Daily rainfall variability controls humid heatwaves in the global tropics and subtropics

Domain: earth_science
Published: 2025-04-29
Editorial outcome: minor_revision

Abstract
Humid heatwaves are a growing risk to human and animal health, especially in tropical regions. While there is established research on dry-bulb temperature heatwaves, greater understanding of the meteorological drivers of extreme humid heat is urgently needed. In this study, we find that recent rainfall is a key control on the occurrence of humid heatwaves in the tropics and subtropics and its effect is regulated by the energy- or moisture-limited state of the land surface. In moisture-limited environments, heatwaves are likely during, or immediately after, enhanced rainfall. In energy-limited environments, heatwaves are likely after suppression of rainfall for two days or longer. The nature of the threat to health from heat stress varies by environment. It depends on local adaptation to temperature or humidity extremes, as well as vulnerability to absolute or anomalous extremes. Early warning systems, which reduce exposure and vulnerability to weather extremes, can benefit from this understanding of humid heatwave drivers, highlighting the possibility of predicting events using satellite-derived rainfall and surface moisture data.

Introduction
Periods of combined high temperature and humidity result in heat stress, which can have a significant impact on human and animal health and restrict economic activity, such as outdoor work. Studies on human physiological responses to humid heat extremes suggest a potential limit to human adaptability to such conditions. After a few hours of exposure to wet-bulb temperature (Twb) of 35 °C, effective thermoregulation may become impossible. Recent empirical studies suggest that health impacts occur around 31 °C for young, healthy individuals, and likely at much lower values for vulnerable groups such as the very young and the elderly. The focus of this study is on the physical processes involved in the occurrence of humid heatwaves, with particular attention to the role of rainfall variability.

Humid heat extremes have intensified since 1979 and become more frequent. Some regions in the subtropics, such as coastal areas around the Persian Gulf, have already experienced short-lived Twb extremes above 35 °C. Climate change is driving the occurrence of more extreme humid heat events, as seen in South and Southeast Asia in April 2023. Most importantly, humid heat stress is projected to become more severe under future climate change. Along with an increased awareness of the risks posed by humid heatwaves there has been a growing focus on their underlying processes. In regions such as the southern Persian Gulf, north-central Pakistan, eastern South Asia, and the western Amazon, strong surface evaporation and the inhibition of convection by atmospheric stability play a key role in the occurrence of humid heat extremes. A study using a pan-Africa convection-permitting climate model found that humid heat is often associated with rainfall, with approximately one-third of humid heatwaves starting on wet days. In addition to rainfall, other factors exerting a control over humid heatwaves in all but the most humid regions of Africa include increases in cloud cover, surface longwave radiation, and surface evaporation. However, in highly humid regions such as the Congo Basin, factors regulating dry-bulb temperature are more significant than rainfall.

Unlike dry heatwaves, extreme Twb events often occur during the monsoon season rather than prior to it, and the association between rainfall and humid heat varies with the local near-surface moisture climatology. In parts of South Asia with relatively low specific humidity, Twb extremes are more likely during periods of enhanced rainfall, whereas Twb extremes are more likely during suppressed rainfall in regions of higher specific humidity. In the arid and semi-arid regions of the global tropics and subtropics, light rain sustains surface evaporation and is associated with more frequent and more intense wet-bulb globe temperature extremes during the hottest four months of the year. Irrigation has been shown to be important for humid heat extremes in India and the northern plains of China, but there is no consensus on the nature of its control, partly due to different regional impacts of irrigation on moisture transport. Coastal regions may be more at risk from extreme humid heat events and, in India for instance, from compound humid heat and rainfall events. Land-atmosphere feedbacks intensify and help the propagation of dry heatwaves, and increasing ecosystem water limitations are linked with intensified future dry heat extremes. A widespread positive correlation between Twb and soil moisture suggests that land-atmosphere feedbacks also play a key role in humid heat extremes.

Much of the existing research on humid heat processes, however, is limited to regional-scale mechanisms, and the understanding of underlying processes at the scale of the global tropics and sub-tropics remains poorly understood.

We have two aims for this study. Our first aim is to characterise the relationship between occurrences of humid heatwaves and rainfall overland across the global tropics and subtropics. Our second aim is to test the hypothesis promulgated by Ivanovich et al. and Zhang et al. that rainfall regulates humid heat extremes through surface moisture flux processes that vary between energy- and moisture-limited environments. Importantly, our study focuses on the global tropics and subtropics, whereas Ivanovich et al. focus on South Asia. Additionally, our study addresses both the promotion and suppression of humid heat extremes, whereas Zhang et al. focus more on the enhancement of extremes.

We use the daily mean Twb as our primary measure of humid heat because it is a useful metric for understanding humid heat dynamics in climate science. It combines both temperature and humidity and has similar thermodynamic properties to equivalent potential temperature (\theta_e), making it robust for analysis on regional scales. Furthermore, Twb is relevant to human heat stress as it provides an upper temperature limit for healthy, well-acclimatised human beings who have access to drinking water, shade, and a strong breeze. Nevertheless, we acknowledge its limitations in representing human heat stress, particularly in relation to health outcomes. The 35 °C threshold for Twb may substantially underestimate the range and severity of heat-related outcomes because it assumes specific conditions that are unlikely to apply in all contexts. Additionally, Twb is a compound metric, and distinguishing between the contributions of temperature and humidity is crucial for understanding their distinct impacts, particularly because high Twb values are often driven by anomalously high humidity, with temperature anomalies playing a secondary role. Furthermore, epidemiological studies have found little evidence for the impact of humidity on heat–health outcomes in some contexts although epidemiological evidence is likely to develop under increasingly extreme future temperatures driven by climate change.

In this study, we prepare a dataset of humid heatwaves using ERA5 reanalysis data, validated against surface station observations, and identify distinct heatwave events using a time-space connected components method that has previously been used in the identification of heatwaves. We use the local 95th percentile of daily mean Twb to capture humid heat events that are high for the locality, with an absolute minimum of 24 °C to exclude events likely low risk for most people while ensuring sufficient data for statistically significant results. The 95th percentile of daily mean Twb is calculated locally for each grid cell, accounting for regional variations, and is based on all days of the year, inherently capturing the seasonal cycle. We prepare a dataset of enhanced and suppressed rainfall days using GPM-IMERG data and assess the significance of the relationship between humid heatwaves and rainfall in years 2001–2022. At the time of each heatwave, we classify the surface environments as energy- or moisture-limited using the Ecosystem Limitation Index, an index of surface energy- and moisture-limitation that has previously been used in the study of dry heat extremes. We find that there is a statistically significant relationship between humid heatwaves and daily rainfall across tropical land areas. Exploring the extent to which this relationship is explained by energy- or moisture-limitations shows the key role of surface evaporation of recent rainfall in many regions of the tropics and subtropics.

Results
Humid heatwaves and seasonal rainfall
The occurrence of humid heatwaves is widespread across the global tropics and subtropics (Fig. 1a). These heatwaves occur in monsoon regions such as West Africa, India, East China, and north Australia, and in equatorial regions such as the Amazon, the Congo basin, and the Maritime Continent. Most of these regions experience 1–2 heatwaves per year. In general, the frequency of occurrence decreases sharply at the northern and southern extent of monsoon regions due to climatologically low humidity (e.g., West Africa, Australia) and in regions at high elevation due to lower dry-bulb temperatures at altitude (e.g., areas within the Himalayan region in India and inland East Africa). The heatwaves are relatively small in size. The minimum size of the heatwaves is approximately 1900 km^2 (by definition), while the median size is approximately 4400 km^2.

The median duration of humid heatwaves is typically between 3 and 6 days (Fig. 1b). Regions with the longest heatwave durations include the equatorial east coast of Africa, the Indian subcontinent, and eastern China. In contrast, heatwaves are relatively short in South America, West and Central Africa, and Southeast Asia. Heatwave intensity, represented by the 95th percentile of daily mean Twb on heatwave days, typically ranges between 24 °C and 27 °C (Fig. 1c). Regions with the most intense heatwaves include the Red Sea and Persian Gulf coastlines, Pakistan, northern India and Bangladesh, and northeast China, where the daily mean Twb 95th percentile ranges between 28 °C and 31 °C. Daily maximum Twb can be much higher.

Humid heatwaves and regional rainfall exhibit a strong seasonal cycle (Fig. 1d, e). Over the western and central regions of the Amazon basin, heatwaves most frequently occur during October-November, marking the transition from the dry to wet season. In equatorial regions (10°S–10°N), humid heatwaves occur at the time of the seasonal migration of the tropical rain-belt, particularly in March-May over eastern South America, Africa, and western Maritime Continent. Regions such as India, Southeast Asia, East and West Africa, and North Australia are farther from the equator and experience strong monsoon seasons (e.g., peak rainfall occurs in July-August over much of India and the West African Sahel). In these regions, humid heatwave occurrence appears to synchronise with monsoon seasons.

To show the relationship between humid heatwaves and seasonal rainfall at the monthly timescale, Fig. 1f shows the number of months separating the seasons of peak rainfall and peak humid heat (i.e., the difference between Fig. 1e and d). In regions beyond latitudes 10°S–10°N that have strong seasonal monsoons, the seasons of rainfall and humid heat are closely synchronised. These are regions shaded cream in Fig. 1f (e.g., West African Sahel). However, it is important to note that this qualitative association between seasonal rainfall and humid heat does not establish a causal relationship between the two phenomena. Furthermore, there are many regions exposed to humid heat in which peak seasonal rainfall and humid heat do not coincide. These regions, where heatwaves can occur before or after seasonal rainfall, include many monsoon areas between 10°S and 10°N and are shaded purple in Fig. 1f.

Rainfall variability as a driver of humid heatwave occurrence
In the previous section, we established a link between the timing of humid heatwaves and of rainfall at the seasonal timescale. As a step towards a process-based understanding, we now examine the relationship on the daily timescale in each grid cell using months in which at least one humid heatwave occurred. We categorised each day into one of four groups based on whether rainfall was higher or lower than a minimum threshold of 5 mm/day in a two-day window, and whether a heatwave started or not. The groups with higher rainfall (High_Rain) included days when rainfall exceeds 5 mm/day on that day, or the previous day, or on both days. The groups with lower rainfall (Low_Rain) included days when rainfall does not exceed 5 mm/day on both that day and the previous day. We used counts of the number of days in each group to calculate empirical probabilities for heatwaves starting on High_Rain days or Low_Rain days (see Methods for more details).

In Fig. 2a, we map the relative risk (the ratio of the two probabilities) in those grid cells where there is a statistically significant difference between the probabilities. Blue shades represent grid cells where heatwaves are more likely on High_Rain days, and red shades represent grid cells where heatwaves are more likely on Low_Rain days. There is a clear geographic pattern which resembles the Köppen-Geiger classification of climate zones; humid heatwaves are more likely to occur on High_Rain days in arid regions (Köppen-Geiger Zone B). In contrast, humid heatwaves are more likely to occur on Low_Rain days in tropical and equatorial regions (Köppen-Geiger Zone A).

