Future increase in compound soil drought-heat extremes exacerbated by vegetation greening

Abstract

Compound soil drought and heat extremes are expected to occur more frequently with global warming, causing wide-ranging socio-ecological repercussions. Vegetation modulates air temperature and soil moisture through biophysical processes, thereby influencing the occurrence of such extremes. Global vegetation cover is broadly expected to increase under climate change, but it remains unclear whether vegetation greening will alleviate or aggravate future increases in compound soil drought-heat events. Here, using a suite of state-of-the-art model simulations, we show that the projected vegetation greening will increase the frequency of global compound soil drought-heat events, equivalent to 12–21% of the total increment at the end of 21st century. This increase is predominantly driven by reduced albedo and enhanced transpiration associated with increased leaf area. Although greening-induced transpiration enhancement has counteracting cooling and drying effects, the excessive water loss in the early growing season can lead to later soil moisture deficits, amplifying compound soil drought-heat extremes during the subsequent warm season. These changes are most pronounced in northern high latitudes and are dominated by the warming effect of CO₂. Our study highlights the necessity of integrating vegetation biophysical effects into mitigation and adaptation strategies for addressing compound climate risks.

This study finds that vegetation greening is expected to exacerbate compound soil drought-heat extreme events, as enhanced transpiration during the early growing season depletes soil moisture leading to deficits in the subsequent warm season.

Introduction

Occurrences of compound soil drought-heat events, i.e., co-occurring low soil moisture and high-temperature extremes, have caused extensive crop failures, wildfires, ecosystem carbon losses, and even human mortality worldwide, posing a growing threat to human society and ecosystem resilience^1–4. Compound soil drought-heat conditions are projected to increase in many regions during the 21^st century, with important socio-ecological impacts^5–7. Given the myriad of consequences, compound soil drought-heat events have gained significant attention from the scientific community, with particular focus on temporal and spatial variations^8,9, mechanisms related to land-atmosphere interactions^10,11, and the impacts on biophysical and biogeochemical processes¹². However, a quantitative understanding of how long-term vegetation changes might impact the occurrence of compound soil drought-heat events is lacking.

Changes in vegetation cover, productivity and water use have multiple impacts on climate, through modifying key surface biophysical properties such as transpiration and albedo¹³ (Figs. 1a and Supplementary Fig. 1). These impacts can be categorized as both positive and negative climate feedbacks. For example, the projected increase in vegetation activity and extension of growing seasons can enhance transpiration, effectively dissipating extra heat and cooling the land surface^14–16. In contrast, a denser vegetation canopy can absorb more heat into the land by reducing albedo, thereby warming the land surface¹⁷. Additionally, enhanced plant transpiration may accelerate soil drying and facilitate the occurrence of droughts^18,19. Such effects may also propagate from previous seasons to later seasons through soil moisture memory effect^20,21. As changes in compound soil drought-heat events are induced by variations in multiple drivers and their dependencies, the effects of vegetation on such events involve complex interactions among the aforementioned processes, which act either in synergy or counteractively. Moreover, while current attribution frameworks for univariate events provide useful insights, they cannot connect the multi-directional processes underlying vegetation effects or quantify compounding characteristics²². These complexities pose a major challenge in quantifying the risk of future compound soil drought-heat events associated with plant biophysics.

Fig. 1. Schematic diagram for quantifying changes in the likelihood of compound soil drought-heat events attributed to vegetation biophysics.

a Illustration of the effects of plant transpiration (Tr) and albedo (α) on compound soil drought-heat events through regulating temperature (Ta) and soil moisture (SM). For a comprehensive description of the processes involved, please refer to Supplementary Fig. 2a. b–c The hypothetical change in the likelihood of compound soil drought-heat events (shift of the bivariate distribution from gray to red) arising from a shift in the trend while holding the variability and dependence constant (b) and a shift in the variability and dependence while holding the trend constant (c). The black solid line in the upper left corner indicates a threshold assumed to be constant for both present and future climate conditions. Schematically, the likelihood of a compound soil drought-heat event (represented by LMF) represents the ratio of the area bounded by the red and black lines to the area enclosed by the gray and black lines.

Here, we develop a framework to quantify the likelihood changes of compound soil drought-heat events from 1850-2100 and attribute these changes to transpiration (Tr) and albedo (α) effects, which are the two key land surface properties²³ through which vegetation regulates the land water and energy balance and thus air temperature (Ta) and soil moisture (SM)^14,24. The compound soil drought-heat events are identified as co-occurring low SM and high Ta over the warm season (the climatologically hottest three consecutive months), which overlaps with the main growing season when plants are most active. By employing 17 state-of-the-art Earth system models (ESMs) from the Coupled Model Intercomparison Project Phase 6 (CMIP6) which incorporate current knowledge of various land processes²⁵, we characterize changes in the frequency of compound soil drought-heat extremes using the likelihood multiplication factor (LMF)²⁶. LMF is defined as the ratio of the joint probability of low SM and high Ta between future and historical periods, which effectively characterizes the changes in the occurrence of compound extremes. We partition the LMF into two components: (1) those related to the trends of Ta and SM, and (2) those related to the variability and dependence of both variables (Figs. 1b–c and Supplementary Figs. 2a–b, Methods). We then attribute the LMF components to vegetation-induced changes in Tr and α. This allows us to comprehensively evaluate the effect of projected greening on the likelihood of compound extremes under future climate change, and identify the underlying processes driving these changes (see “Methods” for details).

Results

Increases in global compound soil drought-heat likelihood from vegetation biophysics

We estimate the changes in the likelihood of compound soil drought-heat events (represented by LMF) and their trend (t) and variability and dependency (vd) components throughout 1851-2100 relative to the 1850-1879 baseline (Fig. 2). For each component, we further delineate the contribution of vegetation change through its impact on α and Tr from both current (cur) and previous (pre) seasons. For the LMF induced by the trends of climate variables, the albedo effect (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$) exhibits a progressive increase during the 21^st century, which dominates the overall increase in the likelihood of compound soil drought-heat extremes (Fig. 2a). The trend of Tr from the previous season contributes to an increase in LMF (i.e., ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{t}}$ steadily increases), while the LMF associated with the Tr trend of the current season (i.e., ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}}$) shows a slight decrease (Fig. 2a) due to the offsetting cooling and drying associated with the current Tr (Supplementary Figs. 2c–f). For the LMF driven by the variability and dependency, only Tr from the previous season (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{vd}}$) shows a large positive contribution (Fig. 2b) because of the synergistic effect of previous season Tr on Ta and SM (Supplementary Figs. 2g–h).

