Intermodel uncertainty in response of the Pacific Walker circulation to global warming

The Pacific Walker circulation (PWC) is one of the major atmospheric circulations that plays an essential role in ocean-atmosphere interactions and global climate. The response of the PWC to greenhouse warming remains a mystery and model results are inconsistent. Based on multimodel simulations from the Coupled Model Intercomparison Project phase 6 (CMIP6), this study explores the intermodel uncertainty of the change in the PWC under global warming. The combination of the El Niño-like warming pattern and the interbasin warming contrast between the Indian and Pacific Oceans strengthens (weakens) the west (east) branch of the Pacific trade winds, resulting in a structural shifting of the PWC. By conducting a set of Atmosphere General Circulation Model (AGCM) experiments, we demonstrate that the western Pacific warming plays a critical role in driving the PWC shift. An intensified western Pacific warming counteracts the effect of Indian Ocean warming on the PWC, leading to a uniformly weakened PWC in the tropical Pacific due to the SST gradient. In contrast, a decreased warming in the western Pacific strengthens the west branch of the PWC, shifting the turning longitude of zonal wind changes eastward. Our finding highlights that the relative warming pattern in the Indian and Pacific Oceans is coupled with the PWC change in a warmer climate.


Introduction
The Pacific Walker circulation (PWC) is a large-scale zonal overturning atmospheric circulation that plays an important role in ocean-atmosphere interactions and the global climate system. It rises over the Maritime Continent and the western Pacific warm pool and descends over the eastern Pacific cold tongue. This system forms a closed structure with easterly trade winds in the lower atmosphere and westerlies in the upper troposphere. Changes in the PWC can influence a while enhanced evaporative damping over the warm pool may reduce the zonal SST gradient in the tropical Pacific (Knutson and Manabe 1995). Meanwhile, a warmer atmosphere retains more moisture (~ 7%/K), consistent with the Clausius-Clapeyron relation, but the precipitation increases much more slowly (~ 2%/K), implying a decrease in convective mass fluxes, resulting in a slowdown of the PWC (Held and Soden 2006;Vecchi and Soden 2007).
The abovementioned mechanisms coexist and have various spatial and temporal effects on the PWC. (Luo et al. 2017;Heede et al. 2020;Heede and Fedorov 2021). Under future climate scenarios, the majority of coupled general circulation models (CGCMs) project a weakening of the SST gradient and the PWC (DiNezio et al. 2013;Power and Kociuba 2015;Ying et al. 2022). However, natural variability (Karnauskas et al. 2009;Dong and Lu 2013;Chung et al. 2019;Wu et al. 2021) and model bias (Seager et al. 2019) may also modulate the PWC change in historical simulations and future projections.
In addition to the oceanic and atmospheric processes in the tropical Pacific, other basins have an impact on the PWC (Luo et al. 2012;McGregor et al. 2014;Cai et al. 2019;Hu and Fedorov 2019;Wang 2019;Kang et al. 2020). Particularly, recent studies have identified the substantial role of the tropical Indian Ocean (TIO) in modulating the Pacific warming pattern and the PWC (Luo et al. 2012;Han et al. 2013;Zhang and Karnauskas 2017;Zhang et al. 2019Zhang et al. , 2021. Besides the SST warming pattern, the land-sea thermal contrast, variations in the western north Pacific monsoon, the Indonesian throughflow, and the Leeuwin current are associated with the response of the PWC to a warming climate (Feng et al. 2011;Zhang and Li 2016;Yim et al. 2017).
Previous studies mostly focused on the general trend of the PWC and distinguished the warming effects of the tropical Indian and Pacific Oceans. It is still challenging to reconcile the relative responsibility of different ocean basins and to investigate the detailed structural change of the PWC. This study aims to combine the warming effects between the Indian and Pacific Oceans and investigate the sources of intermodel uncertainty in projecting the PWC response to greenhouse warming, specifically to evaluate whether the PWC trend is constant throughout the entire Pacific basin. A set of AGCM experiments is conducted to understand the mechanism underlying the combined warming effect of different basins on the PWC.
