Introduction

Since the Industrial Revolution, Global Mean Surface Temperature (GMST) has continued to increase due to anthropogenic carbon emissions (IPCC 2021). Unlike the almost steady increase in atmospheric carbon dioxide, GMST shows a staircase-like increasing trend. Specifically, global warming has slowed down since the 1990 s (Fyfe et al. 2016; Kosaka & Xie 2013). However, GMST has once again shown an accelerating warming rate recently, with 2024 being the hottest year on record (Xie et al. 2025). Climate internal variability is an essential element that drives historical global warming to follow this staircase-like evolution (Kosaka & Xie 2013; England et al. 2014). Internal variability can affect the global energy balance, leading to variations in the short-term warming rate, thereby increasing uncertainty in future projections (Bordbar et al. 2017, 2019; Kang et al. 2013; Wu et al 2024).

As described in previous studies, internal variability also influences atmospheric circulation and precipitation through thermodynamic and dynamic processes (Capotondi et al. 2023; Liu & Di Lorenzo 2018). At the interdecadal time scale, the Interdecadal Pacific Oscillation (IPO) or Pacific Decadal Oscillation (PDO) is a leading pattern of sea surface temperature (SST) anomalies in the tropical Pacific or North Pacific, respectively (Henley et al. 2015; Smith et al. 2016). Recent studies revealed that the negative phase of the IPO has dominated the recent strengthening of the Pacific Walker Circulation, thereby contributing to Pacific cooling and recent “hiatus” (England et al. 2014). By modulating the Atmospheric circulation, Pacific SST anomalies influence precipitation changes (Schneider et al. 2014; Sun et al. 2021; Wang et al. 2018). For example, the tropical Pacific, California, as well as global monsoon precipitation changes are closely linked to the IPO (Dong et al. 2021; Sun et al. 2021; Huang et al. 2020; Jiang & Zhou 2025). This decadal variability could either accelerate or slow down the influence of external forcing, complicating the assessment of precipitation change from limited observations to the sparse temporal length (Fyfe et al. 2016; Kosaka & Xie 2013).

Although the IPO or PDO is the dominant decadal mode in the Pacific, other Pacific decadal modes also play crucial roles in climate impacts. In the extratropical regions, the North Pacific Gyre Oscillation (NPGO) mode exists in the North Pacific while the South Pacific Decadal Oscillation (SPDO) mode prevails in the South Pacific (Capotondi et al. 2023; Liu & Di Lorenzo 2018). Previous studies have demonstrated that these modes are significant in modulating precipitation patterns, ocean currents, and ecological responses. Additionally, the tropical Indian Ocean interacts with the tropical Pacific, also influencing changes in the Walker Circulation, thereby affecting precipitation patterns (Zhang et al. 2019, 2021). Due to limitations in observational records, previous studies have primarily focused on the impacts of IPO or PDO on tropical circulation and precipitation, while research on the synergistic effects between the tropical Pacific and Indian Ocean at decadal timescales remains relatively scarce. This raises a scientific question: Do the tropical Pacific and Indian Ocean exhibit coupled or independent decadal variability that influences atmospheric circulation and precipitation changes?

The recently developed coupled models, especially the large ensemble simulations from a single model, forced by the same external forcing with perturbed initial conditions, present an opportunity to study the roles of internal variabilities in climate changes, mitigating the shortage of observations in time length (Rodgers et al. 2021; Wu et al. 2021, 2024). Using the large ensemble simulations from the Community Earth System Model version 2 (CESM2), this work provides new insight into tropical Indo-Pacific decadal variability and its corresponding impact on atmospheric circulation and precipitation changes. Except for the impact from the traditional interdecadal variability of the IPO, we have identified that the interdecadal Warm Pool Seesaw (WPS) mode also plays a critical role in influencing atmospheric circulation and precipitation patterns. Furthermore, this study has developed a new index to accurately reproduce observed tropical precipitation changes based on these two modes, which is beneficial for predicting future precipitation changes.

