1 Introduction

The western Pacific subtropical high (WPSH) is an anticyclonic circulation located over the western Pacific, mainly in lower- to mid-troposphere in boreal summer, and is always depicted by 5880-gpm isoline (hereafter 5880 line) at 500 hPa (Zhang and Tao 1999; Zhang et al. 2008; Liu et al. 2014). The WPSH exerts significant climatic impact over East Asia. Areas covered by the WPSH are often accompanied with scorching weather (Ding et al. 2010; Peng 2014), and areas at northwestern edge of the WPSH are more likely to experience precipitation owing to moisture transportation (He et al. 2001; He and Gong 2002; Jia et al. 2021). Multiple timescales can be found in the variance of the WPSH. On seasonal timescales, the WPSH advances northward in summer as well as the rain belt due to the seasonal variation of solar radiation (Wang et al. 2011; Yang et al. 2014). On interannual timescales, mainly affected by the interannual forcing change especially the oceanic thermal condition, the intensity and the location of the WPSH vary from year to year, and greatly modify the precipitation pattern over East Asia in summer (Lu 2002; Sui et al. 2007).

Recently, several studies have shown the prominent subseasonal (10–90 days) variability in climate over East Asia and its close relationship with the subseasonal signals of atmospheric circulation including the WPSH. For instance, the persistent extreme precipitation (PEP) events occurring over the Yangtze River region are always accompanied with pronounced westward movement of the WPSH and it is thought that the low-level southwesterly along the northwestern flank of the WPSH enhances the moisture transportation and thus leads to PEP events (Mao and Wu 2006; Mao et al. 2010; Ren et al. 2013; Yang et al. 2010; Chen and Zhai 2015; Yan et al. 2019). Therefore, the subseasonal variability of the WPSH has drawn more attention since its significant impact on the climate over East Asia. Depicted by 5880 line, the WPSH extends westward at first and then retreats eastward, called the subseasonal zonal oscillation of the WPSH (Yu and Yang 1995; Ren et al. 2013; Qian and Shi 2017; Guan et al. 2018, 2019; Yang and Li 2020). Accompanied with the westward extension of the WPSH, an anomalous anticyclone is sustained in lower- to mid-troposphere at the west side of the WPSH. This anomalous anticyclone reaches the strongest when the WPSH stretches to the westernmost position, while in upper-troposphere the South Asian high (SAH) extends eastward during westward extension of the WPSH (Chen and Zhai 2015; Ren et al. 2015; Yao and Ren 2019; Shang et al. 2020).

Efforts have been made to investigate the possible factors causing the subseasonal zonal oscillation of the WPSH. These factors could be simply classified into two categories, namely, the internal forcing and the external forcing. The former contains the low-frequency wave train at different levels (Enomoto et al. 2003; Guan et al. 2019) and anomalous convection (Qian and Yu 1991; Wang et al. 2011; Guan et al. 2018). The low-frequency wave train, such as the Silk Road pattern (SRP) and East Asia–Pacific pattern (EAP), generates subseasonal variability over East Asia by transporting energy and momentum, that is, through a remote way (Enomoto et al. 2003; Guan et al. 2019). While the anomalous convection works more locally. Over the western Pacific the anomalous active (suppressed) convection tends to induce anomalous diabatic heating (cooling) which stimulates an anomalous cyclonic (anticyclonic) circulation at the northwest side of the anomalous convection (Lawrence and Webster 2002; Chen and Sui 2010; Li et al. 2015, 2020; Li and Mao 2019; Kikuchi 2021). Also based on potential vorticity (PV) diagnosis, Guan et al. (2018) emphasized that the anomalous convection-induced PV dominates the total PV variation and its center locates at the west side of the WPSH. With the enhancement of the anomalous PV, the WPSH extends more westward. It seems that the effect of the anomalous convection on the circulation is widely accepted in the subseasonal zonal oscillation of the WPSH. However, it is still questionable whether the circulation anomaly associated with the subseasonal zonal oscillation of the WPSH has feedback on the intensity and propagation of the anomalous convection.

The external forcing, such as the air–sea interaction, also works in the subseasonal zonal oscillation of the WPSH. Over the western Pacific a warm (cold) sea surface temperature anomaly (SSTA) usually appears after the anomalous suppressed (active) convection (Sui et al. 1997; Kemball-Cook and Wang 2001; Wang et al. 2006; Li and Wang 2021). An anomalous suppressed convection tends to induce a warm underlying SSTA by enhancing the downward solar radiation and reducing the evaporation (Hsu and Weng 2001; Kemball-Cook and Wang 2001; Hendon 2012; Mao and Wang 2018; Li and Wang 2021). In turn, the induced warm SSTA acts to directly heat and moisten the air in planetary boundary layer (PBL) by upward surface heat flux anomalies, which destabilize the PBL and further generate upwelling and cyclonic circulation anomalies (Neelin and Held 1987; Roxy and Tanimoto 2012; Roxy et al. 2013; Wang et al. 2018). Studies on the subseasonal zonal oscillation of the WPSH also reveal the in-phase relationship between the SSTA at the west side of the WPSH and the local anomalous convective stability (Ren et al. 2013; Guan et al. 2019; Zi et al. 2021). It demonstrates that the cold SSTA favors more stable condition, and thus enhances anomalous anticyclonic circulation related to the WPSH. However, in these studies the air–sea interaction is mainly investigated qualitatively. The quantitative contribution of the ocean to the atmosphere on subseasonal timescale still needs to be further studied. Wang et al. (2018) proposed a method to distinguish the relative contribution of the ocean and the atmosphere in the air–sea interaction processes by decomposing the turbulent heat flux. It may provide a reference of quantification for our works.

