1 Introduction

Due to the high population density, precipitation variations in China exert substantial impacts on agriculture, water resource, and infrastructure (Fu and Ye 1995; Yang et al. 2005). During the rainy season, precipitation variations over most parts of China are dominated by the East Asian summer monsoon (EASM) (Wang et al. 2000; Wu and Wang 2000; Wang and LinHo 2002; Huang et al. 2012). Extensive efforts have been made to investigate the precipitation over monsoon affected areas, especially for the factors responsible for the precipitation variability (Lau 1992; Wang et al. 2000; Ding 2007; Xie et al. 2009; Huang et al. 2012; Yim et al. 2014; Gu et al. 2015, 2018) and the onset and withdrawal of the monsoon rainy season (Nlu and Li 2008; Xu et al. 2009; Zhang et al. 2013; You and Jia 2018).

Previous studies indicated that winter El Niño-Southern Oscillation (ENSO)-related sea surface temperature (SST) anomalies in the central-eastern tropical Pacific could induce an anomalous anticyclone over the western north Pacific (WNP) during the following summer, via the local air–sea interaction process and/or the Indian Ocean capacitor effect (Wang et al. 2000; Xie et al. 2009). The WNP anticyclonic anomaly would further lead to changes in EASM and associated precipitation anomalies over East China through modulating the location and intensity of the WNP subtropical high (Zhang et al. 1996, 1999; Wang et al. 2000, 2012; Wu et al. 2003; Huang et al. 2004, 2012; Chan and Zhou 2005; Xie et al. 2009; Li et al. 2011). Besides the contribution of SST anomalies in the tropical Pacific, studies have reported that SST anomalies in the North Atlantic also exert significant impacts on EASM and precipitation anomalies over East Asia, via triggering an atmospheric wave train extending from the North Atlantic eastward to East Asia or modifying the anomalous Walker circulation over the tropics (Gu et al. 2009; Liu et al. 2012; Zuo et al. 2013, 2018; Hong et al. 2014; Chen et al. 2015, 2018a; Zhou and Wu 2015; Chang et al. 2016; Lu et al. 2017; Jin and Huo 2018; Li et al. 2018). For example, Gu et al. (2009) pointed out that spring North Atlantic SST anomalies could affect the precipitation and duration of the East Asian Mei-yu rain belt through exciting a stationary atmospheric wave train across Eurasia to East Asia. Zuo et al. (2013) showed that a tripole SST anomaly pattern over the North Atlantic during boreal summer was able to regulate the EASM and related climate anomalies via triggering an atmospheric wave train over the mid-latitudes of Eurasia. Li et al. (2018) reported the important role of a mid-latitude Eurasian atmospheric wave train in linking North Atlantic SST changes and spring precipitation anomalies over the southwestern China, based on observational evidence and atmospheric general circulation model (AGCM) experiments. Additionally, Hong et al. (2014) and Chang et al. (2016) demonstrated that the northern tropical Atlantic (NTA) SST warming could impact the EASM via modulating the tropical Walker circulation.

Previous studies indicated that the onset of rainy seasons in China is significantly linked to the commencement and northward movement of the EASM (Lau 1992; Tanaka 1992; Wang and LinHo 2002; Ding and Chan 2005; Ding 2007; Huang et al. 2012). Accompanied by abrupt changes of large-scale atmospheric circulations including the southerly wind and subtropical jet, pronounced rain belts chronologically occur in South China, Yangzi river Valley, and northern China (Wang et al. 2004; Zhao et al. 2007; Li and Zhang 2009; Zeng et al. 2012; Cao et al. 2018). Studies have also explored the characteristics and forming mechanisms related to the EASM onset. For example, Wu and Wang (2000) found that interannual variations of the WNP summer monsoon onset and the commencement of related monsoon rain were dominated by ENSO. Zhao et al. (2007) highlighted the role of southwesterly winds in modulating precipitation anomalies over eastern China. Zhu et al. (2011) suggested that the atmospheric heating over South China sea (SCS) was the main driver for the onset of the subtropical EASM as well as the summer precipitation increase over South China. Compared to the onset, studies regarding the withdrawal of the EASM rainy season are relatively less. Hu et al. (2018) suggested that the interdecadal delay of the SCS summer monsoon withdrawal around the mid-2000s was mainly attributed to interdecadal increase in the number of the tropical cyclone activity and enhancement of the quasi-biweekly oscillation over the SCS. Cao et al. (2018) pointed out that the advanced rainy season retreatment over many parts of China at the interannual scale was closely associated with the El Niño-like SST warming in the central-eastern tropical Pacific.