Data and methods

Observational dataset and model experiments

To verify the role of decadal variability of SST on precipitation changes, this paper uses the monthly observed Optimum Interpolation SST (OISST) version 2 (Reynolds et al. 2002) and the precipitation datasets (Adler et al. 2003), which are provided by the National Oceanic and Atmospheric Administration (NOAA) and the Global Precipitation Climatology Project (GPCP), respectively.

To estimate the uncertainty of internal variability, this paper uses the outputs of large ensembles from CESM2 (Rodgers et al. 2021). CESM2 Large Ensemble (CESM2-LE) uses a combination of different initial states to create an ensemble spread comprising 100 members at 1-degree spatial resolution under CMIP6 historical and SSP370 future radiative forcing scenarios. More information about the CESM2-LE outputs can be found at https://www.cesm.ucar.edu/community-projects/lens2.

Methods

Firstly, to investigate the diverse decadal variability, we separate the external forcing signal and internal variability. Since the 100 members are driven by the same external forcing, the ensemble mean of 100 members can be presented as the response to external forcing. Thus, the difference between the single member and the ensemble mean can be considered as internal variability, which can be expressed as:

$${X}_{internal}\left(i\right)=X\left(i\right)- {X}_{forced}, i=1 to 100$$
(1)

where X means a certain variable (e.g., SST, precipitation), \({X}_{forced}\) is the ensemble mean of 100 members, \({X}_{internal}(i)\) is the difference between the original \(X(i)\) and forced response \({X}_{forced}\), presenting the internal variability for member i.

Then, this work selects a common period 1985–2014 to calculate a 30 year linear trend for member i \([{X}_{internal}^{trend}\left(i\right)]\), consistent with the observations. In addition, we utilize the period 2041–2060 to calculate the 20 year trend under the SSP370 scenario for comparison with historical results. Next, we further evaluated the fundamental characteristics of the 30 year trend for the 100 members using the Empirical Orthogonal Function (EOF) method.

Based on the EOF results, we define the IPO and WPS index and calculate the 30 year linear trend from 1985 to 2014 for the IPO and WPS index for each ensemble member. The IPO index [\({IPO}_{internal}(i)\)] is defined as follows (Huang et al. 2020): the 7 year running mean of the difference in the averaged SST anomalies [\({SST}_{internal}(i)\)] between the tropical central and eastern Pacific (180°E to 90°W, 10°S to 15°N) and the north Pacific (150°E to 160°W, 30°N to 45°N) for each member i. Similarly, the WPS index [\({WPS}_{internal}(i)\)] is defined as the difference between the tropical western Pacific (150°E to 170°W, 5°S to 5°N) and the southeastern Indian Ocean (90°E to 110°W, 15°S to 5°S). Then we calculate the 30 year linear trend of the IPO \([{IPO}_{internal}^{trend}\left(i\right)]\) and WPS [\({WPS}_{internal}^{trend}\left(i\right)\)] for each member i.

Based on a threshold of ± 0.8 standard deviations from the 30 year trends of the IPO index across 100 ensemble members (± 0.8 σ), this study classified IPO events for each ensemble member. Specifically, A positive IPO event [IPO(+)]: the IPO index exceeding + 0.8 σ; A negative IPO event [IPO(−)]: the IPO index falling below −0.8 σ; All other cases are normal IPO events [IPO(0)]. Similarly, we defined three WPS categories: WPS(+), WPS(−), and WPS(0).

To estimate the contribution of IPO and WPS to the precipitation variability, we calculate the first-order regression coefficients between IPO or WPS and a specific variable X based on 100 members, which can be expressed as:

$${X}_{internal}^{trend}={r}_{X,IPO}\cdot {IPO}_{internal}^{trend}+b$$
(2)

or

$${X}_{internal}^{trend}={r}_{X,WPS}\cdot {WPS}_{internal}^{trend}+b$$
(3)

where \({X}_{internal}^{trend}\), \({IPO}_{internal}^{trend}\), \({WPS}_{internal}^{trend}\) is the same as \({X}_{internal}^{trend}(i)\), \({IPO}_{internal}^{trend}(i)\), \({WPS}_{internal}^{trend}\left(i\right)\), but for the matrix of 100 members, \({r}_{X, IPO}\) and \({r}_{X,WPS}\) presents the regression coefficients of the specific variable X regressed onto the IPO or WPS 30-year trend over the 1985–2014 period, respectively. b is a redundant constant term.