To examine the role of surface energy- and moisture-limitations in modulating the relationship between rainfall and humid heat, we calculated the Ecosystem Limitation Index (ELI) daily for each grid cell. The ELI is calculated as the difference between: (i) the correlation of surface latent heat flux with near-surface soil moisture; and (ii) the correlation of surface latent heat flux with downwelling shortwave (SW) radiation at the surface using variables from ERA5 reanalysis and over a 7-day rolling window (see Methods). Positive values for the ELI mean that soil moisture exerts a stronger control on surface evaporation than downwelling surface SW radiation, signifying that moisture limitation is greater than the energy limitation. Hereafter, we refer to this as moisture limitation. In contrast, negative values indicate greater energy limitation than moisture limitation, which hereafter we refer to simply as energy limitation. In Fig. 2b, the ELI shown is a heatwave-composite mean of values taken two days before the start of humid heatwaves. This ELI, therefore, represents surface energy- and moisture-limitation immediately before and at the start of humid heatwaves and is not necessarily indicative of the local seasonal climatology.

The scatter plot of grid cell data in Fig. 2c shows that humid heatwaves fall into one of four rainfall-ELI regimes (see Methods). Regime 0, in which heatwaves occur in moisture-limited environments and are more likely on Low_Rain days, is relatively rare (0.1% grid cells, red shading). Its grid cells have relatively small ELI values (median 0.27) which could potentially result from noise in other regimes. Therefore, Regime 0 is not examined further, along with grid cells that are not statistically significant (66% of the grid cells, white shading).

Figures 2a, b show that heatwaves occurring in moisture-limited environments generally occur on High_Rain days (Regime 1). These heatwaves occur in 8% of land grid cells between latitudes 35°N and 35°S where humid heatwaves occurred during 1993–2022 (Fig. 2c, d, dark blue shading). Heatwaves occurring in energy-limited environments generally occur on Low_Rain days (Regime 2) and account for 23% of the grid cells (Fig. 2c, d, orange shading). For grid cells with moderate relative risk values (i.e., relative risk < 10), there is a strong linear relationship between relative risk and ELI (Pearson correlation coefficient +0.74). Grid cells on the right-hand side of Fig. 2c with relative risk values > 10 (i.e., where Eq. (3) applies; see “Methods”) have a mean ELI of +0.92 ± 0.01 (± 1 standard error) and are clearly moisture-limited. Similarly, grid cells on the left-hand side of Fig. 2c with relative risk values > 10 (i.e., where Eq. (4) applies; see Methods) have a mean ELI of −1.14 ± 0.02 and are clearly energy-limited.

Grid cells with a negative ELI and a positive relative risk are assigned to Regime 3 (Fig. 2c). This regime occurs in parts of western India, Mozambique, and northern Australia, where the local environment is energy-limited according to the ELI, yet heatwaves are more likely on High_Rain days (Fig. 2c, d, light blue shading). This apparent contradiction is explained in the next section, where we show that surface evaporation in Regime 3 is sensitive to both energy- and moisture-limitations.

Contributions of temperature and specific humidity to humid heatwaves
Figure 3 shows composite timeseries centred on the first day of each heatwave for Twb, 2m temperature, and 2m specific humidity. Grid cell heatwave composites are constructed by averaging daily mean timeseries spanning 7 days before to 7 days after the start of each heatwave. For grid cells where the heatwave-rainfall relationship is statistically significant (Fig. 2), the composites are grouped into the regimes shown in Fig. 2d. The composite for each regime is then calculated as the average of grid cell composites within that regime. The heatwaves in our analysis last a minimum of 3 days (days 0–2) and have a median duration of 4 days (days 0–3). By day 7, ~79% of the heatwaves have dissipated. To maintain consistency in the number of data points across all days, the composites for days 3–7 include data from both ongoing and dissipated heatwaves.

Regions in Regime 1 are climatologically hot and dry, with relatively modest levels of Twb prior to the heatwaves, consistent with the moisture-limited nature of Regime 1 (Fig. 2c). Anomalies in temperature and specific humidity grow strongly starting two days before the heatwaves, coinciding with days of High_Rain immediately before and at the start of the heatwaves. In Regime 1, humid heatwaves result from large positive specific humidity anomalies, partly offset by negative 2m temperature anomalies (~−2 °C).

Regime 2 is energy-limited (Fig. 2c) and is climatologically cooler and more humid than Regime 1. Anomalies in temperature and specific humidity grow during the first two days of the heatwaves following two days of Low_Rain. Unlike Regime 1, humid heatwaves in Regime 2 result from positive anomalies in both 2m temperature and specific humidity. Although heatwaves have the largest absolute Twb in Regime 2, the temperature and specific humidity anomalies are smaller than those in Regime 1.

Regime 3 is climatologically similar to Regime 2, although slightly hotter and less humid. In contrast to Regime 2, heatwaves in Regime 3 primarily result from positive specific humidity anomalies. There is a statistically significant increase in 2m temperatures from day −1 to day 1, although the anomalies during the heatwave are relatively small (<0.5 °C).

The controlling role of surface energy- and moisture limitations
To elucidate the mechanisms underpinning each heatwave regime, Fig. 4 presents composite timeseries centred on the first day of each heatwave for several surface and atmospheric variables.

Rainfall anomalies on day −1 and day 0 differ between the regimes by design. Differences in anomalies on days −7 to −2 and days 1 to 7, however, provide insight into the role of rainfall variability in the occurrence of humid heatwaves. In Regime 1 (moisture-limited), daily mean rainfall is relatively low. The rainfall anomaly increases strongly in the two days before the heatwave, and is enhanced just prior to the start of the heatwave (day −1). For Regimes 2 and 3 (energy-limited), daily mean rainfall is greater three or more days before the start of a heatwave. In Regime 2, rainfall decreases sharply two days before a heatwave, it is suppressed at the start of a heatwave, and returns to its daily climatology over the next three days. In Regime 3, positive rainfall anomalies occur in the run up to a heatwave (days −6 to −1). Rainfall decreases to its climatology at the start of a heatwave followed by a peak in rainfall three days later when the heatwaves start to dissipate (on day 3).

In summary, rainfall variability at the start of a humid heatwave can be characterised as enhanced (Regime 1), suppressed (Regime 2), or neutral (Regime 3).

Regime 1 (ELI moisture-limited and enhanced rainfall)
Prior to rainfall, the environment in these regions is relatively dry characterised by low rainfall, low total column water vapour (TCWV), low soil moisture, and a relatively deep boundary layer (Fig. 4). Rainfall immediately before and/or during the first days of a heatwave, increases soil moisture and promotes humidification of the boundary layer through a strong increase in surface latent heat flux. Specific humidity may also be enhanced aloft by moisture convergence associated with the rain-bearing storms. The overall increase in surface latent heat flux is accompanied by a decrease in surface sensible heat flux, which is characteristic of moisture-limited environments. This decrease in surface sensible heat flux reduces the depth of the boundary layer, concentrating specific humidity near the surface. The increase in atmospheric specific humidity enhances downwelling longwave radiation at the surface, although this increase in surface radiation is more than offset by attenuation of downwelling SW radiation due to increased cloud cover associated with the storms. The associated changes in net surface radiation fluxes are shown in Fig. S1.

Regime 2 (ELI energy-limited and suppressed rainfall)
The environment in these regions is wetter, and the supply of energy and moisture from the surface to the near-surface air differs from regions that are moisture-limited. Prior to a heatwave, rainfall and TCWV are greater than in the moisture-limited regime, and wetter soils support greater latent heat fluxes at the surface. Cloud cover associated with the rainfall prior to heatwaves attenuates downwelling SW radiation at the surface.

The humid heatwaves in these regions are associated with suppressed rainfall from the day before the start of a heatwave to 2 days after the start of the heatwave. The near-surface soil remains moist and the atmosphere humid although changes from climatology are very small. Positive anomalies in downwelling SW radiation, which exceed 25 Wm^−2, promote an increase in surface latent heat flux. Changes in surface sensible heat flux and boundary layer height are very small. Taken together, these are changes characteristic of energy-limited environments, due to climatologically wetter soils.

Regime 3 (ELI energy-limited and neutral rainfall)
Prior to the onset of humid heatwaves (day −7), the environment in these regions resembles that of Regime 2 in terms of rainfall, TCWV, and downwelling SW radiation at the surface. In Regime 3, however, the surface is drier with less near-surface soil moisture.

The critical difference between Regimes 2 and 3 is the response of surface latent heat fluxes to changes in surface moisture and energy, as indicated by the correlations between these variables (Table 1). Over the 15 days centred on the start of the humid heatwaves, Regime 3 has positive correlations for surface latent heat flux anomalies with both soil moisture anomalies (+0.88) and downwelling SW radiation anomalies (+0.54). In contrast, Regime 2 has a negative correlation between surface latent heat anomalies and soil moisture anomalies (−0.76) and a positive correlation between surface latent heat anomalies and downwelling SW radiation anomalies (+0.99). For comparison, Regime 1 (moisture-limited) has correlations of +0.96 between surface latent heat flux anomalies and soil moisture anomalies and −0.47 between surface latent heat flux anomalies and downwelling SW radiation anomalies.

In Regime 3, prior to the onset of a humid heatwave, surface evaporation and Twb are constrained by surface energy and moisture availability. Rainfall prior to a humid heatwave (days −7 to −2) supplies the necessary surface moisture, while a decrease in rainfall around the start of a heatwave (days −1 and 0) is accompanied by an increase in downwelling SW radiation, which increases surface energy. Together, these changes overcome the initial constraints on surface energy and moisture, leading to an increase in surface latent heat flux. This, in turn, raises near-surface specific humidity and Twb. These changes are reinforced by a shallower boundary layer resulting from weaker surface sensible heat fluxes.

In summary, although Regime 3 is energy-limited according to the ELI, both energy- and moisture-limitations actually influence surface evaporation in this regime.

The most extreme humid heatwaves
To examine the most extreme humid heatwaves, we identify the heatwaves in each grid cell where the highest daily mean Twb during the event exceeds the 95th percentile of the highest daily mean Twb values calculated across all humid heatwaves in that grid cell (Fig. 5). Each grid cell is allocated to the same regime as used for all heatwave events. Conditions during extreme heatwaves in each regime (solid circles) have a wide distribution of temperature and relative humidity, with substantial overlap between the three regimes (shading). Daily mean Twb during the most extreme events is between 27 °C and 28 °C in all three regimes. Heat Index (HI) classifications of Extreme Caution (HI > ~33 °C) and Danger (HI > ~39.5 °C) are common in all regimes, although the very highest Twb and HI values occur in Regime 2. The mean maximum daily Twb conditions averaged over all humid heatwaves (crosses) are also similar across the three regimes, ranging from 25 °C to 26 °C and HI 33 °C to 35 °C.