The above studies mainly investigated the precipitation variability and withdrawal/onset of rainy season over the monsoon domain. It is noted that there exists an interactional belt, also called the monsoon transitional zone (MTZ), along the northern border of East Asian Monsoon between monsoon (humid) and non-monsoon (arid) regions (Tao and Chen 1987; Fu and Ye 1995). The MTZ in China is a semi-arid region and its variability exhibits a northeast-southwest oriented pattern (Qian et al. 2007, 2012; Wang et al. 2017). Compared to studies on the EASM domain, fewer studies have focused on investigating the withdrawal/onset of rainy season in the MTZ domain. In particular, the characteristics and mechanisms of the rainy season withdrawal/onset in the MTZ over China remain to be explored. As the MTZ tends to have a fragile ecosystem, which is more sensitive to climate changes and vulnerable to natural disasters (Dai 2011, 2013; Qian et al. 2011; Cook et al. 2014), there are strong societal demand to improve the understanding of changes in the withdrawal/onset of the MTZ rainy season in China, the associated precipitation anomalies, and their generation and maintenance mechanisms. In addition, understanding interannual variations of the withdrawal/onset of the MTZ rainy season have important implications for the precipitation prediction over the MTZ. In this study, we focus on investigating the withdrawal of the MTZ rainy season in China and the related driving factors. The onset of the MTZ rainy season in China would be examined in a future study.

The rest of this paper is organized as follows. Section 2 lists the data and methods used in this study. Section 3 describes the definition of the MTZ rainy season withdrawal. Section 4 presents evolutions of precipitation and atmospheric circulation anomalies in association with the withdrawal of the MTZ rainy season. Section 5 explores possible factors contributed to the interannual variation of the withdrawal. Section 6 gives a summary and discussions.

2 Data and methods

2.1 Data

Three precipitation datasets are used in this paper, including: (1) the daily and monthly 0.5° × 0.5° grid product provided by the National Meteorological Information Center of the Chinese Meteorology Academy (CMA-grid) (Zhao et al. 2014; Zhao and Zhu 2015). This gridded precipitation dataset is constructed based on more than 2400 stations in China and is available during 1961–2013; (2) the daily 609 stations precipitation data provided by the National Climate Center, Chinese Meteorology Academy, which is available from 1979 to 2013 (CMA-station); and (3) the pentad mean precipitation data on 2.5° × 2.5° girds provided by the Climate Prediction Center Merged Analysis of Precipitation of National Oceanic and Atmospheric Administration (NOAA) from 1979 to present (CMAP) (Xie and Arkin 1997). Monthly mean precipitation data over oceanic regions are derived from the Global Precipitation Climatology Project (GPCP), which has a horizontal resolution of 2.5° × 2.5° and covers the period from 1979 to the present (Adler et al. 2003).

This study also employs the monthly mean horizontal wind, specific humidity and geopotential height fields provided by the ERA-Interim reanalysis from 1979 to the present (Dee et al. 2011). This atmospheric dataset has a horizontal resolution of 0.5° × 0.5° and extends from 1000 to 1 hPa (Dee et al. 2011). In addition, the monthly mean SST data is obtained from the NOAA Extended Reconstructed SST version 3b dataset (ERSSTv3b) (Smith et al. 2008), which has a horizontal resolution of 2° × 2° and is available from 1854 to the present. The analysis period of this study is 1979–2013 during which all variables are available.

The statistical significances of correlation and regression analyses are evaluated based on a two-tailed Student’s t test. As this study focuses on interannual variations, all variables are subjected to a 7-year high pass filter via the Fourier analysis technique to obtain their interannual components.

2.2 Wave activity flux

The present study applies the wave activity flux described in Takaya and Nakamura (1997, 2001) to examine the propagation of stationary Rossby wave train. This wave activity flux is phase-independent and parallel to the local group velocity of stationary Rossby wave train. The wave activity flux is expressed as follows:

$${\mathbf{W}} = \frac{1}{{2|\bar{U}|}}\left[ {\begin{array}{*{20}l} {\bar{u}(\psi^{\prime}_{x} - \psi^{\prime}\psi^{\prime}_{xx} ) + \bar{\nu }(\psi^{\prime}_{x} \psi^{\prime}_{y} - \psi^{\prime}\psi^{\prime}_{xy} )} \\ {\bar{u}(\psi^{\prime}_{x} \psi^{\prime}_{y} - \psi^{\prime}\psi^{\prime}_{xy} ) + \bar{\nu }(\psi^{\prime 2}_{y} - \psi^{\prime}\psi^{\prime}_{yy} )} \\ {\frac{{f_{0}^{2} }}{{S^{2} }}\{ \bar{u}(\psi^{\prime}_{x} \psi^{\prime}_{p} - \psi^{\prime}\psi^{\prime}_{xp} ) + \bar{\nu }(\psi^{\prime}_{y} \psi^{\prime}_{p} - \psi^{\prime}\psi^{\prime}_{yp} )\} } \\ \end{array} } \right],$$
$$S^{2} = - \;\alpha \frac{\partial \ln \theta }{\partial p},$$

here, \(\psi^{\prime}\) is the perturbed quasi-geostrophic stream function. u and v with overbars represent basic states of zonal and meridional winds, respectively. f0, α, θ, and p denote the Coriolis parameter at 45°N, specific volume, potential temperature, and pressure standardized by 1000 hPa, respectively. Subscripts x and y indicate the partial derivatives in zonal and meridional directions, respectively. In this study, the basic flow is calculated based on the whole period analysed, 1979–2013, and perturbations are defined as anomalies derived from the regression analysis.

