Introduction

It is well established that past climate change provides a reference for our future climate1,2,3. Recent study has highlighted that a climate similar to that of the Pliocene will appear in near-term climate projections4. As a result, the climate of the Pliocene has received increasing attention in the paleoclimate community. Over the past 15 years, two phases of the Pliocene Model Intercomparison Project (PlioMIP) have been executed. This effort has been made possible by decades of research establishing environmental and geographical conditions of the Pliocene, in particular by means of the Pliocene Research, Interpretation and Synoptic Mapping (PRISM) initiative and has involved continued efforts in quantifying and understanding Pliocene climate from geological reconstructions and modeling5,6,7,8,9,10,11,12,13,14. From PlioMIP we have gained a better understanding of the large-scale features and driving mechanisms of the mid-Piacenzian warm period (MPWP) that may be useful in the context of future climate change. On the other hand the effort has provided opportunities for the cross-validation of regional climate patterns in records and simulations of this time period.

The East Asian summer monsoon (EASM) is a hybrid tropical and subtropical monsoon with characteristics different from a typical tropical monsoon15,16,17,18. Monsoon circulation and precipitation are the two main aspects that characterize monsoon climate19,20, and these are in the focus of studies of monsoon changes in the future by means of climate projections. Simulated future changes in the EASM show behavior that differs from that of other monsoon members21.

Despite the fact that precipitation is projected to increase in both EASM and other monsoon systems, the expected future strengthening of the EASM circulation is in contrast to projected weakening of the circulation in other monsoon regions22,23,24,25. The combined effect of two climate characteristics must be considered in future EASM precipitation. Relative importance of increased water vapor transport, caused by enhanced circulation and surface warming, alternates with the temperature threshold26. This means that the future EASM precipitation increase at lower temperature rise thresholds (i.e., for global warming targets of 1.5 °C and 2 °C above pre-industrial levels) is mainly under thermodynamic control, while dynamic processes related to strengthening of monsoon circulation play a more dominant role for temperature rise beyond 2 °C26. In this study we would like to further explore this topic in the context of the Pliocene. Are thermodynamical or dynamical processes more relevant for EASM change in warmer equilibrium climates? Sun et al.27 quantified the EASM dynamics under the ECP4.5 scenario with reference to the MPWP and yielded a thermodynamically controlled increase in future EASM precipitation27. However, their conclusion is based on only one model from PlioMIP1 because PlioMIP1 lacks the complete set of variables required for moisture budget analysis. This limitation severely hampers the comparability of EASM dynamics between PlioMIP1 and PlioMIP2. Increased climate sensitivity has been documented for some models that contributed to PlioMIP2 but not to PlioMIP113,27,28,29. Consequently, particularly warm climate states may not be represented in the study by ref. 27. The PlioMIP2 ensemble offers the opportunity to re-examine EASM dynamics during the MPWP to improve our understanding of the mechanisms that may drive future EASM precipitation changes. With our study, we also overcome a shortcoming of previous PlioMIP1-based analyses of the EASM that are in lack of quantitative comparisons with reconstructions27,29,30,31,32.

This study quantitatively compares changes in EASM precipitation during the MPWP as reconstructed from pollen records and as simulated by PlioMIP2 models and shows a clear data–model discrepancy. We present a new approach that can be used to reconcile data and models where we decompose the physical processes controlling monsoon precipitation changes and then spatially match proxy–recorded precipitation changes with changes in the decomposed physical processes. Thereby we provide a physical interpretation of precipitation changes in the records. We highlight that thermodynamically controlled increase in water vapor transport leads to an overall enhancement of EASM precipitation, while thermodynamic and dynamical processes show contrasting dominant controls on tropical and subtropical EASM monsoon precipitation in the records and simulations during the MPWP.

Results

Quantitative data–model comparison: data–model disagreement

Towards conducting the data–model comparison, we first examine the mean state of the East Asian summer water vapor cycle for the PI period from the PlioMIP2 multi-model ensemble (MME). Following the definition by ref. 21, the MME PI EASM domain (black+, Fig. 1a–c) is in agreement with observations. We note that a net moisture flux convergence is required to maintain a humid climate in East Asia as precipitation exceeds evaporation in the area (shading, Fig. 1c).

