Stage-dependent influence of PDO on interdecadal summer precipitation anomalies in eastern China

Pacific decadal oscillation (PDO) has been regarded as one of the most important interdecadal factors to the interdecadal summer precipitation in eastern China, which, however, cannot keep a consistent pattern during the same positive or negative PDO phase. Because sea surface temperature (SST) anomalies vary along with PDO evolvement, the PDO impacts are investigated in terms of developing and decaying stages of its positive and negative phases, respectively. It is found that the SST cooling in mid-latitude North Pacific and SST warming in off-equator central-eastern Pacific are generally intensified from the developing stage to the decaying stage for positive PDO phase, and vice versa. Particularly, during the decaying stage of positive (negative) PDO phase, the enhanced SST warming (cooling) in northeastern tropical Pacific triggers a stronger (weaker) large-scale Walker circulation and suppresses (enhances) the convective activities in western tropical Pacific, which favors a meridional wave train like East Asia–Pacific (EAP) teleconnection over East Asia. Meanwhile, the westward extended SST cooling (warming) in mid-latitude North Pacific together with the SST warming (cooling) to its south significantly increases (decreases) the meridional SST gradient and low-level atmospheric baroclinicity, conductive to the strengthened (weakened) and southward (northward) shifted East Asian subtropical westerly jet as well as an equivalent barotropic “cold trough” in western North Pacific. Because of such tropical and extratropical dynamical processes, a meridional tripole pattern of precipitation anomalies occurs in eastern China which dominates the PDO impact in the same phase and distinctly different from the dipole pattern during the developing stage.