To quantitatively assess the combined effect of IPO and WPS, considering the orthogonality between the first and second EOF modes of SST, we develop a novel composite index from the two indices to reconstruct the precipitation trend for each ensemble member i, the reconstructed linear trend of the precipitation [\({Pr}_{\text{reconstruction}}^{trend}\left(i\right)\)] is given by:

$${Pr}_{\text{reconstruction}}^{trend}\left(i\right)=\frac{\sqrt{2}}{2}\cdot [{r}_{Pr,IPO}\cdot {IPO}_{internal}^{trend}\left(i\right) + {r}_{Pr,WPS}\cdot {WPS}_{internal}^{trend}\left(i\right)]$$
(4)

Also, we reconstruct the linear trend of the observed precipitation based on the OISST datasets. Considering the differing responses of precipitation to SST between observations and the model, we make some adjustments based on Eq. (4):

$${Pr}_{\text{reconstruction}}^{trend}\left(obs\right)=\frac{\sqrt{2}}{2}\cdot [{\frac{STD({r}_{Pr,IPO}^{obs})}{STD({r}_{Pr,IPO})}\cdot r}_{Pr,IPO}\cdot {IPO}_{internal}^{trend}\left(obs\right) + {\frac{STD({r}_{Pr,WPS}^{obs})}{STD({r}_{Pr,WPS})}\cdot r}_{Pr,WPS}\cdot {WPS}_{internal}^{trend}\left(obs\right)]$$
(5)

where \(\frac{STD({r}_{Pr,IPO}^{obs})}{STD({r}_{Pr,IPO})}\), \(\frac{STD({r}_{Pr,WPS}^{obs})}{STD({r}_{Pr,WPS})}\) is the ratio of the spatial standard deviation over the tropical Indo-Pacific regions between \({r}_{Pr,IPO}^{obs}\) with \({r}_{Pr,IPO}\) and between \({r}_{Pr,WPS}^{obs}\) with \({r}_{Pr,WPS}\), respectively. The regression coefficient of the 7 year running-mean precipitation anomalies regressed onto the IPO time series from observed OISST during 1985–2014 (\({r}_{Pr,IPO}^{obs}\)) is calculated by:

$$\frac{\partial \text{Pr}(obs)}{\partial t}={r}_{Pr,IPO}^{obs}\frac{\partial IPO(obs)}{\partial t}$$
(6)

\({r}_{Pr,WPS}^{obs}\) is similar to the \({r}_{Pr,IPO}^{obs}\), but using the WPS time series.

Results

IPO and WPS dominate the decadal variability over the tropical Indo-Pacific

To investigate the diverse decadal variabilities and their impacts over the tropical Indo-Pacific, we apply EOF analysis to capture fundamental features through 30-year SST and precipitation trends from the 100-member CESM2 simulations (See Methods). The first SST EOF mode displays an El Niño-like pattern, with positive SST anomalies in the central and eastern tropical Pacific (Fig. 1a). The first principal component (PC1) is remarkably correlated with the IPO trend (r = 0.73), confirming that PC1 represents the traditional IPO pattern (Fig. 1e; Capotondi et al. 2023; Liu & Di Lorenzo 2018). Correspondingly, precipitation PC1 also significantly correlates with SST PC1 (r = 0.78), indicating precipitation’s first EOF mode is dominated by the IPO (Fig. 1c). For a given member in the positive IPO phase, SST warming in the eastern Pacific weakens and shifts the Walker Circulation eastward (Chung et al. 2019; Wu et al. 2021; Zhang & Li 2016). This subsequently causes a weakening of tropical convergence, reducing precipitation over tropical convergence zones like the Maritime Continent (MC) and the Intertropical Convergence Zone (ITCZ), while increasing precipitation in the central and eastern equatorial Pacific, and vice versa for the negative IPO phase (Dong & Dai 2015; Sun et al. 2021). These results are favorable for verifying the influence of IPO on the Walker Circulation and tropical precipitation using the CESM2-LE.