Fig. 2. Projected vegetation-driven changes in global likelihood of compound soil drought-heat events (LMF) in CMIP6 models.

a LMF due to temperature (Ta) and soil moisture (SM) trends related to vegetation biophysics (transpiration (Tr) and albedo (α)) across global vegetated areas. b LMF due to Ta and SM variability and dependence related to Tr and α. The subscript “cur” and “pre” represent current and previous seasons, respectively; the superscript “t” and “vd” represent trend and variability&dependency, respectively. c, LMF attributed to Tr, α, and both (i.e., LMF_Tr, LMF_α, and LMF_Veg), where LMF_Tr is the sum of ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}}$, ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{t}}$, ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{vd}}$ and ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$, LMF_α is the sum of ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{vd}}$, and LMF_Veg is the sum of LMF_Tr and LMF_α. The inset in (c) shows the ratio of LMF_Tr, LMF_α, and LMF_Veg to LMF_Tot during 2071-2100; LMF_Tot represents the overall increase in compound soil drought-heat likelihood (i.e., the increase induced by global climate change) (see “methods”). In (a–c) the solid lines indicate multi-model mean with equal weight, the shaded areas represent ±1 standard deviation across models, and noting that LMF is log transformed and its original values are shown on the right-hand side of the y-axis.

Such vegetation-driven changes have a substantial impact on the overall changes in the likelihood of compound soil drought-heat events. In particular, the likelihood is projected to increase by a factor of 2.2 ± 0.6 (i.e., LMF_Veg) by the end of the 21^st century (Fig. 2c; primarily attributable to ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ and ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$, Fig. 2a, b). This increase is equivalent to 13.9 ± 4.5% of the overall increase in compound soil drought-heat likelihood (i.e., the increase induced by global climate change; LMF_Tot) (inset in Fig. 2c). Our results remain robust when we use evapotranspiration instead of transpiration (Supplementary Figs. 3v–x), or employing different moving window lengths (Supplementary Figs. 3g-l), forcing scenarios (Supplementary Figs. 3m–u), and thresholds to define the compound events (Supplementary Figs. 3a–f). They are also robust if we use optimal weight to calculate multi-model means (Supplementary Figs. 4s–u, Methods), or different depths of soil moisture (Supplementary Fig. 4a-i) and initial conditions of model simulations^27,28 (Supplementary Figs. 4j–r). Additionally, the direction of the LMF_Veg between models is generally consistent across various analyzes (Supplementary Table 1). In particular, the fractional contribution of vegetation to the overall increase in compound event likelihood is similar across various analysis cases, ranging from 12% to 21% across multi-model means (insets in Supplementary Figs. 3–4). However, the magnitude of vegetation-driven LMF intensifies with elevated greenhouse gas emissions (Supplementary Figs. 3m–u), emphasizing the potential of a low-forcing scenario to mitigate vegetation biophysical impacts.

Overall, greening-induced reduction in α, i.e., decreased light reflection, can increase the total energy absorption and warm the land surface²⁴, but this response is instantaneous and mostly affects the trend component of the LMF for the current season (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$, Fig. 2a). Tr can cool the surface at a cost of lowered soil moisture levels, hence, its instantaneous effect on Ta and SM is always contradictory¹³, resulting in a comparably smaller net effect on LMF. Importantly, Tr changes have sizable time-lagged effects on compound climate in subsequent seasons. When Tr increases for the previous season, its effect on SM will be partially retained and propagated to the current season^18,21. We show that both the trend and variability of Tr in the previous season dominate the overall effects of Tr on LMF (Fig. 2a-b). Taken together, our analyzes suggest an amplified effect of vegetation biophysics on the global average risk of future compound soil drought-heat events.

Hotspot regions of increasing compound soil drought-heat likelihood

We identify the global hotspots of the projected changes in the compound soil drought-heat likelihood between 30-year historical (1850-1879) and future (2071-2100) periods. The increased likelihood associated with Tr and α (i.e., LMF_Tr and LMF_α) is detected extensively in northern ecosystems (Fig. 3a, b), where LMF_Veg shows a 5-fold increase (Fig. 3e), equivalent to more than 30% of the overall increase in compound soil drought-heat likelihood due to global change (${\mathrm{LMF}}_{\mathrm{Tot}}$, Fig. 3f). ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ dominates the increased likelihood, contributing to more than 80% of LMF_α in those areas, whereas ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{vd}}$ exhibits little influence (Figs. 3c and Supplementary Fig. 5). Correspondingly, ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$ is the key driving factor of the likelihood increase in LMF_Tr (Fig. 3d). Exceptions are found in semi-arid regions around 30°S, where the Tr trend in the warm season $\left({\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}}\right)$ dominates the likelihood increase from Tr, probably because soil moisture memory is weak and vegetation is more reliant on concurrent precipitation²⁹. In mid-to-low latitudes, the likelihood of compound soil drought-heat events driven by vegetation (LMF_Veg) shows a decrease in some locations (e.g., eastern South America and central Africa), but there is no consensus in the majority of tropical regions (Fig. 3e). This may be due to an increased α and decreased Tr variability and dependence in these regions (Supplementary Figs. 6b, g, and l). Our finding remains consistent when using different thresholds for defining compound events, various baseline periods, and different warming scenarios (Supplementary Fig. 5). Furthermore, the magnitude and extent of the corresponding likelihood progressively intensify with rising levels of greenhouse gas emissions during this century (Supplementary Figs. 5i–n). Overall, vegetation contributes substantially to this likelihood increase particularly in northern ecosystems over this century, with the primary contribution from ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ and ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$.

Fig. 3. Global patterns of projected vegetation-driven changes in the likelihood of compound soil drought-heat event (LMF) in CMIP6 simulations.

a Multi-model mean of LMF_α during the current season from 2071-2100, relative to the historical (1850-1879) periods. b Same as (a) but for LMF_Tr. c Dominant driving components of LMF_α (either ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ or ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{vd}}$) that contributes the most to the increase in LMF_α in each grid cell. d, Same as c, but for LMF_Tr encompassing contributions from ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}}$, ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{t}}$, ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{vd}}$, and ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$. e Multi-model mean of LMF_Veg, note LMF is presented in its original value. f The ratio of LMF_veg to LMF_Tot. Stippling indicates locations where models project a significant (P < 0.1) change in (a, b, and e,) or that more than half of the models show a consistent signal in (c and d) or the ratio is significantly (P < 0.1) larger than 0.2 in (f). White land areas are non-vegetated regions.