The remainder of this paper is organized as follows. Section 2 describes the model outputs, model experiments, observational datasets, and methods used in this study. Section 3 demonstrates the PWC's response to greenhouse warming and its model diversity. Section 4 examines the relationship between the PWC change and the SST warming in different ocean basins. Section 5 is the summary with discussion.

CMIP6 outputs
To evaluate the response of the PWC to greenhouse warming, we analyzed the monthly mean outputs from 24 Coupled Model Intercomparison Project phase 6 (CMIP6) models ( Table 1). This study employs three experiments, including 1% CO 2 (1pctCO 2 ), pre-industrial control (piControl), and historical (Hist) simulations. The 1pctCO 2 experiment is a branch of the piControl experiment, as the global annual mean CO 2 concentration increases exponentially (1% yr − 1 ). Climate change signals are calculated by subtracting the last 30-year mean in the piControl run from the 30-year (#101~#130) mean in the 1pctCO2 run. It should be noted that this study focuses on the long-term response of the PWC to GHG forcing. Thus, we only use 1pctCO2 experiments to ignore the aerosol effects that may play a role in the near-term change in the PWC (Dong et al. 2014;Heede and Fedorov 2021). To examine the robustness of our results, we also investigate the long-term PWC change based on the high-emission (SSP5-8.5) and historical experiments, defined as the differences between the SSP5-8.5 experiment during 2050-2099 and the historical experiment during 1950-1999. The results are similar to those from 1pctCO2 and piControl experiments (not shown).
All model outputs are interpolated into a 2.5° × 2.5° grid, and only the first member of each model is analyzed. The SST changes are normalized by the tropical (25°S-25°N) mean SST warming in each model.

Model experiments
The Community Atmosphere Model (CAM) is the atmosphere component of the Community Earth System Model (CESM). The CAM, version 5 (CAM5) is used for experiments. Experiments are conducted on a horizontal 1.9° × 2.5° grid (f19_f19) with 26 vertical sigma levels. To explore the impacts of interbasin warming contrast and to combine the effect of warming in the Indian and Pacific Oceans, we perform five experiments for comparison. Please refer to appendix A for the detailed experimental design.

Observations
To evaluate the impact of model bias on the PWC projection under global warming, we compare the mean state of SST from Hist simulations with the HadISST (Rayner 2003) and the ERSST version 5 (Huang et al. 2017) datasets. The analysis period is 1979-2014. The precipitation data from the Global Precipitation Climatology Project (GPCP) for the same period is also used for comparison (Adler et al. 2003). The climatological surface winds are taken from ERA5 after the satellite era . All the observational datasets are interpolated to the same horizontal resolution (2.5° × 2.5°).

Changes in the PWC under greenhouse warming
To detect the PWC response to greenhouse warming, we first examine the multimodel ensemble (MME) mean change in the Pacific trade winds and compare it with the climatological mean states (Fig. 1a). The surface westerly changes over the equatorial eastern Pacific (eEP) indicate a weakening of the PWC in this region. In the equatorial western-to-central Pacific (eWCP), however, the change in zonal winds turns to easterlies, indicating that the change in the PWC is not consistent throughout the entire Pacific basin. Though all models capture this feature, there is substantial model disagreement. The turning longitude (TL) of wind change direction ranges from 110°E to 170°W (Fig. 1a). In addition, the intermodel spread of surface zonal wind change is relatively large in the eWCP, with the signal-to-noise ratio (SNR) less than 1.5 (Fig. 1b). Thus, we aim to explore the mechanism of surface wind changes and the source of intermodel uncertainty in this region.
To investigate the characteristics of the PWC change in the eWCP, we perform an intermodel EOF analysis on surface zonal wind changes. The first two leading modes account for 59.7% and 23.8% of the total variance, respectively. The first mode exhibits a uniform change in the domain (Fig. 2a), whereas the second mode shows a zonal dipole pattern (Fig. 2b). Specifically, in their positive (negative) phase, EOF1 displays stronger (weaker) westerlies across the entire domain, while EOF2 displays a convergence (divergence) with westerly (easterly) changes in the west and easterly (westerly) changes in the east.
