al. investigates the impacts of soil moisture-atmosphere feedback (SAF) on\ndry and humid heatwaves using a set of CMIP6 simulations. The derived heatwave characteristics\nfrom CMIP6 are evaluated using ERA5 reanalysis, and SAF impacts are identified by comparing\nall-forcing and prescribed soil moisture simulations. They find that soil moisture feedback could\namplify the dry heatwaves, but reduce humid heatwaves in the tropics and midlatitudes due to\nSAF-induced drying in relative humidity. Overall, this is an interesting study; the methodology is\nstraightforward, and the results are well structured. However, I have a couple of major concerns\nregarding the methodology and physical mechanism of the soil moisture feedback that need to be\naddressed before publication.\nResponse: We are very grateful to the reviewer for the positive and insightful review. These\ncomments have helped improve the manuscript. The reviewer’s comments are italicized and our\nresponses immediatelyfollow (revisions in themanuscript are highlighted in blue).\n2. First, many studies suggest that the characteristics of humid heatwaves, and their sensitivity to\nsoil moisture or humidity, strongly depend on the temperature metrics used. Besides wet-bulb\ntemperature, other common heat metrics include wet-bulb globe temperature, heat index, Universal\nThermal Climate Index, and equivalent temperature. This study, however, relies solely on wet-bulb\ntemperature.. I suggest the authors consider other metrics to explore and discuss the uncertainty of\ntheidentified humid heatwaves.\nResponse: We sincerely appreciate the reviewer's expertise and thoughtful suggestions. In response,\nwe have expanded our analysis to include a wider range of thermal metrics—specifically heat index,\nequivalent temperature, discomfort index and Oxford index, in order to provide a more\ncomprehensive assessment of humid heatwaves. These indices were selected because they rely on a\nrelatively small set of meteorological variables (e.g., temperature, humidity) that are available from\nstandard CMIP6 output, ensuring consistency and feasibility across the multi-model ensemble. The\n“Universal Thermal Climate Index” and “wet-bulb globe temperature” was not adopted as it requires\nnumerous auxiliary variables not routinely provided byCMIP6 experiments.\n(Supplementary Fig. S16), which assign varying weights to dry-bulb temperature versus humidity.\nMetrics in which humidity (or wet-bulb temperature) accounts for a substantial portion of the index,\nor in which the temperature–humidity balance closely resembles that of wet‑bulb temperature,\nproduce patterns similar to those based on wet-bulb temperature alone (e.g., discomfort index and\nequivalent temperature). Conversely, indices that are dominated by dry-bulb temperature naturally\nyield outcomes more aligned with dry-bulb temperature-based heatwaves. These variations are\ntherefore not contradictory to our core findings; rather, they reflect inherent differences in index\nconstruction, confirming that the representation of humid heatwaves depends critically on how a\nmetriccombines temperature and moistureinfluences.\nThe results are incorporated into discussions as: “Results based on alternative heat stress metrics,\nincluding the discomfort index, Oxford index, and equivalent temperature, closely align with those\nfrom the wet-bulb temperature-based index (Supplementary Figs. S16a-f). Conversely, metrics that\nassign greater weight to dry-bulb temperature, such as the heat index (Rachid and Qureshi, 2023),\nexhibit spatial patterns that increasingly resemble those of dry-bulb temperature as their sensitivity\nto temperature increases (Supplementary Figs. S16g-h). These systematic contrasts across metrics\nreveal that changes in humid heatwaves are governed by the competitive interplay between\nSAF-induced warming anddrying effects.” (L355-362 in thetrackedversion ofmanuscript)\nheatstressindexes.SameasFig.2a-2b,butusingthe(a-b)EqT:equivalenttemperature,(c-d)DI:discomfortindex,\n(e-f)OI:Oxfordindex,(g-h)HI:heatindex.TheformulasareprovidedinSupplementaryNote2.\n3. Second, while the study attempts to explain how SAF affects the two types of heatwaves, the\nunderlying reason for the feedback remains unclear. The authors argue that “SAF causes a\ndeclining trend insoil moisture under global warming.” This is a critical argument, as declining soil\nmoisture would subsequently influence surface fluxes, temperature, and humidity, ultimately\naffecting heatwave severity and duration. However, no results are presented to support this\n3\nstatement. If I understand the CMIP experiments correctly, the LFMIP-pdLC experiment uses the\nclimatological soil moisture in 1980–2014 derived from the ALL experiment. In that case, there\nshould be no difference in the long-term mean soil moisture between the two experiments; only soil\nmoisture variability differs. Moreover, even if there is a declining trend, the processes causing soil\ndrying remain unexplored. The authors need to further investigate the mechanisms behind soil\nmoisturevariabilityandits impacts.\nResponse: We sincerely appreciate the expertise and thoughtful comments. Actually, the difference\nbetween the pdLC and ALL experiments lies in that the pdLC experiment uses the climatological\nsoil moisture as a fixed input, therefore, the soil moisture trend in the pdLC experiment is zero. The\ndiscrepancy between the two experiments stems not only from variability in soil moisture but also\nfrom differences in trends. We have analyzed the role of soil moisture trend and variability as\nsuggested, and highlighted therole ofsoil moisture variabilityas follows:\n“SAF-induced dry-bulb warming is typically attributed to the “warmer climate-drier soil” feedback,\nwhereby climate warming exacerbates the precipitation-evapotranspiration deficit, leading to soil\ndrying that further amplifies warming via increased sensible heat (and consequently reduced\nevapotranspiration) and surface solar radiation(Qiao et al., 2023; Seo et al., 2018). However, this\nclimatological-scale feedback alone cannot fully account for the widespread warming observed in\nFig. 5b, as pronounced soil moisture declines are largely confined to subtropical regions during\n1985-2014 (Supplementary Fig. S10). Crucially, at subseasonal to interannual scales, soil moisture\nvariability in response to positive temperature anomalies can also trigger a “warmer-drier”\nfeedback28. This feedback exacerbates negative anomalies insoil moisture and latent heat flux while\nconcurrently amplifying the positive anomalies in sensible heat flux (Figs. 6a, c, e), thereby\nexplaining the stronger temperature anomaly observed when SAF is accounted for (Fig. 6g). Similar\npatterns are observed for dry spells (Supplementary Fig. S11). In contrast, during cold days, although\nsoil moisture variability tends to produce positive soil moisture anomalies, its impact on surface\nenergy fluxes is negligible (Figs. 6b, d, f, h), likely because evapotranspiration is energy-limited\nduring these periods. This asymmetric impact of soil moisture variability between warm and cold\nperiods results in a net positive effect on dry-bulb temperature. Moreover, the amplitude of soil\nmoisture anomalies driven by variability generally exceeds that associated with the long-term trend\n(Fig. 6a and Supplementary Fig. S10). Consequently, even in regions where soil moisture exhibits a\nwetting trend over time, the warming effect induced by soil moisture variability can dominate over\nany cooling tendency arising from the trend itself, thereby still contributing to net surface warming.”\n(L270-293)\nsoil column. The result is based on multi-model mean of the five CMIP6 models. Stippling indicates that no less\nthan80%oftheCMIP6modelsagreeinsignwiththemulti-modelensemblemean.\nanomalies(ALLminusLFMIP-pdLC)for(a)warmdaysand(b)colddaysduring1985–2014.(c–h)Corresponding\ndifferences for latent heat flux (c, d), sensible heat flux (e, f), and dry-bulb temperature (g, h). Anomalies are\ncalculatedrelative to the 1951–1980 climatology from theALLexperiment.Warm(cold) days aredefinedas those\non which the daily mean temperature exceeds (falls below) its climatology. Stippling indicates regions where at\nleast80%oftheCMIP6modelsagreeinsignwiththemulti-modelmean.\n(a) Differences in soil moisture anomalies (ALL minus LFMIP-pdLC) for dry spells during 1985–2014. (c–d)\nCorresponding differences for latent heat flux (b), sensible heat flux (c), and dry-bulb temperature (d).Anomalies\narecalculatedrelativetothe1951–1980climatologyfromtheALLexperiment.Stipplingindicatesregionswhereat\nleast80%oftheCMIP6modelsagreeinsignwiththemulti-modelmean.\ni) L131: All the figures are about the changes in heatwaves. I am a little surprised that there is no\nnegativechange in any case. Can theauthorconfirm?\nResponse: Thanks for the comments. We carefully reviewed our results and used clearer colorbar to\ndisplay them as follows. Only a very small number of grids showed a decrease in heatwaves in the\nERA5 dataset (green color in Fig. R1a-d), which is consistent with previous studies on heatwaves,\nthat is,heatwaves are almost increasing globally (Han et al., 2022;Wang et al., 2024).\nii) L163:How does SAF increasethe risks of globalwarming?\nResponse: We are grateful to the reviewer for highlighting this inaccuracy. There was an error in the\nreferencing, and the statement is supported by Qiao et al. (2023). As Qiao et al. (2023) have\ndemonstrated, “... high GHG emission will result in soil drying and reduced evapotranspiration,\nthereby forcing more heat into the atmosphere via enhanced downward shortwave radiation and\nsensible heat flux. Such soil moisture-atmosphere coupling (SA) conditions will serve to further\namplify theGHG-driven warming.”\nWe have briefly introduced this in the revised manuscript when interpreting SAF’s impacts on dry\nheatwaves as: “A reduction in soil moisture, often initiated by precipitation deficits, can efficiently\nsuppress evaporative cooling, leading to higher surface temperatures and enhanced atmospheric\nheating (Seneviratne et al., 2013; Zhou et al., 2019). This initiates a positive feedback loop, in which\ndrier soils further intensify heatwave conditions by increasing sensible heat flux and reducing latent\nheat flux. Additionally, reduced soil moisture inhibits cloud formation and precipitation, thereby\nexacerbating the persistence and intensity of dry heatwaves (Qiao et al., 2023). These mechanisms\ncollectively explain why soil moisture-atmosphere coupling tends to increase both the duration and\nseverity of dry heatwaves, particularly in regions where evaporation is sensitive to soil moisture\ndeficits.”(L194-202)\n8\niii) L273: Canada would be located in a similar climate regime. Any explanation for why SAF does\nnotincrease dry-bulb there?