Fig. 1: Data and model comparison of EASM precipitation during the MPWP.
figure 1

Left panel: pre-industrial (PI) mean June-July-August (JJA) of three variables (from top to bottom: a precipitation (P), b evaporation (E), c precipitation minus evaporation (P-E); units: mm/day) derived from the PlioMIP2 multi-model ensemble (MME); right panel: as left panel but for differences of three variables between mid-Piacenzian Warm Period (MPWP) and PI (d–f). Black dotted areas in the right panel indicate agreement of the MME with regard to precipitation anomaly, MPWP vs. PI (at least 10 out of 14 models show the same sign of precipitation change as the MME). Towards a quantitative data–model comparison the same color bar is used for recorded (colored circles; 25 pollen-based precipitation records, shown in the δP anomaly MPWP-PI) and simulated precipitation changes. According to the definition of ref. 21, the EASM domain is calculated separately for PI (black “+” symbol, left panel) and MPWP periods (colored “+” symbols, divided into three categories: common areas for both periods (gray “+”, right panel), expanding/shrinking areas during the MPWP relative to PI disentangled by different colors (blue/yellow “+”, right panel)). Black and yellow curves denote the coastlines of PI (left panel) and MPWP (right panel), respectively.

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The MME EASM domain during MPWP is almost unchanged compared to the PI period, apart from a weak expansion of the EASM margin. In contrast to negligible changes in EASM area, changes in the water cycle in the MPWP monsoon region relative to the PI period are evident (Fig. 1d–f). In agreement with elevated temperature in the atmosphere, precipitation and evaporation over East Asia are both simulated to increase in the MPWP compared to the PI period (Fig. 1d, e). As precipitation increases more than evaporation, we find intensified net rainfall, thus leading to a wetter MPWP East Asia (Fig. 1f) which is consistent with earlier studies using qualitative records that revealed a wetter East Asia condition during the MPWP27,29,30,32.

Across the PlioMIP2 MME, there is a spatially consistent increase in EASM precipitation during the MPWP, while the precipitation response from individual model simulations is less in agreement with the MME, especially in the EASM domain (Fig. 1d). Model uncertainty highlights the necessity of employing quantitative precipitation reconstruction as a model-independent source of information to validate reliability of simulated precipitation changes during the MPWP. However, pollen-based precipitation records and simulations are not well matched, as shown by inconsistent precipitation changes among records in contrast to a consistent precipitation increase derived from the climate simulations (Fig. 1d). The important question, that we would like to answer with this study, is how records, showing inconsistent precipitation changes, and models, suggesting a spatially consistent precipitation increase, may be reconciled. Our answer to this question is illustrated in the following section of this paper.

Decomposition of physical processes controlling EASM precipitation changes to reconcile data–model comparison

Using water vapor budget to reveal physical processes of EASM precipitation

Considering the spatial inhomogeneity of recorded precipitation and the multifaceted processes that affect precipitation, the decomposition of physical processes controlling monsoon precipitation is used to reconcile inferences from data and models. We analyze sources and sinks of water vapor in East Asia employing the moisture budget equation. In the mean moisture budget (Fig. 2a), evaporation and vertical moisture transport are the two main sources of water vapor in East Asia for both the PI and MPWP periods. The supply of water vapor to East Asia is largely balanced by precipitation (water vapor sinks), whereas the remaining terms (horizontal moisture transport and residual) contribute little to sources and sinks of water vapor in East Asia (Fig. 2a). As precipitation exceeds evaporation, this in turn leads to a humid East Asian monsoon climate for both periods (Fig. 2a).

Fig. 2: Moisture budget analysis calculated over the EASM monsoon domains (units: mm/day).
figure 2

a Mean JJA budget for MPWP and PI periods and b difference in the mean budget between the two periods; c thermodynamic and dynamic decomposition of moisture transport changes that contribute to MPWP EASM precipitation anomalies. The analysis is based on an average of simulated climate patterns over the monsoon domain.