At present, the researches on the zonal oscillation of the WPSH pay more attention on the whole range of subseasonal (10–90 days) timescale (Ren et al. 2013; Guan et al. 2018, 2019) or only on the quasi-biweekly timescale (Qian and Yu 1991; Yang and Li 2020). However, as we present in the following, the frequency of subseasonal zonal oscillation of the WPSH mainly focus on two bands, that is a 10–25-day period and a 25–50-day period. It remains unclear how the WPSH variabilities in these two periods differ in their evolution characteristics and especially in their corresponding mechanisms.

Thus, the present study aims at investigating the evolution characteristics and the mechanisms, including the convection–circulation interaction and the air–sea interaction, of the subseasonal zonal oscillation of the WPSH with periods of 10–25 days and 25–50 days. The remainder of paper is structed as follow. The data and methods are described in Sect. 2. The evolution characteristics of the subseasonal zonal oscillation of the WPSH in these two periods are presented in Sect. 3. The associated convection–circulation interaction and air–sea interaction processes and their contributions to the subseasonal zonal oscillation of the WPSH are discussed in Sects. 4 and 5, respectively. The paper ends with a summary and discussions for further study in Sect. 6.

2 Data and methods

The atmospheric data is obtained from National Centers for Environmental Prediction–Department of Energy (NCEP-DOE) Reanalysis 2 with the horizonal resolution of 2.5\(^\circ \times \) 2.5\(^\circ \) (Kanamitsu et al. 2002). Daily interpolated outgoing longwave radiation (OLR) data from the National Oceanic and Atmospheric Administration (NOAA) is used as a proxy of the convection activity at 2.5\(^\circ \) spatial resolution (Liebmann and Smith 1996). The sea surface temperature (SST) and the turbulent heat flux-related variables are obtained from Objectively Analyzed Air–Sea Fluxes (OAFlux) daily data with 1\(^\circ \times \) 1\(^\circ \) horizonal resolution (Yu et al. 2008). For all above variables the period of 1985–2020 summer (June–August) is selected in order to cover the time range of the OAFlux data. All variables are processed by 5-day moving average, and then the climatological mean annual cycle and the yearly summer average are removed to obtain subseasonal anomalies.

As shown in Fig. 1a, the variability of subseasonal geopotential height anomaly at 500 hPa (H500) is significant over the region (10\(^\circ \)N–30\(^\circ \)N, 110\(^\circ \)E–140\(^\circ \)E) compared to the rest areas covered by the WPSH. Thus, in this paper we take this region as the core of the subseasonal zonal oscillation of the WPSH, and the WPSH index (WPSHI) is defined by the subseasonal H500 anomaly averaged over this core region as Guan et al. (2019) did. A positive index represents a westward-extending WPSH. The power spectrum of the WPSHI is shown in Fig. 1b, and it illustrates two main periods in the subseasonal zonal oscillation of the WPSH, a 10–25-day period and a 25–50-day period. To better distinguish the features in these two periods, the 6th order butterworth filter is applied to all variables to extract anomalies in corresponding period. For further composite analysis, a positive (negative) event is identified when the filtered WPSHI exceeds (below) the value of 1.5 times the standard deviation, and the day 0 of each event is defined as the day when the filtered WPSHI reaches the maximum (minimum) value. Based on this criteria, 70 positive events and 68 negative events are identified in the 10–25-day period, while 36 positive events and 33 negative events in the 25–50-day period.

Fig. 1
figure 1

a The standard deviation of subseasonal geopotential height anomaly at 500 hPa (H500, shaded) and the climatological mean 5880 line (contour). The red box denotes the core region of the variability of the western Pacific subtropical high (110\(^\circ \)E–140\(^\circ \)E, 10\(^\circ \)N–30\(^\circ \)N). b The power spectrum of the subseasonal WPSH index (WPSHI, black solid line). The red and black dash lines represent the Markov red noise spectrum and the spectrum of 95% confidence level, respectively

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Since the subseasonal zonal oscillation of the WPSH is corresponding to the anomalous circulation signals over the western Pacific, here, we investigate the cause of this signal by diagnosing the vorticity equation:

(1)

where \(\zeta \) is the relative vorticity, \(t\) the time, \(\mathop{{{\bf{V}}}_h}\limits^{\rightharpoonup}\) the horizontal flow (\(u{\mathop{{{\varvec{\iota}}}}\limits^{\rightharpoonup}} + v{\mathop{\varvec{j}}\limits^{\rightharpoonup}}\)), \(\nabla \) the horizontal gradient operator, \(\omega \) the vertical velocity, \(p\) the pressure, \(\beta \) the meridional gradient of the Coriolis parameter \(f\), \(S\) the tilting term associated with velocity shear expressed as \(\left[\left(\partial \omega /\partial y\right)\left(\partial u/\partial p\right)-\left(\partial \omega /\partial x\right)\left(\partial v/\partial p\right)\right]\), and \(D\) the divergence. The first five terms on the right-hand side of the Eq. 1 represent the contributions of the horizontal vorticity advection (a), the vertical vorticity advection (b), the \(\beta \) effect (c), the tilting effect (d) and the horizontal divergence effect (e), respectively. The \(Res\) is the residual term which is mainly attributed to the friction dissipation. The prime denotes the filtered anomalies in corresponding period. The heating condition is also studied as it closely relates to the convection and favors the generation of anomalous circulation as mentioned in Sect. 1. Here, we calculate the diabatic heating rate \(Q\) following Yanai et al. (1973) as:

$$ Q^{\prime} = C_p \left[ {\frac{\partial T}{{\partial t}} + \overrightarrow {{{\varvec{V}}}_h } \cdot \nabla T + \left( {\frac{p}{p_0 }} \right)^{R/C_p } \omega \frac{\partial \theta }{{\partial p}}} \right]^{\prime} $$
(2)

where \({C}_{p}\) is the specific heat of air, \(T\) the air temperature, \(R\) the gas constant, \({p}_{0}\)(= 1000 hPa) the standard atmospheric pressure, and \(\theta \) the potential temperature.

The turbulent heat fluxes, including latent heat flux (LHF) and sensible heat flux (SHF), are important indicators of air–sea interaction. They are simultaneously influenced by both the atmosphere and the ocean, and can be calculated by the bulk algorithm (Yu et al. 2008):

$$\mathrm{LHF}=\rho {L}_{e}{C}_{e}U\left({q}_{s}-{q}_{a}\right)=\rho {L}_{e}{C}_{e}U\Delta q$$
(3)
$$\mathrm{SHF}=\rho {C}_{p}{C}_{h}U\left({T}_{s}-{\theta }_{a}\right)=\rho {C}_{p}{C}_{h}U\Delta T$$
(4)

where \(\rho \) is the density of air, \({L}_{e}\) the latent heat of evaporation. \({C}_{e}\) and \({C}_{h}\) are the transfer coefficients for LHF and SHF, respectively. The rest variables are all from OAFlux dataset, where \(U\) is the wind speed near the sea surface, \({T}_{s}\) the SST, \({q}_{s}\) the interfacial value of specific humidity calculated from saturation humidity at the \({T}_{s}\). The specific humidity and the potential temperature of the atmosphere near the sea surface are denoted by \({q}_{a}\) and \({\theta }_{a}\). To quantify and distinguish the contributions of the ocean and the atmosphere, we decompose the subseasonal anomalies of LHF and SHF as Wang et al. (2018) did. The decompositions can be approximately written as:

$${\mathrm{LHF}}^{{\prime}}\approx \rho {L}_{e}{C}_{e}\left(\overline{U}\Delta {q }^{{\prime}}+{U}^{{\prime}}\overline{\Delta q }\right)$$
(5)
$${\mathrm{SHF}}^{{\prime}}\approx \rho {C}_{p}{C}_{h}\left(\overline{U}\Delta {T }^{{\prime}}+{U}^{{\prime}}\overline{\Delta T }\right)$$
(6)

where a prime denotes the subseasonal filtered component and an overbar denotes the low-frequency basic state (with a longer period than the filtered anomaly). Note that in Eqs. 5 and 6, the small-magnitude terms with second and above order that are mainly contributed by the nonlinear interactions of synoptic-scale components are neglected. The following Eqs. 7 and 8 are decomposed in the same way. Also, the terms \(\rho {L}_{e}{C}_{e}\) and \(\rho {C}_{p}{C}_{h}\) in Eqs. 5 and 6 are the climatological mean value and the overbar there are omitted for convenient description. The above equations means that the LHF and SHF anomalies are largely dependent on two kinds of terms, that is, terms related to the anomalies of air–sea humidity difference and temperature difference (\(\rho L_e C_e \overline{U}\Delta q^{\prime}\) and \(\rho C_p C_h \overline{U}\Delta T^{\prime}\)) that influenced by both oceanic and atmospheric states, and terms related to the anomalous wind speed (\(\rho L_e C_e U^{\prime}\overline{\Delta q}\) and \(\rho C_p C_h U^{\prime}\overline{\Delta T}\)) that is only affected by the atmosphere.

3 Evolution characteristics of zonal oscillation of the WPSH

Composites of 5880 lines shown in Fig. 2 reflect notable zonal oscillation of the WPSH in 10–25-day and 25–50-day periods. For positive events in both two periods, the western edge of the WPSH first moves westward from the location near 145\(^\circ \)E. It reaches the westernmost location near 115\(^\circ \)E at around day 0, and then retreats eastward to the starting location until day + 8 (day + 16) in the 10–25-day (25–50-day) period (Fig. 2a, b, e, f). The evolution characteristics of negative events are completely opposite to those of positive events in each period. That is, the WPSH first moves eastward and then extends westward (Fig. 2c, d, g, h). Owing to their symmetric characteristics, only positive events are analyzed below.

Fig. 2
figure 2

a–d Temporal evolution of the composite 5880 lines for a, b positive events and c, d negative events in 10–25-day period from day −8 to day + 8 with interval of 2 days. e–h Same as a–d, but in 25–50-day period from day −16 to day + 16 with interval of 4 days. Day 0 is defined as the day when the filtered WPSHI in each period reaches the maximum (minimum)

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Figure 3 shows the temporal evolution of composited 10–25-day filtered OLR, geopotential height at 850 hPa (H850), SSTA and vertical velocity at 400 hPa (ω400) for positive events. Accompanied with the westward extension of the WPSH in 10–25-day period, a positive OLR anomaly representing suppressed convection grows and propagates northwestward from the location near 155\(^\circ \)E, with an enhancing positive H850 anomaly at its northwest (left panel in Fig. 3). Both the suppressed convection and H850 anomalies reach the strongest at around day 0 when the WPSH stretches to the westernmost position. Then these anomalies weaken gradually as moving northwestward, followed by the subsequent new active convection and negative H850 anomalies, corresponding to the retreat of the WPSH. Finally, the weakened anomalies disappear near the continent at around day + 4 and the following strengthened active convection and negative H850 anomalies occupy the western Pacific. Moreover, behind the suppressed convection anomaly there is a warm SSTA which get visible at around day 0 near 140\(^\circ \)E (Fig. 3h). It propagates along with the anomalous convection. The descending anomaly represented by ω400 shows great agreement with the suppressed convection anomaly in 10–25-day period (right panel in Fig. 3).