\nResponse: Thanks for the comments. The absence of a strong, consistent SAF-induced dry-bulb\ntemperature increase in northern Canada in our analysis is primarily due to substantial inter-model\nspread. We have discussed this as: “Notably, however, considerable inter-model spread persists in\ncertain high-latitude and coastal regions (especially northern Canada and northern Europe), where\nthe sign and magnitude of SAF-induced changes vary significantly across the ensemble. These\ndiscrepancies likely reflect differences in model physics, resolution, and the representation of\nland-atmosphere coupling processes over complex terrain or under snow-influenced regimes.\nTherefore, while our multi-model mean provides a robust estimate, future efforts should employ\nmore extensive model ensembles (encompassing both a greater diversity of models and single model\ninitial-condition large ensembles) to better isolate the forced response from internal climate noise\nand constrain model uncertainty(Kay et al., 2015).”(L372-381)\nReferences\nHan, Q. et al.Accelerated exacerbation of global extreme heatwaves under warming scenarios. Int. J.\nClimatology42,5430–5441.doi: 10.1002/joc.7541 (2022).\nKay, J. E. et al. The Community Earth System Model (CESM) Large Ensemble Project: A\nCommunity Resource for Studying Climate Change in the Presence of Internal Climate\nVariability.BAm Meteorol Soc96,1333-1349, doi:10.1175/bams-d-13-00255.1 (2015).\nQiao, L. et al. Soil moisture–atmosphere coupling accelerates global warming. Nature\nCommunications14,doi:10.1038/s41467-023-40641-y (2023).\nRachid, A. & Qureshi, A. M. Sensitivity Analysis of Heat Stress Indices. Climate 11,\ndoi:10.3390/cli11090181 (2023).\nSeneviratne, S. I. et al. Impact of soil moisture‐climate feedbacks on CMIP5 projections: First results\nfrom the GLACE‐CMIP5 experiment. Geophysical Research Letters 40, 5212-5217,\ndoi:10.1002/grl.50956 (2013).\nmid-latitude surface air temperature and heat wave events. Clim Dynam 52, 1695-1709,\ndoi:10.1007/s00382-018-4221-4 (2018).\nWang, C. et al. Changes in global heatwave risk and its drivers over one century. Earth's Future 12,\ne2024EF004430,doi:10.1029/2024EF004430 (2024).\nZhou, S. et al. Land–atmosphere feedbacks exacerbate concurrent soil drought and atmospheric\naridity. Proceedings of the National Academy of Sciences 116, 18848-18853,\ndoi:10.1073/pnas.1904955116 (2019).\n1. This study extends the understanding of the impacts and underlying mechanisms of soil\nmoisture–atmosphere feedbacks on humid heatwaves. This paper is been well-written, and the\nresearch presents significant scientific interest. However, I still have some suggestions regarding the\nmethods andconclusions for your reference.\nResponse: We are very grateful to the reviewer for the positive and insightful review. These\ncomments have helped improve the manuscript. The reviewer’s comments are italicized and our\nresponses immediatelyfollow (revisions in themanuscript are highlighted in blue).\n2. In the parts of results and conclusion, the paper attributes the observed differences to distinct\nphenomena occurring at high and low latitudes. However, the study does not clearly define or\nspecify which regions are classified as high-latitude or low-latitude areas. As a result, the\nconclusions remain largely qualitative. It is recommended that the author avoid generalizing results\nbasedonlatitudebandsandinsteadprovide descriptions grounded in specificgeographicregions.\nResponse: We sincerely appreciate the reviewer's expertise and thoughtful suggestions. We have\nprovided descriptions grounded in specific geographic regions as suggested. “SAF substantially\nreduces the annual total duration and severity of humid heatwaves by 10-20 days and 15-20 K,\nrespectively, across low latitudes (–20°S-20°N), southern mid-latitudes (20-60°S), southwestern\nNorth America (20-40°N, 55-91°W) and central and south Europe (20-60°N, 10°W-70°E) (Figs. 2a,\nb). ... In contrast, SAF increases the annual total duration and severity by 5-10 days and 15-20 K,\nrespectively, in northern high-latitudes (60-90°N) regions (e.g., Alaska, northern Asia, and northern\nEurope), therefore amplifying the increasing trends of humid heatwaves by 10-50%. Above results\nhold consistent at regional scales across both the 26 IPCC SREX regions (Supplementary Fig. S3)\nand latitudinally defined zones (low-, mid-, and high-latitudes) (Supplementary Fig. S4).” (L143-156\ninthe tracked version of manuscript)\n(a)SAF-inducedchanges in theannualtotalduration(TDUR) ofhumid heatwaves during1985–2014.(b) Sameas\n(a), but for the annual total severity (TSEV). (c) Relative changes in TDUR induced by SAF, compared to the the\nchanges inducedbyallotherfactors whichwereestimatedfromthe CMIP6-pdLC experiment. (d)Same as(c),but\nfor the TSEV. Stippling indicates that no less than 80% of the CMIP6 models agree in sign with the multi-model\nensemblemean.RedboxesshowingthesouthwesternNorthAmerica(20°N-40°N,55°W-91°W)andthecentraland\nsouthEurope(20°N-60°N,10°W-70°E).\nFig. S3. The same as Fig. 2, but for the regional results. The spatial averaged heatwave changes were first\ncalculatedoverthe26IPCCSREXregions,andthentheeffectandcontributionofSAFweredetermined.\nchanges. Results are aggregated over latitudinally defined zones, including the northern high-latitudes (NHL:\n60-90°N),southwesternNorthAmerica(SW-NA:20-40°N,55-91°W),centralandsouthEurope(CS-EU:20-60°N,\n10°W-70°E),lowlatitudes(LL:20°S-20°N),andsouthernmid-latitudes(SML:20-60°S).\n3. Lines 174-176, the calculation of SAF coupling index is defined as the correlation between\nmonthly soil moisture and surface specific humidity multiplied by the standard deviation of surface\nspecifichumidity. However, in thelisted references, thestandarddeviation ofsoil moisturewasused.\nPleasecheck theresults andthecalculation process.\nResponse: Thank you for the comment. We have checked that, in the listed reference, the standard\ndeviation of surface energy fluxes (e.g., LH or SH) is used instead of the standard deviation of soil\nmoisture. However,as we focused on the influence of soil moisture onrelative humidity, adjustments\nhave been made based on the original approach by using the standard of surface specific humidity.\nWehave clarified this in theMethod as:\n“DefinitionofSAFcoupling index\nThe SAF coupling index is calculated based on the monthly soil moisture ( ) and monthly near\nsurfacespecific humidity( )during 1985-2014 as: w\nϕ\n13\n(5)\n' '\n (wy,m,ϕy,m)\nI(wm,ϕm) = ' 2 = r(wm,ϕm)σ(ϕm)\nn (wy,m)\n, where primes denote anomalies from the mean annual cycle during the total years, and and\nmean the month and year, respectively.The mean correlation the conrrelation betwmeen soiyl\nmoisture and the humidity, while and r(wmi,sϕmth)e standard deviation of humidity. This SAF\ncoupling index shares the formulation ofσp(ϕriomr)terrestrial indices (Dirmeyer, 2011; Dirmeyer et al.,\n2013), but with a focus on humidity instead of surface energy fluxes. The coupling index was\ncalculated for each monthseparately, and then averaged annually.” (L434-444)\n4. This paper applied LFMIP data to analyze the impact of soil moisture- atmosphere feedbacks on\nhumid heatwaves. However, when discussing the soil moisture–atmosphere feedback effect, its\nunderlying drivers—such as vegetation changes, climate change, and other contributing\nfactors—shouldbeexplicitly addressed. Acomprehensiveanalysis of these factors isnecessaryat the\nglobalscale to providecontext for thefeedback mechanism.\nResponse: We sincerely appreciate the reviewer's expertise and thoughtful suggestions. We have\ndiscussed thisin themanuscript as:\n“The SAF inherently integrates multiple co-varying factors over the historical period, including\ninternal climate variability, climate change, and land-cover changes. For instance, the intensity and\npattern of SAF may themselves evolve under a warming climate (Qiao et al., 2023; Seneviratne et al.,\n2006), while land-cover modifications can alter surface drying and locally enhance or weaken\ncoupling strength (Yu et al., 2025). However, SAF can in turn modulate regional climate change and\ninfluence vegetation and land-surface conditions, forming a tightly coupled system. Isolating the\nspecific contribution of any single factor (e.g., climate change versus vegetation dynamics) to the\noverall SAF signal lies beyond the scope of the present study and would require carefully designed\nsensitivityexperiments and novel methodological frameworks.” (L382-391)\nWhile fully attributing the SAF signal to a single underlying factor (e.g., climate change or land\ncover) is out of the scope of current study, we have provided a more detailed characterization by\nseparating the effects of long-term soil moisture trends from those of soil moisture variability.\nThese results helpelucidate themechanisms of thefeedback.\n“SAF-induced dry-bulb warming is typically attributed to the “warmer climate-drier soil” feedback,\n14\nwhereby climate warming exacerbates the precipitation-evapotranspiration deficit, leading to soil\ndrying that further amplifies warming via increased sensible heat (and consequently reduced\nevapotranspiration) and surface solar radiation(Qiao et al., 2023; Seo et al., 2018). However, this\nclimatological-scale feedback alone cannot fully account for the widespread warming observed in\nFig. 5b, as pronounced soil moisture declines are largely confined to subtropical regions during\n1985-2014 (Supplementary Fig. S10). Crucially, at subseasonal to interannual scales, soil moisture\nvariability in response to positive temperature anomalies can also trigger a “warmer-drier”\nfeedback28. This feedback exacerbates negative anomalies insoil moisture and latent heat flux while\nconcurrently amplifying the positive anomalies in sensible heat flux (Figs. 6a, c, e), thereby\nexplaining the stronger temperature anomaly observed when SAF is accounted for (Fig. 6g). Similar\npatterns are observed for dry spells (Supplementary Fig. S11). In contrast, during cold days, although\nsoil moisture variability tends to produce positive soil moisture anomalies, its impact on surface\nenergy fluxes is negligible (Figs. 6b, d, f, h), likely because evapotranspiration is energy-limited\nduring these periods. This asymmetric impact of soil moisture variability between warm and cold\nperiods results in a net positive effect on dry-bulb temperature. Moreover, the amplitude of soil\nmoisture anomalies driven by variability generally exceeds that associated with the long-term trend\n(Fig. 6a and Supplementary Fig. S10). Consequently, even in regions where soil moisture exhibits a\nwetting trend over time, the warming effect induced by soil moisture variability can dominate over\nany cooling tendency arising from the trend itself, thereby still contributing to net surface warming.”\n(L270-293)\nanomalies(ALLminusLFMIP-pdLC)for(a)warmdaysand(b)colddaysduring1985–2014.(c–h)Corresponding\ndifferences for latent heat flux (c, d), sensible heat flux (e, f), and dry-bulb temperature (g, h). Anomalies are\ncalculatedrelative to the 1951–1980 climatology from theALLexperiment.Warm(cold) days aredefinedas those\non which the daily mean temperature exceeds (falls below) its climatology. Stippling indicates regions where at\nleast80%oftheCMIP6modelsagreeinsignwiththemulti-modelmean.