2.3 AGCM experiments

The Community Atmosphere Model (CAM5.3) from the National Center for Atmospheric Research is used to examine the response of atmospheric circulation anomalies to SST anomalies in the NTA. The CAM5.3 has a horizontal resolution of 1.9° × 2.5° and 30 vertical levels with the hybrid pressure-sigma vertical coordinate (Simmons and Burridge 1981). More details about the CAM5.3 are available at http://www.cesm.ucar.edu/models/cesm1.0/cam/docs/description. Detailed descriptions of AGCM experiments are provided in Sect. 5.

3 Definition of the withdrawal index of the MTZ rainy season

We first employ the method proposed by Liu et al. (2009) to identify the MTZ domain over China. According to Liu et al. (2009), monsoon regions over the northern hemisphere are defined as areas where differences in the precipitation between the boreal summer (i.e., MJJAS-averaged) and winter (i.e., NDJFM-averaged) exceed 2 mm day−1 and the local summer (MJJAS) precipitation exceed 55% of the total annual precipitation (Fig. 1). Based on monthly precipitation data from the CMA-grid, borders of monsoon domains can be obtained for each year during 1979–2013. Furthermore, we calculate 7-year running mean land borders of monsoon regions over China (green lines in Fig. 1). Results are almost identical when using the 9- or 11-year running mean. Following the study of Qian et al. (2007), the MTZ over China is defined as overlaid regions covering the range of borders (represented by the black diamond shaped box in Fig. 1).

Fig. 1
figure 1

Definition of the MTZ region in China (represented by the black box). Green lines represent annual range of precipitation that equals to 2 mm day−1 with a 7-year running window for period 1979–2013. Annual range of precipitation is defined as difference in precipitation between boreal summer (MJJAS) and winter (NDJFM). The annual range of precipitation (green lines) is used to denote borders of the monsoon domain over China based on the method proposed by Liu et al. (2009). Areas marked with grey shadings indicate the Tibetan Plateau region

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Climatological annual cycles of precipitation over the MTZ in China based on the three different precipitation datasets are displayed in Fig. 2. As shown in Fig. 2, large precipitation of the MTZ primarily appears in July and August. The amount of precipitation in these 2 months takes account for approximately 50% of the annual total precipitation. Results obtained from the three precipitation datasets are in well agreement with each other, albeit slight differences in the amplitude of the precipitation (Fig. 2).

Fig. 2
figure 2

Climatological monthly precipitation averaged over the MTZ region in China (black box in Fig. 1) for period 1979–2013 derived from three precipitation datasets: CMA-grid (red bars), CMA-station (blue bars), and CMAP (green bars)

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We then examine the onset and withdrawal of the rainy season in the MTZ over China. The pentad mean data is constructed from the daily mean data using the CMA-grid and CMA-station datasets. A precipitation threshold is firstly identified to define the onset and withdrawal pentads of the MTZ rainy season according to the climatological annual cycle of pentad mean precipitation. Specifically, the precipitation threshold is identified when the accumulated precipitation exceeds 50% of the annual total precipitation (Fig. 3). The onset pentad of the MTZ rainy season is then defined as the first pentad when the precipitation during at least three subsequent pentads that exceed the precipitation threshold. Similarly, the withdrawal pentad is defined as the first pentad when the precipitation during at least three subsequent pentads after the onset that are lower than the precipitation threshold, and no more than three consequent pentads higher than the threshold in the following pentads. Notions of “OP” and “WP” in Fig. 3 represent the onset and withdrawal pentad of the MTZ rainy season, respectively. According to the above definition, the onset and withdrawal pentads of the MTZ rainy season in China are respectively on the 34th pentad (15th–19th June) and 49th pentad (22nd–26th August) based on the CMA-grid dataset during 1979–2013. This indicates that July and August are the main rainy season of the MTZ in China. The onset and withdrawal pentads of the MTZ rainy reason obtained from the other two precipitation datasets are similar to those from the CMA-grid dataset (Fig. 3).

Fig. 3
figure 3

Schematic diagram for the definition of the onset and withdrawal pentads of MTZ rainy season based on the smoothed pentad mean precipitation data. Here, smoothed data is the first 12 harmonics of original precipitation annual cycle without high frequency fluctuations. Climatology of the pentad mean precipitation is derived from three datasets [i.e. CMA-grid (red), CMA-station (blue), and CMAP (green)] during 1979–2013. The solid and dashed lines respectively indicate the original and smoothed pentad mean precipitation. “OP” and “WP” denote the onset and withdrawal pentads of the MTZ rainy season, respectively. Definitions of the onset and withdrawal pentads are given in the main text

