1 Introduction

The western Pacific subtropical high (WPSH) is an important component of the East Asian monsoon system. Its area, intensity, north–south position (the northern edge or ridge line), and east–west extension (the western ridge point) play the dominant role in the East Asian monsoon activities, and henceforth dominating the Meiyu/Baiu processes, especially droughts/floods as well as temperature changes in Yangtze River basin, North and South China (Dao and Hsu, 1962; Guan et al., 2010; Zhao et al., 2012; Liu et al., 2013). In the first half of 2016, the WPSH was stronger and extending more westward than normal, which leaded to frequent occurrences of rainstorms and floods in the south of China (Yuan et al., 2016; Zhai et al., 2016). Thereby, researchers in China have been trying all the time to understand the variations of the WPSH intensity and position better.

Previous studies have suggested that many factors can affect the WPSH changes. SST anomalies (SSTAs) over various ocean areas have different impacts on the WPSH (He et al., 2015; Li et al., 2017). Over the Pacific, the subtropical high activity is affected not only by local SSTA in the western Pacific (Kurihara and Kawahara, 1986; Wong et al., 1996; Zhang et al., 1996; Chung et al., 2011; Lu et al., 2014), but also by SSTA in the equatorial central-eastern Pacific. In most of the years when an El Niño event happens, the WPSH is weaker than normal and shifts eastward. In the winter when El Niño reaches its mature stage, an abnormal anticyclonic circulation appears over the western Pacific and maintained there until the subsequent summer (Li and Hu, 1987; Wang et al., 2000; Xiang et al., 2013; Zhang et al., 2017; Qian and Guan, 2018). This anticyclonic circulation promotes abnormal development of the WPSH. During the decaying stage of El Niño, reduced convection over the central Pacific enhances WPSH via Rossby wave response (Wang et al., 2013). This is further reconfirmed in Chen et al. (2016) that the WPSH intensification is induced by the central-eastern Pacific cooling during the rapid transition from El Niño to La Niña. Simultaneously, increased convection over Maritime Continent (MC) motivates easterlies over the western Pacific, leading to WPSH strengthening (Chung et al., 2011; Wang et al., 2017).

SSTA in the Indian Ocean (IO) can also strongly affect the WPSH activities. The Indian Ocean basin mode (IOBM) is the first important factor (Behera et al., 1999), which mainly reflects the lagged response of the Indian Ocean to ENSO (El Niño and Southern Oscillation) signals (Alexander et al., 2002; Ashok et al., 2003). The IOBM reaches its peak in the spring and can maintain until the summer via the ocean–atmosphere interaction (Klein et al., 1999). During positive IOBM phase, the WPSH intensifies due to the two-stage thermodynamic adaptation mechanism (Wu and Liu, 1992; Wu et al., 2000). Terao and Kubota (2005), Xie et al. (2009), and Wu et al. (2009, 2010) argued that SSTA in the tropical Indian Ocean could trigger eastward propagation of warm Kelvin waves; meanwhile, abnormal anticyclonic circulation could occur over the northwestern Pacific (NWP) due to the Ekman pumping, which subsequently affects the WPSH. It is similar to the role of “capacitor”, which transmits the impact of El Niño on WPSH in subsequent summer. And the “capacitor”-effect strengthens in response to global warming (Xie et al., 2010; Tao et al., 2015). As the second mode of SSTA in the Indian Ocean, the Indian Ocean dipole (IOD) is an important SST mode independent of ENSO, though correlated with ENSO signals to a certain extent (Saji et al., 1999; Webster et al., 1999; Ashok et al., 2003). The IOD can affect the summertime East Asian circulation through a triangular correlation mechanism (Guan and Yamagata, 2003). In addition, several previous studies focused on the impact of SSTA in northern Indian Ocean and the Bay of Bengal on the WPSH (Jiang et al., 1992; Huang and Hu, 2008).

According to the different impacts of SSTA in various ocean areas on the WPSH, some recent studies emphasized the combined effect of SSTA in Indo-Pacific. The warming in tropical Indian Ocean–western Pacific is found to be very important in leading to the westward extension of the WPSH since 1970 (Zhou et al., 2009). It is also found that an anomalous strong WPSH can be induced by the anomalous zonal SST gradient between warmer IO and colder Pacific (Ohba and Ueda, 2006; Cao et al., 2013).