Fig. 3
figure 3

a–e Composites of 10–25-day filtered anomalies of geopotential height at 850 hPa (H850, green contours with interval of 2 gpm) and OLR (shaded, unit: W m−2) for positive events from day − 4 to day + 4 with interval of 2 days. f–j Same as a–e, but for anomalies of vertical velocity anomaly at 400 hPa (ω400, black contours with interval of 8 \(\times \) 10–3 Pa s−1) and SSTA (shaded, unit: K). Purple contours denote the 5880 line of the corresponding time. Dots and shade in a–e and f–j denote areas with significance at 95% confidence level for anomalies of H850, ω400, OLR and SSTA, respectively. The yellow line in c represents the propagation path of all variables

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Same as Fig. 3, the temporal evolution of composited 25–50-day filtered variables for positive events is shown in Fig. 4. Accompanied with the westward extension of the WPSH in 25–50-day period, the suppressed convection anomaly, generating northerly compared to 10–25-day period, strengthens and propagates more westward with the positive H850 anomalies at its northwest (left panel in Fig. 4). The suppressed convection and H850 anomalies also reach the strongest at around day 0, then weaken and proceed to move westward. With the weakening of those positive anomalies and the enhancement of subsequent new active convection and negative H850 anomalies, the WPSH retreats eastward. The associated warm SSTA also appears at around day 0 and propagates following anomalous convection (right panel in Fig. 4). What’s more, the magnitude of SSTA in 25–50-day period is much greater than that in 10–25-day period. The 25–50-day descending anomaly also shows consistent distribution with the suppressed convection anomaly (right panel in Fig. 4).

Fig. 4
figure 4

Same as Fig. 3, but for 25–50-day filtered anomalies from day − 8 to day + 8 with interval of 4 days

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Evident propagation of all variables in two periods can also be found in Fig. 5. It reveals that in both two periods the H850 anomalies vary simultaneously with the convection anomaly in temporal (Fig. 5a, c). The SSTA lags the convection anomaly by about 4 days in 10–25-day period, whereas by about 8 days in 25–50-day period (Fig. 5b, d), showing a near-quadrature phase relationship in temporal. Such phase relationship between SSTA and convection anomalies is consistent with that was demonstrated in the research on the subseasonal air–sea interaction (Ren et al. 2013; Wang et al. 2018).

Fig. 5
figure 5

a, b Temporal evolution of 10–25-day filtered anomalies of a H850 (black contours, unit: gpm) and OLR (shaded, unit: W m−2) and b H850 (black contours) and SSTA (shaded, unit: K) along the cross section marked in Fig. 3c. c, d Same as a, b, but for 25–50-day period along the cross section marked in Fig. 4c

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4 The convection–circulation interaction in zonal oscillation of the WPSH

4.1 Effect of the convection on circulation

It can be seen from the discussion in Sect. 3 that the zonal oscillation of the WPSH is related to the generation and movement of the circulation anomaly, so next, the causes of the circulation anomaly are analyzed based on the vorticity equation. We first focus on the 10–25-day zonal oscillation of the WPSH. The left panel in Fig. 6 shows the temporal evolution of the vorticity tendency (the left-hand side of the Eq. 1), the vorticity source terms (the right-hand side of the Eq. 1) as well as the vorticity anomaly at 850 hPa in 10–25-day period, averaged within the core region marked in Fig. 1a. The vorticity tendency precedes the vorticity anomaly by about a quarter of cycle, supporting the periodic oscillation of the vorticity anomaly. Among the vorticity source terms, the vertical vorticity advection and the tilting effect can be neglected because their magnitudes are much smaller than others. The horizontal relative vorticity advection term and the residual term are out-of-phase with the vorticity anomaly, indicating that they always prevent the development of the vorticity anomaly. The \(\beta \) effect term also precedes the vorticity anomaly by about a quarter of cycle, favoring the westward propagation of the vorticity anomaly.