\nsoil column. The result is based on multi-model mean of the five CMIP6 models. Stippling indicates that no less\nthan80%oftheCMIP6modelsagreeinsignwiththemulti-modelensemblemean.\nFig. S11. Impact of SAFon surface anomalies during dry spells (≥3 consecutive days without precipitation).\n(a) Differences in soil moisture anomalies (ALL minus LFMIP-pdLC) for dry spells during 1985–2014. (c–d)\nCorresponding differences for latent heat flux (b), sensible heat flux (c), and dry-bulb temperature (d).Anomalies\narecalculatedrelativetothe1951–1980climatologyfromtheALLexperiment.Stipplingindicatesregionswhereat\nleast80%oftheCMIP6modelsagreeinsignwiththemulti-modelmean.\nDirmeyer, P. A. The terrestrial segment of soil moisture-climate coupling. Geophys Res Lett 38,\nn/a-n/a, doi:10.1029/2011gl048268 (2011).\nDirmeyer, P. A., Jin, Y., Singh, B. & Yan, X. Evolving Land–Atmosphere Interactions over North\nAmerica from CMIP5 Simulations. J Climate 26, 7313-7327, doi:10.1175/jcli-d-12-00454.1\n(2013).\nSeneviratne, S. I. et al. Impact of soil moisture‐climate feedbacks on CMIP5 projections: First results\nfrom the GLACE‐CMIP5 experiment. Geophysical Research Letters 40, 5212-5217,\ndoi:10.1002/grl.50956 (2013).\nSeo, E. et al. Impact of soil moisture initialization on boreal summer subseasonal forecasts:\nmid-latitude surface air temperature and heat wave events. Clim Dynam 52, 1695-1709,\ndoi:10.1007/s00382-018-4221-4 (2018).\nWang, C. et al. Changes in global heatwave risk and its drivers over one century. Earth's Future 12,\ne2024EF004430,doi:10.1029/2024EF004430 (2024).\nYu, L. F. et al. Land-atmosphere interactions mitigate the direct surface-drying effects of land use\nand cover change. OneEarth 8,doi:10.1016/j.oneear.2025.101210 (2025).\n1. This study examines the global scale effects of soil moisture-atmosphere feedback (SAF) on dry\nandhumid heatwaves. Global climate model simulations, both idealised (LFMIP-pdLC) and realistic\n(CMIP6-all), are used to explain the contributions of SAF to historical changes in dry and humid\nheatwaves across the globe, andto disentanglethe mechanisms. CMIP6 models’ abilityto reproduce\nhistorical properties and changes in dry and humid heatwaves is first evaluated with respect to\nERA5. The SAF-induced changes are then quantified by comparing LFMIP-pdLC and CMIP6-all\nsimulations, and the SAF effects are decomposed into contributions from dry-bulb and relative\nhumidity effects. The main outcome of this study are the opposite effects of SAF on humid heatwaves\nin regions of strong and weak land-atmosphere coupling. Although SAF has been extensively studied\nfrom theperspective of dry heatwaves, much less is known about SAF effects on humid heatwaves, as\nis clearly introduced in the paper. In this respect, the contribution of this study is original and of\ninterest for the land-atmosphere/climate community as well as the heat stress/impact community.\nHowever, the methods used in this paper suffer from several approximations and misuses that need\ntobe addressed before thepaper may be considered further forpublication.\nResponse: We are very grateful to the reviewer for the positive and insightful review. These\ncomments have helped improve the manuscript. The reviewer’s comments are italicized and our\nresponses immediatelyfollow (revisions in themanuscript are highlighted in blue).\n2. My main comment relates to the first scientific issue raised by the authors: “How has SAF\nmodulated historical changes in both dry and humid heatwaves?” Comparing models’ capacity to\ncapture heatwave statistics (duration and severity) with respect to ERA5 over the 1951-2014 period\nis meaningful, as it indicates the extent to which each model’s background climate is realistic.\nHowever, comparing the changes between 1980-2014 and 1951-1980 as is done in the paper is less\nso, because the multi-model mean would filter out the part of the change that is due to internal\nvariability, which is large at the grid cell scale. This is illustrated by comparing, for instance, Fig.1a\nwith Fig.1e: in the former, the pattern of change in Tw_TDUR is more speckled than in the latter.\nThe same conclusion holds when comparing each pair of ERA5vsCMIP6-MME panel, and the\ncoefficients of spatial correlation between these pairs of maps are rather low, indicating that the\n19\nforced signal, as estimated by the CMIP6 MME explains only a limited part of the observed spatial\npattern of change. As expected, this analysis is more convincing when looking at regionally or\nzonally averaged values. I think it would make more sense to consider these spatial scales in\nsubsequent analyses, in conjunction toaggregating locations according toland-atmosphere coupling\nregimes, as evaluated withe.g., thecoupling index.\nResponse: We sincerely appreciate the reviewer for this insightful and constructive comment. The\nreviewer correctly points out that the multi-model mean (MME) filters out internal variability,\nmaking direct grid-point-to-grid-point comparison between CMIP6-MME and the single realization\nof ERA5 problematic. Wefully agree that focusing onregional averages provides a more appropriate\nand robust framework for comparing the forced response in models with observations. We would\nlike to clarify that in our original manuscript, the analyses of the soil moisture–atmosphere coupling\nindex and its effect on heatwaves (SAF) were already conducted and presented on regional mean\nscales (e.g., Fig. 3, 6), which inherently reduces the influence of internal variability highlighted by\nthe reviewer. In direct response to the suggestion, we have now further strengthened the\nregional-scaleassessment byperforming two additional sets ofanalyses, as detailed below.\nFirst, we have evaluated the CMIP6 models across the 26 IPCC SREX regions (Supplementary Fig.\nS2). The results demonstrate that the models continue to reasonably capture the changing trends and\nmagnitudes of both heatwave types at regional scales. As anticipated, regional averaging yields\nsubstantially higher spatial correlation coefficients (0.60–0.89) compared to grid-scale values\n(0.5–0.77). However, larger simulation errors are still evident in some coastal and high-latitude\nregions likely due to model-related factors. We have explicitly noted this in the revised manuscript\nas :“... The CMIP6 models continue to reasonably capture the changing trends and magnitudes of\nboth heatwave types at regional scales (Supplementary Fig. S2), with the spatial correlation\ncoefficients increasing to 0.60-0.89 and mean relative errors remaining around 20%. However,\npossibly due to the coarse resolution and biases in surface energy partitioning (Hirsch et al., 2021),\nrelatively larger simulation errors are found in some coastal and high-latitude regions, such as the\nCaribbean, northeastern Brazil, and northern Europe.” (L121-128 in the tracked version of\nmanuscript)\nSecond, we have further assessed the role of soil moisture–atmosphere feedback (SAF) using the\nsame 26-region framework (Supplementary Fig. S3). The regional-aggregated results confirm that\nlatitude regions, while increasing them by more than 20% in high-latitude areas. These\nregional-scale findings are fully consistent with the grid-based patterns presented in the main text\n(Fig. 2), underscoring that our principal conclusions are robust and not sensitive to the choice of\nspatial averaging scale. We have added a corresponding statement in the manuscript: “... Above\nresults hold consistent at regional scales across both the 26 IPCC SREX regions (Supplementary Fig.\nS3)...”(L154-155)\nFig.S2.EvaluationofCMIP6modelsinsimulatingchangesinheatwavecharacteristicsataregionalscale.(a)\nIPCC SREX regions and their acronyms. (b) Scatterplot of observed versus simulated changes in the annual total\nduration of humid heatwaves during 1985–2014. Red circles indicate the multi-model ensemble mean of\nCMIP6-ALL simulations, with blue lines showing the range of individual ensemble members. The mean relative\nabsoluteerror isshowninthebottom-rightcorner,while thespatialcorrelation coefficientis shownbyredtext.(c)\nSameas(b),butfortheannualtotalseverityofhumidheatwaves.(d–e)Sameas(b–c),butfordryheatwaves.\ncalculatedoverthe26IPCCSREXregions,andthentheeffectandcontributionofSAFweredetermined.\nFig.2.Changingpatternsofhumidanddryheatwavesinducedbysoilmoisture-atmospherefeedback(SAF).\n(a)SAF-inducedchanges in theannualtotalduration(TDUR) ofhumid heatwaves during1985–2014.(b) Sameas\n(a), but for the annual total severity (TSEV). (c) Relative changes in TDUR induced by SAF, compared to the the\nchanges inducedbyallotherfactors whichwereestimatedfromthe CMIP6-pdLC experiment. (d)Same as(c),but\nfor the TSEV. Stippling indicates that no less than 80% of the CMIP6 models agree in sign with the multi-model\nensemble mean). Red boxes showing the southwestern North America (20°N-40°N,55°W-91°W) and the central\nandsouthEurope(20°N-60°N,10°W-70°E).\n22\n3. In the following sections, multi-model means from the LFMIP-pbLC and ALL experiments are\ncompared, which allows to quantify the forced effect of SAF on dry and wet heatwaves. Although\ninteresting on its own, this approach doesn’t allow to quantify the contribution of SAF to the\nobserved changes in heatwave duration and severity. Indeed, authors do not link these forced\nchanges to those quantified with ERA5. It should also be noted that considering an ensemble of 5\nsingle-member model runs may not be sufficient to isolate the forced SAF signal robustly, which\nshould bediscussed.\nResponse:Wethank thereviewer forraising thispoint.\nFirst, in our analysis, we indeed quantified the relative contribution of SAF, not only its absolute\neffect. Wehave clarified themethod intheMethod as:\nbl hist\n“For a given heatwave metric M (e.g. annual total duration), let M and M denote its mean\nALL ALL\nvalues in the ALL experiment during the baseline (1951-1980) and historical (1985-2014) periods,\nhist\nrespectively, and let M represent the corresponding mean in the LFMIP-pdLC experiment\npdLC\nduring 1985-2014. The total observed change in the historical period is therefore\nhist bl\nΔM =M −M , which includes the combined influence of all factors (e.g., external forcing,\ntotal ALL ALL\nhist bl\ninternal variability, and SAF). The change in the absence of SAF isΔM =M −M .\nnoSAF pdLC ALL\nHence,\nthe effect of SAF is defined as ΔM =ΔM −ΔM , and its relative contribution is calculated\nSAF total noSAF\nas (ΔM /ΔM )×100%.\nSAF noSAF\nBecause both the sign and magnitude of changes vary across models, ΔM and its relative\nSAF\ncontribution are first computed for each individual model, and the multi-model ensemble mean is\nthen derived from thoseindividual estimates. ...”