1 Introduction

The western Pacific subtropical high (WPSH) is a large-scale anticyclonic circulation located over the subtropical Pacific throughout the year and reaches its peaking phase in summer. The WPSH has large influences on the East Asian summer climate (Zhu et al. 2000). Its low-level western edge features southerlies and southwesterlies that deliver a large quantity of water vapor into East Asia. The intensity, shape and location of the WPSH consequently dominate the large-scale quasi-stationary frontal zones (Huang and Yu 1962; Tao and Xu 1962; Tao and Chen 1987; Chang et al. 2000) and the temperature in East Asia (Hu 1997; Chen et al. 2001). Additionally, the influence of the WPSH can also be examined based on its interactions with other Asian circulations. The WPSH has been identified as a dominant component of the East Asian summer monsoon (EASM). The seasonal northward shifts of the WPSH are closely associated with the onset and withdrawal of the EASM (Tao 1963; Lau and Li 1984; Tao and Chen 1987; Huang and Wu 1989; Ding 1994; Zhu et al. 2010; Wang and Chen 2012; Huang et al. 2013a, b). The seasonal northward advance of the WPSH also corresponds to the seasonal movements of the South Asian high (Tao and Zhu 1964; Zhang and Wu 2001), the westerly jet (Li et al. 2004; Zhao et al. 2005; Kuang and Zhang 2006) and the East Asian blocking situation (Liao and Zhao 1990; Zhang and Tao 2003).

Many factors have been suggested to explain the formation and maintenance of the WPSH. The impact of the Tibet plateau, which acts as a robust heating source to the atmosphere in the summer, was proposed first (Ye and Gao 1979; Ye and Wu 1998). Additionally, anomalies in the sea surface temperature (SST), which can affect the atmospheric convections and trigger dynamic waves, also play an important role (Huang and Sun 1994; Lu and Dong 2001; Wang et al. 2013a). Moreover, the monsoon diabatic heating (Ting 1994; Hoskins 1996; Rodwell and Hoskins 2001), the land-sea heating contrast (Wu and Liu 2003; Miyasaka and Nakamura 2005) and the air–sea interaction (Seager et al. 2003) have also been proposed.

The WPSH has been shown to exhibit multi-scale temporal variations. Its interannual variability (e.g., Huang and Yu 1962; Tao and Xu 1962; Sui et al. 2007; He et al. 2012) and its relationship with tropical cyclone activity over the western North Pacific (Chia and Ropelewski 2002; Zhou and Cui 2008) have been studied for decades. To quantify its interannual variability, the atmospheric variables at 500 hPa have been most commonly used to define the WPSH indices, especially for geopotential height (e.g., Huang 1963; Tao and Chen 1987; Sun and Ying 1999), as well as relative vorticity (Yang and Sun 2003). Recent studies have also used the climate variables at 850 hPa, such as the geopotential height (Lu 2002; Wang et al. 2013a), the horizontal winds (Wang et al. 2001; Huang et al. 2010) and the relative vorticity (Lu et al. 2008).

Based on the investigation of the interdecadal position change in the 588 dagpm contour line at 500 hPa, previous studies have noted that the WPSH has extended westward since the 1970s (Nitta and Hu 1996; Hu 1997; Gong and Ho 2002). Its westward extension has been suggested to contribute to the increased rainfall over the middle and lower reaches of the Yangtze River valley and decreased rainfall over North China since the late 1970s (Gong and Ho 2002), as well as decadal variations of temperature in East Asia (Hu 1997) and typhoon tracks over the western North Pacific (Gong and He 2002; Ho et al. 2004). The Indian Ocean–western Pacific warming has been proposed to be responsible for this westward-extended WPSH (Zhou et al. 2009). However, Yang and Sun (2003), Lu et al. (2008) and Huang and Li (2015) argue that the direct use of the geopotential height field to examine the interdecadal variation of the WPSH may be inappropriate due to global warming, which has produced artificial trends in the lifted isobaric surface at middle and lower latitudes. Huang et al. (2015) reinvestigated the WPSH interdecadal variation in multiple WPSH-associated low-level variables, such as the eddy geopotential height, horizontal winds and relative vorticity. Their results showed that all these variables exhibit consistent signals, suggesting that the WPSH has been recessed eastward during 1979–2009 relative to 1948–1978. They further documented that the Indian summer monsoon played an important role in transporting water vapor into the middle and lower reaches of the Yangtze River valley associated with the eastward recessed WPSH during 1979–2009, possibly contributing to the excessive rainfall over the middle and lower reaches of the Yangtze River valley since the late 1970s.