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Water vapor sources and sinks in East Asia differ between the two periods. Water vapor, which maintains the enhanced EASM precipitation, originates during MPWP mainly from enhanced vertical moisture transport, followed by the contribution of enhanced evaporation (Fig. 2b). However, signs of the horizontal moisture transport and of the residual term are uncertain across the PlioMIP2 models (Fig. 2b). Albeit both precipitation and evaporation in East Asia are elevated during the MPWP, the increase in precipitation outpaces that of evaporation, resulting in raised MPWP net precipitation in East Asia. We find that the vertical component of moisture transport dominates the horizontal component with regard to increased net precipitation during the MPWP (Fig. 2b). Most of the models (12 out of 14, except COSMOS and HadCM3), simulate an increase in EASM precipitation, which is consistent with the increase in precipitation in the MME (Fig. 2b). In contrast, COSMOS and HadCM3 simulate a decrease in EASM precipitation during the MPWP, mainly due to decrease in vertical moisture transport (Fig. 2b).

We separate changes in vertical and horizontal moisture transport into their respective thermodynamic (δTH; changes in specific humidity at constant circulation; Fig. 2c) and dynamic (δDY; changes in circulation at constant specific humidity; Fig. 2c) contributions and co-variations in both (not shown). In order to understand inconsistency in the sign of simulated horizontal moisture transport in the MME, we study their relative contribution to changes in vertical/horizontal moisture transport and MPWP precipitation changes.

Enhanced total water vapor transport (sum of horizontal and vertical moisture transport) is predominantly controlled by thermodynamics. This is inferred from 10 out of 14 models. Nevertheless, dynamic enhancement of total water vapor transport cannot be neglected as it dominates in 4 of the 14 models (Fig. 2c). Thermodynamic enhancement of total water transport is mainly due to increase in vertical water vapor transport, less due to elevated horizontal moisture transport. In contrast, dynamic enhancement of total water vapor transport is mainly related to horizontal moisture transport. Both thermodynamic and dynamic processes increase simulated horizontal moisture transport during the MPWP (Fig. 2c). Inconsistencies in horizontal moisture transport anomaly across the PlioMIP2 MPWP MME can be explained by thermodynamic and dynamical processes, caused by changes in specific humidity and changes in circulation, respectively, and nonlinear processes, caused by changes in both (not shown), contributing to the net horizontal water transport (Fig. 2c).

Contrasting control of thermodynamic and dynamic processes on tropical and subtropical monsoon precipitation: data–model comparison

We quantify relative contribution of different physical processes to monsoon precipitation from the average water vapor budget in the region and identify those that dominate the MPWP EASM precipitation anomaly (Fig. 2). However, our analysis lacks spatial detail due to the applied area average. This caveat impedes comparison of models and records and limits physical interpretation of recorded precipitation anomalies. To enable reconciliation of model- and data-based anomalies, we therefore show in Fig. 3 the spatial distribution of thermodynamically and dynamically controlled enhancement of moisture transports.

Fig. 3: Decomposed physical processes of precipitation used for site-by-site spatial matching with recorded precipitation.
figure 3

As Fig. 2c, but showing the spatial distribution of thermodynamic (a–c) and dynamic processes (d–f) in the MME which are used to decode the physical representations of pollen records by matching the pollen-based inference with thermodynamic and dynamic processes (colored circles).

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The thermally controlled enhancement of water vapor transport facilitates overall enhancement of EASM precipitation during the MPWP (compare Fig. 3a and Fig. 1d) mainly via thermodynamic control on increased vertical water vapor transport. In the tropics enhanced vertical water vapor transport contributes to an increase in EASM precipitation in reconstruction (1 of 25 records) and simulation (Fig. 3c). Although the thermodynamic component of horizontal water vapor transport largely increases area average EASM precipitation during the MPWP (Fig. 2c), its contribution is not spatially uniform (Fig. 3b). The pattern of enhanced horizontal moisture transport due to thermodynamic contribution, which in turn increases EASM precipitation during the MPWP, is opposed by a reduction in the southern part of northern China. Regional decrease in precipitation in 2 of the 25 pollen records may reflect this process (Fig. 3b).

