Introduction

The tropics are home to ~40% of the world’s population and 80% of global biodiversity1,2. By 2050, tropical land is predicted to host most of the world’s people and two-thirds of its children2. As the tropics are already warmer than any other region in the world, any further warming may significantly affect its habitability. This could especially affect low-income and lower-middle-income countries as these are mostly located in the tropics. Although the human-induced warming rate in the tropics is generally smaller than the higher latitudes, the anthropogenically forced signal may emerge earlier from the observation3,4,5 considering the weaker inter-annual variability in the tropics. These motivate an examination of how the tropical climate responds to global warming and whether the forced signal has already emerged in the historical period.

Influenced by the seasonal cycle of solar radiation, precipitation and temperature are closely linked over tropical land throughout the year. As the sun crosses the Equator, the hemisphere experiencing spring heats up rapidly, causing the temperature to rise until the onset of monsoon rainfall, which helps to mitigate the summer heat. Hence, spring is usually the hottest season over tropical land and the timing of monsoon onset has large impacts on how hot the land can get. At the inter-annual time scale, there is a tight relationship between the monsoon onset and spring temperature over the Indian monsoon region6,7. That is, a monsoon onset delay is accompanied by a warmer spring. This tight relationship between precipitation and temperature is also found in South America8,9,10. Hence, the future change in the monsoon onset is important for the temperature change during spring. In a warming climate, previous studies have identified a significant seasonal delay of tropical rainfall11,12, mainly over tropical land monsoon regions13,14,15,16. If the tight relationship between precipitation and temperature still holds under global warming, we may expect higher-than-the-annual mean warming in spring, which is already the hottest season over tropical land. This will be one of the focuses of this study.

Regarding the seasonal delay of tropical rainfall, two views have prevailed17. The first one argues that under global warming, the effective atmospheric heat capacity is enhanced due to the nonlinear dependence of moisture on temperature under the Clausius–Clapeyron relation, which delays the response of tropical rainfall to the seasonal solar forcing as the atmosphere needs more time to accumulate the energy for the monsoon onset. This view emphasizes the role of enhanced moisture demand in the wet season onset under global warming12,13,15,16,18, which can be met via either local evaporation or remote transport. The remote transport would involve large-scale circulation as discussed in many previous studies11,19,20. The other view argues that under global warming, as the dry season gets drier11,21, the soil moisture in the following spring would decrease, so more time is needed for the soil moisture to replenish to support evapotranspiration that enhances the low-level moist static energy (MSE) to meet the convection threshold, thus delaying the onset of wet season22,23,24. This “enhanced convective barrier” mechanism emphasizes the role of reduced moisture sources in the wet season onset under global warming. It is important to note that moisture will be required for the wet season onset in the two views, which can either be provided locally through evapotranspiration or from remote regions. The relative importance of the two views on the rainfall delay remains to be reconciled, which is crucial for understanding the temperature changes over tropical land. This will be the second focus of this study.

A recent study developed a quantitative theory based on convection coupling to explain the amplified warming over tropical land25. It concluded the amplified warming in the hot days over tropical land is linked to the concurrent dry condition of the high-percentile temperature and decreased humidity changes under global warming25. This provides important guidance for understanding the temperature changes over tropical land. Following this, here we aim to examine seasonal warming over tropical land and how it links to seasonal delay of rainfall under global warming. Since there is a higher chance for spring to experience the high-percentile temperature over tropical land, it is pertinent to examine whether the amplified warming of the high-percentile temperature is tied to the seasonal changes in the temperature and precipitation. Here, by combining the climate simulations from the Coupled Model Intercomparison Project Phases 526 and 627 (CMIP5 and CMIP6, see “Model simulations” in Methods), we find that the amplified high-percentile temperature over tropical land is closely linked to the amplified spring warming. We refer to the amplified spring warming as a hot-season-gets-hotter regime. As an evident phenomenon over tropical land under global warming, this hot-season-gets-hotter phenomenon is found to be associated with the seasonal delay of rainfall, i.e., decreased rainfall in spring. Model experiments with fixed soil moisture further reveal that rainfall delay under global warming is initially driven by the enhanced atmospheric heat capacity, then substantially amplified by the soil moisture-atmosphere feedback. During the satellite period, the hot-season-gets-hotter phenomenon has already emerged in the Amazon and Southern Africa, with far-reaching implications for human society and the ecosystems.