Fig. 6
figure 6

a, b Temporal evolution of 10–25-day anomalies of the vorticity at 850 hPa (yellow line, unit: 10−6 s−1), the vorticity tendency (pink line, unit: 10−11 s−2), the vorticity source terms on the right side of Eq. 1 (unit: 10−11 s−2), including the horizontal vorticity advection term (dark blue line), the vertical vorticity advection term (dark green line), the \(\beta \) effect term (black line), the tilting effect term (red line), the horizontal divergence effect term (light green line), and the residual term (light blue line). c, d Same as a, b, but for 25–50-day period. All the variables are averaged within the core region marked in Fig. 1a

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Although the above terms all have certain influence on vorticity variation, the magnitude of the horizontal divergence effect term \(- \left[ {\left( {\zeta + f} \right)D} \right]^{\prime} \) is the largest among the vorticity source terms. It nearly keeps in-phase with the vorticity anomaly in temporal (Fig. 6a) and spatial (left panel in Fig. 7), indicating that the horizontal divergence effect largely favors the generation and the maintenance of vorticity anomaly in 10–25-day period. To further explore what contributes to the horizontal divergence effect term, a decomposition is applied and the first-order approximation of the decomposition can be written as:

$$ - \left[ {\left( {\zeta + f} \right)D} \right]^{\prime} \approx - \overline{{\left( {\zeta + f} \right)}}D^{\prime} - \left( {\zeta + f} \right)^{\prime} \overline{D} $$
(7)

where the terms on the right-hand side represent the anomalous divergence-related term and the anomalous vorticity-related term, respectively. Further diagnosis shows that the horizontal divergence effect term is dominantly contributed by the former \(- \overline{{\left( {\zeta + f} \right)}}D^{\prime}\) (right panel in Fig. 7), which means the divergence anomaly plays more important role in the variation of 10–25-day vorticity.

Fig. 7
figure 7

a–e Composites of 10–25-day filtered anomalies of the vorticity (black contours with interval of 1.5 \(\times \) 10−6 s−1) and the horizontal divergence effect term \(- \left[ {\left( {\zeta + f} \right)D} \right]^{\prime}\) in Eq. 2 (shaded, unit: 10−11 s−2) at 850 hPa from day − 4 to day + 4 with interval of 2 days. f–j Same as a–e, but for anomalies of the horizontal divergence effect term (blue bar) and its two components, the anomalous divergence-related term (\(- \overline{{\left( {\zeta + f} \right)}}D^{\prime}\), red bar) and the anomalous vorticity-related term (\(- \left( {\zeta + f} \right)^{\prime} \overline{D}\), green bar), averaged within the core region marked in Fig. 1a (unit: 10−11 s−2)

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The divergence anomaly determining the horizontal divergence effect is located at the northwest of the convection, in-phase with the vorticity anomaly. Then, what causes this divergence anomaly? Composites of OLR and diabatic heating (\(Q\)) anomalies (Fig. 8) reveals that the diabatic cooling anomaly, coinciding with the suppressed convection, occupies the core region with its strongest cooling at 400 hPa as the WPSH extends westward. This diabatic cooling may shrink the air column, induce local descent and low-level divergence (Wu et al. 2020). The configuration of atmospheric circulation response on the northwest side of the heat source also meets Gill's theoretical results of thermal-driven atmospheric circulation (Gill 1980). Therefore, it is the anomalous convection that results in divergence anomaly and triggers the horizontal divergence effect term.

Fig. 8
figure 8

Temporal evolution of 10–25-day filtered anomalies of a the diabatic heating with height (\({Q}^{{\prime}}\), shaded, unit: K day−1) and b the OLR (black contour, unit: W m−2) averaged within the core region marked in Fig. 1a

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The results above suggest that the convection anomaly from the western Pacific is the direct cause of the 10–25-day zonal oscillation of the WPSH. The suppressed convection causes diabatic cooling, induces divergence anomaly at the northwest side of the convection and further stimulates anticyclonic anomaly by the horizontal divergence effect. Hence, we observe a more westward extending WPSH.

4.2 Feedback of the circulation on convection

In addition to the generation of the anomalous anticyclone by the anomalous convection, the propagation of the anomalous convection and the related anomalous anticyclone is also the key to the subseasonal zonal oscillation of the WPSH. On the one hand, the convection activity itself may have propagation properties, such as the Boreal Summer Intraseasonal Oscillation (BSISO). On the other hand, the convection-induced circulation anomaly and SSTA may also affect the propagation of convection in turn. In this section, we will investigate the feedback of the circulation on the propagation of convection.

The spatial relationship between the boundary layer-integrated vertical moisture advection anomaly \(\left( { - \left( {\omega \frac{\partial q}{{\partial p}}} \right)^{\prime} } \right)\) and the convection anomaly in 10–25-day period can be seen in the left panel of Fig. 9. The center of vertical moisture advection anomaly is always located at the northwest of the suppressed convection, so it is conducive to form a dry condition ahead of the suppressed convection and favors the northwestward propagation of the suppressed convection. Further decomposition is also applied to the vertical moisture advection. Following the method proposed by Hsu and Li (2012), the first-order approximation of the decomposition can be written as:

$$ - \left( {\omega \frac{\partial q}{{\partial p}}} \right)^{{\prime} } \approx - \left( {\frac{\partial \omega q}{{\partial p}}} \right)^{{\prime} } - \overline{q}D^{{\prime} } - q^{{\prime} }\overline{D} $$
(8)

where \(q\) is the specific humidity. The terms on the right-hand side of Eq. 8 respectively represent the vertical moisture flux anomaly, the anomalous divergence-related term and the anomalous humidity-related term. Due to the small magnitude of the anomalous humidity-related term, only the first two terms are shown in the right panel of Fig. 9. We can see that the vertical moisture advection is mainly determined by the anomalous divergence-related term. That is to say, the anomalous wind causes moisture divergence which stimulates the downward dry advection in PBL, and thus conduce to the northwestward propagation of the suppressed convection. It proves that in 10–25-day zonal oscillation of the WPSH the anomalous circulation has feedback on the anomalous convection and steers the propagation of the convection anomaly. As the suppressed convection propagates northwestward, anomalous anticyclone also shows northwestward propagation, corresponding to the westward extension of the WPSH.