Despite the similar conditions experienced during extreme humid heatwaves across the three regimes, the climatological relative humidity and temperature, and their change in the build-up to events are very different. Locations within Regime 1 (moisture-limited) are climatologically hot and arid, with a climatological mean Twb during the heatwave season of 22 °C. A large increase in relative humidity is required for a humid heatwave to occur, and in the most extreme events, much of this occurs more than 7 days before the event. Locations within Regime 2 (energy-limited) are climatologically more humid, cooler in temperature, with a climatological mean Twb between 24 °C and 25 °C (during the heatwave season). A large increase in temperature is required for a humid heatwave to occur, which is accompanied by an increase in specific humidity to sustain the relatively high level of relative humidity, and in the most extreme events, much of this occurs more than 7 days before the event.

The elevated temperatures and relative humidity occurring seven days before the extreme humid heatwave events are likely driven by inter-annual variability. This variability, driven by large-scale environmental factors such as ENSO, preconditions the local environment in part through prior heatwaves. In 34% of extreme heatwave events, a preceding heatwave event occurred seven days before the onset of the extreme event.

Although the humid heat extremes are similar across the three regimes, the nature of the threat to human health from heat stress varies by regime. The threat depends on whether local populations are better adapted to temperature or humidity extremes, and whether they are more vulnerable to absolute or anomalous extremes. Additionally, the impact of a humid heat event at a given magnitude of Twb depends on its composition. Extreme humid heat poses greater danger to human health when driven by high temperatures combined with moderate humidity, rather than high humidity with moderate temperatures.

Methods
Identification of rainy days
To compare heatwaves with rainfall we categorised each day in 2001–2022 into two categories using precipitation data from GPM-IMERG. The category with higher rainfall (High_Rain) includes days when rainfall exceeds 5 mm/day on that day, or the previous day, or on both days. The category with lower rainfall (Low_Rain) includes days when rainfall does not exceed 5 mm/day on both that day and the previous day. The 5 mm/day threshold produced the clearest results for the relative risk of heatwaves on High_Rain versus Low_Rain days. This threshold is physically meaningful; it is the median daily rainfall rate in GPM-IMERG (2001-2022) during the humid heatwave season in regions with humid heatwaves. The 5 mm/day threshold, therefore, represents above-average rainfall, which is sufficiently heavy to promote surface evaporation.

The empirical probability of heatwave occurrence for enhanced and suppressed rainfall days
For each grid cell, we calculate the probability of heatwaves starting on High_Rain days:

Pr(HW|High_Rain) = N1 / N2 (1)

where N1 is the number of High_Rain days on which a heatwave started, and N2 is the total number of High_Rain days. Similarly, we calculate the probability of heatwaves starting on Low_Rain days:

Pr(HW|Low_Rain) = N3 / N4 (2)

where N3 is the number of Low_Rain days on which a heatwave started, and N4 is the total number of Low_Rain days.

The statistical significance of the difference between Pr(HW,j,High_Rain) and Pr(HW,j,Low_Rain) is tested following the method of Welty et al. We use a normal distribution approximation to the binomial test. The significance test is two-tailed and the significance level 5%.

The relative risk, sometimes referred to as the risk ratio, is calculated using one of two formulae:

Relative Risk = Pr(HW|High_Rain) / Pr(HW|Low_Rain) (3)

or

Relative Risk = Pr(HW|Low_rain) / Pr(HW|High_Rain) (4)

Equation (3) is used for grid cells where Pr(HW|High_Rain) is greater than Pr(HW|Low_Rain), and Eq. (4) is used where Pr(HW|Low_Rain) is greater than Pr(HW|High_Rain). We use Eqs. (3) and (4) for presentational purposes so that the relative risk varies over the same range of values (i.e., greater than 1) in all grid cells and all heatwave/rainfall regimes.

Ecosystem Limitation Index (ELI)
The ELI is the difference between two correlation coefficients:

ELI = correlation(SLHF', SM') - correlation(SLHF', SSRD') (5)

where SLHF’, SM’, and SSRD’ are daily anomalies from daily mean climatology for the surface latent heat flux, soil moisture, and surface SW radiation downwards. ELI is calculated daily using a 7-day moving window. We use daily anomalies and a 7-day window to capture variations in the surface environment on the time scale of humid heatwaves. We use a Spearman rank correlation to avoid assuming linear relationships.

The statistical significance of the heatwave composite ELI values was tested using the Wilcoxon signed rank test. This test was applied to the differences between corr(SLHF', SM') and corr(SLHF', SSRD') from values taken two days before each heatwave. Significance was determined at the 5% significance level.

Categorisation of grid cells to rainfall-ELI regimes
The categorisation of grid cells to rainfall-ELI regimes is shown in Fig. 2c. This categorisation is based on the ELI values and relative risk (Table 2). Relative risk is calculated using the Pr(HW|High_Rain) and the Pr(HW|Low_Rain) (see The empirical probability of heatwave occurrence for enhanced and suppressed rainfall days above). For Regimes 1–3, both the ELI and the difference between Pr(HW|High_Rain) and Pr(HW|Low_Rain) are statistically significant at the 5% level. Grid cells categorised as not significant in Fig. 2c fail to meet the 5% significance level for either the ELI or the difference between Pr(HW|High_Rain) and Pr(HW|Low_Rain), or both.

Wet-bulb temperature limitation index (TwbLI)
The Twb limitation index (TwbLI) is motivated by the ELI. This index is analogous to the ELI but replaces surface latent heat flux anomalies with Twb anomalies in its calculation. TwbLI captures the competing influences of soil moisture and surface SW radiation downwards on Twb by comparing the strength of their respective relationships with Twb anomalies.

The evapotranspiration term used by ref. is replaced by Twb. TwbLI is the difference between two correlation coefficients:

TwbLI = correlation(Twb', SM') - correlation(Twb', SSRD') (6)

where Twb’, SM’, and SSRD’ are anomalies from daily mean climatology for Twb, soil moisture, and surface SW radiation downwards. TwbLI is calculated daily using a 7-day moving window. We use a Spearman rank correlation.

The statistical significance of the heatwave composite TwbLI values was tested using the Wilcoxon signed rank test applied in the same way as for the ELI.