Results

The hot season gets hotter due to the rainfall delay under global warming

Here, we utilize the historical and high radiative forcing scenarios (RCP8.5 for CMIP5 and SSP585 for CMIP6) from 30 CMIP5 models and 27 CMIP6 models to represent current and future climates and their differences as the changes under global warming (see “Model simulations” in Methods). Figure 1 shows the annual cycle changes of rainfall and daily-maximum surface air temperature (TX) over tropical land under global warming. Here, TX, defined as the highest temperature recorded at a height of 2 meters across a day, is used as it is more influenced by the changes in the solar radiation, but the results from surface air temperature are consistent with TX (Supplementary Fig. 1). Climatologically, rainfall peaks in the local summer in both hemispheres (Fig. 1a, b), while temperature peaks in the local spring before the onset of wet season and once the wet season starts, temperature decreases (Fig. 1d, e). Under global warming, the local spring receives less rainfall but the local autumn receives more rainfall (Fig. 1a, b), featuring an evident seasonal delay of tropical rainfall as previously noted11,12,13. It is found that there are high inter-model correlations between phase changes of rainfall annual cycle and local spring rainfall changes (0.89 and 0.78 in the northern and southern tropical land, respectively, Supplementary Fig. 2), suggesting the local spring rainfall change is a good indicator of the rainfall delay. Corresponding to the seasonal delay of tropical rainfall, the local spring sees the maximum temperature increases across the year in both hemispheres under global warming (Fig. 1d, e). As the local spring is the hottest season, the increase in the temperature would make the hot season even hotter, which we refer to as the “hot-season-gets-hotter” regime. Regionally, the seasonal delay of rainfall and hot-season-gets-hotter phenomena are evident in almost all tropical land monsoon regions (except northern Australia and northern South America) and are most evident in the Amazon (Fig. 1c, f). This suggests this is a common feature in the tropical land monsoon regions, also consistent with a recent finding of a widespread seasonal delay of rainfall across different monsoons under global warming16. There is also a high spatial correspondence between the seasonal delay of rainfall and hot-season-gets-hotter phenomena, with a pattern correlation of −0.68 (Fig. 1c vs. f). Moreover, there exists a significant inter-model relationship between local spring precipitation changes and temperature changes, with correlations of −0.64 and −0.70 in the northern and southern tropical land respectively (Fig. 1g, h). That is when one model exhibits a stronger rainfall delay under global warming, it would also project a stronger hot-season-gets-hotter phenomenon.

Fig. 1: Changes of precipitation and daily-maximum surface air temperature (TX) annual cycles over tropical land under global warming.
figure 1

a, b Future changes (bars), current (solid line), and future climatology (dashed line) of the annual cycle of precipitation with annual mean changes removed over northern tropical land (NTL) (0°–25°N, a) and southern tropical land (STL) (0°–25°S, b). c Spatial distribution of the changes in precipitation during local spring (April–May–June (AMJ) in the northern hemisphere and September–October–November (SON) in the southern hemisphere) with annual mean changes removed. d–f As in a–c, but for TX. The spatial correlation coefficient between c and f is displayed in the upper right of f. Error bars denote the 25th and 75th of changes among the multimodel ensembles. Diagonal lines in the colored bars of a, b, d, e indicate significance at the 95% confidence level based on a two-sided Student’s t test. Stippling in c, f indicates at least 70% of the models agree on the sign of changes. g, h Inter-model relationship between relative spring changes (annual mean changes subtracted) of precipitation and TX over the NTL (g) and the STL (h). A linear fit (solid black line) is displayed together with the correlation coefficient R and the corresponding P value.