There is regional diversity in the contribution of horizontal and vertical circulation changes to MPWP total water vapor transport anomalies. Dynamical processes significantly increase water vapor transport towards the subtropics, while water vapor transport to the remaining monsoon region is significantly reduced (Fig. 3d).

Enhanced subtropical water vapor transport mainly derives from enhanced horizontal circulation (Supplementary Fig. 2). Regional increase in precipitation in 12 of the 25 records (10 within the EASM domain and 2 outside the EASM domain) can be explained by the dynamically enhanced subtropical water vapor transport (Fig. 3e). In contrast, reduced water vapor transport to the remaining monsoon region is mainly due to reduced vertical transport linked to dynamically weakened vertical motion. This process explains the decrease in EASM precipitation in three records (Fig. 3f). In contrast, dynamics enhance the vertical moisture transport outside the EASM domain, explaining the increase of precipitation in six records in the region (Fig. 3f). Furthermore, reduced precipitation recorded at one location in the northwest margin of the EASM can be explained by weakened horizontal vapor transport due to weakened horizontal circulation (Fig. 3e).

In short, thermally controlled increase in horizontal and vertical moisture transports determines the overall enhancement of EASM precipitation during the MPWP. Enhanced tropical and subtropical EASM precipitation is in both records and simulations controlled by enhanced vertical moisture transport (thermodynamics) and by increased horizontal moisture transport (dynamics), respectively. This reflects two distinct sources of water vapor for enhanced regional monsoon precipitation (Fig. 4): one from the Bay of Bengal (tropical source) and the other from the western Pacific subtropical high (WPSH) (subtropical source). The latter contributes more to the increase in regional monsoon precipitation due to enhanced WPSH (Supplementary Movie 1). In addition to contrasting control of thermodynamic and dynamic processes on enhancement of tropical and subtropical monsoon precipitation, recorded and simulated reduction of tropical and subtropical monsoon precipitation is also controlled by the two different physical processes. Reduced thermodynamic contribution to horizontal water vapor transport explains decreases in subtropical EASM precipitation, whereas reductions in tropical EASM precipitation are dynamically controlled by the reduced vertical water vapor transport due to weakened vertical motion.

Fig. 4: The sources of moisture that enhance tropical and subtropical EASM precipitation during the MPWP through thermodynamic and dynamic processes.
figure 4

Left panel: the vertically integrated water vapor transport throughout the troposphere is represented by the moisture fluxes (\(\langle q\cdot {{\bf{V}}}_{H}\rangle\), units: kg m−1  s−2) in JJA for PI (a) and MPWP periods (c) and the differences between MPWP and PI periods (e). Right panel: horizontal wind vector at 850 hPa (units: m s^−1) in JJA for PI (b), MPWP (d) and differences between MPWP and PI periods (f). The colored circles in (e, f) are 11 proxy records with precipitation increase within EASM domain. The strongest moisture pathway into the EASM domain, sustaining the mean state of EASM precipitation, is depicted by the blue rectangle in (a, c).

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Paleoclimate perspectives constrain near-term future monsoon dynamics

The greenhouse gas single-factor experiments provided by PlioMIP2 and CMIP6 offer the opportunity to compare similarities and differences in the control of physical processes on monsoon for increased greenhouse gases in past and future. We show that elevated greenhouse gases increase monsoon precipitation in two climatic contexts mainly through enhanced moisture transport regulated by thermodynamic effects that follow the Clausius-Clapeyron relationship (Fig. 5). That is, thermodynamics at stable elevated greenhouse forcing are shown to enhance both horizontal and vertical water vapor transport in two climate equilibrium states (Fig. 5, top and middle panels), while thermodynamics of a rapid increase in current greenhouse gas concentrations increases monsoon precipitation mainly through enhanced vertical moisture transport (Fig. 5, bottom panel).