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In this study, we focus on analyzing the withdrawal of the MTZ rainy season in China and examining the related atmospheric circulation and SST anomalies. Variations of the onset of the MTZ rainy season and the associated circulation anomalies will be pursued in another study. Figure 4a displays standardized time series of the withdrawal pentads over the period 1979–2013. In general, the withdrawal pentads derived from the three precipitation datasets are well consistent with each other, and show clear interannual variations. Hence, this study mainly focuses on variations on the interannual timescale. Figure 4b displays the normalized time series of the interannual components of withdrawal pentads, hereafter referred to as the withdraw pentad index (WPI). The correlation coefficients among WPIs derived from the three precipitation datasets are larger than 0.53 and are all significant at the 99% confidence level (Table 1). We further employ the Morlet wavelet technique (Torrence and Compo 1998) to examine the dominant frequency of the WPI. Figure 5 displays the local and global wavelet power spectra of the WPI during 1979–2013. The WPI shows significant power peaks around 2–4 years in all datasets (Fig. 5a–c).

Fig. 4
figure 4

Normalized time series of the a original and b interannual component of the withdrawal pentads index (WPI) during 1979–2013 obtained from three precipitation datasets [i.e., CMA-grid (red), CMA-station (blue), and CMAP (green)]

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Table 1 Correlation coefficients among withdrawal pentad indices (WPI) derived from three precipitation datasets (i.e., CMA-grid, CMA-station, and CMAP) during 1979–2013
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Fig. 5
figure 5

Local and global wavelet power spectra of the WPI based on the Morlet wavelets during 1979–2013 derived from three precipitation different datasets: a CMA-grid, b CMA-station, and c CMAP. Stippling regions indicate the local wavelet power spectra significant at the 95% confidence level. Red dashed lines indicate the global wavelet power spectra significant at the 95% confidence level

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4 Precipitation and atmospheric circulation anomalies associated with the WPI

We first examine the evolution of the precipitation anomalies in association with the WPI. Results obtained from the three precipitation datasets are generally similar, hereafter we only present results based on the CMA-grid dataset, unless otherwise stated. Figure 6 displays monthly evolutions of the precipitation anomalies from June to September regressed upon the WPI. In association with the late withdrawal of the MTZ rainy season (i.e. positive phase of the WPI), the most striking feature is significant precipitation increase appearing over the MTZ and its surrounding regions in August (Fig. 6c). Precipitation anomalies in other months are less well organized and less significant (Fig. 6a, b, d). This suggests that the MTZ precipitation in August tends to be above normal when the withdrawal of the MTZ rainy season is later. It also implies that the interannual variation of the withdrawal of the MTZ rainy season is closely related to the MTZ precipitation in August. We have further examined the pentad evolution of precipitation anomalies in the MTZ. Figure 7 displays the evolution of pentad precipitation anomalies averaged over the MTZ during August obtained by regressions upon the WPI. Significant positive precipitation anomalies can be seen in the MTZ during the last four pentads of August (i.e. from August 12th to 31st). The above-normal precipitation also appears in the first two pentads of August, though less significant (Fig. 7). This suggests that the WPI associated precipitation anomalies over the MTZ have a relatively good consistency during the entire August. In the following, we focus on utilizing monthly data to analyze the potential factors responsible for the interannual variation of the MTZ rainy season withdrawal.

Fig. 6
figure 6

Precipitation anomalies (unit: mm) in a June, b July, c August, and d September obtained by regression upon the WPI. Hereafter, WPI was calculated based on the CMA-grid precipitation data unless otherwise stated. Stippling regions indicate precipitation anomalies are statistically significant at the 95% confidence level. Black boxes in a–d denote the MTZ region

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Fig. 7
figure 7

Pentad evolutions of precipitation anomalies (unit: mm day−1) averaged over the MTZ during August obtained by regression upon the WPI. Bars with slash indicate precipitation anomalies that are significant at the 95% confidence level

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We then examine the atmospheric circulation anomalies related to the WPI to help understand the August precipitation anomalies over the MTZ region. Figure 8 displays the anomalies of horizontal winds and streamfunction at 850 hPa, and geopotential height and wave activity flux at 300 hPa in August regressed upon the WPI. All descriptions below are corresponding to the late withdrawal of the MTZ rainy reason (i.e., positive phase of the WPI) unless otherwise stated. In the lower troposphere, significant cyclonic anomalies appear over the tropical northeastern Pacific and tropical western North Atlantic regions (Fig. 8a). Meanwhile, a significant anticyclonic anomaly can be observed over the tropical WNP. The southerly wind anomalies along the eastern coast of East Asia associated with the anomalous anticyclone over the tropical WNP contribute to the formation of the MTZ precipitation increase by transporting water vapours from southern oceans towards the MTZ (Fig. 8a). In the upper troposphere, a notable atmospheric wave train is found over the Eurasian mid-high latitudes (Fig. 8b). The wave train propagates eastward with negative geopotential height anomalies over the mid-latitudes of central North Atlantic, North Europe, and MTZ region extending northeastward to Kamchatka peninsula, as well as positive anomalies over the North America, West Europe, Central Eurasia and North Pacific (Fig. 8b). The negative height anomalies at 300 hPa around the MTZ may also partly contribute to the MTZ precipitation increase by inducing upward motion anomalies.