Introduction
China is located in the East Asian monsoon region, droughts and floods are the main climate hazards affecting China, and they have different time scales including intraseasonal, interannual and interdecadal scales. The related summer precipitation variabilities are directly influenced by the East Asian summer monsoon (EASM) and indirectly by the oceanic forcing signals (Zhu et al. 2011Dong et al. 2016;Si and Ding 2016;Zhang et al. 2018). And at the same time, interdecadal climate variabilities fall in between interannual variation and long-term trend, and they can provide a slowly changing climate background for the interannual climate variabilities (Lv et al. 2014;Sun et al. 2021). With the increase of social needs and the development of science and technology, people are paying more and more attentions to the interdecadal climate variabilities.
On the interdecadal time scales, North Pacific is dominated by an oscillation with a period of 20-30 years, which is the phenomenon referred to as the Pacific decadal oscillation (PDO) by Mantua et al. (1997). In the positive (negative) phase of PDO, sea surface temperature (SST) anomalies are significantly negative (positive) in the mid-latitude North Pacific and positive (negative) in the off-equator central-eastern Pacific. However, the pattern of SST anomalies is not stable in one phase, it evolves and propagates along with time (Zhu and Yang 2003a). As identified by previous studies (Yang et al. 2004;Newman et al. 2016;Zhang et al. 2020), in the past hundred years, 1890-1924, 1947-1976 and 1999-present are negative phases of PDO, while 1925PDO, while -1946PDO, while and 1977PDO, while -1998 are positive phases.
The timing of phase transition of PDO is well in agreement with that of interdecadal climate variations in eastern China (Zhu and Yang 2003b;Zhu et al. 2015). Associated with the interdecadal changes of EASM, eastern China features remarkable interdecadal changes of spatial pattern of summer precipitation anomalies, which mainly demonstrate a tripole mode in the meridional direction. More precipitation occurs in the Yangtze River basin, while less precipitation appears in North China and South China. (Zhu and Yang 2003b;Kwon et al. 2007;Ding et al. 2008;Deng et al. 2009;Huang et al. 2011;Lv et al. 2014;Chen et al. 2021). Specifically, a tripole mode of "positive-negative-positive" is changed to "negative-positive-negative" around the mid-to-late 1970s, which is consistent with the PDO phase shift from negative to positive accordingly (Ding et al. 2008;Deng et al. 2009;Huang et al. 2011). Mei-yu is the major rainfall belt along the Yangtze River valley during the rainy season, it also shows interdecadal variabilities (Zhu et al. 2007;Zhu and Li 2018;Sun et al. 2019a, b;Ding et al. 2020;Li et al. 2021). Compared to the period of 1961-1980 and 2006-2016, Mei-yu has a delayed peak and a larger intensity during 1985-1997, which may be partially attributed to the influence of the positive phase of PDO (Sun et al. 2019a, b). On the other hand, the linkage between Mei-yu withdrawal date and the previous winter North Pacific SST has intensified since the early 1990s . Extreme events and compound events also experience significant interdecadal variabilities (Coumou and Rahmstorf 2012;Zhu and Li 2017;Apurv et al. 2019;Chen and Zhang 2020;Zhang et al. 2020;Wu et al. 2021;Zang et al. 2021;Liu et al. 2022), and the interdecadal shift of extreme high temperature intensity in North China around 1996 is mainly due to the change in the combination of PDO and Atlantic Multidecadal Oscillation (AMO) .
Many studies have investigated the mechanisms of how PDO influences the interdecadal climate anomalies in eastern China (Huang et al. 2013;Qian and Zhou 2014;Si and Ding 2016), which can be summarized as two pathways that are originated from tropical and mid-to-high latitudes, respectively. One pathway is through the meridional wave train along the East Asian coast from tropical regions (e.g., Pacific-Japan, PJ or East Asia-Pacific, EAP), which may be stimulated by the PDO-related SST anomalies in the Pacific Ocean (Lv et al. 2014;Qian and Zhou 2014;Wu et al. 2016;Si et al. 2021). The other is mainly manifested as the zonal wave train at the mid-to-high latitudes (Si and Ding 2016;Zhang et al. 2018;An et al. 2021). Under the modulation effect of AMO, PDO can produce two different wave trains along the great circle path and along the westerly waveguide, affecting the interdecadal summer precipitation anomalies over East Asia (Zhang et al. 2018). In addition to the abovementioned wave trains, PDO can also affect interdecadal precipitation anomalies in eastern China by altering westerly jet intensity (Kwon et al. 2007;Zhu et al. 2011;Huang et al. 2013). In negative PDO phase, the East Asian subtropical westerly jet is weakened through the air-sea interaction in North Pacific, which in turn can change the interdecadal summer precipitation pattern in eastern China (Kwon et al. 2007).
However, as pointed out by Deng et al. (2009) andHuang et al. (2011), PDO has a phase shift from negative to positive in the mid-late 1970s and remains positive until about 2000, but the pattern of summer precipitation anomalies in eastern China has interdecadal changes in the early 1990s when PDO is still in its positive phase. It has been noted that even if PDO is in the same phase, there are some differences in the pattern of SST anomalies in mid-latitude North Pacific (Zhu and Yang 2003a). Therefore, it is reasonable to deduce that the interdecadal changing precipitation in eastern China may be closely associated with the PDO evolvement, which is the essential scientific issue that this study will address. Accordingly, the positive and negative phases of PDO are divided into their corresponding developing and decaying stages, respectively, and the relationships between four different evolutionary stages of PDO and interdecadal summer precipitation anomalies in eastern China are examined by composite analysis, and the associated mechanisms are further investigated via dynamical processes in tropical and mid-to-high latitudes.
The remainder of this paper is structured as follows. The data and methods used in this study are described in Sect. 2. Section 3 demonstrates the features of the interdecadal anomalies of SST, precipitation and atmospheric circulation in the two phases and the four evolutionary stages of PDO, and investigate the dynamical mechanisms involved. Finally, the findings of this study are summarized and discussed in Sect. 4.