Fig. 5: Comparison of the decomposed physical processes of monsoon precipitation: past warmth vs. future warming.
figure 5

As Fig. 2c, but separating thermodynamic and dynamical contributions to moisture transport (units: mm/day) in response to similar CO2 increase in two climate contexts, including MPWP (top); PI (middle); and current transient warming relative to the PI period (bottom). From left to right: thermodynamic and dynamical decompositions of changes in total moisture transport, changes in horizontal moisture transport, changes in vertical moisture transport.

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Similarly to variable mechanisms by which thermodynamics contribute to increased monsoon precipitation under stable or varying elevated greenhouse forcings, there are also contrasting effects of water vapor dynamics for equilibrium and transient climatic conditions. Dynamic effects increase monsoon precipitation in two equilibrium states while reducing it in transient climate (Fig. 5, left panel). Such distinct dynamical effects arise mainly from very different responses of horizontal circulation in the monsoon region in the two climatic contexts (Fig. 5, middle and right panels). In the two equilibrium states horizontal circulation responds to the increase in greenhouse gases with enhanced horizontal moisture transport. For ongoing rapid increase in greenhouse gases there is no contribution to horizontal moisture transport (Fig. 5, middle panel). The weakening effect of dynamical processes on water vapor transport for warming linked to current rapid increase in greenhouse gases is mainly due to suppressed water vapor transport caused by the reduced vertical circulation (Fig. 5, right panel). In contrast to relatively consistent changes in the area-averaged water budget (Fig. 5), response of monsoon precipitation (Supplementary Fig. 3) and thermodynamic and dynamical contributions to an increase in greenhouse gases is far from spatially uniform in the MME, both for equilibrium and transient climate states (Supplementary Fig. 4, Supplementary Fig. 10, Supplementary Fig. 15). We also find considerable variability among models even in the same climate state (Supplementary Fig. 5, Supplementary Fig. 6, Supplementary Fig. 7, Supplementary Fig. 8, Supplementary Fig. 9; Supplementary Fig. 11, Supplementary Fig. 12, Supplementary Fig. 13, Supplementary Fig. 14; Supplementary Fig. 16, Supplementary Fig. 17, Supplementary Fig. 18, Supplementary Fig. 19, Supplementary Fig. 20). Uncertainty in past and future monsoon dynamics relate to each other.

Discussion

The EASM represents a hybrid tropical and subtropical summer monsoon system in East Asia. This study provides a quantitative model–data comparison of EASM precipitation anomalies MPWP vs. PI, allowing us to obtain information that may help understand and evaluate projections of EASM precipitation. By analyzing the moisture budget balance, we propose a new approach to reconcile the data–model discord of MPWP EASM precipitation anomalies. In addition to precipitation enhancement over the entire monsoon area that is controlled by thermodynamic processes, we highlight that the relative increase in tropical and subtropical MPWP EASM precipitation is controlled by thermodynamic and dynamical processes, respectively. This inference differs from overall enhancement of EASM precipitation under the impact of orbital forcing (mid-Holocene) under dynamic control33. Consequently, we highlight that processes driving EASM behave differently depending on whether climate forcing is more associated to orbital parameters or to geography and substantial differences in greenhouse gas concentrations. We note that at centennial time-scales future climate is controlled more by the overall greenhouse gas concentration than by orbital or tectonic changes. The key findings of our study are summarized as follows:

  1. 1.

    We highlight data–model mismatch of MPWP EASM precipitation anomalies; spatially divergent precipitation changes inferred from records are opposed to a spatially nearly consistent increase in simulated EASM precipitation.

  2. 2.

    We propose the decomposition of monsoonal precipitation into contributions by relevant processes to reconcile inferences from data and model simulations. Overall, MPWP increases in EASM precipitation are controlled by thermodynamically enhanced vertical moisture transport. This is consistent with physical processes enhancing EASM precipitation under the impact of future anthropogenic warming27 but differs from dynamical enhancement of EASM precipitation mainly via enhanced horizontal moisture transport at orbital time scales33.