The location of the TL is determined by the combination of the two modes ( Fig. 2c), which indicates the overall intensity and zonal variation of the PWC change in the eWCP. When PC2 is negative, the spatial pattern of the second mode exhibits easterly in the west of the domain, which may offset the westerly changes of the first mode and shift the TL. For instance, the TL of MCM-UA-1-0 (blue square) is further east than that of BCC-ESM1 (green circle), even though both models have similar PC1 values (Fig. 2c, d).
Similar to the definition of the CP and EP indices used to distinguish two types of El Niño (Takahashi et al. 2011), here we define the TL index ( Fig. 2e) to incorporate the effects of the two modes: The TL index is highly correlated with TL among models (r=-0.91, p < 0.01, Fig. 2d). The linear regression equation is shown in the top-right corner of Fig. 2d. Then we use the TL index to measure the model diversity of zonal change in the PWC. A model with a positive (negative) TL index tends analysis to compare the models with positive and negative values of the TL index. A total of ten models are selected into two groups. One group consists of the models (BCC-CSM2-MR, CanESM5, GFDL-ESM4, IPSL-CM6A-LR, UKESM1-0-LL, hereafter the P-group) with the top five values of the TL index, and the other consists of the models (CNRM-CM6-1-HR, EC-Earth3, GISS-E2-1-H, MIROC-ES2L, NESM3, hereafter the N-group) with the top five negative values. Both groups exhibit westerly wind change in the eEP. However, there are considerable differences in the eWCP between the two groups ( Fig. 4d). In the N-group, the wind change shifts to easterlies, indicating that the structure of the PWC has changed. The peak of positive SLP change occurs further east in the N-group than in the P-group (Fig. 4e), corresponding to an easterly wind change in the warm pool and a westerly in the cold tongue.
Even though both groups exhibit an El Niño-like warming pattern in the tropical Pacific ( Fig. 4a, b), there are some significant differences in the SST warming between the two groups. Specifically, in the P-group, the enhanced equatorial SST warming extends into the western Pacific, leading to a relatively weakened zonal SST gradient, which is associated with the westerly wind change throughout the entire Pacific basin. In the N-group, however, the enhanced equatorial warming is restricted to the central Pacific, whereas to simulate a more (less) westward expansion of the PWC slowdown.

Reconciling the effects of interbasin warming contrast and Pacific SST gradient change
The SST warming pattern in tropical oceans is tightly coupled with the surface wind change. To investigate the coupled warming pattern with the PWC change, we examine the intermodel correlation coefficient between the PCs and the SST change in the Indo-Pacific oceans. The PC1 is highly correlated with the central Pacific warming (Fig. 3a), indicating that a warmer central Pacific tends to amplify westerly changes in the eWCP. The PC2 is significantly correlated with the TIO warming (Fig. 3b), showing that the TIO warming contributes to the zonal variation of the PWC change. The TL index is highly correlated with the eWCP SST (Fig. 3c), which shows large model uncertainty in CMIP6 models (not shown). In addition to the warming of the eEP and TIO SST, the eWCP warming also plays an important role in the PWC change.
To better understand the source of intermodel uncertainty in the TL of the PWC change, we use composite  and correlation coefficient are shown in the top-right corner. e The TL (grey line, right y axis) and TL index (bar, right y axis) of 24 CMIP6 models, blue (red) denote the positive (negative) signal and the TIO and slightly decreases between the eWCP and the eEP (Fig. 5b, c).
The composite results show that the most significant difference between the two groups is the SST warming rate in the western equatorial Pacific, leading to remarkably different responses of local convection and vertical velocity (Fig. 6). For models with less warming in the western Pacific, suppressed local convection induces easterly changes over the Maritime Continent and westerly changes over the central-to-eastern Pacific, resulting in a change in the PWC's structure. The importance of warming in the western Pacific reflects the combined effect of the zonal SST gradient in the equatorial Pacific and the TIO-eWCP interbasin warming contrast on the PWC change. A robust El Niño-like warming pattern can counteract the effect of the TIO warming. In other words, the surface wind changes over the western Pacific are associated with the relative warming between the Indian and Pacific Oceans. the western Pacific is much cooler than that in the P-group (Fig. 4c). In contrast, both groups show comparable warming in the TIO and eEP. Therefore, compared with the P-group, the N-group exhibits a prominent interbasin warming contrast between the TIO and the eWCP (Fig. 4a), which may contribute to the strengthening of the PWC and the increase in zonal SST gradient in the equatorial Pacific (Luo et al. 2012;Zhang and Karnauskas 2017).