Fig. 1
figure 1

EOF results in 30 year SST and precipitation trend. a The first and (b) second EOF modes of 30 year SST trend from 1985 to 2014 (°C) for 100 members in CESM2-LE, (c, d) same as (a, b), but for precipitation (mm/day). e Scatter plots and linear fitted lines between the first principal component of SST with precipitation (red dots and lines) and corresponding IPO trend (black dots and lines) for 100 members in CESM2-LE, with correlations of 0.78 and 0.73, respectively. f same as (e), but for the second principal component of SST with precipitation and the corresponding WPS trend, with correlations of 0.61 and 0.82, respectively

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In contrast to the tropical Pacific-dominated first SST mode, the second mode reveals a synergistic influence between the tropical Pacific and Indian Ocean. It presents a dipole pattern characterized by positive anomalies in the western Pacific and negative anomalies in the southeastern Indian Ocean (Fig. 1b). We define this as the Warm Pool Seesaw (WPS) mode hereafter, using the WPS index to measure it via an SST anomaly difference between the two regions (see Methods).

This WPS index effectively captures the characteristics of the second mode of SST (Fig. 1f), showing a high correlation with the second principal component (PC2) of SST (r = 0.82). Precipitation PC2 also has a significant correlation with the SST PC2 (r = 0.61), demonstrating the impact of the WPS on the decadal precipitation. Specifically, the second precipitation mode (Fig. 1d) reveals robust increases (decreases) in the western Pacific (southeastern Indian Ocean), alongside weaker decreases (increases) in the central and eastern Pacific (western Indian Ocean). Notably, while the variance contribution of the second SST mode (15%) is significantly lower than that of the first mode (46%), the corresponding precipitation exhibits similar variance contribution between the first and second EOF modes (23% vs. 22%). Despite its lower occurrence probability than the first SST mode, the second SST mode exerts a non-negligible influence on precipitation patterns.

Furthermore, we conduct an estimation of the 20 year decadal variability during the mid-term period (2041–2060) in future projections (Figure S1). The results successfully capture both the IPO and WPS modes, consistent with historical 30 year trends (1985–2014). Notably, precipitation exhibits a stronger response to WPS than IPO in this period, with variance contribution rates of 25% versus 18%. This underscores the critical role of WPS mode, further supporting earlier conclusions.

IPO and WPS modulate the Walker circulation and rainfall change

To determine how the IPO and WPS modulate atmospheric circulation and precipitation decadal variability, we regressed their spatial patterns onto indices derived from 100 ensemble members (Fig. 2). During the positive IPO phase, SST warms in the central and eastern Pacific, and alters the zonal gradient, triggering westerly wind anomalies in the Pacific via Bjerknes feedback (Fig. 2c; Bjerknes 1969; Bordbar et al. 2019; Wu et al. 2021). This weakens and shifts Walker circulation eastward, suppressing deep convection in convergence zones while reinforcing convective convergence over the central and eastern Pacific (Fig. 2c). The IPO-regressed precipitation pattern closely matches the 500 hPa vertical velocity field and aligns with the leading EOF mode of precipitation (Figs. 2a, c, and 1c), indicating IPO plays a dominant role in shaping this precipitation pattern through atmospheric convective processes.

Fig. 2
figure 2

The spatial regression onto IPO and WPS index. Precipitation changes (shading, mm/day) regressed onto (a) IPO trend and (b) WPS trend for 100 members in CESM2-LE. c, d same as (a, b), but for 500 hPa vertical velocity (shading, negative means upward anomalies, Pa/s) and 850 hPa horizontal wind (vector, m/s)