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To illustrate how the seasonal delay of tropical rainfall leads to the hot-season-gets-hotter phenomenon, the detailed physical processes are examined through surface energy flux analysis. It is found that surface energy fluxes are closely tied to the seasonal delay of tropical rainfall (Supplementary Fig. 3): the reduced rainfall in the local spring is tied to the reduced cloud cover, which allows more incoming solar radiation (Supplementary Fig. 4a, c, d). Meanwhile, the reduced rainfall also decreases soil moisture, which reduces latent heat flux (Supplementary Fig. 4b, e, f). Hence, the more incoming shortwave radiation can only be balanced by the more upward longwave radiation and sensible heat flux, both associated with more spring warming. The related mechanisms are also consistent with previous findings20,21. The conclusion still holds when the absolute changes in these variables are considered. Hence, the seasonal delay of tropical rainfall produces the hot-season-gets-hotter phenomenon mainly by increasing the incoming solar radiation due to fewer clouds and decreasing the latent heat flux due to lower soil moisture.

The hot percentile gets hotter due to the amplified spring warming

Along with the hot-season-gets-hotter, we would expect the higher percentile temperature to warm more under global warming, which would favor more occurrences of extreme heat events. To confirm this, we also plot the future changes of different percentiles of temperature (Fig. 2). Clearly, the climatological higher percentile temperatures generally warm more in both hemispheres under global warming (Fig. 2a, b), i.e., “hot-percentile-gets-hotter”. For example, the 99th percentile temperature (TX99p) would warm 14% and 25% more than the 1st percentile temperature in the northern and southern tropical land, respectively. Compared to the mean warming, there is 7.4% and 18.5% more warming for TX99p in the northern and southern tropical lands, respectively. As expected, the enhanced TX99p warming is closely linked to the larger warming in the local spring in both hemispheres (Fig. 2c, d), with inter-model correlations of 0.61 and 0.88 for the northern and southern tropical land, respectively. The regional features of this “hot-percentile-gets-hotter” phenomenon are also examined (Supplementary Fig. 5). The enhanced high-percentile warming is evident in almost all the tropical land, including Mexico, Sahel, India, Indochina Peninsula, Amazon, and Southern Africa. The most evident signal occurs in the Amazon, where the local spring warms by 0.93 K more than the annual mean, and the 99th percentile warms by 29% more than the mean temperature. The hot-percentile-gets-hotter phenomenon is also pronounced in the mid- and long-term from the middle and high emission scenarios over tropical land (Supplementary Fig. 6). The enhanced high-percentile temperature warming is consistent with a previous study25, and here we clearly link it to the seasonal temperature changes, which is found to be caused by the seasonal delay of rainfall as examined above.

Fig. 2: The amplified warming in the hot days is closely linked to the hot-season-gets-hotter phenomenon.
figure 2

a, b Future changes (solid red line) and current simulations (solid purple line) of the xth (1st to 99th) percentile of daily-maximum surface air temperature (TX) averaged over northern tropical land (NTL) (a) and southern tropical land (STL) (b). Shading indicates one standard deviation of inter-model spread. c, d Inter-model relationship between relative changes (annual mean changes subtracted) of local spring (April-May-June in NTL, September-October-November in STL) TX and relative changes of the 99th percentile of daily TX (TX99p) warming over the NTL (c, d). A linear fit (solid black line) is shown together with the correlation coefficient R and the corresponding P value.

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Reconciling the two views on the seasonal delay of tropical rainfall