Fig. 8
figure 8

Anomalies of a winds (vectors, m s−1) and stream function (shadings, 10−4 m2 s−1) at 850 hPa, and b wave activity flux (vectors, m2 s−2) and geopotential height (shadings, gpm) at 300 hPa in August obtained by regression upon the WPI. Anomalies of 850 hPa winds less than 0.15 m s−1 in a and 300 hPa wave activity flux less than 0.15 m2 s−2 in b are not shown. Stippling regions in a and b indicate streamfunction and geopotential height anomalies significant at the 95% confidence level, respectively. Black boxes in a and b denote the MTZ region

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Figure 9a shows the anomalies of the water vapour flux (integrated from 1000 to 300 hPa) and its divergence in August regressed upon the WPI. Sufficient water vapours are transported from southern oceans to the MTZ via the southerly wind anomalies to the west fringe of the anomalous anticyclone over the WNP, and significantly convergent with mid-latitude westerlies over most parts of the MTZ during the positive phase of WPI (Figs. 8a, 9a). Furthermore, significant upward motion anomalies (500 hPa) and divergence anomalies in the upper troposphere (200 hPa) occur around the MTZ region (Fig. 9b, c). These conditions are favorable for the formation of the above-normal precipitation over the MTZ during August when the withdrawal of the MTZ rainy season is later than normal.

Fig. 9
figure 9

Anomalies of a water vapour flux (vectors, unit: kg s−1 m−1) and water vapour flux divergence integrated from 1000 to 300 hPa (shadings, unit: 106 kg s−1 m−2), b 500 hPa omega (unit: 10−2 Pa s−1), and c 200 hPa divergence (unit: 105 s−1) in August obtained by regression upon the WPI. Anomalies of water vapour flux less than 0.08 kg s−1 m−1 in a are not shown. Positive (negative) value of omega corresponds to upward (downward) motion anomalies. Stippling regions in a–c indicate anomalies of water vapour flux divergence, 500 hPa omega, and 200 hPa atmospheric divergence, respectively, significant the 95% confidence level. Black boxes denote the MTZ region

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5 Factors of the formation of atmospheric circulation anomalies associated with the WPI

5.1 Observational results

The above analysis suggests that atmospheric circulation anomalies are vital to the withdrawal of the MTZ rainy season and its associated August precipitation anomalies. An immediate question arises as to what are potential factors contributing to the generation of the anomalous anticyclone over the WNP and the wave train extending from North Atlantic to East Asia? Previous studies have demonstrated the importance of SST anomalies over the tropical Pacific, Indian Ocean, and North Atlantic for the formation of the anomalous anticyclone over the WNP (Zhang et al. 1996; Wang et al. 2000; Wu et al. 2009; Xie et al. 2009; Chen et al. 2018a). For example, an El Niño event in preceding winter can induce an anomalous anticyclone over the WNP during the following summer via local air–sea interactions (Wang et al. 2000) or SST anomalies over the Indian Ocean (Xie et al. 2009) and the Atlantic Ocean (Rong et al. 2010). In addition, several studies also reported that North Atlantic SST anomalies can induce an atmospheric wave train from the North Atlantic across Europe to East Asia (Wu et al. 2011; Zuo et al. 2013; Chang et al. 2016). Hence, we further examine SST anomalies related to the WPI in the following.

Figure 10 displays the evolution of SST anomalies from the preceding January to August regressed upon the WPI over the period 1979–2013. In association with the positive WPI, a clear El Niño-like SST warming can be observed over the central-eastern tropical Pacific during the preceding winter (from preceding January to March) (Fig. 10a–c). Previous studies have demonstrated that preceding winter El Niño events could induce an anticyclonic anomaly over the western North Pacific in the following summer via modulating SST anomalies over the Indian Ocean or via the local air–sea interaction over the western North Pacific (Zhang et al. 1999; Wang et al. 2000; Xie et al. 2009). Figure 11a display the evolution of the correlation coefficients between the WPI and the Niño3.4 index from preceding winter to the following August (blue line). Here the Niño3.4 index is employed to characterize the ENSO variability, and is defined as area-averaged SST anomalies over 5°S–5°N, 120°W–170°W as usual. It is expected that significant positive correlations are seen between the WPI and the Niño3.4 index from preceding December to March (Fig. 11a), consistent with the result obtained in Fig. 10. The above evidence suggests that the formation of the WPI related anticyclonic anomaly over the WNP was partly attributed to the preceding winter El Niño-like SST warming in the central-eastern tropical Pacific.