We further examine the temporal revolution of the changes in SST and its zonal gradient in the Indo-Pacific regions. Under global warming, the relative SST (normalized by the tropical mean SST) increases in the P-group but decreases in the N-group over the eWCP (Fig. 5a). In contrast, the SST over the TIO and the eEP increase at a similar rate in both groups (Fig. 4c). Therefore, for the N-group, the SST gradients are both reduced between the eWCP and the TIO, and between the eWCP and the eEP (Fig. 5b, c). For the P-group, the SST gradient increases between the eWCP Fig. 3 The correlation coefficient maps between the SST warming and the a PC1, b PC2, and c TL index. Stippling denotes regions where the relationship is statistically significant at 95% confidence level based on the Student's t test. The grey box represents the EOF domain Fig. 4 The SST warming pattern (shading; K) and the surface winds change (vector; m/s) of a the N-group, b the P-group, and c their difference. Stippling denotes regions where the differences are statistically significant at 95% confidence level based on the Student's t test. The 5°S-5°N mean d surface zonal wind change and e the sea level pressure change of the N-group (pink line) and the P-group (blue line). Shading indicates the model spread on the PWC change is limited to the eWCP. Models with strong TIO warming tend to present easterly changes over 150°E to 160°W. In contrast, the eEP warming is coupled with opposite zonal wind changes that extend to the equatorial central Pacific. As a result, the PWC change over the central Pacific is determined by the relative warming To evaluate the coupling between each basin warming and the PWC change, we examine the intermodel correlation between the SST warming in three regions (the tropical Indian Ocean, the equatorial western-to-central Pacific, and the equatorial eastern Pacific) and the equatorial zonal surface wind changes (Fig. 7). The effect of the TIO warming . However, the intermodel correlation between the IOD-like warming and the PWC change is not statistically significant (Fig. 7), implying that the PWC is modulated by the warming of the entire Indian Ocean basin rather than its east-west gradient change. magnitude of the TIO and the eEP, as the two oceans have an opposing effect.
We notice that the CMIP6 models also show considerable diversity in the Indian Ocean Walker circulation change (Fig. 1a, b). Previous studies suggest that the Indian Ocean Dipole (IOD)-like warming pattern is strongly associated with the zonal wind change over the Indian Ocean (Zheng Fig. 6 Differences of the changes between the N-group and the P-group: a Precipitation; b Surface divergence wind; c 500 hPa vertical velocity; d Total cloud cover. Stippling denotes regions where the differences are statistically significant at 95% confidence level based on the Student's t test over the western Pacific warm pool and the ascending motion over the tropical Indian Ocean have combined to generate a secondary circulation superimposed on the climatological Walker circulation, thus altering the structure of the PWC. As mentioned in Section 4a, both the Indian and Pacific Oceans modulate the PWC. Specifically, the El Niño-like warming in the tropical Pacific counteracts the influence of Indian Ocean warming on the PWC. As the eEP warms in the WP0K experiment, negative SLP anomalies and positive precipitation anomalies in the Indian Ocean decrease substantially (Fig. 8b). Such a warming pattern induces two negative SLP anomalies centered over the TIO and the eEP, respectively. Hence, easterly (westerly) anomalies emerge in the western (eastern) Pacific. Notably, though the imposed SST gradient in the tropical Pacific is smaller in the WP1K than in the WP0K, the WP1K exhibits stronger westerly anomalies. This is because a warmer western Pacific provides a smaller interbasin warming contrast between the Indian and Pacific Oceans, canceling out the effect of TIO warming and leading to the Pacific SST gradient dominating the PWC's shift. As the imposed warm SST increase in the western Pacific, the TL gradually shifts westward (Fig. 8e), resulting in an increase (decrease) in precipitation over the western Pacific (the Maritime Continent and the TIO) (Fig. 9e).