Calculation of the Heat Index
The Heat Index is calculated using the Rothfusz multiple regression formula published by the NOAA/National Weather Service. In this formulation, the Rothfusz formula is modified for conditions of low or high relative humidity and when values of the Heat Index are below 80 °F (26.7 °C).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors evaluate the relationship between daily rainfall variability and humid heatwave dynamics. They particularly isolate the impacts of rainfall intensification and suppression based on categorizing grid cells by evapotranspiration regimes. The results of the study help advance our understanding of these relationships greatly, and are presented cleanly and concisely. Most of my comments are regarding result interpretation, communication, and contextualization with existing literature. I therefore recommend the authors complete minor revisions before the article be accepted.\n\nTitle:\nR1-1. o In the title, I would note that this manuscript focuses on just the tropics and subtropics.\n\nAbstract:\nR1-2. o Here as well, I would include mention that the manuscript will only focus on the tropics and subtropics.\n\nR1-3. o P2L9: Suggested change to “greater understanding of the meteorological drivers of extreme humid heat is urgently needed.”\n\nR1-4. o P2L16: I think of adaptation as a modulator of vulnerability. Perhaps this sentence would make more sense if it mentioned vulnerability vs. exposure to extremes? I’m particularly thinking of the IPCC venn diagrams (see https://www.ipcc.ch/srocc/chapter/technical-summary/ts-0-introduction/ipccsrocc-ts_4/)\n\nIntroduction:\nR1-5. o P4L70: 24°C actually seems quite low, and I’m not sure if you could say it’s a threshold relevant to human health impacts. I know you do a sensitivity test with 26°C, so I would either leave out the final clause of this sentence or mention that you chose this lower threshold for the main analysis in order to retain statistical significance of the results.\n\nR1-6. o P4L77: I would include one or two sentences in this paragraph about the ongoing debate between physiology/epidemiology/economics/climate science regarding using Tw as a heat stress metric. Many epidemiologists and economists disagree that this represents humans experience of heat stress well. I think it is fine to use for climate science applications for understanding humid heat dynamics, but the authors should be upfront about the limitations of using this variable for human health applications (which they are in the discussion section, but I think it’s worth mentioning before the results, as well). Example citations for this would include Baldwin et al. 2023 (https://doi.org/10.1289/EHP11807) and Vanos et al. 2020 (https://doi.org/10.1038/s41467-020-19994-1)\n\nResults:\nR1-7. o P6: I think the detailed discussion of climatologies of humid heatwaves and their seasonal cycle is a nice addition to the literature.\n\nR1-8. o P6L116: Seems to me this conclusion should only be regions which have simultaneous peak rainfall and peak humid heat? I.e., the cream colored grid cells?\n\nR1-9. o P9L168: I think it would be beneficial to provide a more quantitative explanation for how the Regimes are categorized, even if just included in the Methods section at the end of the manuscript. For example, is Regime 1 grid cells which have a positive relative risk and a positive ELI?\n\nR1-10. Additionally, I am having trouble determining how Regime 3 is identified. I think it would be helpful to have this explained in the text, and especially to describe it in the same paragraph above where Regimes 1 and 2 are introduced before the start of the next section (“Contributions of temperature and humidity to humid heatwaves”)\n\nR1-11. o P11L209: I wonder if there is a way to show heatwave length? Especially as the authors begin to discuss what happens “when the heatwaves start to dissipate” (P12L226), it is unclear to me where in the time series these comments refer to. This is particularly important to clarify as it is my understanding that the heatwaves are defined as multiday events, but do not need to be the same duration across events.\n\nR1-12. o P12L228: I find the characterization of Regime 3 as “decreased” rainfall at the start of the humid heatwave to be deceptive. It appears that it is really elevated rainfall (positive anomaly) which decrease to 0 at the start of the heatwave and then rise back up (positive anomaly). Is there a better word to call this? Something like “neutral”?\n\nR1-13. o P12L240: This mention of cloud cover is important for human experience of heat stress, which also depends on direct solar radiation. This relates to my comment below regarding the Discussion section about the need to include more information about the impacts of the heat stress metric you’ve selected.\n\nR1-14. o P13L270: Interesting finding and interpretation about the evolution of these relationships, very nicely described.\n\nR1-15. o Figures 3-4: It would be beneficial to include some measure of significance for these time evolution plots, or at least discussion of this in the text. Some of these anomalies are very small and I would assume indicate that these relationships are not statistically significant.\n\nR1-16. o P15L286: Could you clarify what the “highest 10% of Twb” means? I’m a bit confused on when the analysis is using 95th percentiles, 90th percentiles, and then what this new requirement means in contrast.\n\nR1-17. o P15L299: Could you comment on why this timeline is so far extended? It surprises me that the elevated temperature or moisture is coming >7 days before the event. What do you think is maintaining these changes in the week to follow?\n\nR1-18. o P15L307: Should also mention that the impact of a humid heat event of one magnitude also depends upon how it’s made up – whether it’s very high temperatures in the presence of some moisture vs. very high moisture in the presence of moderate temperatures. Extreme humid heat of a given threshold is more dangerous when we experience the former (high T, moderate q). Citations to include are Vecellio et al. 2021 (https://doi.org/10.1152/japplphysiol.00738.2021) and Ivanovich et al. 2024 (https://doi.org/10.1175/JAS-D-23-0072.1)\n\nR1-19. o Figure 5: I find it interesting that in each subset of events (climatology, all heatwaves, most intense heatwaves), Regime 2 exhibits higher overall Twb than Regime 1. This seems counter to the findings in Ivanovich et al. 2024, for example, which suggest that most extreme humid heat events at the highest magnitudes are experienced due to elevated moisture. Could you comment on why you think there is a disagreement here?\n\nDiscussion:\nR1-20. o P17L338: Could you provide a bit more context in the main text about your calculation of TwbLI? I’m having a bit of trouble with the interpretation in this paragraph even after reading the section in the Methods about it.\n\nR1-21. o P18L365: I think this paragraph needs to acknowledge that we know that humans’ experience of heat stress also depends on incoming solar radiation and wind speed. This is best represented by variables such as wet bulb globe temperature WBGT or the Universal Thermal Climate Index (UTCI). While I think that Twb is a fine choice for the analysis presented here, the relationship between precipitation and humid heat is definitely modulated by cloudiness (as you show in Figure 4) and wind speed. This inherently cannot be addressed by looking at Heat Index or 2m dry bulb temperature, which also do not incorporate these additional variables relevant to heat stress. A few additional sentences here to discuss this as a limitation in terms of how these results can be interpreted from a human health standpoint are important. Potential citations to help could include Grundstein and Vanos 2021(https://doi.org/10.1136/bjsports-2020-102920) and Budd 2008 (https://doi.org/10.1016/j.jsams.2007.07.003)", "reviewer_2": "This is the review for the article “Humid heatwaves are controlled by daily rainfall variability”. The article focuses on evaluating rainfall as a controlling mechanism for humid heatwaves for different regions. The authors identify differences depending on whether the region is energy-limited or moisture-limited. This study presents interesting findings. However, I wonder how these insights could be applied more broadly.\n\nR2-45. The impact of this study could be enhanced if the authors conduct additional analyses using climate models to evaluate the skill of GCMs in simulating this mechanism, assess projected changes in future periods, and explore the implications of these shifts. This is my major comment. I would like to see at least some, if not all, of these suggestions incorporated into the manuscript before I can recommend it.\n\nA few other studies that author may consider citing.\n• Fischer, E. M., & Knutti, R. (2013). Robust projections of combined humidity and temperature extremes. Nature Climate Change, 3(2), 126–130. https://doi.org/10.1038/Nclimate1682\n• Rastogi, D., Lehner, F., & Ashfaq, M. (2020). Revisiting recent US heat waves in a warmer and more humid climate. Geophysical Research Letters, 47(9), e2019GL086736. https://doi.org/10.1029/2019GL086736\n• Coffel, E. D., Thompson, T. R., & Horton, R. M. (2017). The impacts of rising temperatures on aircraft takeoff performance. Climatic Change, 144(2), 381–388. https://doi.org/10.1007/s10584-017-2018-9\n\nLines 169-171: How is the percentage of grids calculated? Does it represent the percentage of all land grid points globally?\nThe legend size and labels are hard to read in Figures especially Figure1d-e and Figure 2c.\n404-406: Have authors considered using other metric such as apparent temperature instead of wet bulb temperature? What is the reason for using the wet bulb temperature?\n411-413: “The 95th percentiles are calculated using daily data in each grid cell for all days during 1993-2022” Does this mean single 95th percentile value is calculated using 30*365 days for each grid cell? Why didn’t the author consider calculating the 95th percentile for each year and then averaging across all years?\n414-416: Additional clarification is needed here.\n426-430: How did the authors determine the 5mm threshold? Shouldn't this threshold vary depending on the region?\n477: It would be beneficial if the authors could make their code publicly available.", "reviewer_3": "This paper investigates the rainfall controls on daily humid heatwaves across the globe using gridded meteorological records by contrasting two regimes, the moisture-limited versus the energy-limited environment conditions. The work employs re-analysis based meteorological input, which itself has bias especially in arid region in capturing humidity term1. Though sparse coverage in certain data constraint areas of the globe, a validation through observational records is required to claim robustness of obtained result.\n\nMy specific comments on the manuscript are below:\n1) Line 51: Other than irrigation, proximity to the coast, see ref.2.\n2) Line 57: “regional scale” could be elusive, for example, spatial heterogeneity could be very prominent within a continental or national scale.\n3) Line 69 and elsewhere (for example, Fig. 1 caption line 126): The paper revolves back and forth between 90th percentile and 95th percentile of threshold selection in their write-up. The choice of threshold selection is not kept uniform throughout the paper. Also, they have used daily mean temperatures, whereas the daily maxima temperature should be used for heatwave analysis. This is because daily mean does not consider the abrupt rise for few hours, which can have fatal consequences for the exposed livelihoods\n4) Line 94: Fig. 1A shows Himalayan region still experience very high frequency of humid heatwaves.\n5) Line 97: regions with longest and persistent heatwaves are also experienced by desert areas of South Asia\n6) Line 117: regional differences are expressed in a qualitative manner rather than quantitative ways.\n7) Line 136: 5 mm/d rainfall threshold? Any references for heavy/moderately heavy rainfall?\n8) Line 215: How these composites are constructed? Is it spatial average across all grid points?\n9) Humid heat is often controlled by surface evaporation3,4, however, the role of surface evaporation is not investigated among list of drivers in Fig. 4.\n10) In Discussion: Lines 342-347: In Fig. 3SD: for south America and vast stretches of peninsular India, both with a strong tropical climate, no significant regime were identified, which is elusive. The same holds for northeast coast of the US, which has tropical climate.\n11) Line 359: Choice of 24℃, as a fixed threshold could be erroneous without considering seasonality of humid heat across the globe. A daily variable threshold with a moving window approach should be considered to account for the seasonality. On page 20, Methodology, they have highlighted pitfalls of using running mean by citing Brunner & Voigt. But the reference never recommends using constant thresholds but rather they recommend for shortening window lengths.\n12) Different Heat indices (HI) use different formulations and are not in agreement with each other. Further, the most widely use HI by Rothfusz is based on polynomial approximation. In their paper, they have neither discussed which approach was followed for Heat index calculation nor the pitfalls of such an index.\n\nIn summary, I can’t recommend that this manuscript to be accepted by NComm.\n\nReferences\n1. Raymond, C., Matthews, T. & Horton, R. M. The emergence of heat and humidity too severe for human tolerance. Sci. Adv. 6, eaaw1838 (2020).