Fig. 9
figure 9

a–e Composites of 10–25-day filtered anomalies of OLR (black contours with interval of 3 W m−2) and the planetary boundary layer (PBL, 1000–850 hPa) integrated vertical moisture advection (\(\left( { - \omega \partial q{/}\partial p} \right)^{{\prime} }\), shade, unit: kg m−2 day−1) from day −4 to day + 4 with interval of 2 days. f–j Same as a–e, but for anomalies of the PBL integrated vertical moisture advection (blue bar) and its two main components, including the vertical moisture flux term (green bar) and the anomalous divergence-related term (red bar), averaged within the core region marked in Fig. 1a (unit: kg m−2 day−1)

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Similar to the 10–25-day period, the convection–circulation interaction also acts in 25–50-day zonal oscillation of the WPSH. As shown in the right panel of Fig. 6, the 25–50-day vorticity variation is also dominated by the horizontal divergence effect term \(- \left[ {\left( {\zeta + f} \right)D} \right]^{\prime}\). Its nearly in-phase relationship with vorticity anomaly in temporal and spatial indicates that the horizontal divergence effect drives the development of anomalous circulation in 25–50-day period (Fig. 6c; left panel in Fig. 10). Further analysis shows that the diabatic cooling anomaly develops simultaneously with convection and reaches the strongest when the WPSH stretches to the westernmost position (Figure not shown). It confirms that in 25–50-day period the suppressed convection-induced diabatic cooling favors the divergence anomaly at the northwest side of the convection and finally intensifies anomalous anticyclone by the horizontal divergence effect. In turn, the anomalous anticyclone favors the vertical moisture advection anomaly at the west side of the suppressed convection in PBL (right panel in Fig. 10), which is beneficial for the westward propagation of the suppressed convection.

Fig. 10
figure 10

a–e Composites of 25–50-day filtered anomalies of the vorticity (black contours with interval of 1.5 \(\times \) 10−6 s−1) and the horizontal divergence effect term \(- \left[ {\left( {\zeta + f} \right)D} \right]^{\prime}\) in Eq. 2 (shaded, unit: 10−11 s−2) at 850 hPa from day − 8 to day + 8 with interval of 4 days. f–j Same as a–e, but for anomalies of OLR (black contours with interval of 3 W m−2) and the PBL integrated vertical moisture advection (\(\left( { - \omega \partial q{/}\partial p} \right)^{\prime}\), shade, unit: kg m−2 day−1)

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Overall, the suppressed convection and anomalous anticyclone are interacted, which contribute to the enhancement and the propagation of anticyclonic anomaly and consequently lead to the subseasonal zonal oscillation of the WPSH. The two main periods may mainly depend on the propagation period of the convection.

5 The oceanic effect on the atmosphere

As mentioned in Sect. 1, Some studies argue that the oceanic feedback also works in the subseasonal zonal oscillation of the WPSH (Ren et al. 2013; Guan et al. 2019; Zi et al. 2021). Since the magnitude of SSTA in 10–25-day period is much smaller than that in 25–50-day period (Fig. 5b, d), whether the ocean has obvious impact in both two periods still needs to be clarified.

Composites of LHF and SHF anomalies as well as their two main components in each period are shown in Figs. 11 and 12, respectively. The anomalous wind speed-related terms (\(\rho L_e C_e U^{\prime}\overline{\Delta q}\) and \(\rho C_p C_h U^{\prime}\overline{\Delta T}\), dark green lines in Figs. 11, 12) always shows an out-of-phase relationship with the OLR anomaly (black lines) in both two periods, which suggests that the suppressed convection tends to reduce the LHF and the SHF by weakening wind speed, and vice versa. The anomalous air–sea humidity difference-related term (\(\rho L_e C_e \overline{U}\Delta q^{\prime}\), light green lines) closely follows the SSTA in both two periods in most of time, indicating that the ocean appears to determine the air–sea humidity difference. A warm SSTA can increase the humidity difference and further strengthen the LHF. For the anomalous air–sea temperature difference-related term (\(\rho {C}_{p}{C}_{h}\overline{U}\Delta {T }^{{\prime}}\)), there is a large phase difference between it and the SSTA in 10–25-day period in most of time, while it varies almost in-phase with the SSTA in spatial in 25–50-day period. This means that the ocean is not decisive in the air–sea temperature difference in shorter period, but can greatly affects the air–sea temperature difference in longer period, with a warm SSTA enlarging the temperature difference and increasing the SHF.

Fig. 11
figure 11

Composites of 10–25-day filtered anomalies of a–c OLR (black line), SST (blue line), upward latent heat flux (LHF, red dash line), the air–sea humidity difference-related term of LHF (\(\rho {L}_{e}{C}_{e}\overline{U}\Delta {q }^{{\prime}}\), light green line), the anomalous wind speed-related term of LHF (\(\rho {L}_{e}{C}_{e}{U}^{{\prime}}\overline{\Delta q }\), dark green line) and the sum of the two components of LHF (pink dash line); and d–f upward sensible heat flux (SHF, red dash line), the air–sea temperature difference-related term of SHF (\(\rho {C}_{p}{C}_{h}\overline{U}\Delta {T }^{{\prime}}\), light green line), the anomalous wind speed-related term of SHF (\(\rho {C}_{p}{C}_{h}{U}^{{\prime}}\overline{\Delta T }\), dark green line) and the sum of the two components of SHF (pink dash line) along the cross section marked in Fig. 3c, averaged from a, d day 0 to + 2, b, e day + 3 to + 5 and c, f day + 6 to + 8. Curves in the figure match the ordinate with the same color