As the hot-season-gets-hotter phenomenon is mainly due to the seasonal delay of tropical rainfall under global warming, it is important to reconcile the two views mentioned above on the causes of the delay. To compare the relative importance of the two mechanisms, we employ two experiments from a subset of models that participated in the CMIP6 LS3MIP (the Land Surface, Snow and Soil Moisture Model Intercomparison Project)28: one featuring land-atmosphere interactions in fully coupled simulations and the other with soil moisture fixed so that the land-atmosphere coupling through interactive soil moisture is disabled (see “Soil moisture-atmosphere coupling experiments” in Methods). By comparing the two experiments, we can examine the relative importance of the enhanced convective barrier mechanism versus the enhanced effective atmospheric heat capacity in causing the rainfall delay. The former would be present in the fully coupled experiments, whereas the latter would be expected in both experiments. Figure 3 shows precipitation and TX annual cycle changes in these two experiments and their differences. Both the seasonal delay of tropical rainfall and hot-season-gets-hotter phenomena are evident in the fully coupled runs, suggesting these two phenomena are robust, regardless of only a subset of models used here. Interestingly, in the fixed soil moisture experiment, the seasonal delay of tropical rainfall and hot-season-gets-hotter phenomena are still evident, albeit with reduced magnitude. However, the local evaporation is even enhanced in the local spring under global warming due to the enhanced humidity difference between air and land in the fixed soil moisture experiment (Supplementary Fig. 7). Hence, the convective barrier mechanism does not work here. These results are consistent with ref. 18, which found the seasonal delay of rainfall is still evident under global warming in aquaplanet model simulations without the soil moisture-atmosphere feedback. Hence, we conclude that the convective barrier mechanism is not fundamental to the rainfall delay and hot-season-gets-hotter phenomena, but it can amplify the initial signal via positive feedback. Instead, the effective atmospheric heat capacity is largely enhanced in both the fully coupled and fixed soil moisture runs (Supplementary Fig. 8; see “Effective atmospheric heat capacity” in Methods). The enhanced effective atmospheric heat capacity would make the atmosphere more sluggish to the seasonal solar forcing. In other words, the atmosphere needs more time to accumulate the MSE, mostly the latent energy, to meet the monsoon onset criterion12,13. There is also a significant relationship between the changes in the inter-seasonal differences between latent energy tendency and precipitation (Supplementary Fig. 9), suggesting a more fundamental role of the effective atmospheric heat capacity mechanism12,13,15,16 in driving the seasonal delay of rainfall, which induces the hot-season-gets-hotter phenomenon. The difference between the two experiments suggests that the soil moisture-atmosphere coupling can amplify the seasonal delay of rainfall and the hot-season-gets-hotter phenomena by 54% and 46%, respectively, over northern tropical land. Over southern tropical land, the corresponding values are 44% and 52%. In most tropical land regions, the effective atmospheric heat capacity and the convective barrier mechanism contribute almost equally, including Amazon, Southern Africa, and Sahel (Supplementary Fig. 10). In conclusion, the tropical rainfall delay is initially driven by the enhanced atmospheric heat capacity as suggested by refs. 12,15, while substantially amplified by the enhanced convective barrier mechanism, which nearly doubles the initial response. Here, we mainly focus on two prevailing views on the seasonal delay of tropical rainfall. Other factors, such as moisture transport due to local circulation response may also play a role in rainfall over some locations, particularly for islands29,30,31. This warrants further investigation in the future.

Fig. 3: Relative contributions of soil moisture-atmosphere coupling (SA) on the seasonal cycle of precipitation and daily-maximum surface air temperature (TX) over tropical land.
figure 3

a, b Multimodel mean changes (bars), current (solid line), and future climatology (dashed line) of precipitation in the fully coupled experiment (a) and the fixed soil moisture (SM) experiment (b) over northern tropical land (NTL). c SA influence on the seasonal cycle of precipitation calculated by subtracting the values in the fixed soil moisture experiment from those of the fully coupled experiment. d–f As in a–c, but over southern tropical land (STL). g–l As in a–f, but for TX. The ratio values in c, f, i, j indicate the contribution of soil moisture to the seasonal delay (c, f) and the hot-season-gets-hotter phenomenon (i, j) calculated as the local spring changes caused by SA relative to the values in the fully coupled experiment. Error bars represent 25th and 75th percentile of multimodel ensembles. The hatched bars denote significance at the 95% confidence level based on Student’s t test.