Fig. 10
figure 10

Anomalies of SST (unit: °C) in a May, b June, c July, and d August obtained by regression upon the WPI. Stippling regions indicate SST anomalies significant at the 95% confidence level

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Fig. 11
figure 11

a Correlation coefficients of the WPI with the Niño3.4 SST index (solid blue line), NTA SST index (solid red line), and NTA_res SST index (dashed red line) from preceding December to following August. Definitions of the Niño3.4 SST index and NTA SST index are provided in the main text. The NTA_res SST index is the part of the NTA SST index that preceding winter Niño3.4 index has been removed by linear regression. Horizontal dashed lines indicate the correlation coefficients are statistically significant at the 95% confidence level. b The original (solid line) and 7-year high pass filtered (dashed line) NTA SST index in August. c The original (solid line) and 7-year high pass filtered (dashed line) NTA_res SST index in August

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In addition, significant positive SST anomalies can be seen in the NTA from preceding March to the simultaneous August in association with the positive WPI (Fig. 10). This implies that the SST anomalies in the NTA may also play a role in modulating the WPI related atmospheric circulation anomalies over the WNP. To further confirm the role of NTA SST anomalies, we calculate the correlations between the WPI and a NTA SST index. The NTA SST index is defined as area-averaged SST anomalies over 0°–20°N, 20°W–60°W (Fig. 11b). It is clear that significant positive correlations can be seen between the WPI and the NTA SST index since preceding March (Fig. 11a), consistent with the results derived from Fig. 10.

It should be noted that preceding winter ENSO events could exert influences on the anticyclone anomalies over the WNP via the ENSO associated SST anomalies in the NTA. For example, studies have shown that positive (negative) SST anomalies tend to occur in the NTA during the following spring and summer when an El Niño (a La Niña) event appeared in preceding winter (Lau and Nath 1996; Klein et al. 1999; Alexander et al. 2002; Chiang and Sobel 2002). The correlation results shown in Fig. 11a also indicate that appearance of the positive Niño3.4 index-WPI correlation leads the positive WPI-NTA SST correlation by several months. This implies that the occurrence of the WPI associated SST anomalies in the NTA may partly attributed to the preceding ENSO variability. Nevertheless, previous studies have also demonstrated that SST anomalies in the NTA can exert impact on the circulation anomalies over the East Asia and related climate anomalies without the impact of ENSO (Hong et al. 2014; Chang et al. 2016; Li et al. 2018). To demonstrate the close NTA SST-WPI connection was independent of preceding ENSO, we further define a residual NTA SST index (indicated by NTA_res SST index) by partially excluding the ENSO impact. The preceding winter Niño3.4 index has been removed in the NTA SST index as follows:

$${\text{NTA}}\_{\text{res }} = {\text{ NTA}} - \, R \times {\text{Ni}}{\tilde{\text{n}}}{\text{o}}3.4,$$

where Niño3.4 represents the preceding winter (DJF-averaged) Niño3.4 index. NTA indicates the normalized NTA SST index in August. The NTA_res is the part of the NTA SST index that excludes the preceding winter ENSO signal (Fig. 11c). We then recalculate the evolution of correlation coefficients between the WPI and NTA_res SST indices from December to the following August (indicated by dashed red line in the Fig. 11a). It is clear that after removing the ENSO impact, significant positive correlations still exist in July and August between the WPI and the NTA SST anomalies. This suggests that the North Atlantic SST anomalies in August impact the formation of atmospheric circulation anomalies related to the WPI even, regardless of the ENSO influence.

It should be mentioned that, in addition to ENSO, previous studies have demonstrated that the interannual SST variability in the NTA was also closely related to other factors, such as the atmospheric forcing over the extratropics (i.e. North Atlantic Oscillation-like atmospheric anomalies; Tanimoto and Xie 1999), and the local oceanic dynamical process in the NTA (i.e. local wind-evaporation-SST feedback process; Chang et al. 1997; Huang and Shukla 2005). Impacts of these factors on the NTA SST-WPI relation remain to be explored.

To further validate the role of SST anomalies in the NTA on WPI, we present the anomalies of winds and streamfunction at 850 hPa, and wave activity flux and geopotential height at 300 hPa regressed upon the August NTA_res SST index in Fig. 12. It is interesting that the atmospheric circulation anomalies related to the NTA_res SST index in both the lower and the upper troposphere bear a close resemblance to those related to the WPI (Fig. 8). At 850 hPa, a pronounced cyclonic anomaly prevails over the tropical northeastern Pacific and western North Atlantic regions, which is a Gill-type Rossby wave atmospheric response to the NTA SST warming (Figs. 10, 12a) (Gill 1980). In addition, significant anticyclonic anomalies are observed over the tropical western north and south Pacific (Fig. 12a). At 300 hPa, a clear wave train extends from the North Atlantic across East Asia to North Pacific. In particular, significant negative geopotential height anomalies are found around the MTZ region, which exert impacts on the MTZ precipitation anomalies.