The above shows that the relationships between the WPSH and SSTA in oceanic regions such as northwestern Pacific, MC, central equatorial Pacific (CEP), and IO have been extensively investigated in the past. However, there are still some important questions of interest to be answered. What are the temporal variations of the joint impacts of the SSTA in the Indian Ocean and Pacific on summertime WPSH as the IO SSTA signals obviously lag to those in the Pacific? What are physical processes that dominate these joint impacts of SSTA? Is it possible to set up a model for predicting the WPSH area in summer? In the present study, we examine these issues with emphasis on area changes of the WPSH.

The present paper is organized as follows. After the brief introduction, we present in Section 2 with descriptions of data and methodology. In Section 3, we examine the relationship between abnormal changes in WPSH area and SSTA over tropical Indian Ocean and Pacific. In Section 4, the mechanism behind the impact of SSTA on the WPSH is investigated. The prediction model for WPSH area variations is presented in Section 5. In the final section, we summarize the present study.

2 Data and methodology

The data used in the present study include: (1) monthly mean SST from the Met Office Hadley Centre observation datasets (Rayner et al., 2003) with a resolution of 1° × 1°; and (2) NCEP/NCAR reanalysis product (Kalnay et al., 1996) of the geopotential height and winds with a resolution of 2.5° × 2.5° at 17 pressure levels. The data cover the period from September 1980 to October 2016.

The variation of area of the WPSH is highly correlated with its intensity with a correlation coefficient up to 0.89 in the summer (Qian et al., 2009). Thereby, in the present study, we focus on changes in the WPSH area to study the characteristics of WPSH activity. The WPSH moves mainly in region (10°–40°N, 90°E–180°), which is denoted by BOX-W. The WPSH area (WPSHA) is defined by surface areas of those 2.5° × 2.5° grids with monthly mean geopotential height not less than 588 dagpm at 500 hPa. For convenience, the WPSH area index is denoted by I_WH, which is expressed as:

${I_{{\rm{WH}}}} = {\frac{1}{\sum}}\iint\limits_{_{{\rm BOX} {\text{-}} {\rm W}}} {\varepsilon \left( {\lambda ,\;\varphi } \right) M\left( {\lambda ,\;\varphi } \right){\rm d}\varphi {\rm d}\lambda } ,$

(1)

where M(λ, φ) is the area weight factor. When H $\left( {\lambda ,\;\varphi } \right) $ ≥ 588 dagpm, ε $\left( {\lambda ,\;\varphi } \right) $ = 1; when H $\left( {\lambda ,\;\varphi } \right) $ < 588 dagpm, ε $\left( {\lambda ,\;\varphi } \right) $ = 0. Therefore, the disturbance of I_WH can be defined as the difference between I_WH and its mean climatology,

$I{'_{{\rm{WH}}}} = {I_{{\rm{WH}}}} - {\bar I_{{\rm{WH}}}}.$

(2)

Besides, the atmospheric apparent heat source <Q1> is computed ( Luo and Yanai, 1984; Li et al., 2016) for analyzing the anomalous thermal forcing in tropical regions.

In the following text, the preceding autumn and winter refers to September–December (SOND); late winter and early spring is February–April (FMA); the spring is March–May (MAM); and the summer is June–August (JJA).

3 The relationship between WPSH area and SSTA over tropical IO and Pacific 3.1 The key region affecting the WPSH area

In order to determine the key regions in the tropical Indian Ocean and Pacific where SSTA most possibly affect variations in the WPSH area, the correlation coefficient between $I{'_{{\rm{WH}}}}$ and tropical SSTA is calculated (Fig. 1a). It is seen from Fig. 1a that preceding SSTA over large areas of the tropical Indian Ocean and Pacific are highly and positively correlated with the summertime WPSH area. In the Pacific, the positive correlation region is mainly located in the central-eastern Pacific (Niño3 region), where the positive correlation can maintain from the preceding summer to the subsequent spring. In particular, the positive correlation coefficient between SSTA in this area during preceding September–December and the WPSH area exceeds 0.7. At the same time, SSTA over the warm pool region is weakly negatively correlated with the WPSH area index. Different to impacts of the Pacific SSTA on the WPSH, SSTA in the Indian Ocean is highly positively correlated with the WPSH area on ocean basin scale, particularly in the spring of the year (0) when the correlation coefficient can be greater than 0.7. Meanwhile, the correlation coefficient over the entire central-eastern Pacific gradually decreases.