(L467-478)\nThe Fig. 2 is revised to include the SAF’s contribution result, and the related description are now as\nfollows: “SAF substantially reduces the annual total duration and severity of humid heatwaves by\n10-20 days and 15-20 K, respectively, ... Compared to the combined influence of other factors (e.g.,\nclimate warming, as estimated by the CMIP6-pdLC experiment), SAF’s reduction effect alleviates\ntheincreasing trends of humidheatwaves by 10-40%, with particularly pronounced values in Europe,\nAustralia, and North Africa (Fig. 2c, d). In contrast, SAF increases the annual total duration and\nseverity by 5-10 days and 15-20 K, respectively, in northern high-latitudes (60-90°N) regions (e.g.,\nAlaska, northern Asia, and northern Europe), therefore amplifying the increasing trends of humid\nheatwaves by 10-50%. ... In contrast, SAF generally enhances the duration and severity of dry\n23\nheatwaves (Supplementary Figs. S5a, b). The impact of SAF exceeds 1.5 times of the combined\ninfluence of other factors over subtropical regions, suggesting that SAF is the dominant driver of dry\nheatwavechanges (Supplementary Figs. S5c, d).”(L143-165)\nFig.2.Changingpatternsofhumidanddryheatwavesinducedbysoilmoisture-atmospherefeedback(SAF).\n(a)SAF-inducedchanges in theannualtotalduration(TDUR) ofhumid heatwaves during1985–2014.(b) Sameas\n(a), but for the annual total severity (TSEV). (c) Relative changes in TDUR induced by SAF, compared to the the\nchanges inducedbyallotherfactors whichwereestimatedfromthe CMIP6-pdLC experiment. (d)Same as(c),but\nfor the TSEV. Stippling indicates that no less than 80% of the CMIP6 models agree in sign with the multi-model\nensemblemean.RedboxesshowingthesouthwesternNorthAmerica(20°N-40°N,55°W-91°W)andthecentraland\nsouthEurope(20°N-60°N,10°W-70°E).\nFig. S5. Changing patterns of dry heatwaves induced by soil moisture-atmosphere feedback (SAF). (a)\nbut for the annual total severity (TSEV). (c) Relative changes in TDUR induced by SAF, compared to the the\nchanges inducedbyallotherfactors whichwereestimatedfromthe CMIP6-pdLC experiment. (d)Same as(c),but\nfor the TSEV. Stippling indicates that no less than 80% of the CMIP6 models agree in sign with the multi-model\nensemblemean.\nSecond, we fully agree that the current contribution result primarily intends to quantify the effect of\nSAF on heatwaves within the climate model framework, and the ensemble size may not be sufficient\nto isolate the forced SAF signal robustly. We have discussed this as suggested: “The SAF’s\ncontribution was quantified directly within the CMIP6 framework rather than scaling the modeled\neffects to observational datasets such as ERA5. This approach avoids the substantial uncertainty\nassociated with attributing a model-based forced signal to an observed trend that inherently\nintertwines external forcing with internal variability, a confounding factor that our five-model\nensemble cannot fully disentangle. Nonetheless, the models’ fidelity in capturing regional heatwave\nchanges and soil moisture-atmosphere coupling strength (Supplementary Figs. S2, S3, S4, S6),\ntogether with the consistent magnitude and sign of SAF's contribution across spatial scales (Figs. 2,\nS3, S4), provides confidence that internal variability does not undermine the core findings. Notably,\nhowever, considerable inter-model spread persists in certain high-latitude and coastal regions\n(especially northern Canada and northern Europe), where the sign and magnitude of SAF-induced\nchanges vary significantly across the ensemble. These discrepancies likely reflect differences in\nmodel physics, resolution, and the representation of land-atmosphere coupling processes over\ncomplex terrain or under snow-influenced regimes. Therefore, while our multi-model mean provides\na robust estimate, future efforts should employ more extensive model ensembles (encompassing both\na greater diversity of models and single model initial-condition large ensembles) to better isolate the\nforced response from internal climate noise and constrain model uncertainty (Kay et al., 2015).”\n(L363-381)\nchanges. Results are aggregated over latitudinally defined zones, including the northern high-latitudes (NHL:\n60-90°N),southwesternNorthAmerica(SW-NA:20-40°N,55-91°W),centralandsouthEurope(CS-EU:20-60°N,\n10°W-70°E),lowlatitudes(LL:20°S-20°N),andsouthernmid-latitudes(SML:20-60°S).\nFig. S6. Intercomparison of soil moisture-atmosphere coupling indices in ERA5 reanalysis and CMIP6\nmodelsoverthe1985-2014period.(a)Couplingstrengthbetweenmonthlysoilmoistureandnear-surfacespecific\nhumidityderivedfromERA5.(b-f)CorrespondingcouplingindicesforfiveCMIP6models.\ninternal variability cautiously. We have revised the first scientific question to avoid any\nmisunderstanding. “... We aim to address two key scientific issues: 1) What is the role of SAF in\nmodulating dry and humid heatwaves? 2) What are the differences in the patterns and the physical\nmechanisms behind?”(L90-92)\n4. I am also not convinced by the decomposition of changes in wet-bulb temperature into mean and\nvariability signals. First, because adding the SAF-induced annual mean temperature change to daily\ntemperature time series doesn’t seem appropriate; authors refer to ref #5, but I couldn’t see a\nsimilarapproach described there.\nResponse: We thank the reviewer for this insightful comment. We agree with the reviewer that\nadding a constant mean offset is not appropriate. Our intended method was, in fact, the established\ndetrending procedure from reference #5 (in the Method section of Wang et al., 2020). Following the\ncore of that methodology, we have used a polynomial fit to define the secular signal, not an annual\nmean, and perform asubtraction from daily data. This procedure ensures aclean separation ofeffects,\nand we have revised the text to eliminate the previous ambiguous phrasing. “Following previous\nresearch (Wang et al., 2020), we fitted separate second-order polynomials to the monthly mean\ntemperature series (1981-2014) from the ALL and LFMIP-pdLC experiments at each grid cell to\ncapture the warming/cooling signal. Their difference, which varies by year and month, is considered\nas the SAF-induced component of warming/cooling and was subtracted from the daily temperature\nrecord of the ALL experiment. The different heatwave metrics between this adjusted ALL series and\nthe original LFMIP-pdLC experiment, reflects SAF-induced variability effects, encompassing\ninterannual, seasonal, intraseasonal, and diurnal components. Consequently, the residual component\nofSAF-induced heatwave changes represents the effect of mean temperature shifts.” (L485-494)\nImportantly, the key findings and scientific conclusions remain unchanged from our original\nsubmission. This consistency reinforces the robustness of our central result that: SAF primarily\nmodulates humid heatwaves through alterations in the mean state of wet-bulb temperature, rather\nthan byaltering its variability.\n27\n5. A second source of concern is the resort to the GEV distribution, which is designed for the\nstatistical modelling of block maxima; however, in this paper, GEV distributions are fitted to “daily\ntemperature data” (L422), without further details about the sampling procedure (but again using ref\n#5). In addition, it is not quite clear to me what the expected outcome of this procedure is, as hot\ndays in this paper are defined based on a percentile calculated on the whole distribution of daily\nvalues, not on the tail of the distribution. In addition, explaining this result in just one sentence\n(L228-231)is not sufficient.So,I wouldencourage authors to clarifytheir objectiveandprocedure.\nResponse:Thank you forthis insightful comment regarding theuse oftheGEV distribution.\nFirst, we fully agree that the GEV is primarily intended for extreme value modeling. Therefore,\nwe have revised our methodology to employ the Normal distribution for fitting the daily temperature\ndata. We have now used the Normal distribution to fit the distribution of daily temperature in each\nmonth. More than 70% of the grids pass the Kolmogorov-Smirnov goodness-of-fit test at the 0.05\nconfidencelevel (80%at the0.01confidence level), suggesting thenormal distributionis suitable.\nSecond, the primary objective of the probabilistic procedure was to provide an independent line\nof evidence, following the approach of reference #5, to corroborate the findings from the\npolynomial-based mean-variance framework that is central to our main analysis. To prevent any\npotential confusion with our primary percentile-based heatwave definition and to maintain focus in\nthe main text, we have now expanded the explanation of both the objective and the procedure as\nsuggested, but put them tothe Supplementary Note 1.\n“We adopt a probabilistic approach to assess how changes in the mean and variability of temperature\ninfluence the likelihood of heatwaves. This method quantifies the probability of exceeding a fixed\nhigh-temperature threshold under different climatic conditions, providing independent evidence that\ncomplements thepolynomial-based mean–variance framework (Wang et al., 2020).\nSpecifically, for each calendar month and grid cell, we fitted a normal distribution to the daily mean\nwet-bulb temperature data from that particular month over the period 1981–2014. The probability\ndensity function is given by:\n(1)\n2\n1 (x−μ)\n2\n,where and represent thelocationy(m=eafn(x)|aμn,dσ)sc=aleσ(2sπtaenxdpa(rd−dev2σiatio)n) parameters, respectively.\nThe fitteσd distrμibutions for the LFMP-pdLC andALL experiments in a given month i are denoted as\n28\nand . The probability of a hot day under each\nNORMi,pdLC(μi,0,σi,0) NORMi,ALL(μi,1,σi,1)\ndistribution— and )—was calculated relative to the\nsame daily thrPes_hNoOldR,Md i e ,p f d in LC e(dμa i,0 s,tσh i e ,0)90th pePrc_eNnOteRnMoi f ,AL te L m(μp i, e 1 r,aσt i u ,1 r)e from the baseline period in ALL\nexperiment.\nTo isolate the influence of changes in the mean state, we constructed a hybrid distribution\nby replacing the location parameter in with from\nNORMi,pdLC(μ, i,1 w,hσi i l ,0 e)retaining the original scale parameter μi,0 .​ TheNOcoRrMres i,p p d o L n C ding proμba i,1 bility is\nPde_nNoOteRdMi,ALL as . The diσff i, e 0 rences\nP_NORMi,pdLC(μi,1,σi,0) P_NORMi,pdLC(μi,1,σi,0)−\nand , reflect the influence\nPof_NSOARFM-i i n ,p d d u LC c(eμd i,0 c,hσa i n ,0 g)es inPt_hNeOtRemMp i, e A r L a L t(uμr i e ,1,mσi e ,1 a)n−aPnd_NvOaRriMab i, i p l d i L ty C(μto i,1 t,hσe i,0 p)robability of hot day\noccurrence.\nThe contributions of changes in the temperature mean ( ) and variability ( ) were\nquantified for each monthas:\nCTi,μ0→μ1 CTi,σ0→σ1\n(2)\nP_NORMi,pdLC(μi,1,σi,0)−P_NORMi,pdLC(μi,0,σi,0)\nCTi,μ0→μ1\n= P_NORMi,ALL(μi,1,σi,1)−P_NORMi,pdLC(μi,0,σi,0)\n(3)\nP_NORMi,ALL(μi,1,σi,1)−P_NORMi,pdLC(μi,1,σi,0)\n, where the overbar denCoTte i s ,σ0 t → h σ e 1 d=aiPly_NOmReMai,nALLp(μrio,1b,σai,b1)i−liPt_yN.OTRMhei,pdfLiCn(μail,0,σcio,0n)tributions were obtained by\naveraging and across all months.”(see Supplementary Note 1)\nThird,CwTi e ,μ0 h → a μ v 1 e exteCnTd i e ,σ d 0→ t σ h 1 e explanation on the result in the main text as: “...We further\nevaluated the role of the mean state by comparing daily wet-bulb temperature distributions between\nthe ALL and LFMIP-pdLC experiments (Supplementary Note 1). The spatial structure of\nSAF-induced changes in the probability of hot humid days closely consistent with changes in actual\nheatwaves (spatial correlation coefficients = 0.73-0.82; Fig. S8a, Figs. 2a, b). A statistical attribution\nshows that shifts in the location parameter (mean) explain >70% of this change in most regions,\nrobust across models (Figs. S8b, d), while the scale parameter (variability) plays a minor role (Fig.