Due to the significant effects of the WPSH, assessing and projecting the WPSH in climate models are important issues, which have been intensively studied for decades. Recently, climate models from the Coupled Model Intercomparison Project Phase 5 (CMIP5), with generally higher resolution and a broader set of experiments compared with CMIP3, have been coordinated for use in the Intergovernmental Panel on Climate Change Fifth Assessment Reports (IPCC AR5) (Taylor et al. 2012). Many researchers have investigated the performances of the CMIP5 models in terms of the Asian summer monsoon (Jiang and Tian 2012; Sperber et al. 2012), regional and global precipitation (Chen and Sun 2013; Chen et al. 2014; Gao et al. 2015), decadal variation of the linkage between the East Asian winter monsoon and the El Niño-Southern Oscillation (Wang et al. 2013b), climate extremes in China (Chen and Sun 2015) and certain other atmospheric and oceanic processes. In terms of the WPSH, the previous evaluation and projection focused mainly on the geopotential height field at 500 hPa (e.g., Huang et al. 2013a, b; Xin et al. 2013; Liu et al. 2014), which could be affected by the artificial trend caused by global warming, as previously mentioned, especially when evaluating decadal variations of the WPSH and projecting WPSH variation in the future. Therefore, re-evaluation and re-projection for the WPSH are necessary after removing the aforementioned artificial influence.

This paper is organized as follows. The data, model and method are introduced in Sect. 2. Section 3 evaluates the performance of the CMIP5 models in capturing the mean state of the WPSH based on the fields of the eddy geopotential height and horizontal winds. The models’ abilities to reproduce the interannual and interdecadal variations of the WPSH are analyzed in Sect. 4. Section 5 discusses the projection of the WPSH in the future. Finally, a summary is provided in Sect. 6.

2 Data and method

The WPSH appears to be much more stable and stronger in the lower troposphere than in the middle troposphere, and its low-level western and northwestern edges feature southerlies or southwesterlies that transport amount of water vapor, influencing significantly the East Asian summer climate (Lu 2002; Lu et al. 2008). Therefore, we predominantly analyze the WPSH at 850 hPa in this study. The historical simulations of 28 CMIP5 models for the period of 1950–2005 are evaluated. Table 1 lists the basic information for these 28 CMIP5 models, including the horizontal resolution of the atmospheric component. The projection simulations for the period of 2006–2100 under the representative concentration pathway leading to a radiative forcing level of 8.5 W/m2 by 2100 (RCP8.5) (van Vuuren et al. 2011) are used to project the future variations in the WPSH. All the model datasets are interpolated into a common horizontal resolution of 2.5° × 2.5° via a bilinear or area-based interpolation algorithm. Additionally, the monthly mean data in the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis 1 (Kalnay et al. 1996) with a horizontal resolution of 2.5° is used as verification data. Our analysis focuses solely on the summer months of June–August (JJA).

Table 1 Description of the 28 CMIP5 models used in this study
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A Taylor diagram with three statistical measures of the spatial correlation coefficient (SCC), the root mean square error (RMSE) and the standard deviation ratio (SDR) is used to quantify model fidelity for the mean state of the WPSH (Taylor 2001). Following Huang et al. (2015), we use the simple difference between means for the periods 1979–2005 and 1950–1978 to characterize the interdecadal variation of the WPSH. The statistical significance is assessed using the Student’s t test.