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Fig. 12
figure 12

Same as Fig. 11, but for 25–50-day filtered anomalies along the cross section marked in Fig. 4c, averaged from a, d day + 1 to + 5, b, e day + 6 to + 10 and c, f day + 11 to + 15

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To better clarify the oceanic effect on the atmosphere, three stages are selected according to the corresponding evolution characteristics of SSTA in two periods (Fig. 5b, d), namely, the SSTA developing stage (day 0 to + 2 for 10–25-day period; day + 1 to + 5 for 25–50-day period), the maximum SSTA stage (day + 3 to + 5 for 10–25-day period; day + 6 to + 10 for 25–50-day period) and the SSTA decaying stage (day + 6 to + 8 for 10–25-day period; day + 11 to + 15 for 25–50-day period). The SSTA developing stage and the SSTA decaying stage correspond to a relatively weak SSTA with an anomalous strong convection, while the maximum SSTA stage corresponds to a maximum SSTA anomaly with an anomalous weak convection.

In 10–25-day period (Fig. 11), the anomalous wind speed-related terms (\(\rho L_e C_e U^{\prime}\overline{\Delta q}\) and \(\rho C_p C_h U^{\prime}\overline{\Delta T}\)) dominates both the LHF and the SHF anomalies in the SSTA developing stage (Fig. 11a, d) and the SSTA decaying stage (Fig. 11c, f). Since the anomalous wind speed-related terms only depend on atmospheric states, it illustrates that the atmospheric process is more of significance when the SSTA is in a weak stage. In the maximum SSTA stage, both the anomalous wind speed-related term (\(\rho {L}_{e}{C}_{e}{U}^{{\prime}}\overline{\Delta q }\)) and the air–sea humidity difference-related term (\(\rho {L}_{e}{C}_{e}\overline{U}\Delta {q }^{{\prime}}\)) favors the anomalous LHF (Fig. 11b). Although the ocean plays a dominant role in the air–sea humidity difference-related term (\(\rho {L}_{e}{C}_{e}\overline{U}\Delta {q }^{{\prime}}\)), it accounts for only half of the LHF anomaly and lasts for a short period. Thus, the oceanic process cannot remarkably influence the LHF anomaly. Meanwhile, due to the large phase difference between the air–sea temperature difference-related term (\(\rho {C}_{p}{C}_{h}\overline{U}\Delta {T }^{{\prime}}\)) and SSTA (Fig. 11e), the ocean is also not decisive in causing the SHF anomaly. Therefore, the ocean has no obvious feedback on the atmospheric circulation in the 10–25-day zonal oscillation of the WPSH.

As for 25–50-day period (Fig. 12), during the SSTA developing stage (Fig. 12a, d), it is similar to 10–25-day period that both the LHF and the SHF anomalies are largely contributed by the anomalous wind speed-related terms (\(\rho {L}_{e}{C}_{e}{U}^{{\prime}}\overline{\Delta q }\) and \(\rho {C}_{p}{C}_{h}{U}^{{\prime}}\overline{\Delta T }\)), while the air–sea difference-related terms (\(\rho {L}_{e}{C}_{e}\overline{U}\Delta {q }^{{\prime}}\) and \(\rho {C}_{p}{C}_{h}\overline{U}\Delta {T }^{{\prime}}\)) tend to restrain the development of the LHF and the SHF anomalies. In this stage, the atmospheric process is more essential in influencing the LHF and the SHF anomalies. When the SSTA develops to the maximum stage (Fig. 12b, e), the anomalous wind speed-related terms (\(\rho {L}_{e}{C}_{e}{U}^{{\prime}}\overline{\Delta q }\) and \(\rho {C}_{p}{C}_{h}{U}^{{\prime}}\overline{\Delta T }\)) weaken evidently, while the air–sea difference-related terms (\(\rho {L}_{e}{C}_{e}\overline{U}\Delta {q }^{{\prime}}\) and \(\rho {C}_{p}{C}_{h}\overline{U}\Delta {T }^{{\prime}}\)) strengthen and dominate the LHF and the SHF anomalies. The nearly in-phase relationship between the anomalous air–sea difference-related terms and the SSTA indicates that the ocean inclines to affect the atmosphere through moistening and heating processes during the maximum SST stage. After that, the SSTA dampens due to the heat flux transfer to the atmosphere (Fig. 12c, f), and the air–sea difference-related terms (\(\rho {L}_{e}{C}_{e}\overline{U}\Delta {q }^{{\prime}}\) and \(\rho {C}_{p}{C}_{h}\overline{U}\Delta {T }^{{\prime}}\)) decay correspondingly. Meanwhile, the anomalous wind speed-related terms (\(\rho {L}_{e}{C}_{e}{U}^{{\prime}}\overline{\Delta q }\) and \(\rho {C}_{p}{C}_{h}{U}^{{\prime}}\overline{\Delta T }\)) increase again. The former (\(\rho {L}_{e}{C}_{e}{U}^{{\prime}}\overline{\Delta q }\)) takes a leading part of the LHF anomaly, whereas the latter (\(\rho {C}_{p}{C}_{h}{U}^{{\prime}}\overline{\Delta T }\)) has a comparable contribution with the air–sea temperature difference-related term (\(\rho {C}_{p}{C}_{h}\overline{U}\Delta {T }^{{\prime}}\)) to the SHF anomaly.