The dominant role of leaf area in the increasing compound soil drought-heat likelihood

Although Tr and α variation are dominated by vegetation leaf area^23,24, other covarying climatic and environmental factors other than vegetation, such as radiation, vapor pressure deficit, and cloud cover, may also play a role. To elucidate the contribution from vegetation leaf area to LMF, we further explore the physical linkage associated with the two key contributors, i.e., ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$. To do so, we decompose the associated changes in Tr (or $\alpha$) into several additive components related to leaf area index (LAI) and other climate factors, followed by the quantification of LMF attributable to LAI and the other factors (see “Methods”).

Our results reveal that the projected increase in both ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ is predominantly driven by LAI shifts for the corresponding periods (Fig. 4a, b). The aggregate of the two LAI-driven components exhibits a progressive increase during the 21^st century, contributing to more than 90% of LMF_Veg, equivalent to 13 ± 3.7% of LMF_Tot during 2071–2100 (Fig. 4c). Specifically, the additional growth of pre-season LAI is projected to enhance Tr variability and simultaneously intensify the negative dependence of Tr between the pre-season and the warm season (Supplementary Figs. 6a and f). A negative dependence suggests that excessive water extraction during pre-season reduces water availability and inhibits Tr cooling during subsequent warm seasons, thereby increasing the compound soil drought-heat likelihood. Regarding the spatial pattern, the LAI-driven hotspots are also primarily concentrated in the northern ecosystems (Figs. 4d–f), which well (P < 0.1) coincided with the most substantial relative increases in LAI (Supplementary Fig. 7). These analyzes highlight the importance of LAI in modulating compound soil drought-heat extremes.

Fig. 4. Drivers of the changes in the likelihood of compound soil drought-heat event (LMF) associated with vegetation biophysics in CMIP6 models.

a Global ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$ attributed to LAI (i.e., ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{vd}}$), stomatal conductance (gs), vapor pressure deficit (VPD), precipitation (Pr), and net radiation (Rn). b Global ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ attributed to LAI (i.e., ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{t}}$), Pr, and cloud cover (Cl). c Global LMF attributed to LAI (LMF_LAI), represented by the summation of ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{vd}}$ and ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{t}}$. d–f The spatial pattern of ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{vd}}$ (d) ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{t}}$ (e) and LMF_LAI (f) between historical (1850-1879) and future periods (2071-2100). The inset in (a–c) shows the ratio of ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{vd}}$ to ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$ (a) ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{t}}$ to ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ (b), and LMF_LAI to LMF_Tot in future periods (c), respectively; LMF is log transformed and its original values are shown on the right-hand side of the y-axis. The inset in (d-f) shows the spatial correlation between ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{vd}}$ and LAI-induced variability (orange) /dependence (brown) changes (d), ${\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{t}}$ and LAI-induced α changes (e), as well as LMF_LAI and LMF_Veg (f), respectively. Stippling in (d–f) indicates a significant change (P < 0.1).

Compound soil drought-heat impact on northern ecosystems

Our analyzes highlight that vegetation-induced changes in compound soil drought-heat extremes are most evident in northern ecosystems. Despite often being considered energy-limited, northern ecosystems can still suffer from these extreme events. For example, we observe a much weaker greening trend in the current season (i.e., peak growing season) than in the previous season (i.e., early growing season) (Fig. 5a). This is also associated with an enhancement of the negative correlation between peak season LAI anomaly and early season LAI anomaly (Fig. 5b), suggesting that the better-than-average early season growth often led to a worse-than-average peak season growth. Both lines of evidence imply that the peak season may be more productive if compound soil drought-heat extremes do not increase. Additionally, the enhanced compound soil drought-heat risk also jeopardizes the ecosystem stability, as evidenced by increased variability in peak season LAI (Fig. 5b). These results are consistent in both CMIP6 models and satellite observations of LAI, with slight differences in their absolute values.

Fig. 5. Changes in vegetation leaf area index (LAI) across northern ecosystems (> 23° N).

a The difference of the relative change in LAI (%) between the current and previous seasons. b The changes in LAI variability for the current season (∆v, m⁴ m⁻⁴) and the covariance of LAI (∆d, m⁴ m^-4) between the previous and current seasons. c–d Same as (a–b) but for the three CO₂ experiments. The dependence is represented by covariance, and variability is denoted by variance. Changes in CMIP6 and 1pctCO2 are calculated using a 30-year moving window, while the observed LAI changes from 1982–2018 are computed using a 10-year moving window. For a better comparison between the observed and modeled LAI, the changes in CMIP6 are relative to the baseline of 1963–1992. The lower left inset in (a–b) shows trends indicated by Z values of the Mann-Kendall test, while the upper-middle inset shows a zoom-in during 1992–2018. The shaded areas represent the mean of ±1 standard deviation across models.

The magnitude and spatial extent of the LAI-driven increase in the compound likelihood are greater under high emissions scenarios (Supplementary Figs. 8), implying that compound soil drought-heat events are exacerbated by vegetation greening as atmospheric CO₂ concentrations continue to rise. Using ESMs configured with three distinct CO₂ sensitivity experiments (see “Methods”), We further demonstrate that CO₂ radiative effect dominates the increase in compound soil drought-heat extremes (Supplementary Fig. 9), and the associated impact on LAI trend and variability changes in these northern regions (Figs. 5c, d).

Discussion

Our results demonstrate that the greening-induced shifts in land biophysical processes, particularly Tr and α, are expected to increase the global likelihood of compound soil drought-heat events. This is equivalent to 12–21% of the total increment in global compound event likelihood at the end of the 21^st century. More than 90% of the projected increases are caused by an increase in the magnitude of LAI and its seasonal dynamics. The enhanced vegetation growth reduces α and triggers additional pre-season Tr increases that further enhance soil moisture depletion and high temperature during the subsequent warm season, amplifying the likelihood of compound extremes. The rise in LAI-induced likelihood is predominantly found in northern ecosystems and is dominated by the indirect response of leaf area to CO₂, suggesting that the CO₂-induced water-saving effect is limited and cannot fully compensate for the warming effect^30,31.

Almost one-fifth of the increase in compound soil drought-heat likelihood is associated with increased vegetation activity in the northern regions. This “greening but warming-drying” phenomenon seems contradictory but can be explained from two perspectives. First, the negative impacts from the compound soil drought-heat extremes may be overridden by the strong positive carryover effect from the previous season. This is supported by a much weaker LAI increase during the peak growing season than the early growing season (Fig. 5a). Second, although compound soil drought-heat extremes have caused a large increase in fire occurrences^32–34 and forest mortality^35,36 in these boreal regions, these changes are most scattered and obscured by the overall greenness increase at coarse spatial resolution³⁷. However, these greenness increases contributed by young and fast-growing species are not likely to fully compensate for ecosystem carbon and biodiversity loss. The compound soil drought-heat extremes are likely to decrease ecosystem stability in boreal regions.