In the WP1K experiment, precipitation significantly increases over the eWCP, consistent with the warmer-getwetter mechanism . However, the spatial pattern of precipitation change in the tropical Pacific is inconsistent with the PWC shift, which may be attributed to

The dominant role of the western Pacific warming
The above results show that the large intermodel spread in the PWC changes is due primarily to the warming of the eWCP. Additionally, the TIO and the eEP warmings, particularly their contrast with the eWCP warming, are essential to the PWC change. To further verify our proposed mechanism that the warming in the Indian and Pacific Oceans, especially the western Pacific warming, modulates the PWC change, we conduct a set of atmospheric model experiments. To simulate the impact of the TIO warming on the PWC change (the WARMIO experiment), we first add an idealized SST warming to the TIO and compare it with the control run (CTRL, forced by climatology SST). Then we add an El Niño-like warming to the equatorial Pacific to examine the combined effect of the TIO and eEP warmings. In particular, we investigate the effect of the western Pacific warming on the PWC by varying the magnitude (0 K, 0.5 K, 1 K) of the SST warming in the eWCP (named as WP0K, WP0.5 K, and WP1K experiments). Please refer to Appendix A for the details of the model experiments.
Comparing the WARMIO with the CTRL, the TIO warming induces local negative SLP anomalies that extend to the western Pacific through Kelvin waves. Thus easterly wind response can be found throughout the entire tropical Pacific basin, indicating that the low-level branch of the PWC has strengthened (Fig. 8a, e). Notably, precipitation in the Maritime Continent does not increase significantly (Fig. 9a, e), consistent with the enhanced trade winds tied to the convection center shifting to the TIO. The anomalous subsidence

Summary and discussion
In this study, we use CMIP6 outputs to analyze the PWC change in response to greenhouse warming, revealing the relative importance of SST warming in the Indian and Pacific Oceans. In particular, we highlight the critical role of the eWCP warming in the PWC change. The major findings are summarized as follows.
The CMIP6 models project westerly winds change over the central-to-eastern Pacific under global warming, indicating a weakening of the PWC in this region. However, models show a large intermodel diversity in the trade wind change over the eWCP, with the SNR less than 1.5. To explore the the changes in water vapor transport and Hadley circulation (Sohn et al. 2019).
Under global warming, precipitation generally increases over the climatological wet regions (Held and Soden 2006), such as the western Pacific, and the magnitude of increased precipitation is associated with local warming relative to the tropical mean value (Johnson and Xie 2010;Xie et al.). Convection in the western Pacific can alter the atmospheric circulation. Meanwhile, the eWCP warming contributes to both the TIO-eWCP and the Pacific SST gradients, which are crucial for the west and east branches of the PWC, respectively. Fig. 8 Spatial patterns of the change in sea level pressure (shading; hPa) and surface wind (vector; m/s) in a WARMIO, b WP0K, c WP0.5 K, and d WP1K experiments. The 5°S-5°N mean e surface zonal wind change and the f sea level pressure change. The green line, blue line, brown line, and red line denote the WARMIO, the WP0K, the WP0.5 K, and the WP1K, respectively Fig. 9 As in Fig. 8, but for the precipitation (shading) the intermodel uncertainty in the PWC change, although it indeed acts to weaken the atmospheric circulation generally.
Another important issue is that the uncertainty in model projections may originate from the intermodel spread in historical simulations. Climate models with unrealistic simulations of mean states tend to project spurious patterns of future climate changes (Huang and Ying 2015). CMIP6 models exhibit a variety of SST and precipitation biases in the tropical Pacific (Fig. 11a), such as the cold tongue and the double-Intertropical Convergence Zone (ITCZ) biases (Mechoso et al. 1995;Marx et al. 2008;Zheng et al. 2012;Li and Xie 2014;Wang et al. 2014). Despite both P-and N-groups suffering from these well-recognized biases, their simulations have significant differences (Fig. 11b, c). The P-group presents a much colder and drier cold tongue, as well as a much warmer and wetter ITCZ and South Pacific Convergence Zone (SPCZ). In other words, the N-group simulates more realistic mean states than the P-group in most regions where common biases exist (Fig. 11d).