3 Simulation of the climatology of the WPSH

To avoid the artificial influences caused by global warming, we first examine the features of the eddy geopotential height (H′) field at 850 hPa (hereafter H′850), in which H′ = H− \({\bar{\text{H}}}\), where H is the geopotential height and \({\bar{\text{H}}}\) is the zonal mean of H. Figure 1 shows the climatology of the observed and simulated summer H′850. The WPSH indicated by the positive eddy geopotential height is a dominant high-pressure system over Pacific, accompanied by a negative eddy geopotential height over East Asia, which represents the Asian low system (Fig. 1a). The CMIP5 models generally reproduce the positive H′850 over Asia and the negative H′850 over the Pacific, although biases exist in intensity and position (Fig. 1b1–r2). Figure 2 shows the position of the western edge of the WPSH (the contour line of 0 gpm over the western Pacific) in the CMIP5 model simulations and NCEP. Compared with the position of the western edge of the WPSH in the NCEP, i.e., near 140°E and 20°N, a more westward-extended WPSH appears in the FGOALS-g2, MIROC5 and the MIROC-ESM models and a somewhat eastward- or northward-recessed WPSH is produced by bcc-csm1-1, CanESM2, GFDL-CM3, inmcm4, and MPI models. Additionally, a dramatic underestimation of the WPSH is found in three IPSL models and the MRI-CGCM3 model, with the positive eddy geopotential height only appearing east of 170°E over the Pacific. The other CMIP5 models, such as ACCESS1, CNRM–CM5, HadCM3 and NorESM1 models, perform generally well in capturing the intensity and the position of the climatological H′850 over Pacific, which is indicative of a reasonable ability reproducing the mean state of the WPSH (Figs. 1, 2). Similarly, the CMIP5 models’ abilities to capture the climatological WPSH can also be observed in the climatology maps of the summer 850-hPa geopotential height and horizontal winds (figures not shown). Moreover, it should be noticed that most of the CMIP5 models fail to capture the mean state of the WPSH described in the climatology map of the 500-hPa geopotential height due to larger systematic errors (Liu et al. 2014). Therefore, compared with the 500-hPa geopotential height, the use of the 850-hPa eddy geopotential height field in the CMIP5 models to project the future variations of the WPSH seems to be more creditable.

Fig. 1
figure 1

The climatology of the JJA-mean eddy geopotential height at 850 hPa (H′850) (gpm) during 1950–2005 from the NCEP/NCAR reanalysis data (a) and CMIP5 model simulations (b1–r2). The shaded regions denote H′850 values >0 gpm, and the thick dashed lines indicate the topographic contour of 1500 m

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Fig. 2
figure 2

The westernmost location of the contour line of 0 gpm in the climatological JJA 850-hPa eddy geopotential height over the western Pacific in the CMIP5 models and NCEP (red dot)

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More quantitative measurements can be obtained from a Taylor diagram (Fig. 3). Specifically, the azimuthal angle represents the spatial correlation coefficient (SCC), the distance apart between the model code and REF (reference, namely observation) indicates the root mean square error (RMSE) and the radial distance from the origin is the standard deviation ratio (SDR) between a simulation and an observation. The SCC and RMSE measure the model quality with respect to the variable’s spatial distribution, whereas the SDR reflects the model quality with respect to the variable’s amplitude or spatial variability. Smaller distances between the model code and the REF in the Taylor diagram indicate better performances for the corresponding model. For the climatological summer H’850 over the western Pacific (0°–145°N, 110°–180°E) (Fig. 3a), the SCCs in all 28 CMIP5 models are above 0.80, and half are above 0.95, which are statistically significant at the 99.9 % confidence level (0.14). The RMSEs are generally <0.65 gpm, except the IPSL-CM5B-LR and MRI-CGCM3 models, which have slightly larger values of 0.79 and 0.75 gpm, respectively. These results represent the CMIP5 models’ capacity in reproducing the geographical distribution of H′850 over the western Pacific. Meanwhile, the CMIP5 models with SDRs between 0.75 and 1.28 also well capture the spatial variability of the climatological H′850. Most CMIP5 models, with SCCs of 0.73–0.98, RMSEs of 0.38–0.76 and SDRs of 0.78–1.32, reasonably reproduce the main features of the spatial distribution and amplitude of the climatological summer zonal wind at 850 hPa over the western Pacific (Fig. 3b). One significant outlier is the MIROC-ESM model with an SDR of 1.62 and a relatively high RMSE value of 1.12. Overall, according to Fig. 3, most CMIP5 models reliably reproduced the spatial distribution and variability of the WPSH.