Our analysis also highlights the large influence of lagged ecosystem dynamics on the prevalence of compound soil drought-heat extremes. From the pre-season to the warm season, extra water consumption not only leads to lower subsequent soil moisture levels, but the enhanced vegetation growth also increases the water demand^38,39. When this imbalance between demand and supply accumulates and surpasses the ecosystem carrying capacity, a peculiar type of compound soil drought-heat extreme happens, known as “structural overshoot”⁴⁰. Additionally, such overshoot, when interacting with climate change, can further exacerbate climate events^38,39. Northern high latitudes have been shown to have the highest likelihood of experiencing structural overshoot drought¹⁸, and our study further projects a much stronger increase in the associated compound extremes in these regions.

The projected increase in compound drought-heat extremes induced by greening has important implications for both ecosystem stability and human wellbeing. Vegetation-driven drought-heat events can have cascading effects on agriculture ecosystems through interactions between plants and various agents in the ecosystem^41–43. Crops during the critical grain-filling period may also be more frequently affected by drought-heat extremes, both locally due to enhanced early-season growth and remotely through heat advection⁴⁴ and water competition⁴⁵ from neighboring natural vegetation, potentially jeopardizing global food production. Moreover, in many regions globally with strong vegetation-atmosphere coupling, surface climate conditions are influenced by large-scale atmospheric circulation patterns and local vegetation conditions^14,46. Our findings emphasize the significance of also considering the pre-existing conditions of vegetation growth in compound event forecasts during the subsequent warm season^18,47.

While our study focuses on natural ecosystems, these insights are relevant for nature-based solutions in urban environment. This is due to the consistent effects of vegetation on climate at both macro and micro scales, particularly through mechanisms such as modifications of albedo and transpiration^13,48. Urban green initiatives can mitigate urban heat by enhancing albedo and transpiration, especially in mid-to-low latitudes^49,50. Consistently, we show that vegetation greening will mitigate compound soil drought-heat in these regions, implying potential climate benefits from nature-based solutions in urban settings. Conversely, in high-latitude or arid regions, urban greening might not yield the expected benefits, likely due to the projected exacerbation of dry and heat extremes by climate change and urban development^51,52. Whether urban greening can mitigate the compound soil drought-heat extremes also depends on human management practices, such as irrigation and species selections, and faces large uncertainties in model simulations. Therefore, effective future urban climate mitigation efforts should incorporate high-resolution modeling and delicate management to ensure the success of these interventions in the face of ongoing climate change.

Compound soil drought-heat extremes may disproportionately impact the global carbon cycle compared to univariate extremes, not only through the direct effect on vegetation photosynthesis, but through other processes including enhanced fire emission⁵³, permafrost thaw⁵⁴, variation in boundary layer⁵⁵, and the complex positive interactions therein⁵⁶. However, these processes lack robust observational constraints and are still not well-represented in the state-of-the-art models, contributing to the uncertainties in future global compound soil drought-heat extremes predictions. Our global quantification of the effects of vegetation fingerprint on compound soil drought-heat events emphasizes the importance of accurately representing land processes for future projections of compound extremes, and motivates the need to incorporate vegetation biophysics into climate decision-making and adaptation strategies related to compound extremes.

Methods

CMIP6 model simulations

We used outputs from 17 state-of-the-art ESMs that participate in CMIP6 (Supplementary Table 2). We use CMIP6 models since a lengthy time series is necessary to acquire an adequeate number of samples for estimating compound event likelihood, and evaluate its trend attributed to vegetation changes^8,22,26,28. Remote sensing observations are limited in temporal coverage and do not have the capability to predict the changes of compound extremes in the future. Moreover, our analyzes (Supplementary Fig. 10) and ample evidence suggest that the overall trends in historical drought^57–59, temperature^60–62, and vegetation characteristics^13,63 (such as LAI, transpiration, and others) simulated by the ESMs are generally consistent with observations. The various output variables from this consistent modeling framework also allow us to reliably investigate the underlying processes and mechanisms driving such changes. Hence, we utilize ESMs from CMIP6, which integrate the latest human understanding of knowledge on various land surface processes²⁵, to project the vegetation-driven compound soil drought-heat likelihood.

The selected CMIP6 models all report the required variables and incorporate the dynamic responses of stomatal conductance and vegetation cover to climate change and increased CO₂. We used monthly total soil moisture (mrso), near-surface air temperature (tas), transpiration (tran), evapotranspiration (evspsbl), runoff (mrro), precipitation (pr), relative humidity (hurs), leaf area index (lai), sensible heat flux (hfss), latent heat flux (hfls), total cloud cover percentage (clt), surface downwelling shortwave radiation (rsds), and surface upwelling shortwave radiation (rsus) from the historical (1850-2014), SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 (2015-2100) simulations. Surface albedo (α) was computed as the ratio of rsus to rsds. From CanESM5, CanESM5-1, and MPI-ESM1-2-LR, we extracted all ensemble members (i.e., 50, 20, and 20), respectively, to assess the effect of initial conditions on the estimated compound soil drought-heat likelihood. Relative humidity was not available for the BCC-CSM2-MR, and was calculated from specific humidity, near-surface air pressure, and Ta. Considering the divergent depth of soil moisture across model^64,65, multiple layer soil moisture (mrsol) is also used to obtain surface SM and SM at 1 m and 2 m. We linearly interpolate the profiles of each model and then extract the soil moisture at 1 m and 2m⁶⁶. The satellite LAI are from GIMMS LAI3g⁶⁷ and GLASS LAI⁶⁸. We also used three idealized single-forcing CMIP6 experiments (i.e., 1pctCO2, 1pctCO2-rad and 1pctCO2-bgc) that participate in the coupled carbon-climate ESMs⁶⁹. In these experiments, the influence of atmospheric CO₂ was separated into the radiation effect and vegetation physiological effect. In 1pctCO2, both the atmospheric and land surface modules experience a 1% annual increase of atmospheric CO₂ starting from 280 ppm (pre-industrial) to 1140 ppm (4 × CO₂) over a 140-year period. The rate of CO₂ increase is similar to that in historical and SSP5-8.5 simulations. In 1pctCO2-bgc, only the vegetation module experiences the increase in CO₂, while the atmosphere continuously experiences pre-industrial CO₂ levels. By contrast, in 1pctCO2-rad, only the atmospheric module is subjected to the increase in CO₂, while the vegetation module is set to a fixed CO₂ concentration at the pre-industrial level. These simulations have been commonly used to investigate the impact of CO₂ radiative and physiological effects on climate extremes^31,66,70. Ten climate models that participated in the three idealized single-forcing CMIP6 (Supplementary Table 2) were used. In these simulations, we also used the above-mentioned monthly outputs. All the model outputs utilized in this study were resampled to a common spatial resolution of 1.5° × 1.5° by using bilinear interpolation.