Recently, an "emergent constraint" approach aims to reduce the uncertainty among climate models and correct future projections (Cox et al. 2018;Hall et al. 2019;Brient 2020). We find that the excessive cold tongue bias potentially impacts future PWC projections. Models with an excessive cold tongue tend to project much stronger warming in the eWCP (Fig. 12a) due to the too weak SST-convection feedback (Ramanathan and Collins 1991;Li et al. 2016Li et al. , 2017Ying et al. 2018), resulting in the error of SST warming pattern and the coupled surface winds change. The spurious La Niña-like warming is coupled with the erroneous easterly change in the central Pacific. On the other hand, the interbasin warming contrast between the TIO and the eWCP is significantly reduced by the strong eWCP warming. Then the tropical Pacific SST gradient will dominate the PWC change, resulting in an underestimated TIO effect. The opposite effects of the interbasin warming contrast and the El Niño-like warming pattern result in the zonal difference of the PWC change (i.e., opposite changes between the west and east sides of 155°E, shown in Fig. 2b). Additionally, the PC2 in Fig. 2 is significantly correlated with the climatological precipitation in the eWCP (Fig. 12b), consistent with the above hypothesis.
Based on the intermodel correlation between mean state simulations and changes, we attempted to use a simple "observational constraint" approach (see Appendix B) to remove the effect of cold tongue bias and calibrate the PWC change among models. Comparing the corrected and uncorrected results, we found that models present spurious westerly (easterly) anomalies on the west (east) side of 155°E (Fig. 13a), consistent with the zonal dipole pattern in EOF2 (Fig. 2b). The SST change exhibits a pronounced warm error in the eWCP, coupled with the spurious winds associated source of this model uncertainty, we define the TL index to represent the TL of zonal wind change based on the intermodel EOF analysis, and then separate models into the P-group and the N-group, respectively, according to this index.
The PWC change is closely coupled with the Indo-Pacific SST warming pattern. We find that the TIO and the Pacific warming modulate different branches of the PWC change. In addition, the western Pacific warming is crucial for the zonal wind change in the EOF domain. Further comparison of the SST warming pattern for the two groups reveals that the eWCP is much colder in the N-group, but both groups show similar TIO and eEP warming, implying that the SST gradients between the three regions are quite different, which are closely associated with the difference of the PWC change.
Then, this study investigates the combined effects of the TIO and Pacific warming on the PWC change. We hypothesize that the warming of the two basins modulates the west and east branches of the PWC, respectively. In addition, a warmer Pacific reduces the interbasin warming contrast, which may mitigate the impact of TIO warming on the PWC. Based on the CAM experiments, we suggest that the western Pacific warming is crucial to the PWC change, especially for its TL. Furthermore, the response of the PWC to global warming deviates from its original structure due to the uncertainty of SST warming. The western and eastern branches may change in opposite directions.
In this study, we focus on the coupling between the PWC change and Indo-Pacific SST warming, while other factors may potentially impact the PWC change and contribute to the intermodel uncertainty. Particularly, the static stability of the troposphere will increase under global warming, leading to a slowdown of general atmospheric circulation (Held and Soden 2006). Indeed, previous studies suggested that increased atmospheric static stability acts to weaken the Walker circulation (Vecchi and Soden 2007;Ma et al. 2012;Sohn et al. 2016) and the atmospheric circulation stimulated by the Indian Ocean SST anomaly (He et al. 2022). Here, CMIP6 models show intermodel agreements in responses of the water vapor and precipitation to global warming (Fig. 10a). Moreover, the increase rate of precipitation (2.1%/K) is much lower than that of water vapor (7.7%/K), indicating a more stable atmosphere under global warming. As a result, the general circulation will slow down (Fig. 10a). In the tropics (20°S-20°N), the increase in static stability (quantified by the vertical warming contrast in the troposphere) is tightly associated with the climate sensitivity among models (Fig. 10b). However, there is no significant correlation between the PWC change and the increase in static stability (Fig. 10c, d), indicating that the increased static stability of the troposphere is not the main source of future PWC change are too complicated to be fully explained by a single linear process. Other physical mechanisms on how the model biases affect future PWC projections remain unclear. The relevant processes that may lead to uncertainty in the PWC change need further investigation.