  3. 3.

    In addition to the overall thermal control, thermodynamic and dynamic processes tend to dominate with respect to tropical and subtropical MPWP EASM precipitation anomalies. The thermodynamic increase of vertical moisture transport towards the tropical EASM region enhances precipitation recorded and simulated there. Dynamical enhancement of precipitation on the other hand is evident in recorded and simulated subtropical EASM. In addition to enhancing tropical and subtropical EASM precipitation, both thermodynamic and dynamic processes control regional decrease in EASM precipitation. Reduced vertical water vapor transport under dynamic control may explain recorded decrease of subtropical EASM precipitation, while thermodynamic decrease in horizontal moisture transport provides an explanation of recorded reduction in another part of subtropical EASM precipitation.

  4. 4.

    Both thermodynamic and dynamical effects enhance regional tropical and subtropical EASM precipitation in records and simulations during the MPWP, reflecting the two different sources of water vapor that enhance monsoon precipitation. The thermodynamic enhancement of tropical EASM precipitation originates from enhanced water vapor transport in the tropical Indian Ocean and the dynamic increase in subtropical EASM precipitation due to enhanced water vapor transport by western Pacific subtropical high.

  5. 5.

    The dynamics of the EASM under elevated greenhouse gases in the past warm period exhibit similar traits to those anticipated under increasing greenhouse gases in future projection scenarios. In both cases, a thermally controlled increase in EASM precipitation is observed. This insight stands as a significant outcome from our investigation into monsoon dynamics during the past warm period.

In conclusion, through the decomposition of physical processes controlling EASM precipitation, we identified that (i) certain physical processes do align with the changes in recorded precipitation. (ii) Areas, where the sum of the decomposed physical processes does not align with the sign of the recorded precipitation, are indicative of biases in the simulated magnitude of the relative contribution of the decomposed physical processes to the total simulated precipitation response. These biases require improvement in the models. (iii) The proposed decomposition of the monsoon precipitation process in this study serves not only to reconcile the comparison between records and simulations in the East Asian monsoon region but also facilitates the comparison of precipitation records and simulations in tropical monsoon areas. Moreover, it extends its utility to the comparison of precipitation records and simulations outside the monsoon region.

The variations in orbital parameters during the Pliocene can influence monsoon precipitation34,35. While the PlioMIP2 protocol did not consider changes in orbital parameters, this will be an optional experiment in the upcoming PlioMIP336. In addition, the inclusion of aerosol emissions during the Pliocene37 and the growth of the Antarctic ice sheet from the Miocene to the Pliocene38 in the models could provide potential opportunities to improve consistency between simulations and records. In addition, the number of model members used for ensemble average may also influence the spatial distribution of the Pliocene monsoon precipitation response (Fig. 1d and Supplementary Fig. 21).

Methods

Proxy records of East Asian during the MPWP

We compiled 25 published MPWP fossil pollen records across East Asia, ensuring that they exhibit clear and complete pollen spectra with a resolution higher than 60 ka. All records are based on paleomagnetic or other precise dating methods (e.g., Electron Spin Resonance - ESR) to provide reliable age data, with the paleomagnetic age dates calibrated according to the latest geomagnetic polarity time scale39.

Precipitation is quantitatively derived using the Modern Analogue Technique40 due to its advantages in large-scale reconstructions41. To address the lack of modern analogs42,43, we utilize Plant Functional Type scores in the calculation of squared chord distance44. More detailed descriptions can be found in the Supplementary Text 1 and Supplementary table 1.

PlioMIP2 core simulations

Precipitation differences in MPWP (Eoi400) with regard to pre-industrial (E280) as simulated in the PlioMIP2 are quantitatively compared with pollen-based reconstructed precipitation. This analysis is supported with climate dynamics analysis methods to extract the physical representation of precipitation in the records.