\n2. Ganguli, P. & Merz, B. Observational Evidence Reveals Compound Humid Heat Stress-Extreme Rainfall Hotspots in India. Earths Future 12, e2023EF004074 (2024).\n3. Bu, L., Zuo, Z., Zhang, K. & Yuan, J. Impact of Evaporation in Yangtze River Valley on Heat Stress in North China. (2023) doi:10.1175/JCLI-D-22-0573.1.\n4. Zhang, Z. et al. Light rain exacerbates extreme humid heat. Nat. Commun. 15, 7326 (2024)."}, "author_response": "Response to Reviewers\nReviewer #1\nIn this manuscript, the authors evaluate the relationship between daily rainfall variability and humid\nheatwave dynamics. They particularly isolate the impacts of rainfall intensification and suppression\nbased on categorizing grid cells by evapotranspiration regimes. The results of the study help advance\nour understanding of these relationships greatly, and are presented cleanly and concisely. Most of\nmy comments are regarding result interpretation, communication, and contextualization with\nexisting literature. I therefore recommend the authors complete minor revisions before the article\nbe accepted.\nWe thank the reviewer for their thoughtful and thorough review. Our responses to your specific\ncomments are set out below.\nTitle:\nR1-1. o In the title, I would note that this manuscript focuses on just the tropics and subtropics.\nWe have changed the title to mention the tropics and subtropics.\nAbstract:\nR1-2. o Here as well, I would include mention that the manuscript will only focus on the tropics and\nsubtropics.\nWe now include mention of the tropics and subtropics.\nR1-3. o P2L9: Suggested change to “greater understanding of the meteorological drivers of extreme\nhumid heat is urgently needed.”\nWe have inserted the text “ … of extreme humid heat …”.\nR1-4. o P2L16: I think of adaptation as a modulator of vulnerability. Perhaps this sentence would\nmake more sense if it mentioned vulnerability vs. exposure to extremes? I’m particularly thinking of\nthe IPCC venn diagrams (see https://www.ipcc.ch/srocc/chapter/technical-summary/ts-0-\nintroduction/ipccsrocc-ts_4/)\nWe have replaced the term “adaptation” with explicit reference to vulnerability and exposure.\nIntroduction:\nR1-5. o P4L70: 24°C actually seems quite low, and I’m not sure if you could say it’s a threshold\nrelevant to human health impacts. I know you do a sensitivity test with 26°C, so I would either leave\nout the final clause of this sentence or mention that you chose this lower threshold for the main\nanalysis in order to retain statistical significance of the results.\nWe agree there is limited evidence for the 24°C threshold being relevant to the effect of humid heat\non human health and, where it is relevant, it will apply to vulnerable groups such as the elderly\n(Vanos et al., 2023). We have changed the sentence to state that the 24°C threshold is applied to:\n exclude conditions likely low risk for most people. We have also added references to\nVecellio et al. (2023) and Vanos et al. (2023). We point the reviewer to Figure 4 in these\npapers.\n1\n and, as suggested by the reviewer, to ensure there are sufficient data for statistically\nsignificant results.\nVanos, J., Guzman-Echavarria, G., Baldwin, J.W. et al. A physiological approach for assessing human\nsurvivability and liveability to heat in a changing climate. Nat Commun 14, 7653 (2023).\nhttps://doi.org/10.1038/s41467-023-43121-5.\nVecellio, D. J., Kong, Q., Kenney, W., L. & Huber, M. Greatly enhanced risk to humans as a\nconsequence of empirically determined lower moist heat stress tolerance. PNAS 120, 42,\ne2305427120 https://doi.org/10.1073/pnas.2305427120 (2023).\nR1-6. o P4L77: I would include one or two sentences in this paragraph about the ongoing debate\nbetween physiology/epidemiology/economics/climate science regarding using Tw as a heat stress\nmetric. Many epidemiologists and economists disagree that this represents humans experience of\nheat stress well. I think it is fine to use for climate science applications for understanding humid heat\ndynamics, but the authors should be upfront about the limitations of using this variable for human\nhealth applications (which they are in the discussion section, but I think it’s worth mentioning before\nthe results, as well). Example citations for this would include Baldwin et al. 2023\n(https://doi.org/10.1289/EHP11807) and Vanos et al. 2020 (https://doi.org/10.1038/s41467-020-\n19994-1)\nWe thank the reviewer for recommending citations. We have added a few sentences to\nacknowledge the limitations of Twb in representing human heat stress. We have added the following\nspecific points to the text:\n The 35°C threshold for Twb is an upper limit and may underestimate the health impacts in\nsome contexts (Vanos et al., 2020).\n Twb does not separately identify the contributions of temperature and humidity, a\ndistinction which can be important for health impacts (Ivanovich et al., 2024).\n Epidemiological studies fail to identify evidence for the impact of humidity on human health\n(Baldwin et al., 2023) although epidemiological evidence is likely to develop under\nincreasingly extreme future temperatures driven by climate change.\nBaldwin, J. W., Benmarhnia, T., Ebi, K. L., Jay, O., Lutsko, N. J. & Vanos, J. K. Humidity’s Role in Heat-\nRelated Health Outcomes: A Heated Debate. Environmental Health Perspectives 131(5), 055001 1-14\nhttps://doi.org/10.1289/EHP11807 (2023).\nIvanovich, C. C., Horton, R. M., Sobel, A. H. & Singh, D. Subseasonal variability of humid heat during\nthe South Asian summer monsoon. Geophysical Research Letters 51, e2023GL107382\nhttps://doi.org/10.1029/2023GL107382 (2024).\nVanos, J. K., Baldwin, J. W., Jay, O. & Ebi, K. L. Simplicity lacks robustness when projecting heat-\nhealth outcomes in a changing climate. Nature Communications 11, 6079\nhttps://doi.org/10.1038/s41467-020-19994-1 (2020).\nResults:\nR1-7. o P6: I think the detailed discussion of climatologies of humid heatwaves and their seasonal\ncycle is a nice addition to the literature.\nThank you, this was our motivation for including Figure 1 and the accompanying text.\nrainfall and peak humid heat? I.e., the cream colored grid cells?\nWe agree with the reviewer and have changed the text to refer specifically to the cream coloured\ngrid cells.\nR1-9. o P9L168: I think it would be beneficial to provide a more quantitative explanation for how the\nRegimes are categorized, even if just included in the Methods section at the end of the manuscript.\nFor example, is Regime 1 grid cells which have a positive relative risk and a positive ELI?\nYes, Regime 1 includes grid cells that have a positive ELI and positive relative risk. As requested, we\nhave added a sub-section under Methods (“Categorisation of grid cells to rainfall-ELI regimes”) which\nexplains in more quantitative terms how the grid cells are categorised.\nR1-10. Additionally, I am having trouble determining how Regime 3 is identified. I think it would be\nhelpful to have this explained in the text, and especially to describe it in the same paragraph above\nwhere Regimes 1 and 2 are introduced before the start of the next section (“Contributions of\ntemperature and humidity to humid heatwaves”)\nFor clarity, we prefer to describe Regime 3 in its own paragraph, positioned immediately after the\ndescription of Regimes 1 and 2 and before the start of the next section (“Contributions of\ntemperature and humidity to humid heatwaves”). The updated paragraph explains in more detail\nhow Regime 3 is identified (i.e., grid cells with negative ELI and positive relative risk). Additionally, a\nmore detailed explanation of the regime categorisation is now provided in the methods section. We\nbelieve these changes make clearer how Regime 3 is identified.\nR1-11. o P11L209: I wonder if there is a way to show heatwave length? Especially as the authors\nbegin to discuss what happens “when the heatwaves start to dissipate” (P12L226), it is unclear to me\nwhere in the time series these comments refer to. This is particularly important to clarify as it is my\nunderstanding that the heatwaves are defined as multiday events, but do not need to be the same\nduration across events.\nYour understanding is correct: the heatwaves are multiday events lasting a minimum of 3 days with\ndurations varying between events. The median duration is 4 days and, by day 7 in Figure 3,\napproximately 79% of the heatwaves have dissipated. Heatwave durations do not very greatly\nbetween the regimes with median durations of 4, 4, and 4.5 days for Regimes 1, 2, and 3\nrespectively.\nTo avoid complicating Figures 3 and 4, we prefer not to add heatwave duration to these figures. We\nhave changed the text, however, to explain more clearly how the composites are calculated and\ndescribe the dissipation of the heatwaves using the statistics quoted above. We also now state\nexplicitly that the heatwaves start to dissipate on day 3. We have updated Figure 1b to show the\nmedian heatwave durations rather than mean durations. Median durations are shorter and indicate\nmore clearly the dissipation of heatwave events over the timescales shown in Figures 3 and 4.\nR1-12. o P12L228: I find the characterization of Regime 3 as “decreased” rainfall at the start of the\nhumid heatwave to be deceptive. It appears that it is really elevated rainfall (positive anomaly)\nwhich decrease to 0 at the start of the heatwave and then rise back up (positive anomaly). Is there a\nbetter word to call this? Something like “neutral”?\nWe thank the reviewer for the suggestion and have changed the description from “decreased” to\n“neutral”.\nwhich also depends on direct solar radiation. This relates to my comment below regarding the\nDiscussion section about the need to include more information about the impacts of the heat stress\nmetric you’ve selected.\nWhile we acknowledge the importance of cloud cover for the human experience of heat stress, we\nhave not made changes to this specific paragraph. As part of the Results section, this paragraph\nfocuses on the dynamics of heatwaves, which is the primary scope of our study, rather than health\nimpacts. However, we have addressed this point in the updated Discussion section, elaborating on\nthe human experience of heat stress, particularly in relation to incoming solar radiation and wind\nspeed. We also draw attention to the role of clouds in Figure 4h and the relevance for the human\nexperience of heat stress.\nR1-14. o P13L270: Interesting finding and interpretation about the evolution of these relationships,\nvery nicely described.\nThank you.\nR1-15. o Figures 3-4: It would be beneficial to include some measure of significance for these time\nevolution plots, or at least discussion of this in the text. Some of these anomalies are very small and I\nwould assume indicate that these relationships are not statistically significant.\nWe have added a 95% confidence interval to the composite anomaly time series in Figures 3 and 4.\nThis shows which variables have statistically significant composite anomalies and the days on which\nthe significant changes occur.\nAll anomaly time series in Figure 3 are statistically significant at the 5% level. The anomalies are\nparticularly small, however, for 2m temperature in Regime 3. Although previously noted in the text,\nwe now emphasise this point by stating explicitly that the anomalies are less than 0.5°C (the\nmaximum anomaly occurs on day 1 and is 0.41°C).\nWe have changed the text describing the results for Regime 2 in Figure 4 to make clear that the\nanomalies for TCWV, surface sensible heat flux, and boundary layer height are very small.\nR1-16. o P15L286: Could you clarify what the “highest 10% of Twb” means? I’m a bit confused on\nwhen the analysis is using 95th percentiles, 90th percentiles, and then what this new requirement\nmeans in contrast.\nWe have expanded the description in the text to improve its clarity. To improve consistency\nthroughout the manuscript and reduce the potential for confusion, we have also changed the\ndefinition to use the top 5% of heatwaves as measured by the maximum daily mean Twb in the\nheatwaves.\nTo help you assess the clarity of the revised description, a step-by-step description of the\ncalculations is provided below:\n1. For each grid cell, determine the periods classified as humid heatwaves.\n2. Within each humid heatwave in a grid cell, find the highest daily mean Twb.\n3. Collect the maximum daily mean Twb values for all humid heatwaves in a grid cell.\n4. Calculate the 95th percentile of these maximum values for the grid cell.\n5. Identify the heatwaves in which the maximum daily mean Twb exceeds the 95th percentile\nof the maximum Twb values in the grid cell.\n6. Compute mean statistics for Figure 5 using this subset of extreme heatwaves.\nthe elevated temperature or moisture is coming >7 days before the event. What do you think is\nmaintaining these changes in the week to follow?\nThe elevated temperatures or humidity seven days before extreme humid heatwave events are\nprimarily due to inter-annual variability and preconditioning by prior heatwaves, likely driven by\nlarge-scale environmental conditions.\nThere is notable inter-annual variability in the number of humid heatwaves across the land grid cells\nin our analysis, with 39% of these cells having statistically significant variance in annual heatwave\ncounts at the 5% significance level. This variability is driven by phenomena such as ENSO, which\nmodulates near-surface temperature and humidity on inter-annual timescales. Unpublished\nresearch on our ERA5 dataset further reveals that humid heatwaves are significantly more frequent\nduring El Niño years than La Niña years.