This study investigates the combined effects of the Indian and Pacific Oceans warming on the PWC change. However, the quantitative contributions of the two basins remain unclear. To better understand the mechanisms of the PWC change and the consequently climatic effects, further analysis should be conducted. In addition, this study focuses on the ocean-atmosphere dynamics in the tropical Indian and Pacific Oceans, whereas Atlantic and high-latitudes regions may potentially influence the PWC change. The detailed (Fig. 13a). We further examine the corrected results of the N-and P-group. The N-group models simulate a more realistic climatological precipitation in the eWCP than the P-group models (Fig. 12). Therefore, the N-group exhibits a negligible error in the PWC projections, while the P-group exhibits a relatively large one (Fig. 13c, d). However, the disagreement between the two groups remains distinct after constraint, indicating the intermodel spread in the climatological precipitation in the eWCP is not the only source of the intermodel uncertainty in the PWC change.
Overall, the magnitude of the error induced by cold tongue bias is relatively small, and there is no significant reduction in the uncertainty among models (Fig. 13b). The physical connections between the present-day climate and Fig. 10 a Response of water vapor (blue), precipitation (green), and 500 hPa upward pressure velocity (red) to global-mean surface warming. b Scatterplot of the global-mean surface warming and the vertical warming contrast. Relationships between vertical warming contrast and c east-west sea level pressure gradient change in tropi-cal Pacific, and d TL index. The vertical warming contrast is defined as the difference between potential temperature increase at the upper (~ 300 hPa) troposphere and lower-middle (700 hPa) troposphere in tropics (20°S-20°N) response of the PWC to the combination of different oceans is another important issue that needs to investigate in the future. Fig. 11 Spatial patterns of the model bias in mean-state precipitation (shading; mm/day) and SST (contour; K) for a MME, b the N-group, c the P-group, and d differences between the two groups. Solid (dashed) gray contours denote the warm (cold) bias. The IPO signal is removed using partial regression. Stippling denotes the regions where the precipitation bias in the N-group is relatively smaller than that in the P-group Fig. 12 Climatological precipitation (mm/day) in the eWCP versus a relative SST warming in the eWCP and b PC2. The pink (blue) pentagram represent the N-(P-) group. The Red line denotes the value from observation. The intermodel correlation is shown in each panel Fig. 13 a Spatial pattern of the change errors in surface zonal winds (shading; m/s) and SST (contour; K) for CMIP6 models. The uncorrected and corrected changes in Pacific trade winds for b MME, c the N-group, and d the P-group. Shading denotes the model spread Most CMIP6 models project an El Niño-like warming over the Pacific Ocean. To investigate the combined effect of the Indian Ocean warming and the El Niño-like warming on the PWC, we then design another series of experiments, imposing both 1-K Indian Ocean warming and 2-K equatorial Pacific (5°S-5°N, 130°E-90°W) warming. The imposed warming is largest in the eastern Pacific cold tongue (100°W, equator) and gradually decreases westward as a sine function. Considering the large intermodel diversity of the western Pacific warming, we set three different drop rates to simulate the various patterns of the SST warming in the tropical Pacific, with the imposed warming decreasing to 0 K, 0.5 K, and 1 K at 160°E, named WP0K, WP0.5 K, and WP1K, respectively (Fig. 14b, c, d). The SST warming is constant throughout the year. Each experiment runs for 30 years. The climatological mean of the last 20-year of each experiment is analyzed.

Design of the CAM5 experiments.
Previous studies have demonstrated that the enhanced tropical Indian Ocean warming plays an important role in modulating the Pacific trade winds (Luo et al. 2012;Zhang et al. 2019). We firstly conduct two experiments to verify the effect of Indian Ocean warming on the PWC. In addition to the control run (CTRL), which is forced by the observed monthly climatological SST and sea ice concentration, an experiment named WARMIO impose 1-K warming in the tropical Indian Ocean (25°S-25°N, 30°E-130°E) to mimic the Indian Ocean warming (Fig. 14a). As a cosine function, the imposed warming is largest in the center of the basin (80°E, equator) and gradually decreases in the surrounding areas.