The PlioMIP2 protocol12 required modeling groups to follow a common procedure towards the setup of MPWP simulations. PlioMIP2 simulations selected for our study (Supplementary Table 2) focus on some of the key changes including: a) the atmospheric CO2 concentration is set to 400 ppm; b) Greenland ice cover is reduced to 25% of the pre-industrial (PI) period9; c) terrestrial vegetation is derived from reconstruction by ref. 45; d) minor tectonic changes with regard to modern geography include the closure of the Bering Strait, Hudson Bay and Canadian Arctic Archipelago, as well as further reconfigurations of coastlines and ocean bathymetry as a result of strongly reduced West Antarctic Ice Sheet and changes at Kara Strait, Java Sea, Torres Strait, and South China Sea12. However, not all groups implemented all of these tectonic changes13, and HadGEM3 did not implement any of them46. Fourteen models who contributed MPWP simulations to PlioMIP2 were considered in this study (Supplementary table 2). Importantly, all PlioMIP2 models used in this study show robust performance in simulating the East Asian monsoon climate, as demonstrated in the works27,30,47,48,49,50,51. The last 30 years of simulations served to analyze EASM and related climate patterns.

Nevertheless, state-of-the-art climate models exhibit biases in the simulation of regional precipitation, and although high-resolution models are recommended for improvement52, their universal added value is not guaranteed53. Analysis of high-resolution MIP models54 shows that even with high-resolution simulations attempting to address these issues, the prevalent dry biases persist in low-resolution simulations in core Asian monsoon regions. Increasing model resolution alone has limited effectiveness in improving total mean precipitation but can improve the model’s ability to simulate extreme precipitation54,55.

To reduce uncertainty in individual model simulations, a MME mean of PlioMIP2 models is employed for comparison with proxy data. This approach is considered superior, as the ensemble mean’s skill can exceed that of individual models52.

Individual greenhouse gas (GHG) experiment following the PlioMIP2 and CMIP6 protocols

To isolate the effects of increased greenhouse gas concentrations (relative to PI) on monsoonal precipitation and its physical processes, we additionally analyzed single-factor greenhouse gas experiments conducted in three different climate contexts in PlioMIP2 and Coupled Model Intercomparison Project Phase 6 (CMIP6) (Supplementary table 3). These include an experiment conducted at equilibrium with MPWP geography as PlioMIP2 core simulation Eoi400 but where CO2 concentrations were reduced to the same level as in the PI (Eoi280); an experiment based on PI geography as E280, but where CO2 concentrations were increased to the same level as in the MPWP core simulation (E400); and experiments with similar increases in CO2 concentrations (compared to the PI) taken from ongoing transient climate (2006–2025).

Diagnostic methodology

The moisture budget equation is suitable to identify the mechanism causing EASM precipitation anomalies, MPWP with respect to PI, because it incorporates the physical processes that affect precipitation33,56,57. The time–mean air column integral of this equation throughout the troposphere can be written as:

$$P=E-\left\langle \omega {\partial }_{P}q\right\rangle -\left\langle {{\bf{V}}}_{H}\,\cdot\, \nabla q\right\rangle +{\rm{Res}}$$
(1)

where P is the precipitation, E is the evaporation, ω is the vertical velocity, q is the atmospheric specific humidity, VH is the horizontal wind, and Res is the residual term that includes transient eddy effects and deformation of the surface moisture transport by the surface pressure gradient33,58. The bracket notation refers to the vertical integral of the atmospheric column across the troposphere. \(\left\langle\, \cdot\, \right\rangle =\frac{1}{{{gp}}_{w}}\mathop{\int }\nolimits_{0}^{Ps}\,\cdot\, {dp}\), where Ps is the surface pressure, ρw is the density of water, and g is the gravitational acceleration. The first bracket on the right-hand side of Eq. (1) refers to vertical moisture advection whereas the second term describes horizontal transport of water vapor.