Full size image

Similarly, WPS-regressed precipitation mirrors its corresponding 500 hPa vertical velocity pattern and matches the second EOF mode (Figs. 2b, d, and 1d). In contrast to the IPO, positive WPS features SST warming in the western Pacific and cooling in the southeastern Indian Ocean. This indicates that the atmospheric circulation exhibits strong westerly wind anomalies in the western Pacific, pronounced southeasterly wind anomalies in the southeastern Indian Ocean, and weakened easterly wind anomalies in the tropical eastern Pacific. These drive the dipole-like precipitation pattern, characterized by robust increases in the western Pacific and decreases in the southeastern Indian Ocean, accompanied by weaker precipitation declines in the central and eastern Pacific (Good et al. 2021). Notably, the WPS-regressed precipitation pattern exhibits significantly stronger intensity than the IPO-regressed pattern, particularly over the western Pacific and southeastern Indian Ocean (Figs. 2a and b). These provide compelling evidence that WPS is also a key driver of precipitation decadal variability in the tropical Indo-Pacific.

Joint effect of the IPO and WPS on the precipitation changes

In the real world, IPO and WPS events do not always occur independently, and their phases are often misaligned. However, observational limitations hinder understanding of their combined precipitation impacts. Fortunately, Large ensemble simulations help overcome this by revealing the likelihood of different phase configurations.

To investigate IPO-WPS joint influences on decadal precipitation variability, we composite SST, precipitation, and circulation fields under different phase combinations (Figs. 3 and S2). For independent IPO events (28 cases) or WPS events (27 cases), SST and precipitation patterns closely resemble those derived from the EOF analysis (Figs. 1a, b, and 3c, d), and Sect. “IPO and WPS modulate the Walker circulation and rainfall change” explains their impacts on precipitation, avoiding repetition. Here, we focus on the SST characteristics and the underlying factors affecting precipitation when IPO and WPS occur either in the same phase or in opposite phases.

Fig. 3
figure 3

The composites of anomalous fields for different phases of IPO and WPD. a the difference between positive IPO with positive WPS events and negative IPO with negative WPS events, (b) the difference between positive IPO with negative WPS events and negative IPO with positive WPS events, (c) the difference between positive IPO with normal WPS events and negative IPO with normal WPS events, and (d) the difference between positive WPS with normal IPO events and negative WPS with normal IPO events in SST (lines, ℃) and precipitation (shading, mm/day) for 100 members in CESM2-LE

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During the positive IPO co-occurring with positive WPS events, SST warms across the tropical Pacific while cooling in the southeastern Indian Ocean (Fig. 3a). Unlike an independent IPO, the strongest SST warming occurs in the western Pacific, resembling a La Niña-like pattern (Lian et al. 2018). In the Indian Ocean, the SST anomalies exhibit a Dipole-like structure, characterized by cooling in the southeastern Indian Ocean and warming in the tropical western Indian Ocean. These SST configurations modulate atmospheric circulation over the Indo-Pacific, with robust westerly (southeasterly) wind anomalies in the tropical western Pacific (tropical Indian Ocean) and weak easterly wind anomalies in the eastern Pacific (Figure S2a). They also intensify deep convection in the western Pacific while suppressing the convection in the southeastern Indian Ocean. Consequently, precipitation increases in the western Pacific and decreases in the southeastern Indian Ocean, a pattern largely consistent with the precipitation patterns from independent WPS events but with stronger amplitude (Figs. 3a and d). This underscores WPS's significance and its combined IPO role in shaping decadal precipitation variability.

Compared to the 10 cases where IPO and WPD events occurred in the same phase, there were only 4 cases where IPO and WPD were in opposite phases, suggesting a relatively low likelihood of such asymmetric occurrences. Under opposite phases, SST anomalies mirror a combined pattern of these two modes, featuring warming in the central and eastern Pacific, alongside a negative WPS phase (cooling in the western Pacific, warming in the southeastern Indian Ocean). Consequently, Precipitation displays a stronger increase (decrease) in the central and eastern Pacific (Western Pacific and ITCZ) due to the compounding effects of the two phases. In contrast, the southeastern Indian Ocean shows relatively weaker precipitation increases due to offsetting influences. These results demonstrate the complex precipitation impacts driven by IPO-WPS phase interactions.