The regions of high correlation coefficient between SSTA from January of the last year to the June of the present year and the summertime WPSH area, i.e., (5°S–5°N, 160°–140°W) in CEP and (10°S–5°N, 60°–80°E) in the central tropical Indian Ocean (CTI), are identified to be the key regions where SSTA can significantly affect the interannual variability of WPSH. Lead–lag correlations between SSTA in the two key regions and the WPSH area are calculated (Fig. 1b). It shows that the WPSHA in summer is affected by the preceding SOND ENSO signals in the tropical central Pacific, while it is more significantly affected by CTI-SSTA in the early spring (FMA) of the same year. This result indicates that positive SSTA often occurs in the CEP since the preceding autumn and winter. In response, warm SSTA appears in the Indian Ocean in the subsequent spring. The correlation coefficient between the CEP-SSTA averaged over preceding SOND and the CTI-SSTA averaged over subsequent FMA is up to 0.84 (above 99% confidence level). As a result, the WPSH area in the summer is larger than normal. The above results suggest that SST over CEP and CTI and the WPSH area are closely related to each other.

Time series of CEP-SSTA averaged over the preceding SOND and CTI-SSTA averaged over the subsequent FMA during the 36-yr period are calculated and defined as the SSTA indices ${I'_{{\rm{CEP}}(- 1)}}$ for the central equatorial Pacific and ${I'_{{\rm{CTI}}(0)}}$ for central tropical Indian Ocean, respectively. These two indices are then used to investigate the joint effects of SSTA in the Pacific and Indian Ocean on the WPSHA.

3.2 Variations of WPSH area in association with SSTA

In order to further reveal the impacts of CTI-SSTA and CEP-SSTA on the WPSH and the possible mechanisms behind them, the linear trends during 1981–2016 are first removed from ${I'_{{\rm{CEP}}(- 1)}}$ and ${I'_{{\rm{CTI}}(0)}}$ . The normalized time-series ${\tilde I_{{\rm{CTI}}(0)}}$ and ${\tilde I_{{\rm{CEP}}(- 1)}}$ are then obtained. One strong SSTA event is identified when the absolute value of the index is greater than 0.75. A positive SSTA event is denoted by “P” and a negative one by “N”. Using the above definitions, six types of SSTA are identified; they are P-P type for cases of both ${\tilde I_{{\rm{CTI}}(0)}}$ and ${\tilde I_{{\rm{CEP}}( - 1)}}$ larger than 0.75, N-N type for cases of both ${\tilde I_{{\rm{CTI}}(0)}}$ and ${\tilde I_{{\rm{CEP}}( - 1)}}$ smaller than −0.75, P-0 type for cases when ${\tilde I_{{\rm{CTI}}(0)}}$ ≥ 0.75 and $\left| {{{\tilde I}_{{\rm{CEP}}( - 1)}}} \right|$ < 0.5, 0-P type for cases if $\left| {{{\tilde I}_{{\rm{CTI}}(0)}}} \right|$ < 0.5 and ${\tilde I_{{\rm{CEP}}( - 1)}}$ ≥ 0.75, N-0 type if ${\tilde I_{{\rm{CTI}}(0)}}$ ≤ –0.75 and $\left| {{{\tilde I}_{{\rm{CEP}}( - 1)}}} \right|$ < 0.5, and 0-N type if $\left| {{{\tilde I}_{{\rm{CTI}}(0)}}} \right|$ < 0.5 and ${\tilde I_{{\rm{CEP}}( - 1)}}$ ≤ –0.75. Similarly, the normalized time series of ${\tilde I_{{\rm{WH}}}}$ can be obtained after removing the linear trend from $I{'_{{\rm{WH}}}}$ . Note that in the following analysis, linear trends have been removed from all the time series unless specifically stated.