The relative importance of each physical process In Eq. (1) for differences in precipitation between two climates (e.g., MPWP relative to the PI), i.e., δP, can be derived from the difference in the water vapor budget balance between the two periods (Eqs. 2 and 3).

$$\delta P=\delta E-\delta \left\langle \omega {\partial }_{P}q\right\rangle -\delta \left\langle {{\bf{V}}}_{H}\,\cdot\, \nabla q\right\rangle +\delta {Res}$$
(2)
$$\begin{array}{l}\approx \delta E-\left\langle \delta \omega {\partial }_{P}q\right\rangle -\left\langle \omega {\partial }_{P}\delta q\right\rangle -\left\langle \delta \omega {\partial }_{P}\delta q\right\rangle -\left\langle \delta {{\bf{V}}}_{H}\,\cdot\, \nabla q\right\rangle \\\qquad\,-\,\left\langle {{\bf{V}}}_{H}\,\cdot\, \nabla \delta q\right\rangle -\left\langle \delta {{\bf{V}}}_{H}\,\cdot\, \nabla \delta q\right\rangle +\delta {\rm{Res}}\end{array}$$
(3)

Thermodynamic and dynamic decomposition of changes in second and third terms on the right hand side of Eq. (2) are conducted to further distinguish between relative contributions of changes in water vapor transport by thermodynamic and dynamic processes. For example, the thermodynamic contribution results from changes in specific humidity at fixed atmospheric circulation (due to increased water holding capacity of warmer air according to the Clausius-Clapeyron equation) whereas the dynamic contribution is caused by atmospheric circulation changes at constant specific humidity. The contribution of both changes in atmospheric circulation and changes in specific humidity to changes in water vapor transport is called the nonlinear term and is usually neglected because it is smaller compared to the other terms.

Thermodynamic (TH), dynamic (DY) and nonlinear (NL) components of changes in vertical moisture transport can be written as follows:

$$\delta {\rm{TH}}=-\left\langle \omega {\partial }_{P}\delta q\right\rangle =-\frac{1}{g{\rho }_{w}}\mathop{\int }\nolimits_{0}^{Ps}{\rm{\omega }}{\partial }_{P}\delta q\,{dp}$$
(4)
$$\delta {\rm{DY}}=-\left\langle \delta \omega {\partial }_{P}q\right\rangle =-\frac{1}{g{\rho }_{w}}\mathop{\int }\nolimits_{0}^{Ps}\delta \omega {\partial }_{P}q\,{dp}$$
(5)
$$\delta {\rm{NL}}=-\left\langle \delta \omega {\partial }_{P}\delta q\right\rangle =-\frac{1}{g{\rho }_{w}}\mathop{\int }\nolimits_{0}^{Ps}\delta \omega {\partial }_{P}\delta q\,{dp}$$
(6)

Here we extend the work of Chou and Lan57 and decompose horizontal moisture transport in addition to vertical moisture transport33,59. Changes in horizontal moisture transport were further decomposed into thermodynamic(δTH) and dynamic contributions (δDY):

$$\delta {\rm{TH}}=-\left\langle {{\bf{V}}}_{H}\,\cdot\, \nabla \delta q\right\rangle =-\frac{1}{g{\rho }_{w}}\mathop{\int }\nolimits_{0}^{Ps}{{\bf{V}}}_{H}\cdot \nabla {\rm{\delta }}q\,{dp}$$
(7)
$$\delta {\rm{DY}}=-\left\langle \delta {{\bf{V}}}_{H}\,\cdot\, \nabla q\right\rangle =-\frac{1}{g{\rho }_{w}}\mathop{\int }\nolimits_{0}^{Ps}{\delta {\bf{V}}}_{H}\cdot \nabla q\,{dp}$$
(8)
$$\delta {\rm{NL}}=-\left\langle \delta {{\bf{V}}}_{H}\,\cdot\, \nabla \delta q\right\rangle =-\frac{1}{g{\rho }_{w}}\mathop{\int }\nolimits_{0}^{Ps}{\delta {\bf{V}}}_{H}\cdot \nabla \delta q\,{dp}$$
(9)