Fig. 3
figure 3

Taylor diagram of simulated climatological JJA eddy geopotential height (a) and zonal wind (b) at 850 hPa during 1950–2005 over the western Pacific (0°–45°N, 110°–180°E) with respective to observation (namely Reference, REF). The radial distance of the model code from the origin is the standard deviation ratio of the model relative to the observation. The spatial correlation coefficient between the model simulation and the observation is expressed as the azimuthal position of the model code. The root-mean-square error is given by the distance between themodel code and the REF

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4 Performance with respect to the interdecadal variations of the WPSH

Following Huang et al. (2015), we defined the WPSH index (WPSHI) as the regionally averaged summer H′850 over the maximum interannual variability center (15°–30°N, 120°–150°E) of the western edge of the WPSH to characterize the variability of the WPSH. Figure 4 shows the linear trend of the normalized summer WPSHI from 1950 to 2005 for the NCEP data and CMIP5 model simulations. The NCEP WPSHI displays a significant decreasing trend of −0.027 (significant at the 99.9 % confidence level) during 1950–2005, indicating a weakened and eastward-recessed WPSH in the late 1970s (Fig. 4). As shown in Fig. 4, 11 CMIP5 models generally capture this decreasing trend. In particular, the trends of the simulated WPSHIs in the models bcc-csm1-1, CESM1-CAM5, GFDL-ESM2G, inmcm4, and MPI-ESM-Pare −0.018, −0.011, −0.014, −0.011, and −0.015, which are significant at the 97, 80, 90, 83, and 92 % confidence levels, respectively. However, the rest of CMIP5 models fail to capture this decreasing trend, with no interdecadal variation in 8 models and even opposite increasing trends in 9 models (Fig. 4). For example, the ACCESS1-0, GISS-E2-H, and IPSL-CM5A-LR models exhibit no trends in the WPSHIs, and the MIROC5 and MRI-CGCM3 models exhibit significant increasing trends of 0.026 and 0.019, respectively.

Fig. 4
figure 4

The linear trend of the normalized JJA WPSH index (WPSHI) (%) during 1950–2005 in the NCEP and the CMIP5 model simulations

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The interdecadal signals of the WPSH can be further observed in the difference map of the 850-hPa winds between 1979–2005 and 1950–1978. A significant anomalous cyclone appears over the western Pacific, suggesting a weakened WPSH during 1979–2005 relative to 1950–1978 (Fig. 5a). Meanwhile, the anomalous northeasterly winds prevail from North to South China in observation, indicating a weakened EASM in 1979–2005 compared to 1950–1978 (Wang 2001) (Fig. 5a). The anomalous cyclone over the western Pacific is generally reproduced by 9 CMIP5 models, but with the biases in position and intensity relative to the observation. In particular, the bcc-csm1-1, CESM1-CAM5, GFDL-ESM2G and inmcm4 models exhibit the best performances, with the significant anomalous cyclone appearing over the western Pacific. The ACCESS1-0, CanESM2, CESM1-BGC, GFDL-CM3 and NorESM1-ME models also capture the anomalous cyclone over the western Pacific, but the intensities of the simulated cyclonic anomalies are weaker than the observation and are not statistically significant. Interestingly, the 9 models that produce an anomalous cyclone over the western Pacific are the same models that capture the decreasing trend of the WPSH index. The four best models is the models with most significant decreasing trends (Fig. 4). However, the remaining19 CMIP5 models perform very poorly in representing this anomalous cyclone, with no interdecadal signals or even significant anomalous anticyclone over the western Pacific (e.g., the MIROC5 model).