To quantify the joint effect of IPO and WPS on precipitation, we developed a novel composite index to reconstruct the decadal precipitation changes based on the IPO and WPS indices (see Methods). Firstly, we reconstruct the precipitation trends based on the observed OISST to compare with the observed precipitation (Figs. 4a and b). The reconstructed precipitation changes align well with observations throughout the tropical Indo-Pacific. In particular, precipitation decreases in the central Pacific and increases in the MC, ITCZ, and southeastern Indian Ocean. This pattern closely resembles the influence of an independent negative phase of IPO (Figs. 2a and 3c). The observed OISST trend further corroborates this, showing a strong negative IPO index (−0.99) and negligible WPS index (0.04), reinforcing the confidence of this methodology. Notably, the reconstructed precipitation trend exhibits significant discrepancies compared to observational data in the northeastern Pacific (Figs. 4a and b). Our analysis reveals that in the CESM2 model, tropical IPO and WPS mode show relatively weak influences on precipitation there (Figs. 2a and b). Subtropical decadal variability modes—particularly the POD and NPGO—may exert stronger control over precipitation patterns. Furthermore, external forcings (e.g., greenhouse gases) may significantly alter precipitation patterns in this region. The discrepancies need to be studied in the future.

Fig. 4
figure 4

Reconstructed precipitation between the observations and models. a Observed GPCP 30 year precipitation trend (shading, mm/day) from 1985 to 2014, (b) using the new index reconstructed the 30 year precipitation trend (shading, mm/day) from 1985 to 2014 based on the OISST observed datasets, (c) reconstructed the 30-year precipitation trend (shading, mm/day) from 1985 to 2014 for the difference between positive IPO with normal WPS events and negative IPO with normal WPS events based on SST in CESM2-LE, and (d) the spatial correlation between the reconstructed tropical precipitation trend and CESM2-LE 100 members’ tropical precipitation trend using the new index (blue bar) and EOF results (red bar)

Full size image

Furthermore, we apply this method to reconstruct 30 year precipitation trends for each ensemble member. For independent IPO events, results exhibit spatial patterns consistent with composite and EOF analyses (Figs. 1c and 3c), yet display an opposite sign to the recently observed precipitation trend (Fig. 4a), confirming that recent decadal precipitation changes are primarily driven by the negative IPO phase, aligning with prior studies (Sun et al. 2021; Wu et al. 2021). Notably, for the majority of ensemble members, this method effectively captures the spatial patterns of precipitation changes (Fig. 4d). However, a subset of members displays poor performance or even inverse trends, mainly attributed to weak IPO and WPS indices. These results indirectly highlight the significant influence of these two modes on precipitation variability.

Conclusions with discussions

This study investigates the diverse decadal variability in the tropical Indo-Pacific region, with a focus on the impacts of the IPO and the newly identified WPS mode on atmospheric circulation and precipitation patterns, utilizing large ensemble simulations of CESM2. The IPO, characterized by an El Niño-like pattern, affects the Walker Circulation and precipitation distribution, leading to reduced precipitation in convergence zones and increased rainfall in the central and eastern Pacific. The WPS mode, which represents a dipole pattern with positive anomalies in the western Pacific while negative anomalies in the southeastern Indian Ocean, also modulates regional precipitation patterns.

The study further demonstrates that the combined effect of IPO and WPS modes can lead to more complex and pronounced changes in precipitation patterns. When these modes occur in the same phase, their impacts are amplified, resulting in stronger precipitation anomalies, consistent with the impact of the independent WPS mode. Conversely, when they are in opposite phases, the IPO’s impact is enhanced over the Pacific, while their effects can partially offset each other in the southeastern Indian Ocean, leading to more moderate changes there. To capture the combined influence of these two modes, the novel combined index, which effectively integrates the IPO and WPS indices, offers valuable insights into the physical mechanisms underlying historical precipitation variations and provides a framework for predicting future precipitation changes.

Nevertheless, our new index framework still yields unsatisfactory results when evaluating weak events, with notable deviations observed in certain regions. Moving forward, we hope to leverage Artificial Intelligence technology to enhance the accuracy of our method and extend its applicability beyond tropical regions. Additionally, due to limitations in observational duration, we were unable to assess other possible phase combinations in this work. We hope similar events will occur in the future to validate our methodology.