Data
The monthly gridded precipitation used in this study is obtained from both Climatic Research Unit (Harris et al. 2020) and Global Precipitation Climatology Project (GPCP) version 2.3 (Adler et al. 2003), which have latitude-longitude horizontal resolutions of 0.5° × 0.5° and 2.5° × 2.5° and time ranges of 1901-2019 and 1979-2021, respectively. The twentieth century monthly reanalysis data with a horizontal resolution of 1° × 1° from 1836 to 2015 is provided by NOAA's Physical Sciences Laboratory and CIRES at the University of Colorado (Compo et al. 2011), of which variables including zonal and meridional winds, geopotential height are used in this study. The monthly SST data from 1870 to the present are provided by Hadley Centre Sea Ice and Sea Surface Temperature dataset, version 1.1 (HadISST1), with a horizontal resolution of 1° × 1° (Rayner et al. 2003). PDO index is defined by Mantua et al. (1997) and Zhang et al. (1997), as the leading standardized principal component of monthly SST anomalies in the North Pacific (20°-70°N). According to the common time period covered by the above data, the time period of 1901-2015 is selected for analysis in this study, and the summertime is defined as the three-month average of June-July-August (JJA).

Methods
In order to eliminate the effects of global warming and better analyze the interdecadal variations, the linear trends are firstly removed from all variables. Then, nine-year running means are applied to extract the interdecadal variations.
PDO index together with its nine-year running mean are shown in Fig. 1. Consistent with previous studies, the whole study period can be divided into positive and negative PDO phases when its nine-year running mean is above and below zero accordingly. Furthermore, because one cycle of PDO index is much similar to the sine function, it is approximately divided into four evolutionary stages in terms of its peak point, valley point and transition point, i.e., the developing stage of positive PDO phase (1901-1904, 1926-1938, 1979-1983), the decaying stage of positive PDO phase (1904-1909, 1938-1944, 1983-1996), the developing stage of negative PDO phase (1910-1920, 1945-1952, 1961-1971, 1997-2009) and the decaying stage of negative PDO phase (1920-1925, 1952-1961, 1971-1978, 2009-2011). Composites for the four PDO evolutionary stages can reveal the stage-dependent impact of PDO, while linear regressions on nine-year running mean of PDO index are used to obtain the PDO impact for its two phases in a traditional way, serving as the reference. Before composite analysis, SST anomalies of certain stage for each period have been checked up, and their major features are generally consistent with each other in Pacific, which assures the robustness of composite results.

PDO impact in two phases
Consistent with previous studies (Zhu and Yang 2003b), PDO impacts on China summer precipitation and its associated atmospheric circulations are firstly demonstrated by linear regressions on the nine-year running mean of PDO index (Fig. 2). In positive PDO phase, SST anomalies are significantly negative in the mid-latitude western-central North Pacific while obviously positive in the off-equator central-eastern Pacific with relatively smaller amplitude, besides, they also display weak warming in the Indian Ocean with the large centers in southern hemisphere (Fig. 2a). Corresponding to the PDO-related SST anomalies in the tropical regions, there are two major centers of anomalous 200 hPa potential velocity (Fig. 2d). The negative center with anomalous divergent wind is located in the centraleastern tropical Pacific, which indicates an obvious upward motion triggered by the local warm SST anomalies. The positive one with anomalous convergent wind is located in the western Indian Ocean, which implies an obvious local downward motion as well as a process of the atmosphere forcing the ocean because of the odd relationship of depressed convection and warm ocean over there (Xue et al. 2022;Wang et al. 2005;Dong et al. 2016). Besides, relatively weaker active and inactive convection anomalies associated with the anomalous 200 hPa potential velocity also appear in the western tropical Pacific and the westerncentral tropical Pacific, respectively, and they are closely connected with the two stronger centers of convective activities and responsible for the cyclonic wind anomalies in northwestern Pacific, which further causes a meridional tripole pattern of precipitation anomalies in eastern China, i.e., much less precipitation in both Huang-Huai River valley and South China and more precipitation in Yangtze River valley. Besides, there are also some more precipitation in Northeast China (Fig. 2f;Zhu and Yang 2003a).
On the other hand, the significant negative SST anomalies in mid-latitude North Pacific can greatly increase the meridional SST gradients on their southern edges, which favors enhanced storm track activities by increasing the low-level atmospheric baroclinicity (Fig. 2b). In turn, an equivalent barotropic structure of "cold trough" forms due to the transient eddy vorticity forcing (Fang and Yang 2016;Tao et al. 2020), which manifests prominent low geopotential height and cyclonic wind anomalies over the North Pacific and its surrounding areas (Fig. 2e, f). Meanwhile, a meridional dipole pattern of zonal wind anomalies at 200 hPa appears over East Asia and North Pacific according to the quasi-geostrophic balance relationship, and it precisely locates to the south of climatological East Asian subtropical westerly jet (EASWJ) (Fig. 2c), indicating the southward shift of EASWJ, which can further induce more precipitation in Yangtze River valley and less precipitation in North China ( Fig. 2f; Sun et al. 2019a, b). Since the method of linear regression is linear, the regression patterns of anomalous SST, precipitation and atmospheric circulation are expected to be reversed in negative PDO phase.