\nExtreme humid heatwaves tend to occur more frequently in years with a higher overall frequency of\nheatwaves. In 75% of the land grid cells analysed, years with at least one extreme humid heatwave\nhave a greater number of heatwaves overall compared to years without extreme events.\nAdditionally, in 34% of extreme humid heatwave events, a preceding heatwave event occurs seven\ndays prior to the start of the extreme heatwave event. These preceding heatwave events likely\ncontribute to elevated temperatures and humidity, which are maintained by persistent large-scale\nenvironmental conditions favourable to heatwave formation.\nR1-18. o P15L307: Should also mention that the impact of a humid heat event of one magnitude also\ndepends upon how it’s made up – whether it’s very high temperatures in the presence of some\nmoisture vs. very high moisture in the presence of moderate temperatures. Extreme humid heat of a\ngiven threshold is more dangerous when we experience the former (high T, moderate q). Citations to\ninclude are Vecellio et al. 2021 (https://doi.org/10.1152/japplphysiol.00738.2021) and Ivanovich et\nal. 2024 (https://doi.org/10.1175/JAS-D-23-0072.1)\nWe have updated the manuscript to include mention of the dependence of humid heatwave impact\non the individual contributions from temperature and humidity.\nR1-19. o Figure 5: I find it interesting that in each subset of events (climatology, all heatwaves,\nmost intense heatwaves), Regime 2 exhibits higher overall Twb than Regime 1. This seems counter to the\nfindings in Ivanovich et al. 2024, for example, which suggest that most extreme humid heat events at\nthe highest magnitudes are experienced due to elevated moisture. Could you comment on why you\nthink there is a disagreement here?\nYou raise a very interesting issue, and we appreciate the opportunity to discuss the apparent\ndifferences between our findings and those of Ivanovich et al. (2024). Your comment highlights two\nkey points: (1) why extreme humid heat events appear to differ in their dependence on elevated\nmoisture, and (2) why Twb is greater in Regime 2 than in Regime 1.\n1. Extreme Humid Heat Events and Elevated Moisture\nThe apparent differences between our results and those of Ivanovich et al. (2024) may be partly\nexplained by the use of different measures of moisture. Ivanovich et al. (2024) use specific\nhumidity to calculate their “stickiness” metric, whereas our results are presented using relative\n5\nhumidity. Importantly, specific humidity is increased when temperature is increased under\nconditions of constant relative humidity. For example, in Figure 5 of our manuscript, Twb\nheatwaves in Regime 2 appear to be primarily temperature-driven, as there is only a small\ndifference between climatological relative humidity and relative humidity during heatwaves.\nHowever, the large increase in temperature, coupled with near-constant relative humidity,\nimplies that specific humidity is substantially above climatology during these events.\nIvanovich et al. (2024) present results for four regions, two of which (the Persian Gulf and South\nAsia) overlap geographically with our study. In the Persian Gulf region (likely corresponding to\nRegime 1 in our study), Ivanovich et al. (2024) find that extreme events are driven by increases\nin both specific and relative humidity, with little change in temperature compared to\nclimatology. Similarly, in Figure 5 of our study, we find that extreme events in Regime 2 are\nassociated with elevated relative humidity and only minor temperature changes, suggesting\nbroad consistency between the two studies.\nFor South Asia (likely corresponding to Regime 2 in our study), Ivanovich et al. (2024) show that\nextreme events are driven by increases in both specific humidity and temperature. Relative\nhumidity, however, differs little between extreme and all day events with the change\napproximately parallel to the relative humidity isopleths. This behaviour aligns with our findings\nin Figure 5, where relative humidity differs little between climatology and extreme events, but\ntemperature is significantly elevated during extreme events.\n2. Twb in Regime 2 vs. Regime 1\nThe observation that Twb is greater in Regime 2 than in Regime 1 is apparently inconsistent with\nthe results presented in Figure 4 of Ivanovich et al. (2024). They report higher Twb for extreme\nevents in the Persian Gulf region compared to South Asia. In contrast, our results in Figure 5\nshow extreme Twb to be greater for Regime 2 (which includes South Asia) than for Regime 1\n(which includes parts of the Persian Gulf). The comparison of Regime 1 with the Persian Gulf and\nRegime 2 with South Asia should be interpreted with caution. Regimes 1 includes parts of West\nAfrica and North West India (amongst others) and 2 includes much of South America, tropical\nAfrica, and northeast China. Further, the difference between Twb for extreme events in Regimes\n1 and 2 is small (Figure 5).\nDifferences in Data and Methods\nWhile the distinctions between specific and relative humidity partly explain the apparent differences\nbetween the two studies, several methodological differences may also be crucial.\n Meteorological Data Sources: Ivanovich et al. (2024) use station observations, whereas we\nuse reanalysis data. In our validation of ERA5 reanalysis data against weather station\nobservations, however, we found good overall consistency between ERA5 reanalysis and\nHadISD station observations for wet-bulb and 2m temperatures.\n Definitions of Twb: Ivanovich et al. (2024) analyse daily maximum Twb, whereas we focus on\ndaily mean Twb. This distinction not only affects the magnitude of Twb but also likely alters\nthe relative contributions of temperature and humidity to Twb.\n Time Periods: Differences in the time periods analysed further contribute to the apparent\ndifferences in findings.\nIn light of these thought-provoking issues, we have reviewed the language used in our manuscript\nregarding the contributions of temperature and humidity to humid heatwave events. We do not\nrefer to temperature-driven or humidity-driven events. We have made one change in the section\n“The most extreme humid heatwaves”, where we have updated the description of Regime 2\nextreme heatwaves to note that specific humidity, as well as temperature, is elevated.\nDiscussion:\nR1-20. o P17L338: Could you provide a bit more context in the main text about your calculation of\nTwbLI? I’m having a bit of trouble with the interpretation in this paragraph even after reading the\nsection in the Methods about it.\nELI captures the competing influences of soil moisture and surface SW radiation downwards on\nsurface latent heat fluxes. To test our findings that surface energy- and moisture-limitations\nmodulate the relationship between rainfall and humid heat, we defined a wet-bulb temperature\nenergy-moisture limitation index (TwbLI). TwbLI captures more directly than ELI the competing\ninfluences of soil moisture and surface SW radiation downwards on Twb.\nWe have amended the relevant paragraph in the discussion section and the description in the\nmethods section to include more explanation of the interpretation of the TwbLI.\nR1-21. o P18L365: I think this paragraph needs to acknowledge that we know that humans’\nexperience of heat stress also depends on incoming solar radiation and wind speed. This is best\nrepresented by variables such as wet bulb globe temperature WBGT or the Universal Thermal\nClimate Index (UTCI). While I think that Twb is a fine choice for the analysis presented here, the\nrelationship between precipitation and humid heat is definitely modulated by cloudiness (as you\nshow in Figure 4) and wind speed. This inherently cannot be addressed by looking at Heat Index or\n2m dry bulb temperature, which also do not incorporate these additional variables relevant to heat\nstress. A few additional sentences here to discuss this as a limitation in terms of how these results\ncan be interpreted from a human health standpoint are important. Potential citations to help could\ninclude Grundstein and Vanos 2021(https://doi.org/10.1136/bjsports-2020-102920) and Budd 2008\n(https://doi.org/10.1016/j.jsams.2007.07.003)\nWe have updated this paragraph to address the limitations of our research regarding human health\nand heat stress. We specifically discuss the influence of incoming solar radiation and wind speed, as\nhighlighted in your comment, and have incorporated the references you kindly suggested (Budd\n2008; Grundstein and Vanos, 2021).\nBudd, G. M. Wet-bulb globe temperature (WBGT)—its history and its limitations. Journal of Science\nand Medicine in Sport 11, 1, 20 – 32 https://doi.org/10.1016/j.jsams.2007.07.003 (2008).\nGrundstein, A. & Vanos, J. There is no ‘Swiss Army Knife’ of thermal indices: the importance of\nconsidering ‘why?’ and ‘for whom?’ when modelling heat stress in sport. British Journal of Sports\nMedicine 55, 15, 822-824 https://doi.org/10.1136/bjsports-2020-102920 (2021)\nThis is the review for the article “Humid heatwaves are controlled by daily rainfall variability”. The\narticle focuses on evaluating rainfall as a controlling mechanism for humid heatwaves for different\nregions. The authors identify differences depending on whether the region is energy-limited or\nmoisture-limited. This study presents interesting findings. However, I wonder how these insights\ncould be applied more broadly.\nR2-45. The impact of this study could be enhanced if the authors conduct additional analyses using\nclimate models to evaluate the skill of GCMs in simulating this mechanism, assess projected changes\nin future periods, and explore the implications of these shifts. This is my major comment. I would\nlike to see at least some, if not all, of these suggestions incorporated into the manuscript before I\ncan recommend it.\nWe thank the reviewer for their thoughtful review. We agree that the proposed analyses are\nimportant and would greatly enhance understanding of the mechanisms and their implications in a\nchanging climate. However, our current study is focused on analysing the observed relationships and\ndynamics in the recent climate using reanalysis data which, to our knowledge, is lacking in the\nliterature at the scale of the global (sub) tropics. We view this as a foundational step in\nunderstanding the humid heat-rainfall relationships. While incorporating climate model simulations\nand future projections is beyond the scope of the present study, we have plans for such work in the\nnext stages of our project.\nTo acknowledge the importance of the reviewer’s suggestion, we have updated the final paragraph\nof the Discussion section to emphasise the opportunity for extending this work to climate change\nprojections. We hope this provides clarity on the scope of our current work and its potential to\ninform further research.\nOur responses to the detailed comments are set out below.\nR2-22. A few other studies that author may consider citing.\nThank you for suggesting further studies to cite. We consider each study in turn below.\n• Fischer, E. M., & Knutti, R. (2013). Robust projections of combined humidity and temperature\nextremes. Nature Climate Change, 3(2), 126–130. https://doi.org/10.1038/Nclimate1682\nAlthough we appreciate the significance of this study, we have not added a citation because its focus\nis not directly relevant to the objectives and methods of our research. Fischer & Knutti (2013) focus\non CMIP climate model outputs, which are not used in our study, and principally address climate\nchange, which is beyond the scope of our study. Additionally, Fischer & Knutti (2013) use equivalent\ntemperature and simplified wet-bulb globe temperatures to quantify the combined effects of\ntemperature and humidity whereas we use wet-bulb temperature in our analysis.\n• Rastogi, D., Lehner, F., & Ashfaq, M. (2020). Revisiting recent US heat waves in a warmer and more\nhumid climate. Geophysical Research Letters, 47(9), e2019GL086736.\nhttps://doi.org/10.1029/2019GL086736\nWe have not added a citation for this study because its focus is the United States of America,\nwhereas our study examines the global tropics and sub-tropics. Additionally, Rastogi et al. (2020)\naddress climate change, which lies beyond the scope of our study.\n8\n• Coffel, E. D., Thompson, T. R., & Horton, R. M. (2017). The impacts of rising temperatures on\naircraft takeoff performance. Climatic Change, 144(2), 381–388. https://doi.org/10.1007/s10584-\n017-2018-9\nWe have not added a citation for this study because its focus is on aircraft performance changes\nunder climate change, neither of these issues are addressed in our study.\nR2-23. Lines 169-171: How is the percentage of grids calculated? Does it represent the percentage of\nall land grid points globally?\nThe percentage of grid cells relates to land grid cells between latitudes 35°N and 35°S where humid\nheatwaves occurred during 1993-2022. We have amended the text to make this clear. We have also\nmade the same change to the caption for Figure 2.\nR2-24. The legend size and labels are hard to read in Figures especially Figure1d-e and Figure 2c.\nWe have increased the font size for legends and axis labels in all figures with specific attention paid\nto Figure 1 and Figure 2c. While the legends and axis labels are clearer in the individual figure files,\nthey do not always appear so in the figures embedded in the manuscript document. We believe this\nis an issue with displaying figure files in Word documents and will not affect the figure quality in the\npublished manuscript.