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The observed emergence of hot-season-gets-hotter along with rainfall delay

The above investigation into the hot-season-gets-hotter phenomenon and the seasonal delay of rainfall is based on a future warming scenario. It is important to examine whether they have emerged in the historical period, which is challenging due to the short record of good-quality observations, the relatively weak external forcings, and large internal variability. A previous study suggested the seasonal delay of tropical rainfall has already emerged in the satellite period15, so it is natural to inquire whether the hot-season-gets-hotter phenomenon has also emerged, given their causal relationship. To examine this, we employ all available precipitation and temperature observational datasets (see “Observational data” in Methods) and find that enhanced spring warming has already emerged in the Amazon and Southern Africa (Fig. 4), where the response projected under global warming is also the strongest (Fig. 1f). Over the Amazon, the observations show that spring has warmed by 0.47 K more than the annual mean and precipitated −0.14 mm day−1 fewer than the annual mean. Most of the observed changes are accounted for by the multimodel ensemble mean of CMIP (0.37 K and −0.24 mm day−1, respectively, Fig. 4a), which represents the external forcings (including GHGs, aerosols, solar radiation, and volcanic eruptions). This suggests the dominant role of external forces. Over Southern Africa, the external forcing accounts for less of the observed changes: about half of the precipitation changes and one-third of the temperature changes can be attributed to the external forcings. Moreover, the enhanced spring warming is closely tied to the reduced rainfall in spring, with inter-model correlations of −0.69 and −0.68 in the Amazon and Southern Africa, respectively. The reduced rainfall in spring over the recent decades over the Amazon is consistent with previous studies32,33, but here we highlight it is closely tied to the enhanced spring warming and both of them are mainly accounted for by the external forcing.

Fig. 4: Observed emergence of the hot-season-gets-hotter phenomenon along with rainfall delay during 1979–2022.
figure 4

a, b Inter-model relationship between relative spring trends in precipitation and daily-maximum surface air temperature (TX) over the Amazon (0°–20°S, 40°W–80°W, a) and the Southern Africa (8°S–25°S, 10°E–42°E, b). The black dots and stars indicate the average trend of observational datasets and model simulations, respectively. A linear fit (solid black line) is displayed together with the correlation coefficient R and the corresponding P value. Error bars denote one standard deviation of observational datasets and multimodel ensembles.

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The delayed rainfall and hot-season-gets-hotter phenomena would make the future spring drier and hotter, which poses a heightened challenge for local residents’ daily lives and creates more favorable conditions for wildfires. The Standardized Dry and Hot Index (SDHI)34, broadly used to represent the hot and dry climate as an indicator of the weather and climate conditions for the wildfire, is calculated and shown in Supplementary Fig. 11 (see “Standardized Dry and Hot Index” in Methods). The lower SDHI indicates a higher risk for wildfire. One can see that the SDHI becomes significantly lower during spring in the satellite period in the southern tropical land, corresponding to the hotter and drier spring. The SDHI change is well correlated with the decreased rainfall in spring over the southern tropical land, with an inter-model correlation of 0.75 (Supplementary Fig. 11a). Regionally, the SDHI changes are also evident over the Amazon and Southern Africa, which are also closely tied to the rainfall delay (Supplementary Fig. 11b-c). Along with the future amplified rainfall delay and hot-season-gets-hotter phenomena, we would expect harsher living conditions for the populations in the tropics and an enhanced likelihood of wildfire over tropical land.

Under global warming, seasonal delay of rainfall and amplified warming of extreme temperatures are reported over tropical land, which urges us to investigate the possible link between the two. Here, it is found that the warming in the hot season (local spring) would get amplified over tropical land, referred to as the “hot-season-gets-hotter” phenomenon under global warming. The hot-season-gets-hotter phenomenon is also closely tied to the amplified warming in the hot days previously suggested25. The high spatial resemblance and close inter-model relationship between the hot-season-gets-hotter phenomenon and the spring rainfall changes implies a close link between them. The rainfall delay causes the hot-season-gets-hotter by reducing evapotranspiration due to drier soil and increasing incoming solar radiation due to reduced cloudiness. It should be noted that the seasonal delay of rainfall and hot-season-gets-hotter are evident across different warming scenarios and periods. Based on the fixed soil moisture experiments, it is further found that the rainfall delay is initially caused by the enhanced effective atmospheric heat capacity, then substantially amplified by the soil moisture-atmosphere feedback, which nearly doubles the initial response. During the satellite period, the hot-season-gets-hotter phenomenon has already emerged in the observations along with the rainfall delay, mainly evident in the Amazon and Southern Africa.