Fig. 5
figure 5

The difference in the JJA horizontal winds at 850 hPa between 1979–2005 and 1950–1978 for the NCEP (a) and the CMIP5 model simulations (b1–r2). Shading indicates significance at the 95 % confidence level using Student’s t test

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The cause of the differences in the ability to simulate the interdecadal WPSH variations between the 9 good models and the other 19 bad models is further analyzed. It has been confirmed that the Indian Ocean-Western Pacific warming can induce a strong and westward extended WPSH (e.g., Yang et al. 2007; Li et al. 2008; Zhou et al. 2009). All CMIP5 models successfully capture the interdecadal increased SSTs in the late 1970s in the Indian ocean-western Pacific regions (figure not shown). It seems to imply that all CMIP5 models should consequently produce an westward extended WPSH, however, it is contrary to the above evaluated results. For the SST role in affecting the interdecadal variation of the WPSH, Huang et al. (2015) suggested the different active roles between the North Indian Ocean (NIO) and the western North Pacific (WNP). Particularly, they examined the interdecadal signal in the 500-hPa vertical p velocity. The dominant descent over the NIO suggests a recharging phase of the NIO on the interdecadal scale, and the large ascent area over the WNP indicates the vital role of the WNP in affecting the atmospheric circulations over that region (Fig. 6a). Through local wind-evaporation-SST feedback, the cool western north Pacific favors a westward and enhanced WPSH (Wang et al. 2000, 2013a; Wu et al. 2010). Therefore, they suggested that the recharging phase of the Indian ocean and the western north Pacific warming in the late 1970s may together contribute to the interdecadal weakening of the WPSH. Considering this speculation, we compare the model performances in simulating the interdecadal signal in the 500-hPa vertical p velocity to examine the model ability for capturing the different active role of SST. The multi-model ensemble of the 9 good models generally reproduce the interdecadal signals of the 500-hPa vertical p velocity, with descent appearing over the NIO and ascent locating over the WNP, although certain biases exist in position and intensity (Fig. 6b). However, the 19 bad models simulate a consistent descent spanning from the NIO to the WNP, thus failing to reproduce the ascent over the WNP (Fig. 6c). Thus, the ability of the 9 good models to reproduce the interdecadal WPSH variation may be attributed to the ability of these models in capturing the different roles of the NIO and the WNP in affecting atmospheric circulations on the interdecadal scale.

Fig. 6
figure 6

The difference in JJA 500-hPa vertical p velocity (× 0.001 Pa s−1) between 1979–2005 and 1950–1978 in the NCEP (a), the multi-model ensemble of the 9 good models (b) and the multi-model ensemble of the 19 bad models. The contour interval is 4 Pa s−1 (2 Pa s−1) in Panel a (Panel b and c). Dark, medium and light blue and red shading indicate significance at the 99, 95 and 90 % confidence levels, respectively, using Student’s t test. The 9 good models are ACCESS1-0, bcc-csm1-1, CanESM2, CESM1-CAM5, CESM1–BGC, GFDL–CM3, GFDL–ESM2G, inmcm4 and NorESM1-ME

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5 Projection of the WPSH under RCP8.5

Based on the above analyses, the four CMIP5 models that were best able to reproduce the interdecadal WPSH variations (including the decreasing trend of the WPSH index and the anomalous cyclone over western Pacific)—bcc-csm1-1, CESM1-CAM5, GFDL-ESM2G and inmcm4—were selected to make future projections for the 21st century under the RCP 8.5 scenario. The results of the multi-model ensemble (MME), calculated as the simple average of the bcc-csm1-1, CESM1-CAM5, GFDL-ESM2G and inmcm4 model projections, are analyzed in this section.