\nS8c). These results independently corroborate that mean-state shifts dominate SAF’s impact on\nhumidheatwaves.”(L231-239)\ncontributionsfromchangesinlocationandscaleparameters.(a)Themeanchangesofprobabilityofhothumid\ndays induced by soil moisture-atmosphere feedback. (b) Contributions of changes in location parameter to the\nchanges in humid heatwave frequency. (c) Same as (b), but for the contributions from the scale parameter. (d)\nGlobal mean contributions based on (b) and (c), with error bars indicating the range (i.e., the minimum and\nmaximum)acrossallindividualmonths.\n6. In sum, this article has merit in dealing with an important knowledge gap but, in my opinion, it\nfalls short of providing robust answers to the first key scientific question raised – mainly because\nit is not formulated correctly. The second issue, which is about how SAF controls heatwaves\nproperties across the globe, is more consistently addressed but may suffer from methodological\ncaveats that should be addressed. It would also be interesting to see whether the two mechanistic\napproaches (the statistical oneandthephysical one) can be linked.\nResponse: Thank you for the comment. We have revised the manuscript according to your\ncomments and suggestion. The first question have been revised to better focus on the influence of\nSAF, instead of pointing to an attribution framework. We have strengthened methodological clarity\nand robustness as suggested, including adding a detailed information to some Methods and revising\nsomemethods tokeep constant withthe reference. (Please see ourresponse above fordetails).\nThere are close linkages between the statistical and physical approaches. The statistical analysis first\nidentified that SAF influences humid heatwaves primarily by shifting the mean state of wet-bulb\ntemperature rather than its variability. Such statistical-based result is approved by the CMIP6-based\nresults (or the physical simulation). This statistical-based key finding did not merely stand as a result\nbut directly guided and focused our subsequent physical mechanism investigation. This finding\nprompted a focused investigation into why and how SAF alters the mean thermodynamic state,\nthereby streamlining the mechanistic inquiry by avoiding unnecessary complexity. In turn, the\nphysical experiments (LFMIP-pbLC vs. ALL), quantified the causal pathways that explain the\nSAF-induced mean-state shifts, namely, the competitive interplay between SAF-induced warming\nand drying effects. This did not just confirm the statistical pattern, but also provided the\nprocess-based understanding behind it, turning correlation into causation. Thus, the two approaches\nform a coherent, reinforcing cycle: statistical patterns pointed to the most relevant physical question,\nand physical mechanisms elucidated the processes behind those patterns. We have strengthened this\nnarrative in the text to highlight how this integration allows us to more confidently address the\nscientific questions raised. “... Figure 5a further illustrates the SAF-driven shifts in mean daily\nwet-bulb temperature during 1985-2014, which closely aligns with SAF-induced changes in TDUR\nand TSEV of humid heatwaves with spatial correlation coefficients ranging from 0.6 to 0.75.”\n(L225-228)\n“... Critically, in these regions the drying influence of SAF outweighs its warming effect, leading to\nlower wet-bulb temperatures and a corresponding decrease in humid heatwaves. By contrast, in\nhigh-latitude regions ... the warming effect of SAF dominates, producing a net increase in wet-bulb\ntemperatureand contributingtomore frequent humidheatwaves.”(L301-308)\ni) Authors refer to refs. #21 and 22, where heatwaves’ definitions are based on daily maximum\nvalues, but it is unclear how a heatwaveis defined here. My guess is thatdaily mean values areused,\ninwhich case thecitations arenot relevant. In addition, authors may consider removing theseasonal\ncycle of T and Tw before calculating the 90th percentile on 15-day moving window, as recommend\nbyBrunner andVoigt (2024).\nResponse: Thank you for the careful comment. We have revised the references and clarified the use\nof daily temperature in the manuscript as follows: “Dry and humid heatwave events are defined as\nperiods of three or more consecutive days during which daily mean dry-bulb or wet-bulb\ntemperatures exceed their respective 90th percentile thresholds (Raghavendra et al., 2018; Xu et al.,\n2016)”(L96-98).\nIn addition, the seasonal cycles have been removed from the T and Twet prior to heatwave\ncalculation as suggested, and the results remain robust. We have discussed this in the manuscript: “In\naddition, the results remain robust when using a more complex algorithm for estimating wet-bulb\ntemperature (Stipanuk, 1973), or removing the seasonal cycle of temperatures before calculating the\n90th percentile (Brunner and Voigt, 2024), or applying a 95th percentile threshold for identifying\nhumidheatwaves (Supplementary Fig. S15).”(L351-354)\nFig.S15.Patternsofhumidheatwavechangesinducedbysoilmoisture-atmospherefeedbackusing different\ndefinitions. (a-b) Same as Fig. 2a-2b, but the wet-bulb temperature was estimated from dry-bulb temperature,\nsurfacepressure,andrelativehumidityusingthealgorithmproposedbyStipanuk(1973).(c-d)SameasFig. 2a-2b,\nbut removing the seasonal cycle of temperatures before calculating the 90th percentile following the method\nintroduced by Brunner and Voigt (2024). (e-f) Same as Fig. 2a-2b, but using the 95th percentile threshold for\ndetecting humid heatwaves. Stippling indicates that no less than 80% of the CMIP6 models agree in sign with the\nmulti-modelensemblemean.\n31\nii) It is not clear how the statistical significance of changes between ALL and LFMIP experiments is\nassessed (see stipplinginFigures).\nResponse: Thanks for the comment. We have added corresponding descriptions in the Method\nsection and figure caption as follows: “Because both the sign and magnitude of changes vary across\nmodels, ΔM and its relative contribution are first computed for each individual model, and the\nSAF\nmulti-model ensemble mean is then derived from those individual estimates. A signal is considered\nstatistically significant when at least four of the five models agree on the sign of the ensemble-mean\nresult(Jiand Yuan, 2024; Qiao et al., 2023;Zhouet al., 2022)”(L476-480)\n“... Stippling indicates that no less than 80% of the CMIP6 models agree in sign with the\nmulti-modelensemble mean. ...”(L175-176)\niii) The coupling index in ref #24 is defined as the linear regression (or coefficient of correlation)\nbetween a flux (e.g., latent heat) and soil moisture, multiplied by the standard deviation of soil\nmoisture; so, the description in L174 may be incorrect. In addition, it is not clear whether the\ncalculation isbased ondailyvalues anddone monthly, orif it isbased onmonthlyvalues?\nResponse: Thank you for the comment. The coupling index is based on monthly values. The index\nin ref #24 is mathematically equivalent to the product of the standard deviation of the flux and the\ncorrelation between soil moisture and the flux (Dirmeyer et al., 2013). We used specific humidity\ninstead of surface energy flux because the study focuses on the influence of soil moisture to the\nhumidity. Wehaveclarified thedefinitionand calculationprocedure intheMethod section as:\n“DefinitionofSAFcoupling index\nThe SAF coupling index is calculated based on the monthly soil moisture ( ) and monthly near\nsurfacerelative humidity ( )during 1985-2014 as: w\nϕ\n(5)\n' '\n (wy,m,ϕy,m)\nI(wm,ϕm) = ' 2 = r(wm,ϕm)σ(ϕm)\nn (wy,m)\n, where primes denote anomalies from the mean annual cycle during the total years, and and\nmean the month and year, respectively.The mean correlation the conrrelation betwmeen soiyl\nmoisture and the humidity, while and r(wm,ϕmis) the standard deviation of humidity. This\nhumidity-based coupling index shares theσfo(ϕrmmu)lation of prior terrestrial indices(Dirmeyer, 2011;\nDirmeyer et al., 2013), but with a focus on humidity instead of surface energy fluxes. The coupling\n32\nindex was calculated foreach month separately,and thenaveraged annually.” (L434-444)\niv) Authors indicate in L324-326 that “The strong performance of CMIP6 models to capture SAF\nacross most regions —as indicated by previous studies28,30 and confirmed by our evaluation (Fig. 1\nand Supplementary Fig. S1-S2)— further strengthens the credibility of our findings.” This statement\nmay be wrong, as the evaluation performed here and shown in Figs. 1, S1, S2 does not relate to the\nSAF. Evaluating the ability of the five GCMs used here to capture coupling regimes across the globe\nwouldindeed beauseful additionto this paper.\nResponse: Thank you for the insightful comment. We agree that the Fig. 1 and Fig. S1-S2 are not\nfocus on the SAF. We have evaluated the CMIP6’s ability to capture SAF regimes by comparing the\nSAF coupling index (CI) from ERA5 reanalysis to the simulation from CMIP6 models. The R2\nbetween ERA5 and CMIP6 reaches 0.65-0.79. To further strengthen this conclusion, we have also\ndrawn on studies that examined these GCM’s ability in capturing soil moisture feedbacks on water\navailability (e.g., precipitation and evapotranspiration) based on MERRA-2&ERA5 reanalysis\ndatasets (Zhou et al., 2022). These independent analyses corroborate the ability of the models used\nhere to capture coupling regimes at the global scale. The relevant changes have been incorporated in\ntherevised manuscript as follows:\n“These patterns are consistent with ERA5 reanalysis using the same coupling index (Supplementary\nFig.S6,S7), ...”(L185-186)\n“Nonetheless, the models’ fidelity in capturing regional heatwave changes and soil\nmoisture-atmosphere coupling strength (Supplementary Figs. S2, S3, S4, S6), together with the\nconsistent magnitude and sign of SAF's contribution across spatial scales (Figs. 2, S3, S4) ...”\n(L368-371)\nmodelsoverthe1985-2014period.(a)Couplingstrengthbetweenmonthlysoilmoistureandnear-surfacespecific\nhumidityderivedfromERA5.(b-f)CorrespondingcouplingindicesforfiveCMIP6models.\nFig. S7. Scatter density plots comparing soil moisture-atmosphere coupling indices between ERA5 and\nCMIP6 models. Each panel displays global land grid cells, with color intensity indicating the density of points.\nThe red line denotes the linear regression fit, and the coefficient of determination (R²) is shown in the upper left\ncornerofeachsubplot.\n34\nv) The resolution of the figures is low, authors are encouraged to generate higher-resolution figures\nwhen possible.\nResponse: Thank you for the suggestion. All figures in the revised manuscript have been\nregenerated with a resolution of 1000 dpi (or higher) to ensure optimal clarity in both print and\ndigital formats.\nReferences\nBrunner, L. & Voigt, A. Pitfalls in diagnosing temperature extremes. Nat Commun 15,\ndoi:10.1038/s41467-024-46349-x (2024).\nDirmeyer, P. A. The terrestrial segment of soil moisture-climate coupling. Geophys Res Lett 38,\nn/a-n/a, doi:10.1029/2011gl048268 (2011).