Drier and hotter springs would create climate conditions unfavorable for humans, but favorable for wildfires, presenting a challenge for the already vulnerable ecosystems in tropical regions. Extreme temperatures are among the most dangerous natural hazards with serious societal impacts35. A recent study found that from 2000–2019 approximately 489,000 heat-related deaths occurred each year36. The projected hot season gets hotter, and the intensification of temperature extremes will undoubtedly escalate the risks of human fatality related to heat waves. As dry and warm conditions will also exacerbate the risks of wildfires37, the intensified hot-dry season would pose huge threats to tropical forests, particularly significant for the Amazon. The strengthened hot-dry season will also increase the risks of drought with severe implications for crop yields and ecosystem services (e.g., ref. 38). These widespread impacts caused by the seasonal rainfall and temperature changes deserve additional attention besides the annual mean changes.

Methods

Model simulations

To detect seasonal delay of tropical rainfall and hot-season-gets-hotter phenomena, we analyze monthly outputs of precipitation and daily-maximum surface air TX from 30 CMIP5 models and 27 CMIP6 models26,27, as listed in Supplementary Table 1. We include most of the available model datasets to enlarge sample sizes. Given the various variables used in our study, some models are not included due to the lack of necessary outputs. We use one realization from each model to compose multimodel ensembles, which contain both CMIP5 models and CMIP6 models. Our results are not sensitive to the number of realizations. All model outputs are interpolated onto a common 2.5° × 2.5° grid.

We use 1986–2005 of historical simulation to represent the current climate, 2080–2099 of the high radiative forcing scenarios (RCP8.5 for CMIP5 and SSP585 for CMIP6) simulation to define the future climate and the difference between the latter and the former to represent the future changes in a warming climate. The RCP8.5 simulations from CMIP5 and SSP585 simulations from CMIP6 have additional radiative forcing of 8.5 W m−2 by 2100, representing the highest range of emission scenarios of CMIP5 and CMIP6, respectively. SSP585 additionally encompasses factors like non-CO2 greenhouse gases, aerosols, and land use changes based on socio-economic development pathways39, but CMIP5 and CMIP6 simulations show very similar results. Furthermore, the RCP4.5 simulations from CMIP5 and SSP245 simulations from CMIP6 are used to examine our results in middle emission scenarios. To estimate the hot-season-gets-hotter phenomenon during the satellite period (1979–2022), we combine historical simulation and high radiative forcing scenarios simulation for each model to compute trends in the recent four decades.

In addition to the monthly TX, daily mean TX from both CMIP5 and CMIP6 models are also utilized to estimate enhanced high-percentile warming. Percentiles in current and future climate are computed by all daily TX averaged over the corresponding tropical land during 1986–2005 and 2080–2099, respectively, consistent with ref. 25. Ninety-nine percentiles of TX between 1st and 99th percentiles are computed for each model. The difference between the xth percentile of TX (TXxp) in the future and that in the current is defined as the future changes of TXxp.