In addition to the above-defined WPSHI based on H’850, the traditional WPSH index, similar to the WPSHI but based on the 850-hPa geopotential height, was also analyzed for comparison. Figure 7 shows the 9-year running mean of the normalized traditional WPSH index and WPSHI from 2006 to 2100. Not surprisingly, due to the exacerbated effects of global warming on the increased geopotential height in twentyfirst century, the traditional WPSH indice in four CMIP5 models and in the MME all exhibit significant increasing trends (e.g. the trend in MME is 0.030, significant at 99.9 % confidence level) and predict a gradually strengthening WPSH (Fig. 7a). In fact, based on the projections using the geopotential height field, the strengthened and westward-extended features of the future WPSH have been illustrated by many researchers (e.g., Seo et al. 2013; Xin et al. 2013; Liu et al. 2014). However, after removing the artificial trends caused by global warming, no significant linear trend exists in the WPSHIs. This result is consistent with those of He and Zhou (2015), who documented that the projected changes in the WPSH intensity are approximately zero under both RCP4.5 and RCP8.5 scenarios. In addition, deriving from the inmcm4 model with different projected phase or magnitude, the MME’s uncertainty before 2045 is larger than it after 2045 for both traditional WPSH index case and WPSHI case.

Fig. 7
figure 7

The 9-year running mean of the JJA the traditional WPSH index based on the 850-hPa geopotential height (a) and the WPSHI based on the 850-hPa eddy geopotential height (b) from 2006 to 2100 under the RCP8.5 scenario from the projections of the four best CMIP5 models (thin dash lines) and the multi-model ensemble (MME) (thick solid line). Shaded areas represent the MME’s uncertainty which is obtained from one standard deviation of individual models departure from MME

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According the interdecadal signals in WPSHI, the MME projects the WPSH is in a positive phase during 2010–2025 and 2071–2100 and in a negative phase during 2026–2070. To verify this WPSH future interdecadal variation, we examined the differences in the 850-hPa horizontal winds between the positive phase periods (2010–2025 and 2071–2100) and the negative phase period (2026–2070) in the MME (Fig. 8). In Fig. 8a, significant anticyclonic anomalies appear over the western Pacific. For each positive phase period, the significant anticyclone anomalous can also been seen in the difference maps (Fig. 8b, c). In the difference maps for the relative vorticity at middle-lower levels (1000–500 hPa) along 15°–30°N, the remarkable significant negative anomalies of the relative vorticity span the western Pacific region (Fig. 9). Based on a stronger WPSH corresponding to stronger anticyclonic circulation and higher negative vorticity over the western Pacific, the significant anticyclonic anomalies in the 850-hPa winds and the negative anomalies in the relative vorticity suggest that the WPSH may not gradually strengthen in the twentyfirst century (as projected by the traditional WPSH index) and may instead to weaken during 2026–2070 relative to 2010–2025 and 2071–2100. These consistent interdecadal WPSH variations in the future 850-hPa winds and relative vorticity imply that the projections based on the WPSHI are reliable. Therefore, compared the traditional WPSH index based on geopotential height, which can be affected by the artificial trends caused by global warming, the WPSHI based on the eddy geopotential height is better suited to project future WPSH variations.

Fig. 8
figure 8

Differences in the horizontal winds at 850 hPa in the four best CMIP5 models’ ensemble between the WPSH positive periods (2010–2025 and 2071–2100) and the negative period (2026–2070) (a). Panels b and c are same as in panel a but for the positive period of 2010–2025 in panel b, and 2071–2100 in panel c. Shading indicates significance at the 95 % confidence level using Student’s t test

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Fig. 9
figure 9

Same as in Fig. 8, but for the difference in the cross-section of the JJA relative vorticity along 15°–30°N at the middle and lower levels (1000–500 hPa). Dark, medium and light blue and red shading indicate significance at the 99, 95, and 90 % confidence levels, respectively, using Student’s t test