\nR2-25. 404-406: Have authors considered using other metric such as apparent temperature instead\nof wet bulb temperature? What is the reason for using the wet bulb temperature?\nAt the outset of our study, we considered available options for humid heat metrics and settled on\nwet-bulb temperature as our primary measure of humid heat for several reasons:\n It combines both temperature and humidity.\n It has similar thermodynamic properties to equivalent potential temperature (θe), making it\nrobust for analysis on regional scales and for a study which focuses on the physical processes\nby which rainfall regulates the occurrence of humid heatwaves.\n It is relevant to human heat stress. Wet-bulb temperature provides an upper temperature\nlimit for healthy, well-acclimatised human beings who have access to drinking water, shade,\nand a strong breeze.\nWe recognise there are alternative humid heat metrics that will exhibit different sensitivities to\nchanges in temperature and humidity than wet-bulb temperature. To address this, we show the\nsensitivity of our results to different humid heat metrics in Figure S7 of the revised manuscript. Panel\nc shows the relative risk of heatwaves given rainfall based on the Heat Index (one apparent\ntemperature metric) while panel d shows the same results based on 2m dry-bulb temperature.\nR2-26. 411-413: “The 95th percentiles are calculated using daily data in each grid cell for all days\nduring 1993-2022” Does this mean single 95th percentile value is calculated using 30*365 days for\neach grid cell? Why didn’t the author consider calculating the 95th percentile for each year and then\naveraging across all years?\nYes, the 95th percentiles used in our study are calculated using daily data for all days in all years (i.e.,\n30×365 days).\nWe have re-calculated the 95th percentiles using the reviewer’s suggested method. A comparison of\npercentiles from the two approaches is shown below in Figure RR1. For land grid cells where humid\nheatwaves occurred during 1993-2022, the method used in the manuscript yields percentile values a\n9\nlittle greater than the alternative method with a median difference of 0.09°C (Figure 1a, b). Figure 1c\nshows that the differences are broadly evenly distributed across the tropical land areas.\nBased on this comparison, we have decided to retain our method for calculating the 95th percentiles.\nThe results of our study would not change materially if we changed the method for calculating the\n95th percentiles.\nFigure RR1. Comparison of 95th percentiles for daily mean wet-bulb temperature. The percentiles\nused in the manuscript are calculated using the 95th percentile of values in all days and years and are\nreferred to as “percentiles calculated over all years”. Alternatively, percentiles calculated separately\nfor each of the 30 years and then averaged are referred to as “percentiles calculated as the mean of\nannual percentiles”.\nR2-27. 414-416: Additional clarification is needed here.\nWe have clarified the description of the 3-dimensional connected components algorithm.\nSpecifically, we now explain how the algorithm identifies spatially and temporally contiguous\nheatwave events using 26 points of connectivity, and we provide additional details on the definition\nof connectivity in 3-dimensions.\nR2-28. 426-430: How did the authors determine the 5mm threshold? Shouldn't this threshold vary\ndepending on the region?\nthe clearest results for the relative risk of heatwaves occurring on “High_Rain” versus “Low_Rain”\ndays. The 5 mm/day threshold is physically relevant: it is the median daily rainfall during 2001-2022\nin GPM-IMERG in the humid heatwave season in regions with humid heatwaves (Figure 1). We\ninterpret the threshold as representing above average rainfall which is sufficiently heavy to promote\nevaporation.\nOur study focuses on the global tropics and subtropics, emphasising processes operating at these\nlarge scales. While region-specific thresholds might enhance results in certain areas, they would\ncomplicate direct comparisons between different regions. By using a single threshold of 5 mm/day,\nwe maintain consistency and comparability across the global tropics and subtropics. Despite using a\ncommon threshold for all regions, we find our results to be robust and compelling at the scale of our\nanalysis.\nWe have added more justification for the 5 m/day threshold in the methods section of the\nmanuscript. We present the results of sensitivity tests using different rainfall thresholds in Figure S6.\nR2-29. 477: It would be beneficial if the authors could make their code publicly available.\nWhile we understand the value of sharing code, we have decided not to make our code publicly\navailable for this study because there is no novel methodology in our code. The analysis relies on\nstandard data processing techniques and established statistical methods, which are implemented\nusing widely available Python packages. For the calculation of wet-bulb temperature, we used the\nestablished method of Davies-Jones and Python code published by Raymond. For the identification\nof heatwave events, we used a 3D-connected components algorithm published in Python by\nSilversmith. Replicating the analysis should be straightforward using the details provided in the\nmanuscript.\nDavies-Jones, R. An efficient and accurate method for computing the wet-bulb temperature along\npseudoadiabats. Monthly Weather Review 136, 7, 2764-2785 DOI: 10.1175/2007MWR2224.1 (2008).\nRaymond, C. https://github.com/cr2630git/wetbulb_dj08_spedup, accessed 16 October 2023.\nSilversmith, W. connected-components-3d-3.12.1, https://pypi.org/project/connected-components-\n3d/, downloaded 15 January 2024.\nThis paper investigates the rainfall controls on daily humid heatwaves across the globe using gridded\nmeteorological records by contrasting two regimes, the moisture-limited versus the energy-limited\nenvironment conditions.\nR3-44. The work employs re-analysis based meteorological input, which itself has bias especially in\narid region in capturing humidity term. Though sparse coverage in certain data constraint areas of\nthe globe, a validation through observational records is required to claim robustness of obtained\nresult.\nWe have validated our analysis using hourly station observations from the HadISD dataset. In a new\nfigure, Figure S2 in supplementary information, we compare daily mean wet-bulb temperatures\nfrom station observations and ERA5 grid cells with which the stations are “paired”. We show\nseparate results for the three heatwave-rainfall regimes identified in this study and for the\nremaining stations at which the local heatwave-rainfall relationship is not statistically significant at\nthe 95% confidence level. There is a substantial degree of overlap of the confidence intervals for the\nstation and ERA5 composite time series. Further, important features of the ERA5 results are also\npresent in the station observations:\n1. The marked increase in wet-bulb temperatures (on day -1 and day 0);\n2. The greatest increase in wet-bulb temperatures occurs in Regime 1;\n3. The highest absolute wet-bulb temperatures occurs in Regime 2; and\n4. The subsequent decrease in wet-bulb temperatures (from day +3).\nWe conclude that the results of Figure S2 validate both the wet-bulb temperatures derived from\nERA5 data and the heatwave-rainfall relationships characterised by Regimes 1-3.\nWe have added a paragraph to the Discussion section summarising the rational for this validation\ntest and our findings. We have added a section in Supplementary Information summarising the\nmethods we used.\nWe have repeated the comparison of ERA5 and HadISD station observations for 2m temperatures to\ncheck that the results for Twb are not masking large opposing errors in 2m temperatures and\nhumidity. Reassuringly, there is a substantial degree of overlap of the confidence intervals for the\nstation and ERA5 composite time series (Figure RR2).\nFor rainfall in our analysis, we used GPM-IMERG, a satellite-based observational product. We also\ntested its consistency with ERA5 precipitation. The relative risk results using ERA5 precipitation\n(Figure S7a) align closely with those obtained using GPM-IMERG precipitation (Figure 2a).\nfrom 7 days before the start of each heatwave (day -7) to 7 days after the start of each heatwave\n(day 7). Day 0 is the heatwave start day. The number of stations with sufficient data in each rainfall-\nheatwave regime is shown in the top right of each panel.\nMy specific comments on the manuscript are below:\nR3-30. 1) Line 51: Other than irrigation, proximity to the coast, see ref.2.\nThank you for highlighting the work of Ganguli and Merz (2024). We have included a sentence\ndescribing the role played by proximity to the coast in the relationship between humid heat and\nrainfall.\nR3-31. 2) Line 57: “regional scale” could be elusive, for example, spatial heterogeneity could be very\nprominent within a continental or national scale.\nWe agree that spatial heterogeneity can be very pronounced at continental or national scales. In our\nstudy, we use the term 'regional scale' to refer to areas smaller than the tropical and subtropical\ndomains. We argue that the processes underlying humid heatwaves at the regional scale may not\nnecessarily generalise to the broader tropical/subtropical scales, which underscores the value of\nconducting a global study focused on the tropics and subtropics.\nWe have amended the sentence to make clear the distinction between regional scales and the global\ntropics and subtropics.\nR3-32. 3) Line 69 and elsewhere (for example, Fig. 1 caption line 126): The paper revolves back and\nforth between 90th percentile and 95th percentile of threshold selection in their write-up. The\nchoice of threshold selection is not kept uniform throughout the paper.\nFigure 1c, we now use the 95th percentile instead of the 90th percentile to represent the intensity of\nhumid heatwaves. We have added 95% confidence intervals to Figures 3 and 4. In Figure 5, we now\nuse the 95th percentile instead of the 90th to identify the extreme heatwave events (see R1-16).\nR3-33. Also, they have used daily mean temperatures, whereas the daily maxima temperature\nshould be used for heatwave analysis. This is because daily mean does not consider the abrupt rise\nfor few hours, which can have fatal consequences for the exposed livelihoods\nWe believe that the choice of using daily mean temperatures or daily maximum temperatures\ndepends on the purpose of the study. We concluded that daily mean temperature rather than daily\nmaximum temperature is the most appropriate for this study. It captures the effects of both daytime\nheating and night-time cooling which are important for a study of processes at daily timescales. In\nterms of exposure to heat stress, daily mean temperatures capture accumulative exposure over\nlonger periods than daily maxima and, importantly, it includes night-time temperatures which can\nmake a substantial contribution to heat stress. In studies of the relationship between temperature\nand human health, daily mean temperatures are often used because they can provide robust results\nthat are more easily interpreted in a policy context (Yang et al., 2012).\nThe reviewer makes a valid point, however. Heatwave definitions are frequently based on daily\nmaximum temperatures and the most acute impacts of heat stress are often related to daily\nmaximum temperatures. We have, therefore, repeated our analysis using daily maximum wet-bulb\ntemperatures. The methods used are identical to those we used for daily mean temperature except\nthat the minimum threshold was changed from 24°C to 24.75°C to approximately maintain the same\nnumber of heatwave days. We show the principle results in Figure S8 (which is equivalent to Figure 2\nin the main manuscript) and Figure RR3 (which is equivalent to Figure 3a). The use of daily maximum\ntemperature does not change the key results or conclusions of our study although the proportion of\ngrid cells with statistically significant results is lower than for results based on daily mean\ntemperatures.\nFigure RR3. Reproduction of Figure 3a in the main manuscript but using daily maximum instead of\ndaily mean wet-bulb temperatures.\ncomment on our supplementary results using daily maximum Twb.\nYang, J., Ou, CQ., Ding, Y. et al. Daily temperature and mortality: a study of distributed lag non-linear\neffect and effect modification in Guangzhou. Environ Health 11, 63 (2012).\nhttps://doi.org/10.1186/1476-069X-11-63.\nR3-34. 4) Line 94: Fig. 1A shows Himalayan region still experience very high frequency of humid\nheatwaves.\nWe have amended the text to refer to “areas within the Himalayan region …”.\nR3-35. 5) Line 97: regions with longest and persistent heatwaves are also experienced by desert\nareas of South Asia\nWe have updated Figure 1b to show the median heatwave durations (instead of mean durations)\nand have amended the accompanying text accordingly. The median duration is more representative\nof regional heatwave durations. A few long heatwaves in some locations greatly inflates the mean\nduration (e.g. near the eastern coast of South America).\nWe have updated the text to describe more precisely regional differences in humid heatwave\ndurations.\nR3-36. 