Fig. 12
figure 12

As in Fig. 7, but for anomalies in August regressed upon the normalized NTA_res SST index in simultaneous August

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We speculate that the formation mechanism of the anomalous anticyclone over the WNP related to the NTA SST warming may be attributed to the anomalous Walker circulation induced by the NTA SST warming. To confirm this, we examine the NTA_res SST associated anomalies of omega at 500 hPa, and velocity potentials at 850 hPa and 200 hPa (Fig. 13). In association with the NTA SST warming, significant ascending anomalies are found over the tropical Atlantic (Fig. 13a), which induce an anomalous Walker circulation with anomalous upward motion (convergence in the lower troposphere and divergence in the upper troposphere) over the tropical Atlantic and anomalous downward motion (divergence in the lower troposphere and convergence in the upper troposphere) over the tropical central Pacific (Fig. 13b, c). The pronounced downward motion anomaly over the tropical central Pacific would further trigger a pair of significant anticyclonic anomalies over the tropical western south and north Pacific, respectively, following a Gill-type atmospheric response (Gill 1980) (Fig. 13b, c). The results hence indicate that the NTA SST warming in August can induce low-level anticyclonic anomalies over the tropical WNP, basically in consistent with previous findings (Chen et al. 2015, 2016, 2018b; Chang et al. 2016; Chen and Wu 2017). The circulation anomalies subsequently contribute to interannual variations of the withdrawal of the MTZ rainy season and related precipitation anomalies.

Fig. 13
figure 13

Anomalies of a 500 hPa omega (unit: 10−2 Pa s−1), and b 850 hPa and c 200 hPa divergent wind (vectors, unit: m s−1) and velocity potential (shadings, unit: 106 m2 s−1) obtained by regression upon the normalized NTA_res SST index. Values over the land in a are masked. Stippling regions in a–c indicate anomalies of 500 hPa omega, velocity potential at 850 hPa and 200 hPa significant at the 95% confidence level, respectively

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5.2 Numerical evidence

To further verify the contribution of observed NTA SST warming in initiating the anomalous anticyclone over the WNP and atmospheric wave train over North Atlantic-Eurasia, three numerical experiments are conducted by using CESM–CAM5.3. Details of the experiments are listed in Table 2. The control experiment with observed monthly climatological SST forcing is referred to as EXP_CLIM. The sensitive experiments, referred to as EXP_NTAPOS and EXP_NTANEG, are respectively forced by the positive and negative SST anomalies in the NTA region in associated with one standard deviation of the NTA SST index in August superimposed on the climatological SST. Each simulation has run for 30 model years. The difference between the control run and a sensitivity run (i.e. EXP_NTAPOS or EXP_NTANEG) is estimated to represent the model response to observed NTA SST anomalies.

Table 2 Details of numerical experiments
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Figure 14 displays the model results derived from the variable differences of experiments EXP_NTAPOS and EXP_NTANEG, and have been divided by two in order to compare with observations. Results obtained in the AGCM experiments are well consistent with the observation results (Figs. 8, 11, 14). Corresponding to the SST warming in the NTA, a significant anomalous cyclone appears in the tropical northeastern Pacific and northwestern Atlantic. In addition, a pair of anticyclonic anomalies is found over the tropical western Pacific (Fig. 14a). The formation of these anomalous anticyclones is related to the anomalous Walker circulation over the tropics induced by the NTA SST warming (Fig. 14c, d), with significant uprising motions over the tropical Atlantic and downwelling motions over the tropical central Pacific. The induced downwelling anomaly over the tropical central Pacific can in turn trigger a pair of anticyclonic anomalies over the tropical western Pacific (Fig. 14a, c, d). In addition, a significant atmospheric wave train can be found over the North Atlantic extending eastward across Eurasia to East Asia, and then eastward to North Pacific at 300 hPa (Fig. 14b). This wave train forced with NTA SST anomalies is similar to that in the observation, despite some slight differences in the amplitude and locations of the relevant action centers. The negative geopotential height anomalies to the northwest of the MTZ are also well simulated in the AGCM experiments. The AGCM experiments hence provide further evidence in linking the NTA SST anomalies to the interannual variation of the MTZ rainy season withdrawal and related precipitation anomalies.

Fig. 14
figure 14

Differences of August a 850 hPa winds (vector, unit: m s−1) and streamfunction (shadings, unit: 10−4 m2 s−1), b 300 hPa wave activity flux (vectors: m2 s−2) and geopotential height (shadings; gpm), c 850 hPa and d 200 hPa divergent winds (vectors, unit: m s−1) and velocity potential (shadings, unit: 106 m2 s−1) between experiments EXP_NTAPOS and EXP_NTANEG. Anomalies of 850 hPa wind less than 0.15 m s−1 in a and 300 hPa wave activity flux less than 0.15 m2 s−2 in b are not shown. Stippling regions in a–d indicate differences in 850 hPa streamfunction, 300 hPa geopotential height, 850 hPa and 200 hPa velocity potentials significant at the 95% confidence level, respectively

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6 Summary and discussion

In the present study, we investigate the interannual variation of the MTZ rainy season withdrawal during 1979–2013 and its associated physical processes based on observational data and AGCM numerical experiments. An index (WPI) is defined to characterize the variation of the MTZ rainy season withdrawal. Firstly, a precipitation threshold is identified according to the climatological annual cycle of the pentad mean precipitation. The threshold is determined when the accumulated precipitation exceeds 50% of the annual total precipitation. The withdrawal pentad is then considered as the first pentad when the precipitation during at least three subsequent pentads after the onset that are lower than the precipitation threshold, and no more than three consequent pentads higher than the thresholds in the following pentads. Over the period 1979–2013, the withdrawal of the MTZ rainy season in China tends to occur on the 49th pentad (22nd–26th August) on average. In addition, the WPI shows pronounced interannual variations, with a dominant period around 2–4 years.