\nDirmeyer, P. A., Jin, Y., Singh, B. & Yan, X. Evolving Land–Atmosphere Interactions over North\nAmerica from CMIP5 Simulations. J Climate 26, 7313-7327, doi:10.1175/jcli-d-12-00454.1\n(2013).\nHirsch,A. L., Ridder,N. N., Perkins‐Kirkpatrick, S. E. & Ukkola,A. CMIP6 MultiModel Evaluation\nof Present‐Day Heatwave Attributes. Geophysical Research Letters 48,\ndoi:10.1029/2021gl095161 (2021).\nJi, P. &Yuan, X. Spatially varying effect of soil moisture-atmosphere feedback on spring streamflow\nunder future warming in China. Commun Earth Environ 5, doi:10.1038/s43247-024-01701-3\n(2024).\nKay, J. E. et al. The Community Earth System Model (CESM) Large Ensemble Project: A\nCommunity Resource for Studying Climate Change in the Presence of Internal Climate\nVariability.BAm Meteorol Soc96,1333-1349, doi:10.1175/bams-d-13-00255.1 (2015).\nQiao, L. et al. Soil moisture–atmosphere coupling accelerates global warming. Nat Commun 14,\ndoi:10.1038/s41467-023-40641-y (2023).\nRaghavendra, A., Dai, A., Milrad, S. M. & Cloutier-Bisbee, S. R. Floridian heatwaves and extreme\nprecipitation: future climate projections. Clim Dynam 52, 495-508,\ndoi:10.1007/s00382-018-4148-9 (2018).\nmeteorological quantities.Report No. ECOM-5515, (1973).\nWang, J. et al. Anthropogenically-driven increases in the risks of summertime compound hot\nextremes. Nature Communications 11,doi:10.1038/s41467-019-14233-8 (2020).\nWang, Y.-N. et al.Amplification effect of intra-seasonal variability of soil moisture on heat extremes\nover Eurasia. Advances in Climate Change Research 15, 1-8, doi:10.1016/j.accre.2024.01.008\n(2024).\nXu, Z., FitzGerald, G., Guo, Y., Jalaludin, B. & Tong, S. Impact of heatwave on mortality under\ndifferent heatwave definitions: A systematic review and meta-analysis. Environment\nInternational 89-90, 193-203, doi:10.1016/j.envint.2016.02.007(2016).\nYu, L. F. et al. Land-atmosphere interactions mitigate the direct surface-drying effects of land use\nand cover change. OneEarth 8,doi:10.1016/j.oneear.2025.101210 (2025).\nZhou, S. et al. Diminishing seasonality of subtropical water availability in a warmer world\ndominated by soil moisture-atmosphere feedbacks. Nat Commun 13,\ndoi:10.1038/s41467-022-33473-9 (2022)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have thoroughly addressed my concerns on the previous submission. I am pleased with the revisions and have\nno further concerns.", "reviewer_2": "The authors have provided sound responses to the questions of my concern, and I have no further questions.", "reviewer_3": "I thank the authors for their detailed responses and the additional work they have done to improve the framing of their study\nand to address some methodological issues. I keep thinking that the paper has merit in addressing a complex, timely, and as\nyet overlooked issue, but I would like to encourage authors to address a few more points, as detailed below. As a general\ncomment, the paper deals with several inter-related issue but, based on my understanding, in a way that is still not\nconvincing enough.\n1- I keep thinking that comparing changes in heatwaves duration and severity in ERA5 vs the CMIP6 ensemble mean is not\nmeaningful for the purpose of this study, which is not about attributing the observed (ERA5) signals but quantifying the role\nof SAF in these changes, after assessing GCMs’ performances. In this respect I find Fig. S1 more relevant to the subsequent\nanalysis.\n2- Why do authors focus their analyses of mean vs variability and the underlying physical mechanisms on humid heatwaves\nonly? Since the first part of the paper is about both dry and humid heatwaves, I would expect some consistency throughout\nthe paper, if only because contrasting these two types of events might help better understand the distinct role of SAF.\nOtherwise, this focus should be justified somehow.\n3- I remain somewhat sceptical about the ability of the methodology utilized here to detect any influence of changing Twb\nmean vs Twb variability on heatwave duration and severity. I would like to see papers that have used this method alongside\ndiscussing its limitations cited – Wang et al (2020) indicate that “The trends for these re-computed frequency and intensity\nare assumed to be dictated by evolving variabilities of summertime Tmax/Tmin (including interannual variability, seasonal\ncycle, intraseasonal, and diurnal variability)” without further discussions or references about this assumption, which, in my\nopinion, is too important a point to be overlooked. In addition, the robustness of this analysis to using other percentile\nthreshold for defining a heatwave day (e.g., 95th or 99th percentiles) deserves to be assessed. Ultimately, an estimation of\nstatistical significance/uncertainty is needed.\n4- It is stated that “More than 70% of the grids pass the Kolmogorov-Smirnov goodness-of-fit test at the 0.05 confidence level\n(80% at the 0.01 confidence level)”, so I wonder how the confidence level is defined, as more grid point pass the goodness-\nof-fit test with a more demanding level of significance (smaller p-value); please clarify. Which level is used and how the\nfailing grid points are treated?\n5- Authors are encouraged to double check the consistency between equations 2 and 3, in particular the numerator in Eq.3.\n6- Figures 5 and 6 illustrate changes in all-days and warm/cold days (defined as days above/below the mean), respectively;\nhow would authors link these to heatwave days, as defined in the paper? In other words, what if the low latitude regions are\ndrier in general but wetter during a humid heatwave, as indeed suggested by recent studies linking Twb extremes to\nenhanced soil moisture and subsequent evapotranspiration in regions of strong land-atmosphere coupling? (Monteiro and\nCaballero 2019, Mishra 2020, Jackson 2025, to cite but a few).\n7- Related to minor comment #4 and to the previous comment: the ability of CMIP6 models to reproduce the SM-q coupling\nindex is assessed on the annual scale, which tells little about the coupling regime during heatwaves. An analysis for the\nheatwave season/month would be a minimum, on heatwave days would be ideal. More generally, a discussion that\ncontrasts the results of this study to the ability of GCMs to represent land-atmosphere interactions is needed. Authors are\nright in saying that locally, GCMs may not agree due to small-scale land-atmosphere processes being ill-represented,\nprimarily for horizontal resolution reasons (e.g. mesoscale circulations such as land-sea breezes). But this ill-representation\nmay also be found in places where GCMs agree, for instance due to the parameterisation of convection and turbulence,\nthat control the boundary layer heat and moisture budgets (see for instance the representation of the SM-precipitation\nfeedback in a convection-permitting model vs GCMs; Lee & Hohenegger, 2024). Unfortunately, there is little information in the\nliterature on this topic, especially (and critically) in the Tropics due to the lack of sufficient land-atmosphere observations –\nyet, the (implicit) assumption that GCMs provide a realistic depictions of the effects of L-A interactions on humid heat\nextremes is likely a strong one, which needs to be discussed.\n8- The point of discussion about attribution (L363-372) is not very useful insofar as the objectives of the paper have been\nclearly stated in the introduction, which avoids any confusion.\nReferences\nMonteiro, J. M., & Caballero, R. (2019). Characterization of extreme wet‐bulb temperature events in southern Pakistan.\nGeophysical Research Letters, 46(17-18), 10659-10668.\nMishra, V., Ambika, A. K., Asoka, A., Aadhar, S., Buzan, J., Kumar, R., & Huber, M. (2020). Moist heat stress extremes in\nIndia enhanced by irrigation. Nature Geoscience, 13(11), 722-728.\nJackson, L. S., Birch, C. E., Chagnaud, G., Marsham, J. H., & Taylor, C. M. (2025). Daily rainfall variability controls humid\nheatwaves in the global tropics and subtropics. Nature Communications, 16(1), 3461.\nLee, J., & Hohenegger, C. (2024). Weaker land–atmosphere coupling in global storm-resolving simulation. Proceedings of\nthe National Academy of Sciences, 121(12), e2314265121."}, "author_response": "Responses to the comments from Reviewer #3\nI thank the authors for their detailed responses and the additional work they have done to improve\nthe framing of their study and to address some methodological issues. I keep thinking that the paper\nhas merit in addressing a complex, timely, and as yet overlooked issue, but I would like to encourage\nauthors to address a few more points, as detailed below. As a general comment, the paper deals with\nseveral inter-related issue but, based on my understanding, in a way that is still not\nconvincing enough.\nResponse: Thank you very much for your constructive and insightful comments. We sincerely\nappreciate the time and effort you have dedicated to reviewing our manuscript. These comments\nhave helped improve the manuscript. The reviewer’s comments are italicized and our\nresponses immediately follow (revisions in the manuscript are highlighted in blue).\n1. I keep thinking that comparing changes in heatwaves duration and severity in ERA5 vs the CMIP6\nensemble mean is not meaningful for the purpose of this study, which is not about attributing the\nobserved (ERA5) signals but quantifying the role of SAF in these changes, after assessing GCMs’\nperformances. In this respect I find Fig. S1 more relevant to the subsequent analysis.\nResponse: Thank you for raising this important point. We fully agree that assessing GCM\nperformance is crucial before quantifying the role of soil moisture–atmosphere feedback (SAF). In\nour original design, Fig. S1 evaluates the models’ ability to capture the climatological mean state of\nheatwave characteristics, while Fig. 1 assesses their performance in simulating historical changes in\nheatwave duration and severity.\nConsidering that simulating historical changes is generally more challenging for GCMs than\nsimulating the mean state (Rivera et al., 2020; Liu et al., 2023), we have retained Fig. 1 in the main\ntext. This allows us to explicitly demonstrate that the CMIP6 ensemble captures not only the\nclimatology but also the observed trends (as further supported by Figs. S2 and S3), thereby\nstrengthening the foundation for the subsequent mechanism-based analysis.\nWe hope this explanation clarifies our rationale and is acceptable for the purpose of the manuscript.\n1\n2. Why do authors focus their analyses of mean vs variability and the underlying physical\nmechanisms on humid heatwaves only? Since the first part of the paper is about both dry and humid\nheatwaves, I would expect some consistency throughout the paper, if only because contrasting these\ntwo types of events might help better understand the distinct role of SAF. Otherwise, this focus\nshould be justified somehow.