6) Line 117: regional differences are expressed in a qualitative manner rather than\nquantitative ways.\nWe have amended the text to state explicitly that the comparison is qualitative. We have not\nupdated Figure 1f to present a more quantitative comparison because, as explained in the first\nparagraph of the section “Rainfall variability as a driver of humid heatwave occurrence”, we\nsubsequently proceed to present a quantitative analysis on daily timescales.\nR3-37. 7) Line 136: 5 mm/d rainfall threshold? Any references for heavy/moderately heavy rainfall?\nWe selected a threshold of 5 mm/day for enhanced rainfall days because that threshold produced\nthe clearest results for the relative risk of heatwaves occurring on “High_Rain” versus “Low_Rain”\ndays. The 5 mm/day threshold is physically relevant: it is the median daily rainfall during 2001-2022\nin GPM-IMERG in the humid heatwave season in regions with humid heatwaves (Figure 1). We\ninterpret the threshold as representing above average rainfall which is sufficiently heavy to promote\nsurface evaporation.\nIn the manuscript, we have amended the discussion on rainfall thresholds to include this additional\nexplanation and interpretation. We have also included additional explanation in the methods\nsection.\nR3-38. 8) Line 215: How these composites are constructed? Is it spatial average across all grid\npoints?\nGrid cell heatwave composites are constructed by averaging daily mean time series spanning 7 days\nbefore to 7 days after the start of each heatwave. For grid cells where the heatwave-rainfall\nrelationship is statistically significant (Figure 2), the composites are grouped into the regimes shown\n15\nin Figure 2d. The composite for each regime is then calculated as the average of grid cell composites\nwithin that regime.\nWe have added text to the beginning of the results sub-section “Contributions of temperature and\nhumidity to humid heatwaves” to provide a more detailed explanation for the reader.\nRegime composites are calculated by averaging the values of grid cells within each regime, without\napplying area weighting to individual grid cells. Since our analysis focuses on the characteristics of\neach regime rather than on contiguous geographic regions within those regimes, area weighting was\nnot used. We tested the effect of area weighting, however, and found its impact to be negligible\n(Figure RR4).\nFigure RR4. Heatwave composite time series from 7 days before the start of each heatwave (day -7)\nto 7 days after the start of each heatwave (day 7). Day 0 is the heatwave start day. Solid lines show\ndaily mean values as presented in Figure 3 of the manuscript (i.e., with no area weighting of grid\ncells). Crosses show the equivalent values when the grid cells in each regime are area weighted.\nR3-39. 9) Humid heat is often controlled by surface evaporation3,4, however, the role of surface\nevaporation is not investigated among list of drivers in Fig. 4.\nWhile we do not explicitly use the term \"surface evaporation,\" we investigate its role through\nsurface latent heat fluxes, which are equivalent but expressed in terms of energy flux rather than\nmoisture flux. We prefer to show the surface latent heat flux because it provides consistency with\nother terms in the surface energy budget investigated in Figure 4; namely the sensible heat flux and\ndownwelling radiation fluxes.\nR3-40. 10) In Discussion: Lines 342-347: In Fig. 3SD: for south America and vast stretches of\npeninsular India, both with a strong tropical climate, no significant regime were identified, which is\nelusive.\nin regions such as South America, peninsular India, and the southeast coast of the US, despite their\ntropical climate. There are several potential reasons for this outcome:\n Insufficient Heatwave Events: In some regions, the number of heatwave events may be too\nsmall for the underlying signal to emerge from the noise introduced by sub-seasonal and\ninter-annual variability. This can hinder statistical significance despite the presence of\nphysical processes linking heatwaves and rainfall.\n Regional Variability in Heatwave-Rainfall Relationships: The specific heatwave-rainfall\nrelationships identified in many regions may not prevail universally. It is plausible that, in\nsome locations, other processes dominate the dynamics of humid heatwaves, leading to\nweaker or different associations with rainfall.\n Seasonal Cycle Effects: The relationship between heatwaves and rainfall may vary at\ndifferent times in the seasonal cycle. For example, in parts of peninsular India, the local\nenvironment may be moisture-limited during the pre-monsoon period but energy-limited\nafter the onset of the monsoon. This seasonal variation could obscure consistent heatwave-\nrainfall associations when analysed over the entire season. Additionally, in some regions,\nsuch as parts of India, central Africa, and South America, our analysis shows that the humid\nheatwave season spans several months. This extended season further increases the\nlikelihood of intra-seasonal variations in heatwave dynamics, which may dilute the statistical\ncoherence of a single relationship over the entire period.\nAlthough the reviewer raised this point in relation to Figure S3 in the supplementary information, it\napplies equally to our main results in Figure 2. Consequently, we have updated the paragraph\ndiscussing our Figure 2 results in the Discussion section to address these issues in greater detail.\nR3-41. 11) Line 359: Choice of 24℃, as a fixed threshold could be erroneous without considering\nseasonality of humid heat across the globe. A daily variable threshold with a moving window\napproach should be considered to account for the seasonality. On page 20, Methodology, they have\nhighlighted pitfalls of using running mean by citing Brunner & Voigt. But the reference never\nrecommends using constant thresholds but rather they recommend for shortening window lengths.\nWe appreciate the reviewer’s comment, which highlights the need for clearer explanation of how\nhumid heatwaves are defined in the main text. To summarise, we use the local 95th percentile of\ndaily mean Twb, with an absolute minimum of 24°C, to capture humid heat events that are both\nhigh for the locality and to exclude events that are unlikely to pose a threat to human health. The\n95th percentile of daily mean Twb is calculated locally for each grid cell, accounting for regional\nvariations, and is based on all days of the year, inherently capturing the seasonal cycle.\nWhile the methods section provides a detailed definition, we recognise that additional context in the\nintroduction and discussion sections would help ensure the approach is clear to readers. To address\nthis, we have revised the introduction to briefly summarise the definition of humid heatwaves and\nclarified the paragraph in the discussion section where the reviewer’s comment highlighted this\nissue.\nR3-42. 12) Different Heat indices (HI) use different formulations and are not in agreement with each\nother. Further, the most widely use HI by Rothfusz is based on polynomial approximation. In their\npaper, they have neither discussed which approach was followed for Heat index calculation nor the\npitfalls of such an index.\nreference to the specific formulae. In the discussion section, we now discuss the limitations of Twb\nas a measure of human heat stress in greater detail.\nIn summary, I can’t recommend that this manuscript to be accepted by NComm.\nWe appreciate the time and effort you have taken to review our manuscript. We hope that the\nrevisions made to the manuscript, in response to comments from all three reviewers, have\nsubstantially improved its clarity, robustness, and overall contribution to the field.\nReferences\n1. Raymond, C., Matthews, T. & Horton, R. M. The emergence of heat and humidity too severe for\nhuman tolerance. Sci. Adv. 6, eaaw1838 (2020).\n2. Ganguli, P. & Merz, B. Observational Evidence Reveals Compound Humid Heat Stress-Extreme\nRainfall Hotspots in India. Earths Future 12, e2023EF004074 (2024).\nR3-43. 3. Bu, L., Zuo, Z., Zhang, K. & Yuan, J. Impact of Evaporation in Yangtze River Valley on Heat\nStress in North China. (2023) doi:10.1175/JCLI-D-22-0573.1.\nThank you for drawing this paper to our attention. We have included a reference to it in the\ndiscussion section.\n4. Zhang, Z. et al. Light rain exacerbates extreme humid heat. Nat. Commun. 15, 7326 (2024)\nR3-44. See the top of page 15.\nReviewer #1 (Remarks to the Author):\nI thank the authors for their thorough responses to my comments, including their extended\ndiscussion of how these results fit into currently published literature.\nWe thank the reviewer for considering our responses and providing additional comments. Our\nresponses to your specific comments are set out below.\nMy final suggestion for the paper relates to the use of the term \"humidity\" throughout the text.\nSome of the confusion in my initial reading was associated with assuming the authors were\ndiscussing relative vs. specific humidity, when they meant the opposite. I would suggest that the\nauthors should change all mentions of general \"humidity\" to \"relative humidity\" or \"specific\nhumidity,\" where appropriate.\nWe have revised the manuscript to address the reviewer's comment by specifying \"specific\nhumidity\" when discussing Figure 3 and \"relative humidity\" when referring to Figure 5, as these\nterms more accurately reflect the variables depicted in these figures. We have left other uses of the\nterm \"humidity\" unchanged, as we believe its general usage is more appropriate in those contexts.\nAdditionally, in several instances, we adhere to the terminology used in the literature we cite, where\n\"humidity\" is used in a broader sense.\nI believe that all of my other comments have been addressed.\nThe revised paper has addressed and clarified several of my comments. However, there are a few\nminor issues, which can be addressed easily:\nWe thank the reviewer for considering our responses and providing additional comments. Our\nresponses to your specific comments are set out below.\n1) Regime 1 and Regime 2, show distinct differences in wet-bulb temperatures in HadISD\nobservations relative to ERA5 (Figure RR2). While Regime 1 shows substantial differences within the\ntime window t ∈ (-1,5)-day, Regime 2 shows substantial differences across all time lags and leads,\nwith ERA5 largely underestimate at-site measurements. This should be highlighted as caveats in the\ndiscussion section. Also, possible physical mechanisms behind this underestimation should be\ndiscussed.\nTo address the reviewer’s comment, we have added a paragraph to the Discussion section and\nadded the relevant figure to Supplement Information (previously it was only disclosed in the\nresponse to reviewers). The additional text is quoted below:\n“A comparison of ERA5 reanalysis and the HadISD 2m temperature dataset shows broad agreement,\nalthough ERA5 exhibits a cold bias in both Regimes 1 and 2. This bias may result from factors such as\nthe averaging of ERA5 grid cell temperatures versus station point measurements, elevation\ndifferences, unresolved local topography48, and the influence of land use/land cover on station\nobservations. Additionally, ERA5 has been shown to underestimate daily maximum temperatures\nand extremes in some regions49,50. Unlike Regime 1, the cold bias in Regime 2 is consistent across all\nlead-lag times. Regime 2 primarily occurs in moist tropical environments and in one such\nenvironment, tropical oceans, ERA5 has been found to underestimate temperatures and\noverestimate humidity, possibly due to deficiencies in relative humidity-dependent entrainment51.\nThis mechanism could potentially contribute to the consistent bias in Regime 2.”\n2) The authors have not discussed the limitations of using Rothfusz's formulation in defining heat\nindex, which is largely based on assumptions of polynomial approximation in its calculation, rather\nthan physiological limits for withstanding heat stress, and its possible influence in their findings\nWe have revised the manuscript to address the reviewer's comment by including discussion of\nlimitations in the Rothfusz formulation in the relevant paragraph of the Discussion section. The\nrevised paragraph is quoted below:\n“Although an assessment of human heat stress is beyond the scope of this study, we recalculated\nrelative risk using the Rothfusz formulation of the Heat Index (Figure S8c) and also 2m dry-bulb\ntemperature (Figure S8d) to contextualise our results using two widely used temperature metrics. In\nenergy-limited regions where heatwaves are more likely to follow suppressed rainfall, we obtain\nsimilar but more strongly significant results using the Heat Index or 2m dry-bulb temperature. In\ncontrast, in moisture-limited regions the strength of the relationship between heatwaves and rainfall\nis much weaker. This supports our choice of Twb for this study and highlights differences in the\nsensitivity of different heat stress measures to humidity58,25,20. The Rothfusz formulation for the Heat\nIndex is an empirical polynomial approximation based on Steadman’s physiological data59,60 and is\nnot a comprehensive model of human heat tolerance. Its validity is limited under extreme\ntemperature and humidity conditions, particularly beyond its original dataset61,62. Furthermore, both\nthe Rothfusz Heat Index and 2m dry-bulb temperature overlook factors such as incoming solar\nradiation and variations in wind speed, which are critical in outdoor environments55.”\n2"}]

Decision letter