We have further examined the precipitation, atmospheric circulation and SST anomalies in association with the WPI variability. Results indicate that the interannual variation of the MTZ rainy season withdrawal has a close relation with the precipitation anomalies over the MTZ in August. When the MTZ rainy season retreats later than normal, above-normal precipitation appears in MTZ in August, accompanied by the anomalous anticyclone over the WNP and an eastward propagating wave train in the mid-high latitudes over Eurasia. The southerly wind to the west fringe of the anomalous anticyclone over the WNP transports water vapours from southern oceans towards the MTZ, leading to significant water vapour convergence anomalies in low-level troposphere over the MTZ. The anomalous cyclone resulting from this mid-high latitude teleconnection also facilitates the MTZ precipitation by providing ascending anomalies there.

The potential drivers of precipitation and circulation anomalies in August in association with the withdrawal of the MTZ rainy season are further explored. It is found that preceding winter El Niño events impact the anomalous anticyclone over the WNP via modulating the SST anomalies in the NTA. However, significant NTA SST anomalies on WPI can also be observed without ENSO, indicating that the impact of the NTA SST anomalies on WPI is independent of ENSO. The impact of NTA SST anomalies on atmospheric circulation anomalies related to the WPI is mainly via two pathways, which are schematically depicted in Fig. 15. The first is the tropical pathway. The NTA SST warming may induce an anomalous Walker circulation over the tropics, with uprising anomalies in the tropical Atlantic and downwelling anomalies in the tropical central Pacific. The precipitation decrease and its related atmospheric heating anomalies induced by the anomalous downward motion over the tropical central Pacific would trigger an anomalous anticyclone over the tropical WNP via a Gill-type atmospheric response. The second is the mid-latitude pathway. The NTA SST warming could induce a significant atmospheric wave train originating from the North Atlantic and flowing across the Eurasia to East Asia. In particular, pronounced negative geopotential height anomalies around the MTZ in this wave train would contribute to the formation of positive MTZ precipitation anomalies in August via the local upward motion anomalies. Both observational analyses and numerical experiments confirm the contribution of the NTA SST warming to the formation of the atmospheric wave train over the Eurasian mid-high latitudes and the anomalous anticyclone over the WNP.

Fig. 15
figure 15

Schematic diagram illustrates impacts of the tropical northern Atlantic SST anomalies on the MTZ precipitation anomalies in August and the associated withdrawal of MTZ rainy season. a NTA SST anomalies impact MTZ precipitation variation in August via atmospheric teleconnection over mid-latitudes of Eurasia. Red circle and green circle respectively represent the positive and negative anomalies of 300 hPa geopotential height. b NTA SST anomalies impact MTZ precipitation variation in August via tropical pathway. Blue arrows indicate anomalous Walker circulation induced by NTA SST warming with ascending branch in the NTA and descending branch over the tropical central Pacific. Red circle over the WNP denote the anticyclonic circulation in lower troposphere. Red arrows in a and b indicate wind anomalies. Black boxes in a and b denote the MTZ region

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This study indicated that SST anomalies in the NTA could exert significant influences on the interannual variation of the MTZ rainy season withdrawal and the associated precipitation anomalies in August via triggering an atmospheric wave train over the mid-high latitudes of Eurasia as well as through modulating the atmospheric circulation anomalies over the WNP. The relative contributions of the atmospheric wave train over Eurasia and the atmospheric circulation over the WNP to the MTZ rainy season withdrawal need to be further investigated. In addition, the individual and combined impacts of preceding winter ENSO and SST anomalies in the NTA on the formation of the MTZ related anticyclone anomalies over the WNP are also unclear and remain to be explored.

Furthermore, previous studies suggested that the Eurasian snow cover and Arctic sea ice may have significant impacts on the EASM and its associated climate anomalies over East Asia (Yim et al. 2010; Wu et al. 2014, 2016; Jia et al. 2018; Chen and Wu 2018). For example, Yim et al. (2010) found that the summer precipitation variation over East Asia has a close relation with the snow cover anomalies over western and eastern Eurasia. Wu et al. (2016) indicated that the change in Arctic sea ice during preceding winter has a pronounced influence on the spring precipitation over East Asia via triggering an atmospheric wave train over mid-high latitudes Eurasia that propagates southeastward to East Asia. Contributions of the Eurasian snow cover and Arctic sea ice changes on the interannual variation of the MTZ rainy season withdrawal remain to be explored.