The variations of WPSH area are examined for cases with the above six types of SSTA events. It is seen from Fig. 2 that positive WPSH area anomalies (denoted by red marks) most possibly occur in the years when both ${\tilde I_{{\rm{CTI}}(0)}}$ and ${\tilde I_{{\rm{CEP}}( - 1)}}$ are positive (70.6%), especially in type P-P years. On the contrary, negative WPSH area anomalies (denoted by black marks) are most possible when both ${\tilde I_{{\rm{CTI}}(0)}}$ and ${\tilde I_{{\rm{CEP}}( - 1)}}$ are negative (73.7%). The N-N type of SSTA always corresponds to smaller than normal WPSH area in the summer.

As described previously, the variations of SSTA in CTI are influenced by the SSTA in CEP; the lagged correlation coefficient of ${I'_{{\rm{CTI}}(0)}}$ and ${I'_{{\rm{CEP}}(- 1)}}$ is up to 0.84. In the recent 36 years, there are 30 yr (83.3%) when SSTA in the two key regions are same signed whereas there are 6 yr (16.7%) when SSTA in these two regions are oppositely signed. As observed in Fig. 2, when the strong SSTA event (absolute normalized index value greater than 0.75) appears in one region, the typical SSTA event with opposite sign will never appear in the other region, i.e., there exist no P-N and N-P types of strong SSTA events. More than this, it is found that El Niño event as denoted by “×” in Fig. 2 only occurs when ${\tilde I_{{\rm{CEP}}( - 1)}}$ in the autumn–winter is up to 0.5 and above. This El Niño signal can be confirmed by the response of the Indian Ocean where the CTI-SSTA arises later. In contrast, La Niña event as denoted by “•” in Fig. 2 only occurs when ${\tilde I_{{\rm{CEP}}( - 1)}}$ is equal to or smaller than –0.5, which also induces the SSTA in CTI to drop anomalously in the subsequent spring. As the consequence, the WPSH area is larger (smaller) than normal in the summer when the P-P (N-N) type of SSTA that correspond to El Niño (La Niña) occurs.

Note that there are no cases of P-N and N-P types of SSTA appearing during the study period, reconfirming that the CTI-SSTA in current year is almost a result of IO response to the CEP-SSTA in the preceding autumn–winter. Interestingly, there are some particular cases when significant SSTA occurs in one region while SSTA in the other region is not large enough. These situations are indeed observed in Fig.2, denoted as cases of P-0, 0-P, and N-0 types of SSTA. When these cases occur, the relations of WPSH area variations are not highly correlated with ${\tilde I_{{\rm{CTI}}(0)}}$ or ${\tilde I_{{\rm{CEP}}( - 1)}}$ . After removing the years of P-P and N-N types of SSTA, the correlation coefficient between ${\tilde I_{{\rm{CTI}}(0)}}$ and ${\tilde I_{{\rm{CEP}}( - 1)}}$ in the remaining years is 0.46, indicating that the response of IO to the remote forcing of SSTA in CEP is still significant though weak. In this situation, the correlation coefficient between ${\tilde I_{{\rm{WH}}}}$ and ${\tilde I_{{\rm{CTI}}(0)}}$ is 0.46 while that between ${\tilde I_{{\rm{WH}}}}$ and ${\tilde I_{{\rm{CEP}}( - 1)}}$ is 0.54, suggesting that the basic relationship between SSTA and WPSH area does not change much.

4 The mechanism behind the impact of SSTA on the WPSH 4.1 SSTA patterns related to WPSH variations

The SSTA patterns related to WPSH area variations can be displayed by the composites of SSTA differences between P-P and N-N cases, which are presented in Fig 3. It is seen that when warm SSTA occurs over CEP in the preceding autumn and winter (SOND) (Fig. 3a), abnormally cold SSTA occurs in the western Pacific and the MC region. At this time, SST warming at CTI is weak. According to the Delayed Oscillator theory (Suarez and Schopf, 1988), accompanied with the eastward propagation of Kelvin waves and westward propagation of Rossby waves in the ocean, El Niño enters decaying stage in the subsequent spring (Fig. 3b), with CEP-SSTA gradually weakening. During the entire period of the ENSO cycle, continuous ocean–air interaction leads to the lagged response of CTI to ENSO signals through the “Atmospheric Bridge” (Klein et al., 1999; Alexander et al., 2002; Lau and Nath, 2003) and results in significant warm CTI-SSTA in spring (FMA) (Fig. 3b) (Ashok et al., 2003; Zhou et al., 2004).