A framework for quantifying the likelihood of compound soil drought-heat events from vegetation biophysics

The total LMF

Compound soil drought-heat extremes are expected to have large impacts on natural ecosystems and human society, especially for those happen during the warm season. Additionally, the warm season also overlaps with the main growing season for most regions, during which vegetation change through modifying α and Tr can substantially regulate SM and Ta^13,21. We thus focus on global vegetated regions during the warm season. Following ref. ²⁶, the warm season is defined as the average hottest three consecutive months during study periods in each model grid cell.

Following ref. ²⁶, we used the likelihood multiplication factor (LMF) to quantify the change in the frequency of compound soil drought-heat events driven by Ta and SM (hereafter referred to as LMF_Tot). We first employed the commonly used bivariate copulas to calculate the joint probability of a compound soil drought-heat event. Accordingly, our two variables are monthly Ta and the opposite of SM (-SM) over the warm season. Given two random variables X (i.e., Ta) and Y (i.e., -SM), the joint probability distribution function of X and Y with a copula C can be expressed as

$$\mathrm{F}\left(x,y\right)=\mathrm{P}\left(X\le x,Y\le y\right)=\mathrm{C}\left(u,v\right)$$ 1

Where P is the joint cumulative probability; u and v are the uniform distribution of X and Y, respectively. The joint probability of a compound soil drought-heat event during the historical period, defined by both variables exceeding their specific thresholds, can be expressed as

$${\mathrm{p}}_{\mathrm{his}}={\mathrm{P}}_{\mathrm{his}}\left(u>{\mathrm{u}}_{\mathrm{his}}\bigcap v>{\mathrm{v}}_{\mathrm{his}}\right)=1-{\mathrm{u}}_{\mathrm{his}}-{\mathrm{v}}_{\mathrm{his}}+{\mathrm{C}}_{\mathrm{his}}\left({\mathrm{u}}_{\mathrm{his}},{\mathrm{v}}_{\mathrm{his}}\right)$$ 2

where C_his is the copula during the historical period. u_his and v_his are Ta and SM thresholds, respectively, and both are set at 0.9, which is a common threshold to define climate extremes.

Subsequently, we calculated the future thresholds of X and Y, corresponding to the 90^th quantile values during the historical period. For example, future thresholds of X (u_fut) can be expressed as

$${\mathrm{u}}_{\mathrm{fut}}={\mathrm{F}}_{\mathrm{fut}}\left({\mathrm{X}}_{90-\mathrm{his}}\right)$$ 3

Where X_90-his is the 90^th percentile value of X during the historical period, ${\mathrm{F}}_{\mathrm{fut}}$ is the normal cumulative distribution function (CDF) of X during the future period. We then recomputed a new copula driven by future X and Y, and used Eq. (2) to calculate the future joint probability $\left({\mathrm{p}}_{\mathrm{fut}}\right)$. The LMF_Tot is defined as the ratio of ${\mathrm{p}}_{\mathrm{fut}}$ to ${\mathrm{p}}_{\mathrm{his}}$

$${\mathrm{LMF}}_{\mathrm{Tot}}=\frac{{\mathrm{p}}_{\mathrm{fut}}}{{\mathrm{p}}_{\mathrm{his}}}$$ 4

An increase in likelihood is indicated by a value greater than one. We used the function “BiCopCDF” in R VineCopula package⁷¹ to calculate the joint probability.

The decomposition of LMF

Following ref. ²², changes in trend, variability, and dependence of relevant drivers can affect the likelihood of all types of compound events. For example, an increase (reduction) in Ta (SM), an escalation in variability, or an intensification of negative dependence between Ta and SM can increase the compound event likelihood²². We partition LMF_Tot into components attributed to Ta trend, SM trend, variability, and dependence.

We first calculated the LMF attributed to changes in variability (referred to as ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{v}}$). Using Eq. (3), but with the CDF that fixes the mean values of Ta (SM) in accordance with the historical period while allowing standard deviation to change, we calculated the future Ta (SM) threshold (i.e., ${\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}$ and ${\mathrm{v}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{SM}}$, where the superscript v stands for variability). With this, we obtained the joint probability only encompassing information on the variability of Ta and SM $\left({\mathrm{p}}_{\mathrm{fut}}^{\mathrm{v}}\right)$. ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{v}}$ is given by

$${\mathrm{p}}_{\mathrm{fut}}^{\mathrm{v}}={\mathrm{P}}_{\mathrm{fut}}\left(\mathrm{u}>{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}\bigcap \mathrm{v}>\underset{\mathrm{fut}}{\overset{\mathrm{v}-\mathrm{SM}}{\mathrm{u}}}\right)=1-{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}-{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{SM}}+{\mathrm{C}}_{\mathrm{fut}}\left({\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}},{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{SM}}\right)$$ 5

$$\mathrm{LM}{\mathrm{F}}_{\mathrm{Tot}}^{\mathrm{v}}=\frac{{\mathrm{p}}_{\mathrm{fut}}^{\mathrm{v}}}{{\mathrm{p}}_{\mathrm{fut}}}$$ 6

Where ${\mathrm{C}}_{\mathrm{fut}}$ is the newly recalculated copula driven by future Ta and SM. We then calculated the LMF related to trends in Ta and SM (i.e., ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{Ta}}$ and ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{SM}}$), using Ta as an example. We derived a new Ta threshold $\left({\mathrm{u}}_{\mathrm{fut}}^{\mathrm{t}-\mathrm{v}-\mathrm{Ta}}\right)$, employing a CDF calculated from future Ta which contains both changes in mean and variability of Ta. We then obtained the joint probability containing information on Ta’s variability and trend $\left({\mathrm{p}}_{\mathrm{fut}}^{\mathrm{t}-\mathrm{v}-\mathrm{Ta}}\right)$, by setting the threshold for SM to 0.9, as well as the joint probability for Ta’s variability only $\left({\mathrm{p}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}\right)$. The ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{Ta}}$ is given by

$${\mathrm{p}}_{\mathrm{fut}}^{\mathrm{t}-\mathrm{v}-\mathrm{Ta}}={\mathrm{P}}_{\mathrm{fut}}\left(\mathrm{u}>{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{t}-\mathrm{v}-\mathrm{Ta}}\bigcap \mathrm{v}>0.9\right)=1-{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{t}-\mathrm{v}-\mathrm{Ta}}-0.9+{\mathrm{C}}_{\mathrm{fut}}\left({\mathrm{u}}_{\mathrm{fut}}^{\mathrm{t}-\mathrm{v}-\mathrm{Ta}},0.9\right)$$ 7

$${\mathrm{p}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}={\mathrm{P}}_{\mathrm{fut}}\left(\mathrm{u}>{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}\bigcap \mathrm{v}>0.9\right)=1-{\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}-0.9+{\mathrm{C}}_{\mathrm{fut}}\left({\mathrm{u}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}},0.9\right)$$ 8

$$\mathrm{LM}{\mathrm{F}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{Ta}}=\frac{{\mathrm{p}}_{\mathrm{fut}}^{\mathrm{t}-\mathrm{v}-\mathrm{Ta}}}{{\mathrm{p}}_{\mathrm{fut}}^{\mathrm{v}-\mathrm{Ta}}}$$ 9