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6 Summary and discussion

The western Pacific subtropical high is a dominant anticyclonic circulation over the subtropical Pacific and exerts large influences on the East Asian summer climate, especially the low-level WPSH with southerlies or southwesterlies along its lower-level western or southern edges. This study assesses the ability of 28 CMIP5 models to simulate the summer low-level WPSH during 1950–2005. We primarily investigated the fields of eddy geopotential height and horizontal winds at 850 hPa to avoid the artificial influences caused by global warming. The results show that most of the models generally performed well in reproducing the spatial distribution and amplitude of the WPSH, excluding three IPSL models with significant underestimations and the MIROC5 model with a significant overestimation. Four models (bcc-csm1-1, CESM1-CAM5, GFDL-ESM2G and inmcm4) successfully captured the significant cyclonic anomalies in the 850-hPa winds over the western Pacific during 1979–2005 relative to 1950–1978 and the significant decreasing trend in the WPSH index (WPSHI) during 1950–2005. Therefore, these models generally captured the eastward recession of the WPSH in the late of 1970s, which may be attributed to the models’ ability to reproduce the recharging phase of the North Indian Ocean and the vital role of the western North Pacific in affecting the atmospheric circulations on the interdecadal scale.

The four models that performed best in reproducing the historical interdecadal WPSH variation were selected to project the WPSH variation into the future of the twentyfirst century under RCP8.5. Using the WPSHI based on eddy geopotential height, the WPSH is projected to be weaker during 2026–2070 relative to 2010–2025 and 2071–2100. These future WPSH interdecadal variations are further verified by the significant anticyclonic anomalies in the 850-hPa winds and the significant negative anomalies in the relative vorticity at middle-lower levels (1000–500 hPa) along 15°–30°N over the western Pacific in the difference maps between the positive phase periods (2010–2025 and 2071–2100) and the negative phase period (2026–2070). Considering the isobaric surface at the middle-lower latitudes could be further lifted in global future further warming, the artificial trends in the increased geopotential height would be exacerbated, thus the traditional WPSH index based upon geopotential height may not be suitable for projecting future WPSH changes.

The possible reason for the weakened WPSH during 2025–2070 is now discussed. Using the diagnostic study and numerical simulation, He and Zhou (2014) suggested that the SST gradient between the tropical Indian Ocean and the tropical western Pacific dominates the projected WPSH intensity under both the RCP4.5 and RCP 8.5 scenarios. A stronger (weaker) warming in the tropical Indian Ocean—TIO, 10°S–10°N, 50°E–100°E—stimulates warm (cold) Kelvin waves, which increase (decrease) the WPSH intensity via wave-induced Ekman divergence (convergence). A weaker (stronger) warming in the tropical western Pacific—TWP, 10°S–10°N, 150°E–180°E—increases (decreases) the WPSH intensity via an anticyclonic (cyclonic) Rossby wave response to the northwest. Therefore, we examine the future changes of the differences in the normalized regionally averaged SST between the TIO and the TWP (i.e., the TIO-TWP zonal SST gradient) during 2006–2100 (Fig. 10). The correlation coefficient between the 9-year running mean WPSHI and TIO-TWP SST zonal gradient is 0.50 during 2006–2100 in the MME, exceeding the 99.9 % confidence level. Based on this significant positive correlation, the general negative phase of the TIO-TWP zonal SST gradient during 2025-2070 may give a clue for the weakened WPSH (Fig. 10). However, the primarily negative phase of the TIO-TWP zonal SST gradient is not completely consistent with the negative phase of the WPSH. This disagreement means that there may still be other factors responsible for the weakened WPSH during 2025-2070. Therefore, further analysis based on more quantitative diagnose, as well as state-of-the art climate models, is needed in the future work.

Fig. 10
figure 10

Same as in Fig. 7, but for the TIO-TWP SST zonal gradient, which is defined as the difference in the normalized regionally averaged SST between the TIO (10°S–10°N, 50°E–100°E) and the TWP (10°S–10°N, 150°E–180°E)

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