In the following summer (JJA) (Fig. 3c), El Niño disappears; CEP-SSTA is very weak and the tropical western Pacific starts to become warming. Meanwhile the abnormal warm center in the CTI shifts northward to the Arabian Sea and Bay of Bengal, which is due to both the more absorption of solar radiation and the anomalous oceanic convergence of warm water by the anomalous anticyclonic circulations near the ocean surface. However, SSTA still remains high in the west and low in the east from the equatorial Indian Ocean to western Pacific. Such an SSTA pattern is favorable for the intensification and maintenance of the WPSH (Ohba and Ueda, 2006; Wu et al., 2014).

4.2 Mechanisms for the WPSH area change

Due to the joint influence of SSTA in the Pacific and Indian Ocean, significant convergence and divergence anomalies appear over the entire Indo-Pacific sector (Fig. 4). In the autumn and winter, surface air pressure over the CEP decreases following the abnormal increase in SST. As a result, the pressure difference between eastern and western sides of the CEP decreases, leading to weakened equatorial easterlies. Anomalous convergence occurs over the eastern Pacific (EP) around 140°W, while abnormal divergence occurs above the MC (120°–130°E). The Walker circulation is weakened (Fig. 4a). The intensities of the convergence and divergence anomalies are associated with the amplitude of SSTA. Anomalous cyclonic circulations symmetric about the equator occur to the west of the convergence center in EP, while anomalous anti-cyclonic circulations symmetric about the equator appear to the west of the divergence anomaly over the MC. This phenomenon is consistent to the results of Gill (1980) and Sardeshmukh and Hoskins (1988). The situation at 200 hPa in the upper troposphere is almost opposite to that at 850 hPa (Fig. 4d).

In the early spring, following the decrease in CEP-SSTA and the lagged response of warm CTI-SSTA to CEP thermal forcing, the convergence and divergence anomalies at 850 hPa over the Pacific weakens and the centers of them displace northeastward because of both the eastward shifting of the thermal forcing centers (Fig. 5) and the poleward moving of the sun during seasonal cycle. The northern branch of the anomalous anticyclonic circulations resulted from the Gill response extends to the northeast with the center locating above the South China Sea (SCS) (e.g., Wang and Zhang, 2002) (Fig. 4b). Then it moves further northeastward to Northwest Pacific (NWP) in following summer. These partly explain the increase of the WPSH area.

However, in JJA, El Niño disappearing or La Niña developing (Fig. 3c), although the anomalous divergence near MC region is weakened (Fig. 4c), the anomalous anticyclonic circulation over NWP is still strong; the anomalous vorticity (multiplied by –1) averaged over the region (10°–30°N, 90°–160°E) at 850 hPa in July of (0) year reaches its second peak phase (Fig. 6). The areal averaged geopotential height anomaly at 500 hPa over 10°–30°N, 90°–160°E also increases as compared to those in May and June of (0) year (Fig. 6). This kind of intensification over NWP is induced by the remote forcing of CTI-SSTA, which is the second mechanism for the summertime strengthening of the WPSH.

In both spring and summer during El Niño decaying phase, IOBM develops as a lagged response to CEP warming. The atmosphere above tropical IO responds to the warmed SSTA over there, leading to sea level pressure decreasing and tropospheric warming by enhanced convection (Figs. 6, 7).

The warm equatorial Kelvin wave is excited and maintained via moist-adiabatic adjustment (Emanuel et al., 1997; Neelin and Su, 2005), inducing the anomalous easterlies in equatorial region due to eastward propagation of the wave in the lower troposphere. In the northeast of tropical IO and even NWP, the easterlies associated with the Kelvin wave are trapped in equatorial region and weaken from the equator to the polar (Fig. 7). The anomalous gradient of easterly winds in meridional is hence to intensify the anticyclonic shear over the SCS. Therefore, via the Ekman pumping in atmospheric boundary layer, significant descending motions develop in the lower troposphere over NWP (Fig. 4c). These downward motions as a feedback will induce the negative vorticity there, being favorable for further intensification and enlargement of WPSH (Wu et al., 2009; Xie et al., 2009).