The LMF changes resulting from SM’s trend can be calculated in a similar way. To quantify the LMF due to dependence changes $\left({\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{d}}\right)$, we set future thresholds $\left({\mathrm{u}}_{\mathrm{fut}}^{\mathrm{d}-\mathrm{Ta}},{\mathrm{v}}_{\mathrm{fut}}^{\mathrm{d}-\mathrm{SM}}\right)$ being 90^th quantile for both SM and Ta based on model prediction for future period, and used the Eq. (2) and C_fut to obtain the future joint probability due to shifts in dependence $\left({\mathrm{p}}_{\mathrm{fut}}^{\mathrm{d}}\right)$. ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{d}}$ is given by

$$\mathrm{LM}{\mathrm{F}}_{\mathrm{Tot}}^{\mathrm{d}}=\frac{{\mathrm{p}}_{\mathrm{fut}}^{\mathrm{d}}}{{\mathrm{p}}_{\mathrm{his}}}$$ 10

Since LMF_Tot is overall driven by changes in trend, variability and dependence²², it can also be calculated from the as the summation of the individual components after logarithm transformed:

$$\log \left({\mathrm{LMF}}_{\mathrm{Tot}}\right)=\log \left({\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{SM}}\right)+\log \left({\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{Ta}}\right)+\log \left({\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{v}}\right)+\log \left({\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{d}}\right)$$ 11

In particular, we find a very high consistency between $\log \left({\mathrm{LMF}}_{\mathrm{Tot}}\right)$ estimated from Eq. (4) and the summation of all components in Eq. (11) (Supplementary Fig. 11). Additionally, $\log \left({\mathrm{LMF}}_{\mathrm{Tot}}\right)$ and the summation exhibit good spatial consistency at a global scale. These analyzes suggest that our decomposition method is in line with theoretical principles.

The changes in each individual LMF component predominantly stem from the anomalies of the respective element. For example, ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{SM}}$ is caused by shifts in SM trends, and ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{v}}$ is caused by changes in the product of Ta and SM standard deviation. To establish the relationship between LFM components and the variability characteristics (trend, variation, dependency) of the two variables, we computed each individual LMF component for each consecutive 30-year period from 1850–2100, in relation to the first 30-year period (1850-1879) within each model grid cell (a total of 221 points). We then build a piecewise function to predict each LMF component (after log-transformation) from Ta and SM variability characteristics using the function “segmented.lm” in R package “segmented”⁷².

Ta and SM changes associated with Tr and α

Tr is expected to affect both Ta and SM simultaneously^24,73,74. Additionally, evidence from observations and models also indicates lagged effects of spring Tr on summer SM^20,75–77, such as increased summer drying due to enhanced spring Tr²¹. Moreover, the change in α can also regulate the land energy balance and further affect Ta. We incorporated changes in trend, variability, and dependence of SM and Ta from Tr of the previous season and current season, and the associated changes due to current α (Supplementary Figs. 2a,b).

Given the additive nature of the $\log \left(\mathrm{LMF}\right)$, we performed separate calculations for each pertinent item related to Tr and α. Following refs. ^14,78, we applied the surface energy balance equation to assess the impact of changes in Tr and α on Ta. Briefly, changes in Tr can modify the surface energy budget and alter land surface temperature, further warming or cooling the local Ta. The surface energy balance equation is given by

$${\mathrm{S}}_{\mathrm{in}}\left(1-\alpha \right)+{\mathrm{\epsilon }}_{\mathrm{s}}\sigma \left({\mathrm{\epsilon }}_{\mathrm{a}}\mathrm{T}{\mathrm{a}}^4-\mathrm{T}{\mathrm{s}}^4\right)=\lambda \left(\mathrm{Tr}+\mathrm{Ei}+\mathrm{Es}\right)+H+G$$ 12

Where S_in represents surface downward shortwave radiation, $\lambda$ is the latent heat of vaporization, Ei is canopy evaporation, Es is soil evaporation, H is sensible heat flux, and G is ground heat flux. ${\mathrm{\epsilon }}_{\mathrm{s}}$, $\sigma$, ${\mathrm{\epsilon }}_{\mathrm{a}}$, and Ts denote land surface emissivity, Stephan-Boltzmann constant, atmospheric air emissivity, and land surface temperature, respectively.

By differentiating Eq. (12), we obtained the sensitivity of Ta to Tr (i.e., $\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}$), and calculated the effect of changes in Tr’s trend on Ta (${\mathrm{\Delta }\mathrm{t}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{Ta}}$).

$$\mathrm{\Delta }{\mathrm{t}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{Ta}}=\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}\left({\mathrm{Tr}}^{\mathrm{fut}}-{\mathrm{Tr}}^{\mathrm{his}}\right)$$ 13

Where ${\mathrm{Tr}}^{\mathrm{fut}}$ and ${\mathrm{Tr}}^{\mathrm{his}}$ denote the average of Tr during historical and future periods. Similarly, combing the sensitivity of Ta to α from Eq. (12) (i.e., $\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{\alpha }}$) and the long-term α trends, we obtained the effect of changes in α’s trend on Ta $\left({\mathrm{\Delta }\mathrm{t}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{Ta}}\right)$.