\nResponse: Thank you for the question. We have conducted parallel analyses for dry heatwaves using\nthe same methodology as applied to humid heatwaves. Given that the role of SAF in dry heatwaves and\ndry-bulb temperature has been studied in recent literature, the present study focuses primarily on\nhumid heatwaves, which remain comparatively underexplored, as well as the differences between dry\nand humid heatwaves. Therefore, the figures are presented in the supplementary. We have revised the\nmanuscript to make it more consistent as suggested:\n“... These findings suggest that, SAF’s spatial varying effect on humid heatwaves is primarily\nattributed through alterations in the mean state of wet-bulb temperature, rather than by altering its\nvariability. Similarly, for dry heatwaves, SAF influences primarily through shifts in the mean state of\ndry-bulb temperature, though both mean-state and variability changes act in concert to increase\nheatwave duration and intensity globally (Fig. S8), resulting in a net positive influence of SAF\nobserved in Figure S5.” (L226-232 in the tracked version of manuscript)\n“The spatial structure of SAF-induced changes in the probability of hot humid days and hot dry days\nclosely consistent with SAF’s impacts in actual heatwaves (spatial correlation coefficients = 0.78–\n0.87; Figs. S8a-b, 2a-b, and S5a-b). A statistical attribution shows that shifts in the location\nparameter (mean) explain >70% of this change in most regions, robust across models (Figs. S9c-d,\ng-h), while the scale parameter (variability) plays a minor role (Fig. S9e-f). These results\nindependently corroborate that SAF exerts distinct influences on dry and humid heatwaves primarily\nvia its modification of the mean states of dry-bulb and wet-bulb temperature, respectively.”\n(L235-243)\ntotal severity of dry heatwaves during 1985-2014 resulting from SAF-induced alterations to the mean state of\ndry-bulb temperature. (c-d) Same as (a-b), but resulting from SAF-induced variability changes in dry-bulb\ntemperature.\nWe also clarified why the study focuses more specifically on humid heatwaves in the results and\nconclusion as follows:\n“... These mechanisms collectively explain why soil moisture-atmosphere coupling tends to increase\nboth the duration and severity of dry heatwaves, particularly in regions where evaporation is\nsensitive to soil moisture deficits. However, they fail to explain the effect of SAF on the humid\nheatwave changes, potentially because the wet-bulb temperature reflects both thermal and moisture\nconditions.” (L198-202)\n“Although SAF is well known to amplify dry heatwaves, our results reveal its regionally dependent\ninfluence on humid heatwaves with suppression of their frequency and severity in low-to-mid\nlatitudes but intensification in high-latitude regions. ...”. (L367-370)\ncontributions from changes in location and scale parameters. (a) The mean changes of probability of hot humid\ndays induced by soil moisture-atmosphere feedback. (c) Contributions of changes in location parameter to the\nchanges in humid heatwave frequency. (e) Same as (c), but for the contributions from the scale parameter. (g)\nGlobal mean contributions based on (c) and (e), with error bars indicating the range (i.e., the minimum and\nmaximum) across all individual months. The right panel is the same as left, but for the hot dry days.\n4\n3. I remain somewhat sceptical about the ability of the methodology utilized here to detect any\ninfluence of changing Twb mean vs Twb variability on heatwave duration and severity. I would like\nto see papers that have used this method alongside discussing its limitations cited—Wang et al (2020)\nindicate that “The trends for these re-computed frequency and intensity are assumed to be dictated\nby evolving variabilities of summertime Tmax/Tmin (including interannual variability, seasonal\ncycle, intraseasonal, and diurnal variability)” without further discussions or references about this\nassumption, which, in my opinion, is too important a point to be overlooked. In addition, the\nrobustness of this analysis to using other percentile threshold for defining a heatwave day (e.g., 95th\nor 99th percentiles) deserves to be assessed. Ultimately, an estimation of\nstatistical significance/uncertainty is needed.\nResponse: We thank the reviewer for raising these important methodological points. We have added\nmore citations about this methods and discussed the method’s assumption and limitation as\nsuggested.\n“Similar methods have been widely used to examine the relative roles of mean shifts versus variability\nchanges in climate extremes(Argüeso et al 2016; Meng et al., 2025; Patel et al., 2024; van der Wiel &\nBintanja 2021; You et al., 2023), although approaches to estimating the mean shifts vary (e.g., using\npolynomial fittings of different orders).” (L575-577)\n“Our approach to decomposing heatwave changes into mean shifts and variability changes of\ntemperature follows an additive assumption commonly adopted in previous studies (Argüeso et al\n2016; van der Wiel & Bintanja 2021; You et al., 2023). While this assumption enables a tractable\nseparation of the two components, we acknowledge that it simplifies potential nonlinear interactions\nbetween mean and variability under sustained warming. Recent work suggests that changes in the\ntemperature mean state may also modulate temperature variability in a warming future (Brown et al.,\n2017), which could introduce uncertainty in the exact attribution of extremes. Nevertheless, changes\nin temperature variability in historical period are much smaller that in mean state (Alizadeh et al.,\n2023), suggesting their interaction can not strong enough to influence the robustness of the role of\nmean state changes.” (L399-408)\nIn addition, we have tested the robustness and uncertainties of this analysis and clarified this in the\ndiscussion as: “Additionally, we tested the sensitivity of our results to the heatwave definition\nthreshold (e.g., 95th versus 99th percentiles) and the method used to estimate warming signals (e.g.,\n5\nlinear versus third-order polynomials fittings), finding the result remains robust across these\nmethodological choices (Fig. S18).” (L408-412)\nFig. S18. Robustness assessment of the dominant role of mean-state shifts over variability changes, tested\nagainst alternative heatwave definitions and polynomial fits. (a-d) and (e-h) The same as Fig. 4, but using the\n95th and 99th percentile thresholds for detecting humid heatwaves, respectively. (i-l) and (m-p) The same as Fig. 4,\nbut using the linear and third-order polynomials fittings for estimating the mean-state shifts, respectively.\n4. It is stated that “More than 70% of the grids pass the Kolmogorov-Smirnov goodness-of-fit test at\nthe 0.05 confidence level (80% at the 0.01 confidence level)”, so I wonder how the confidence level\nis defined, as more grid point pass the goodness-of-fit test with a more demanding level of\nsignificance (smaller p-value); please clarify. Which level is used and how the failing grid points are\ntreated?\nResponse: Thank you for the comment. The confusion stems from the interpretation of \"passing\"\nthe test. The null hypothesis (H ) of the Kolmogorov-Smirnov test is that the sample data follow the\n0\nspecified reference distribution (here, a normal distribution). A larger p-value indicates weaker\nevidence against H . Therefore, to \"pass\" the test (i.e., to fail to reject normality), the p-value must be\n0\ngreater than or equal to the chosen significance level (α). At α = 0.05, a grid passes if its K-S test\nyields p ≥ 0.05. At the more stringent α = 0.01, the passing condition becomes p ≥ 0.01. This is a\nmuch wider criterion for passing. All grids that passed at α=0.01 automatically include those that\npassed at α=0.05 , plus an additional set of grids with p-values between 0.01 and 0.05. Consequently,\nthe number of grids \"passing\" (failing to be rejected as non-normal) is always greater for a smaller α\n(0.01) than for a larger α (0.05). Therefore, in our analysis, more than 70% of the grids pass the K-S\ngoodness-of-fit test at the 0.05 significance level (i.e., p ≥ 0.05), while about 80% of the grids pass\nthe test at the 0.01 significance level (i.e., p ≥ 0.01).\nWe apologize for the ambiguous phrasing in the previous sentence. In the revised manuscript, we\nhave removed this ambiguous sentence, clarified both the significance level used and the treatment\nof failing grid points as follows: “Note, the Kolmogorov–Smirnov test was applied to assess the\ngoodness of fit. At the 0.01 significance level, the null hypothesis of normality could not be rejected\nfor approximately 80% of the grid cells (i.e., p ≥ 0.01). Grid points for which the test was significant\n(p < 0.01) were excluded from subsequent analysis.” (L38-41 in the supplementary materials)\n5. Authors are encouraged to double check the consistency between equations 2 and 3, in particular\nthe numerator in Eq.3.\nResponse: Thank you for the suggestion. We have carefully reviewed Equations (2) and (3) in the\nSupplementary Note 1. The previous version included explicit experimental labels (e.g., ALL,\nLFMIP) in the distribution notation, which introduced unnecessary complexity and could lead to\nambiguity in the numerator of Equation (3).\nWe have now simplified the notation by removing these labels from the distribution descriptors,\nmaking the relationship between the two equations mathematically direct and clear. The revised\nformulation ensures full consistency between Equations (2) and (3), and the numerator in Equation\n(3) now correctly follows from the definition provided in Equation (2). The revised contents are:\n“The fitted distributions for the LFMP-pdLC and ALL experiments in a given month i are denoted as\nNORM (μ ,σ ) and NORM (μ ,σ ). ....\ni i,0 i,0 i i,1 i,1\nThe contributions of changes in the temperature mean (CT ) and variability (CT ) were\ni,μ0→μ1 i,σ0→σ1\nquantified for each month as:\nCT =\nP_NORMi(μi,1,σi,0)−P_NORMi(μi,0,σi,0)\n(2)\ni,μ0→μ1\nP_NORMi(μi,1,σi,1)−P_NORMi(μi,0,σi,0)\nP_NORMi(μi,1,σi,1)−P_NORMi(μi,1,σi,0)\n(3)\ni,σ0→σ1\nP_NORMi(μi,1,σi,1)−P_NORMi(μi,0,σi,0)\n... The sum of CT and CT equals to 100%.” (L33-55 in the supplementary materials)\ni,μ0→μ1 i,σ0→σ1\n6. Figures 5 and 6 illustrate changes in all-days and warm/cold days (defined as days above/below\nthe mean), respectively; how would authors link these to heatwave days, as defined in the paper?\nIn other words, what if the low latitude regions are drier in general but wetter during a humid\nheatwave, as indeed suggested by recent studies linking Twb extremes to enhanced soil moisture\nand subsequent evapotranspiration in regions of strong land-atmosphere coupling? (Monteiro and\nCaballero 2019, Mishra 2020, Jackson 2025, to cite but a few).\nResponse: Thank you for the comment and for the relevant references. We apologize for any\nconfusion regarding the linkage between the analysis of Figures 5 (intend to analyze SAF’s influence\non wet-bulb temperature) & 6 (intend to analyze SAF’s influence on dry-bulb temperature). Our core\nfinding is that the distinct impacts of SAF on dry versus humid heatwaves primarily stem from its\ndiffering effects on dry-bulb and wet-bulb temperature mean states. Therefore, the subsequent\nmechanistic analysis was designed to separately elucidate these pathways.