Thus, the anomalous anticyclonic circulation over the western Pacific is induced by the anomalous divergence over MC in (–1) year SOND, and intensified in (0) year spring to summer, due to the anomalous anticyclonic vorticity above the SCS and western Pacific as a result of anomalous easterly wind motivated by the eastward propagating Kelvin waves. The joint effect of the two mechanisms results in an intensified WPSH that expanded over a larger area. The intensified anticyclonic anomaly will reinforce the horizontal divergence in the planetary boundary layer via Ekman pumping and lead to stronger meridional monsoon circulation (e.g., Xie et al., 2009; Zhang et al., 2017).

Figure 8 displays zonal–vertical cross-section of circulation anomalies averaged over 15°–25°N and meridional–vertical cross-section of circulation anomalies averaged over 100°–140°E. Significant descending motions appear over 15°–25°N, 100°–160°E, which promote increases in negative vorticity in the lower troposphere and help maintain the WPSH over a large area.

Furthermore, these descending motions can not only intensify the positive vorticity at 200 hPa in the upper troposphere over the South China Sea–western Pacific (Fig. 8), but also transport climatological negative vorticity from the upper troposphere to the middle and lower troposphere. It is found that $ - \omega '{{\partial \bar \zeta } / {\partial p}}$ averaged over 10°–30°N, 90°–150°E at 500 hPa is –3 × 10^–13 s^–2, which is favorable for the maintenance and intensification of the WPSH.

5 Prediction model for the WPSH area

The joint effect of preceding CEP and CTI SSTA is extremely important for changes in the WPSH area in the subsequent summer. The WPSH area changes will directly affect summertime precipitation and temperature in China. Thereby, it is necessary to construct a statistical prediction model for the WPSH area. In the present study, a multiple regression model is constructed to predict the summertime WPSH area index. For this purpose, 25-yr observations over the period of 1981–2005 are used for model training. Since linearly independent predictors are required for multiple regression model, ${I'_{{\rm{CEP}}{\rm{(- 1)}}}}$ in the preceding autumn and winter (SOND) and ${I'_{{\rm{CTI}}(0)\_{\rm{R}}}}$ in the early spring (FMA) with ENSO signal removed (see Appendix A) are taken as predictors to construct the prediction model for the WPSH area index (Table 1).

Based on the constructed prediction model, it is clear that among those factors affecting the summertime WPSH area index, CEP-SSTA has a greater ratio, i.e., with every one σ increase in ${\hat I'_{{\rm{CEP}}(- 1)}}$ , the summertime WPSH area increases by 0.76σ; however, with every one σ increase in ${\hat I'_{{\rm{CTI}}(0)\_{\rm{R}}}}$ , ${\hat I'_{{\rm{WH}}}}$ increases by 0.24σ. The complex correlation coefficient between estimated ${\hat I'_{{\rm{WH}}}}$ by the model and observations during 1981–2005 is 0.77, which is significant above the 99% confidence level. The F value is up to 44.33 and F_0.01 = 5.72. It is obviously seen from Fig. 9 that the model simulates variations of WPSH area well. This model is then applied for prediction of the WPSH area for 11-yr period from 2006 to 2016, as seen in Fig. 9. The correlation coefficient between the model results and observations is 0.99, indicating that this model may be useful in the prediction of summertime WPSH area changes for practical application.

6 Summary and discussion

Significant positive correlations exist between preceding CEP and CTI SSTA, and between these SSTA and area of subsequent summertime WPSH. The CEP-SSTA averaged over the preceding SOND along with the CTI-SSTA averaged over FMA of the same year is important.

There exist two mechanisms for the joint effect of CTI and CEP SSTA on the summertime WPSH (Fig.10). First, during preceding SOND, the cold SSTA in the western Pacific and MC can lead to divergence anomalies in this region. The warm SSTA in CEP induces anomalous convergence there, facilitating the anomalous divergence in the western Pacific. This anomalous divergence subsequently forces the development of anomalous anticyclonic circulation over Bay of Bengal to northwestern Pacific via the Gill-type response. Since the divergence center near equator over the western Pacific displaces eastward following the thermal forcing center, the anomalous anticyclonic circulation is located eastward over the subtropical northwestern Pacific, intensifying the negative vorticity there. Second, the lagged response of CTI-SSTA to CEP-SSTA triggers the eastward propagating Kelvin wave, which leads to tropical easterly wind anomalies and subsequently intensifies the anticyclonic shear over the SCS and NWP. As a result, the anticyclonic anomaly above the northwestern Pacific further intensifies and expands. The joint effect of the above two mechanisms strengthens the anomalous anticyclone over the northwestern Pacific, which subsequently results in stronger monsoonal meridional-vertical circulation via the Ekman pumping. Significant anomalous descending motions are generated in the middle and upper troposphere, inducing negative vorticity anomalies in the lower troposphere, and henceforth leading to the intensification and enlargement of WPSH.