As for SM, we need to consider both Tr of current period (k) and previous period (k-1). We used a simple water balance equation to characterize the impact of Tr on SM. The water balance equation is given by

$$\mathrm{S}{\mathrm{M}}_{\mathrm{k}}=\mathrm{S}{\mathrm{M}}_{\mathrm{k}-1}+{\mathrm{Pr}}_{\mathrm{k}-1}-{\mathrm{Tr}}_{\mathrm{k}-1}-{\mathrm{Q}}_{\mathrm{k}-1}$$ 14

Where SM_k is SM at time k. SM_k-1, Pr_k-1, Tr_k-1, and Q_k-1 are the average SM, precipitation, Tr, and runoff from the previous three months, respectively. Using three-month average values can consider the potential collective effects of spring vegetation water use and longer timescales of droughts⁷⁵. Due to the different surface and climate characteristics, the effect of ${\mathrm{Tr}}_{\mathrm{k}-1}$ to $\mathrm{S}{\mathrm{M}}_{\mathrm{k}}$ can be different across grid cells. For example, in very wet regions with abundant precipitation, water losses from Tr will be fully replenished, and will have little effect on SM. We therefore build a linear model for each grid cell to quantify the sensitivity of SM to Tr (i.e., $\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}$) using observations from both historical and future periods. If we consider the precipitation events as randomly occurring, such a sensitivity can also be applied to calculate the effect of current Tr on SM. With this, the SM changes due to the trend of warm season Tr $\left({\mathrm{\Delta }\mathrm{t}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{SM}}\right)$ can be calculated as:

$$\mathrm{\Delta }{\mathrm{t}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{SM}}=\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}\left({\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{fut}}-{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{his}}\right)$$ 15

The Eq. (15) can also be used to calculate the SM changes due to trend of previous season $\left({\mathrm{\Delta }\mathrm{t}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{SM}}\right)$ using ${\mathrm{Tr}}_{\mathrm{k}-1}$ from historical and future periods. We then calculated the antecedent and current effects of a Tr anomaly $\left({\mathrm{Tr}}_{\mathrm{ano}}\right)$ on dependence using both $\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}$ estimated from Eq. (14) and $\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}$ estimated from Eq. (12):

$${\mathrm{\Delta }\mathrm{d}}_{\mathrm{cur}-\mathrm{Tr}}=\mathrm{cov}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}},\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}\right)-\mathrm{cov}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}},\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}\right)$$ 16

$$\mathrm{\Delta }{\mathrm{d}}_{\mathrm{pre}-\mathrm{Tr}}=\mathrm{cov}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{fut}},\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}\right)-\mathrm{cov}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{his}},\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}\right)$$ 17

Where cov is the covariance that quantifies the direction and magnitude of dependence between two variables. $\mathrm{\Delta }{\mathrm{d}}_{\mathrm{cur}-\mathrm{Tr}}$ represents dependence change due to current ${\mathrm{Tr}}_{\mathrm{ano}}$, while $\mathrm{\Delta }{\mathrm{d}}_{\mathrm{pre}-\mathrm{Tr}}$ denotes changes in dependence between SM (caused by preseason ${\mathrm{Tr}}_{\mathrm{ano}}$) and Ta (caused by current ${\mathrm{Tr}}_{\mathrm{ano}}$). ${\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}$ and ${\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}$ are monthly ${\mathrm{Tr}}_{\mathrm{ano}}$ at time k during historical and future periods, respectively. ${\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{his}}$ and ${\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{fut}}$ was calculated by averaging monthly ${\mathrm{Tr}}_{\mathrm{ano}}$ from time k-1 to k-3 during historical and future periods, respectively.

We finally calculated the changes in variability related to Tr. The Tr-driven change in variability is defined as the products between Tr-driven Ta and SM anomalies, given that ${\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{v}}$ is driven by changes in the product of Ta and SM standard deviation (see following section), and this definition facilitates the comparison with LMF pairs related to Tr-driven variability and dependence.

$$\mathrm{\Delta }{\mathrm{v}}_{\mathrm{cur}-\mathrm{Tr}}=\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}\right)\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}\right)-\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}\right)\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}\right)$$ 18

$$\mathrm{\Delta }{\mathrm{v}}_{\mathrm{pre}-\mathrm{Tr}}=\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{fut}}\right)\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{fut}}\right)-\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{his}}\right)\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}-1}^{\mathrm{v},\mathrm{his}}\right)$$ 19

Where sd denotes standard deviation. $\mathrm{\Delta }{\mathrm{v}}_{\mathrm{cur}-\mathrm{Tr}}$ represents the variability change due to current ${\mathrm{Tr}}_{\mathrm{ano}}$, while $\mathrm{\Delta }{\mathrm{v}}_{\mathrm{pre}-\mathrm{Tr}}$ denotes the variability change induced by preseason and current ${\mathrm{Tr}}_{\mathrm{ano}}$. Using the Eqs. (16 and 18) and considering the changes in Ta variability associated with α, we obtained changes in variability and dependence induced by α anomalies (i.e., ${\mathrm{\Delta }\mathrm{v}}_{\mathrm{cur}-\mathrm{\alpha }}$ and ${\mathrm{\Delta }\mathrm{d}}_{\mathrm{cur}-\mathrm{\alpha }}$):

$$\mathrm{\Delta }{\mathrm{v}}_{\mathrm{cur}-\mathrm{\alpha }}=\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}\right)\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{\alpha }}{\mathrm{\alpha }}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}\right)-\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}\right)\mathrm{sd}\left(\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{\alpha }}{\mathrm{\alpha }}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}\right)$$ 20

$${\mathrm{\Delta }\mathrm{d}}_{\mathrm{cur}-\mathrm{\alpha }}=\mathrm{cov}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}},\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{\alpha }}{\mathrm{\alpha }}_{\mathrm{k}}^{\mathrm{v},\mathrm{fut}}\right)-\mathrm{cov}\left(\frac{\mathrm{\delta }\mathrm{SM}}{\mathrm{\delta }\mathrm{Tr}}{\mathrm{Tr}}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}},\frac{\mathrm{\delta }\mathrm{Ta}}{\mathrm{\delta }\mathrm{\alpha }}{\mathrm{\alpha }}_{\mathrm{k}}^{\mathrm{v},\mathrm{his}}\right)$$ 21

The LMF caused by changes in Tr and α

In the previous sections, we calculated the LMF and its components related to the trend, variability, and dependence of Ta and SM. We employed a piecewise regression function to characterize these relationships for each model and for each grid cell. We also used energy balance equations and water balance equations to quantify the changes in Ta and SM trend, variability and dependence associated with Tr and α. With these, we can use the “chain rule” to calculate the changes in Tr and α and their contribution to LMF, i.e., LMF from ${\mathrm{\Delta }\mathrm{t}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{Ta}}$ and ${\mathrm{\Delta }\mathrm{t}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{SM}}$ (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}-\mathrm{Ta}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}-\mathrm{SM}}$), ∆d_cur-Tr and ∆v_cur-Tr (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{d}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{v}}$), ∆d_pre-Tr and ∆v_pre-Tr (${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{d}}$ and ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{v}}$), ∆d_cur-α and ∆v_cur-α (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{d}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{v}}$), ${\mathrm{\Delta }\mathrm{t}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{Ta}}$ (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$), and ${\mathrm{\Delta }\mathrm{t}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{SM}}$ (${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}-\mathrm{Ta}}$). For example, ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}-\mathrm{Ta}}$ is given by

$$\log \left({\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}-\mathrm{Ta}}\right){=\mathrm{f}}_{\mathrm{t}-\mathrm{Ta}}\left({\mathrm{\Delta }\mathrm{t}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{Ta}}\right)$$ 22

Where ${\mathrm{f}}_{\mathrm{t}-\mathrm{Ta}}$ denotes the piecewise function formulated by $\log \left({\mathrm{LMF}}_{\mathrm{Tot}}^{\mathrm{t}-\mathrm{Ta}}\right)$ and the change in Ta’s trend.