Observational data

To estimate seasonal delay of tropical rainfall in the satellite period (1979–2022), we use the following five precipitation datasets: (1) the Climate Prediction Center (CPC) merged analysis of precipitation dataset (CMAP) with a 2.5° grid40; (2) the Global Precipitation Climatology Project dataset (GPCP) with a 2.5° grid41; (3) CPC global unified gauge-based analysis of daily precipitation (CPC)42; (4) Climatic Research Unit gridded Time Series version 4.07 (CRU v.4.07) with a 0.5° grid43; (5) the Precipitation Reconstruction over Land dataset with a 2.5° grid44. We also use three observational datasets to detect the observed hot-season-gets-hotter phenomenon, including the monthly-mean TX from (1) the Climate Prediction Center global daily surface air temperature dataset (CPC) with a 0.5° grid45; (2) Berkeley Earth monthly temperature dataset (BEST) with a 1° grid46, as well as (3) CRU v.4.0743. Monthly CPC datasets are obtained by averaging daily values. To compute observational Standardized Dry and Hot Index, we use five precipitation datasets described and following three near-surface air temperature: (1) CRU v.4.0743; (2) BEST46; (3) HadCRUT5 data with a 5° grid47. All observation datasets used in this study are interpolated onto a 2.5° × 2.5° grid to form observation ensembles.

Soil moisture-atmosphere coupling experiments

We use the Land Feedback Model Intercomparison Project with prescribed Land Conditions (LFMIP-pdLC) experiment (1980–2099) in the Land Surface, Snow and Soil Moisture Model Intercomparison Project (LS3MIP) to analyze the impact of soil moisture-atmosphere feedback28. LS3MIP simulations are only available from seven CMIP6 models (CESM2, CMCC-ESM2, CNRM-CM6-1, EC-Earth3, IPSL-CM6A-LR, MIROC6, MPI-ESM1-2-LR) so far. Meanwhile, not all the models provide the necessary variables, but we use all the models with the needed data in the corresponding analyses. See Supplementary Table 1 for the details. The LFMIP-pdLC experiment is performed by fixing the soil moisture based on the climatological annual cycle for the period 1980–2014 derived from historical simulation outputs of the corresponding CMIP6 model. In this study, we use the r1i1p1f2 member in the LFMIP-pdLC experiment, in which the external forcings are consistent with the historical (1980–2014) and the SSP585 (2015–2099) simulations except for fixing the soil moisture. Therefore, the difference between the fully coupled experiments (historical and SSP585 simulations) and the fixed soil moisture experiment (LFMIP-pdLC experiment) represents the soil moisture-atmosphere coupling effects. This experiment has been widely used in recent studies to diagnose the role of land-atmosphere feedback on air temperature response in climate change48,49,50.

Effective atmospheric heat capacity

Increased effective atmospheric heat capacity (\({C}_{A}\)) contributes to the seasonal delay of tropical rainfall. To determine the \({C}_{A}\) increases in both fully coupled and fixed soil moisture experiments, following refs. 13,51, we calculate \({C}_{A}\) as:

$${C}_{A}=\frac{\partial \, < \, h \, > \, /\partial t}{\partial \, < \, T \, > \, /\partial t}$$
(1)

where the angle bracket denotes vertical integration between surface and top of the atmosphere. \(h={c}_{p}T+{gz}+{L}_{v}q\) is MSE, \({c}_{p}\) is specific heat of dry air at constant pressure, \(T\) is air temperature, \(g\) is gravity acceleration, \(z\) is geopotemtial height, \({L}_{v}\) is latent heat of vaporization, \(q\) is specific humidity and \(t\) is time.

Standardized dry and hot index

The precipitation delay and hot-season-gets-hotter phenomena may induce compound dry and hot events over tropical land in a warming climate. To evaluate the severity of compound dry and hot conditions, we use the SDHI34, which can be expressed as:

$${SDHI}={\varPhi }^{-1}\left\{F\left[\frac{{G}_{1}(P)}{{G}_{2}(T)}\right]\right\}$$
(2)

where \(\varPhi\) is the standard normal distribution, \(F\) is the marginal cumulative distribution, which transforms the joint probability into the uniform distribution, \({G}_{1}(P)\) and \({G}_{2}(T)\) are the marginal probabilities of precipitation and near-surface air temperature, respectively. Marginal distribution functions (\(F\), \({G}_{1}\), \({G}_{2}\)) can be fitted based on the Gringorten plotting position formula52: \({GF}=\left(i-0.44\right)/\left(n+0.12\right),\) where \(i\) is the rank of the data in the series sorted from the smallest to the largest values, \(n\) is the length of the series.