Using the preceding autumn and winter (SOND) ${I'_{{\rm{CEP}}(- 1)}}$ , and the subsequent early spring (FMA) ${I'_{{\rm{CTI}}(0)\_{\rm{R}}}}$ with ENSO signals removed (see Appendix A) as predictors, a multiple regression model is very well constructed for simulation of the WPSH area index for period 1981–2005. Using this statistical model, the predicted summertime $I{'_{{\rm{WH}}}}$ for period 2006–16 is highly correlated with observational time-series of WPSH area, suggesting a very good potential of this model in prediction of summertime WPSH area.

However, it is worth noting that, the correlation coefficient between ${I'_{{\rm{CTI}}(0)}}$ and ${I'_{{\rm{CEP}}(- 1)}}$ is 0.84 (Appendix), suggesting that most part of the CTI SST variability is possibly attributed to the IO response to preceding CEP-SSTA. How does the part of CTI-SSTA independent of CEP-SSTA signal influence the summertime WPSH? This question deserves more researches in the future.

In addition, in the present study, we study the SSTA–WPSH relations statistically in a dynamical context. But, the deep insight into the SSTA–WPSH relations should be further examined by using the numerical models. This also deserves further investigations.

Acknowledgment. Authors are very thankful to the two anonymous reviewers for their helpful comments and the staff at the NUIST Data Service Center under the Geoscience Division of NSFC for their data services. The SST data are from the Met Office Hadley Centre observations datasets (https://www.metoffice.gov.uk/hadobs/hadisst/data/download.html) and the NCEP-NCAR reanalysis data are from https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html. All the figures in this paper were plotted by using Grads software package.

Appendix

Index ${I'_{{\rm{CTI}}(0)}}$ can be decomposed into two parts:

${I'_{{\rm{CTI}}(0)}} = \beta {I'_{{\rm{CEP}}(- 1)}} + {I'_{{\rm{CTI}}(0)\_{\rm{R}}}},$

(A1)

where ${I'_{{\rm{CTI}}(0)\_{\rm{R}}}}$ is the remainder part after ${I'_{{\rm{CEP}}(- 1)}}$ is removed from ${I'_{{\rm{CTI}}(0)}}$ , which is linearly independent of ${I'_{{\rm{CEP}}(- 1)}}$ ; β (= 0.84) is the regression coefficient for ${I'_{{\rm{CTI}}(0)}}$ to be regressed on ${I'_{{\rm{CEP}}(- 1)}}$ . Similarly,

${I'_{{\rm{WH}}}} = \gamma {I'_{{\rm{CEP}}(- 1)}} + {I'_{{\rm WH}\_{\rm{R}}}},$

(A2)

where $\gamma $ (= 0.75) is the regression coefficient when $I{'_{{\rm{WH}}}}$ is regressed on ${I'_{{\rm{CEP}}(- 1)}}$ .

Relative contributions of SSTA in the two key regions (Table A1) are different. ${I'_{{\rm{CTI}}(0)}}$ made the largest contribution (75.69%) to WPSH area change in the summer, followed by ${I'_{{\rm{CEP}}(- 1)}}$ . However, after the ENSO signal is removed from ${I'_{{\rm{CTI}}(0)}}$ , the contribution of ${I'_{{\rm{CTI}}(0)\_{\rm{R}}}}$ to $I{'_{{\rm{WH}}}}$ reduces to 19.36%. Note that ${I'_{{\rm{CTI}}(0)\_{\rm{R}}}}$ is significantly positively correlated with ${I'_{{\rm WH}\_{\rm{R}}}}$ with a correlation of 0.67, suggesting that the CTI-SSTA independent of the preceding CEP-SSTA can contribute to the WPSH area variation that is independent of ${I'_{{\rm{CEP}}(- 1)}}$ by up to 44.89%.