To assess the impacts of the current Tr trend on compound event likelihood, we added ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}-\mathrm{Ta}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}-\mathrm{SM}}$ to get ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{t}}$. Given that Tr-driven (or α-driven) variability and dependence are quantified by variance and covariance, respectively, and are therefore compatible, we combined the ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{v}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{d}}$ $\left({\mathrm{LMF}}_{\mathrm{cur}-\mathrm{Tr}}^{\mathrm{vd}}\right)$, ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{v}}$ and ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{d}}$ $\left({\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}\right)$, ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{v}}$ and ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{d}}\left({\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{vd}}\right)$, to represent the influences of variability and dependence on compound event likelihood. We set any the modeled log(LMF) values larger (smaller) than 4.6 (−4.6) to missing (a very small proportion, 0.29%), given that log(LMF_Tot) is generally less than 4.6 (its value before logarithmic transformation is 100)^6,26. Our evaluation shows that the prediction model satisfactorily captures the linkage between response and predictive variables (Supplementary Figs. 12). Specifically, the simulation and observation exhibit satisfactory correlation alongside minimal error, and present strong spatial consistency across a global scale.

We tested whether the ensemble median of the models shows a change in likelihood with the one-sided sign test²⁶. We highlighted regions for which the model ensemble median of the LMF is significantly larger than or less than 0 with stippling. Global statistics such as means and quantiles are based on the arithmetic mean for a balanced reflection of the frequency of events, since LMF represents the frequency of compound events independent of the area size^6,8,26.

The contribution of LAI in Tr- and α- driven LMF

Changes in ${\mathrm{Tr}}_{\mathrm{ano}}$ can be linked to factors such as leaf area index (LAI), precipitation (Pr), net radiation (Rn), stomatal conductance (gs), and vapor pressure deficit (VPD). Following ref.⁷⁹, we used a multivariate regression framework to investigate the ${\mathrm{Tr}}_{\mathrm{ano}}$ associated with these factors. This approach adeptly factors out the direct impacts of alterations in climatic and vegetation factors on terrestrial energy fluxes⁷⁹ and can be consistently applied to various ESM outputs⁸⁰. Partial least-squares regression was used to overcome the potential multicollinearity problem of drivers for each model grid cell and each month⁸¹. The ${\mathrm{Tr}}_{\mathrm{ano}}$ was expressed as

$${\mathrm{Tr}}_{\mathrm{ano}}=\frac{\mathrm{\delta }{\mathrm{Tr}}_{\mathrm{ano}}}{\mathrm{\delta }\mathrm{LAI}}\mathrm{LAI}+\frac{\mathrm{\delta }{\mathrm{Tr}}_{\mathrm{ano}}}{\mathrm{\delta }\mathrm{gs}}\mathrm{gs}+\frac{\mathrm{\delta }{\mathrm{Tr}}_{\mathrm{ano}}}{\mathrm{\delta }\mathrm{Rn}}\mathrm{Rn}+\frac{\mathrm{\delta }{\mathrm{Tr}}_{\mathrm{ano}}}{\mathrm{\delta }\mathrm{Pr}}\mathrm{Pr}+\frac{\mathrm{\delta }{\mathrm{Tr}}_{\mathrm{ano}}}{\mathrm{\delta }\mathrm{VPD}}\mathrm{VPD}$$ 23

Where LAI, gs, Rn, Pr and VPD are detrended and deseasonalized sequences. VPD was calculated from Ta and relative humidity. gs was estimated by $\mathrm{Tr}$ per leaf area following ref.⁸². We calculated the changes in the corresponding variability and dependence (i.e., ∆v and ∆d), and subsequently obtained ∆v attributed to LAI, gs, VPD, Pr, and Rn, as well as ∆d attributed to these factors. Combining these factors with the above framework, we further partition ${\mathrm{LMF}}_{\mathrm{pre}-\mathrm{Tr}}^{\mathrm{vd}}$ associated with LAI $\left({\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{vd}}\right)$, gs, VPD, Pr, and Rn. We also employed the consistent methods to calculate the change in α’s trend associated with LAI, Pr, and Cl, as well as partition ${\mathrm{LMF}}_{\mathrm{cur}-\mathrm{\alpha }}^{\mathrm{t}}$ related to LAI $\left({\mathrm{LMF}}_{\mathrm{LAI}}^{\mathrm{t}}\right)$ and other factors.

Our evaluation shows that this approach can effectively replicate the correctly associated changes in $\mathrm{Tr}$ and α at the global scale (Supplementary Fig. 13). This calculation was conducted for each consecutive 30-year period from 1851 to 2100, relative to the first 30-year period (1850-1879) within each model grid cell. We utilized the pls R packages to execute the partial least-squares regression. In the three CO₂ sensitivity experiments, we assessed the changes in LAI between the first (years 1-30) and last (years 111-140) 30-year periods, and performed a similar analysis to separate the effect of LAI on ${\mathrm{Tr}}_{\mathrm{ano}}$ and α.

Author contributions

Y.Z. conceived the idea. Y.Z. and J.L. designed the study, with contributions from S.P. J.L. performed the analysis, J.L. and Y.Z. wrote the manuscript. J.L., Y.Z., E.B., J.Z., T.F.K., X.L., S.Z., H.Z., M.H., S.P. discussed and commented on the results and the manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

The original CMIP6 model simulations are publicly available from the CMIP6 data portal (https://esgf-node.llnl.gov/search/cmip6/). Earth system models and simulations used in this study are listed in Supplementary Table 1. The data generated in this study are provided in the Source Data file (10.6084/m9.figshare.27889785.v1). Source data are provided with this paper.

Code availability

The code used for the calculation of Tr- and α-induced LMF is available at GitHub (https://github.com/jlyfine/comveg), and have been archived on figshare (10.6084/m9.figshare.27889749.v1)

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-55175-0.