The above analyses demonstrate that the air–sea interaction is more evident in 25–50-day zonal oscillation of the WPSH compared to the 10–25-day period, and the oceanic anomaly can fully develop and impact on the atmosphere more effectively in a longer period.

6 Summary and discussion

The subseasonal zonal oscillation of the WPSH is essential in modulating the persistent climate anomalies over East Asia. From the power spectrum of the WPSHI, it can be seen clearly that the frequency of zonal oscillation of the WPSH is mainly concentrated in two bands, a 10–25-day period and a 25–50-day period. To better distinguish the WPSH variabilities, in this paper, we investigate the evolution characteristics and mechanisms of the zonal oscillation of the WPSH in these two periods, respectively.

Accompanied with westward extension of the WPSH in 10–25-day period, a suppressed convection anomaly propagates northwestward over the western Pacific with a positive H850 anomaly at its northwest side. The intensity of both suppressed convection and positive H850 anomalies reach the strongest when the WPSH stretches to the westernmost position. Subsequently, these anomalies continue to move northwestward followed by another active convection and negative H850 anomalies, corresponding to the eastward retreat of the WPSH. Compared to 10–25-day period, the anomalous suppressed convection in 25–50-day period generates more northly with a more westward propagation path. The WPSH also gets the westernmost when the anomalous suppressed convection reaches the strongest, and retreats eastward with its weakening in 25–50-day period. In both periods, a warm SSTA lags the suppressed convective anomaly, showing a near-quadrature phase relationship in temporal. What’s more, the magnitude of SSTA in 25–50-day period is much greater than that in 10–25-day period.

The zonal oscillation of the WPSH is mainly attributed to the convection–circulation interaction in both two periods, as shown in schematic diagram of Fig. 13. Diagnosis based on the vorticity equation (Eq. 1) indicates that the horizontal divergence effect term \(\left[ { - \left( {\zeta + f} \right)D} \right]^{{\prime} }\) plays a leading role in the vorticity variation. The in-phase relationship between the horizontal divergence effect term and vorticity anomaly suggests the horizontal divergence effect is conducive to the development of anomalous circulation in lower-troposphere. Further analysis shows that the suppressed convection-induced diabatic cooling stimulates the divergence anomaly at the northwest side of the suppressed convection, and further strengthens anticyclonic anomaly through the horizontal divergence effect. In turn, the anticyclonic anomaly motivates the downward dry advection in PBL ahead of the convection anomaly, which benefits the propagation of the suppressed convection. Therefore, through interaction, the convection and circulation anomalies are combined and propagate together, leading to the zonal oscillation of the WPSH.

Fig. 13
figure 13

Schematic diagram of the convection–circulation interaction in the zonal oscillation of the WPSH

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Moreover, though the convection–circulation interaction processes in these two periods are similar, the spatial patterns and propagation paths of OLR anomalies in these two periods are different if we consider the whole tropical Indian Ocean-Western Pacific region. In 10–25-day period, the OLR anomaly displays a northeast-southwest tilted horizontal structure, which resembles the characteristics of the boreal summer short-period convective activities (like BSISO2, Lee et al. 2013). While in 25–50-day period it displays a northwest-southeast tilted structure which is similar to the long-period convective activities (like BSISO1, Lee et al. 2013). The two main periods may be determined by the propagation period of the convection.

Attention has also been paid to the role of air–sea interaction in the subseasonal variability of the WPSH (Ren et al. 2013; Guan et al. 2019; Zi et al. 2021). Our findings suggest that when the SSTA is weak, the LHF and SHF anomalies are primarily driven by the atmospheric processes in both periods. The suppressed (active) convection decreases (increases) the LHF and SHF by weakening (enhancing) the wind speed. When the SSTA enhances to the maximum, the oceanic effect on the LHF and SHF anomalies is still weak in 10–25-day period, but it dominates the LHF and SHF anomalies in 25–50-day period by changing the air–sea humidity and temperature difference. This demonstrates that the air–sea interaction is more evident in longer-period zonal oscillation of the WPSH. In 10–25-day period, the ocean has no obvious feedback on the atmospheric circulation, while in 25–50-day period, the oceanic anomaly can fully develop and impact on the atmosphere more effectively.

Currently, our work reveals the role of the anomalous convection and the evident SSTA in the zonal oscillation of the WPSH in two distinct periods based on observation study. However, what causes the convection anomaly, whether the convection anomaly belongs to some kind of intra-seasonal oscillation such as BSISO, and how the zonal oscillation of the WPSH influences the summer climate over East Asia, these questions still need further analyses. The proposed mechanism of the zonal oscillation of the WPSH in this study is also need to be further explored and validated based on model experiment results. In addition to these factors, there is also a close connection between the zonal oscillation of the WPSH and that of the SAH in upper-troposphere. As documented in lots of researches, the SAH tends to extends eastward during the westward extension of the WPSH, and vice versa (Chen and Zhai 2015; Ren et al. 2015). Our preliminary analysis suggests that this connection may not be contributed by the anomalous vertical vorticity advection due to its negligible magnitude in the lower-troposphere in both two periods (Fig. 5). Then, it is still puzzling that what processe leads to this connection. Moreover, from our investigation we find that the subseasonal zonal oscillation of the WPSH also has significant interannual variability. The characteristics and the cause of this interannual variation also need to be fully revealed.