\nTo clarify this logic and resolve the potential misinterpretation, we have revised the manuscript as\nfollows:\n1) We now directly state that the analysis aims to explain how SAF influences dry and humid\nheatwaves through its effect on the respective temperature mean states. “These results independently\ncorroborate that SAF exerts distinct influences on dry and humid heatwaves primarily via its\nmodification of the mean states of dry-bulb and wet-bulb temperature, respectively. Therefore, the\ndivergent responses can be mechanistically understood and are directly linked to SAF's modulation\nof these mean conditions.” (L241-245)\n2) We have swapped the original Figures 5 and 6. The new Figure 5 first presents the mechanism for\ndry heatwaves, emphasizing that in addition to changes in soil moisture, the variability of soil\nmoisture plays a significant role in amplifying mean state of dry-bulb temperature. The new Figure 6\ndetails the mechanism for humid heatwaves, highlighting SAF's cooling effect on wet-bulb\ntemperature (mediated through reduced surface relative humidity) dominates its concurrent warming\neffect (via temperature increase).\nyet become wetter during humid heatwaves due to enhanced soil moisture and evapotranspiration\nunder strong land–atmosphere coupling. We have discussed this as follows: “It should be clarified\nthat the primary focus of our study is the climatological-scale effect of SAF on humid heatwaves. At\nthis scale, SAF substantially reduces the mean wet-bulb temperature across low-latitude and\nsubtropical regions, leading to an overall suppression of humid heatwave occurrence (Fig. 4). This\nclimatological cooling effect has been largely overlooked in previous studies, which instead\nemphasize the event-scale role of SAF in triggering humid heatwaves through enhanced\nevapotranspiration following precipitation in strongly coupled regions (Jackson et al., 2025; Mishra\net al., 2020; Monteiro and Caballero, 2019). Importantly, these event-based findings are not\ncontradictory to our results. As shown in Figure 4c, when the mean wet-bulb temperature is held\nconstant, SAF enhances wet-bulb temperature variability, resulting in more frequent humid heatwave\ndays, particularly over India and equatorial Africa. However, our results further demonstrate that, at\nthe climatological scale, the suppressing effect of SAF on the mean state of wet-bulb temperature\noutweighs its enhancing effect on variability, thereby reducing humid heatwave occurrence overall.\nThis implies that, although individual humid heatwaves can still be promoted by event-scale wet\nanomalies in precipitation and soil moisture, the background atmospheric drying induced by SAF\nraises the threshold for their initiation. How such climatological shifts in mean wet-bulb temperature\ninteract with event-scale triggering mechanisms of SAF warrants further investigation.” (L413-430)\n7. Related to minor comment #4 and to the previous comment: the ability of CMIP6 models to\nreproduce the SM-q coupling index is assessed on the annual scale, which tells little about the\ncoupling regime during heatwaves. An analysis for the heatwave season/month would be a minimum,\non heatwave days would be ideal. More generally, a discussion that contrasts the results of this study\nto the ability of GCMs to represent land-atmosphere interactions is needed. Authors are right in\nsaying that locally, GCMs may not agree due to small-scale land-atmosphere processes being\nill-represented, primarily for horizontal resolution reasons (e.g. mesoscale circulations such as\nland-sea breezes). But this ill-representation may also be found in places where GCMs agree, for\ninstance due to the parameterisation of convection and turbulence, that control the boundary layer\nheat and moisture budgets (see for instance the representation of the SM-precipitation feedback in a\n9\nconvection-permitting model vs GCMs; Lee & Hohenegger, 2024). Unfortunately, there is little\ninformation in the literature on this topic, especially (and critically) in the Tropics due to the lack of\nsufficient land-atmosphere observations–yet, the (implicit) assumption that GCMs provide a\nrealistic depictions of the effects of L-A interactions on humid heat extremes is likely a strong one,\nwhich needs to be discussed.\nResponse: Thank you for the comment. Following your suggestion, we have re-evaluated the SM-q\ncoupling index seasonally (JJA for the Northern Hemisphere and DJF for the Southern Hemisphere)\nand updated Fig. S7 accordingly. The R2 between the CMIP6 ensemble and ERA5 ranges from 0.62\nto 0.75 across seasons. More importantly, during summer and autumn seasons when heatwaves occur\nmost frequently, the R2 reaches 0.72-0.75, indicating that the models capture the seasonal coupling\nregime reasonably well.\nRegarding the calculation of the coupling index specifically on heatwave days, we acknowledge that\nsuch an analysis would be insightful. However, we opted not to pursue this for practical reasons: (1)\nmost heatwave events are too short (typically ≤5 days) to robustly estimate a correlation coefficient\nbetween soil moisture and specific humidity; (2) the variable duration of individual events would\nintroduce unequal weighting across events, complicating the interpretation of an aggregated index;\nand (3) land–atmosphere coupling prior to a heatwave can significantly influence its evolution, yet\nthere is no consensus on an appropriate time window for capturing this pre‑event coupling.\nFinally, we have added a discussion that contrasts the results of this study to the ability of GCMs to\nrepresent land-atmosphere interactions. “We also acknowledge that quantitative estimates of SAF’s\nrole are subject to model structural uncertainties. For example considerable inter-model spread\npersists in certain high-latitude and coastal regions (especially northern Canada and northern Europe),\nwhere the sign and magnitude of SAF-induced changes vary significantly across the ensemble. These\ndiscrepancies likely reflect differences in model physics, resolution, and the representation of\nland-atmosphere coupling processes over complex terrain or under snow-influenced regimes.\nMoreover, uncertainties in physical parameterizations, particularly for convection and\nboundary-layer processes, may introduce coherent biases in simulated heat and moisture budgets\n(Lee & Hohenegger, 2024). This issue is especially pronounced in the wet tropics, where\nobservational constraints on land-atmosphere interactions remain sparse, and models exhibit large\nuncertainties. Nevertheless, the overall direction and spatial pattern of SAF's impact on humid\n10\nheatwaves are credible for several reasons. First, CMIP6 models reproduce SAF-related processes\nreasonably well, as seen in our evaluation (Supplementary Fig. S6, S7) and in prior literature (Qiao\net al., 2023; Zhou et al., 2022). Second, the spatial structure of SAF’s effect on humid heatwaves is\nconsistent across models despite differing physics, pointing to a physical signal rather than a model\nartifact. Third, our conclusions are robust to varying heatwave definitions and analytical approaches.\nTo further constrain remaining uncertainties, future work should combine multi-model,\nhigh-resolution, convection-permitting simulation with expanded observational networks, especially\nin data-sparse regions where land-atmosphere interactions are critical.” (L431-461)\nFig. S7. Scatter density plots comparing soil moisture-atmosphere coupling indices between ERA5 and\nCMIP6 models during different seasons. Each panel displays global land grid cells, with color intensity\nindicating the density of points. The red line denotes the linear regression fit, and the coefficient of determination\n(R²) is shown in the upper left corner of each subplot. The simulation is from the ensemble mean of five CMIP6.\n11\n8. The point of discussion about attribution (L363-372) is not very useful insofar as the objectives of\nthe paper have been clearly stated in the introduction, which avoids any confusion.\nResponse: Thank you for the comment. We have deleted this discussion as suggested.\nReferences\nLiu, S., Raghavan, S. V., Ona, B. J. & Nguyen, N. S. Bias evaluation in rainfall over Southeast Asia in\nCMIP6 models. J Hydrol 621, doi:10.1016/j.jhydrol.2023.129593 (2023).\nRivera, J. A. & Arnould, G. Evaluation of the ability of CMIP6 models to simulate precipitation over\nSouthwestern South America: Climatic features and long-term trends (1901–2014). Atmos Res\n241, doi:10.1016/j.atmosres.2020.104953 (2020).\nYou, J., Wang, S., Zhang, B., Raymond, C. & Matthews, T. Growing Threats From Swings Between\nHot and Wet Extremes in a Warmer World. Geophys Res Lett 50, doi:10.1029/2023gl104075\n(2023).\nvan der Wiel, K. & Bintanja, R. Contribution of climatic changes in mean and variability to monthly\ntemperature and precipitation extremes. Commun Earth Environ 2,\ndoi:10.1038/s43247-020-00077-4 (2021).\nArgüeso, D., Di Luca, A., Perkins‐Kirkpatrick, S. E. & Evans, J. P. Seasonal mean temperature\nchanges control future heat waves. Geophys Res Lett 43, 7653-7660, doi:10.1002/2016gl069408\n(2016).\nPatel, R. N., Bonan, D. B. & Schneider, T. Changes in the Frequency of Observed Temperature\nExtremes Largely Driven by a Distribution Shift. Geophys Res Lett 51,\ndoi:10.1029/2024gl110707 (2024).\nMeng, C. et al. Identification of compound flood-heatwave extremes in the Yangtze River Basin and\ntheir socio-economic exposure. J Hydrol 649, doi:10.1016/j.jhydrol.2024.132387 (2025).\nBrown, P. T., Ming, Y., Li, W. & Hill, S. A. Change in the magnitude and mechanisms of global\ntemperature variability with warming. Nat Clim Change 7, 743-748, doi:10.1038/nclimate3381\n(2017).\nAlizadeh, O. Changes in the mean and variability of temperature and precipitation over global land\nareas. Environmental Research: Climate 2, doi:10.1088/2752-5295/ace279 (2023).\n722-728, doi:10.1038/s41561-020-00650-8 (2020).\nJackson, L. S., Birch, C. E., Chagnaud, G., Marsham, J. H. & Taylor, C. M. Daily rainfall variability\ncontrols humid heatwaves in the global tropics and subtropics. Nat Commun 16,\ndoi:10.1038/s41467-025-58694-6 (2025).\nMonteiro, J. M. & Caballero, R. Characterization of Extreme Wet‐Bulb Temperature Events in\nSouthern Pakistan. Geophys Res Lett 46, 10659-10668, doi:10.1029/2019gl084711 (2019).\nLee, J. & Hohenegger, C. Weaker land–atmosphere coupling in global storm-resolving simulation.\nProceedings of the National Academy of Sciences 121, e2314265121,\ndoi:doi:10.1073/pnas.2314265121 (2024).\nZhou, S. et al. Diminishing seasonality of subtropical water availability in a warmer world dominated\nby soil moisture-atmosphere feedbacks. Nat Commun 13, doi:10.1038/s41467-022-33473-9 (2022).\nQiao, L. et al. Soil moisture–atmosphere coupling accelerates global warming. Nat Commun 14,\ndoi:10.1038/s41467-023-40641-y (2023).\n13"}, {"round": 3, "reviewer_comments": {"reviewer_3": "I thank the authors for addressing all my comments and have no further comment to make."}, "author_response": ""}]

Decision letter