PDO impact in four evolutionary stages
Since both SST and atmospheric circulations are jointly propagating along with the evolution of PDO (Zhu ang Yang 2003a), PDO impacts on interdecadal summer precipitation anomalies in eastern China are examined in the following in terms of its four evolutionary stages based on the composite analysis.

SST anomalies
During the developing and decaying stages of positive PDO phase (Fig. 3a, b), similar to the those in positive PDO phase, there are significant negative SST anomalies in the mid-latitude western-central North Pacific and positive SST anomalies in the off-equator central-eastern Pacific. However, during the developing stage of positive PDO phase (Fig. 3a), both intensity and area of warming SST anomalies in the southeastern tropical Pacific are m/s, arrow) and precipitation field (units: mm/month, shaded). 90% confidence level is indicated by black mesh lines (a, b, c, f) and black heavy arrows (f). Black thick isoline of 0.35 1/day in (b) indicates the climatological eady growth rate and black thick isoline of 26 m/s in (c) indicates the core of climatological EASWJ more remarkable, and notable positive SST anomalies can be also observed in the western tropical Atlantic Ocean. In comparison, during the decaying stage of positive PDO phase (Fig. 3b), the negative SST anomalies in mid-latitude North Pacific are further developed in both intensity and area, and the positive SST anomalies in Indian Ocean clearly extend from southern hemisphere to northern hemisphere with much larger amplitude, while the large SST warming originally located in the southeastern tropical Pacific during the developing stage moves to the northeastern tropical Pacific including the North America western coast. Besides, the western tropical Atlantic Ocean is getter cooler. From the evolutionary perspective in positive PDO phase, the differences of decaying and developing stages are mainly manifested as the strengthened cooling in mid-latitude western North Pacific and as the enhanced warming in northeastern tropical Pacific as well as eastern tropical Indian Ocean and western tropical Pacific, together with obviously cooling development in both southeastern tropical Pacific and western tropical Atlantic Ocean (Fig. 3c).
Compared to that in positive PDO phase (Fig. 3a), the developing stage in negative PDO phase has almost the opposite patterns of SST anomalies (Fig. 3d), so does the decaying stage as well as the corresponding differences of decaying and developing stages (Fig. 3b, c, e, f). However, during the decaying stage of negative PDO phase, the negative SST anomalies in central tropical Pacific are more prominent while the positive SST anomalies in western tropical Atlantic Ocean are much weaker or even insignificant (Fig. 3e), which are the big differences from those in positive PDO phases (Fig. 3b).

Summer precipitation in eastern China
In association with the SST anomalies, during the developing stage of positive PDO phase (Fig. 4a), much less precipitation appears in Huang-huai River valley whereas more precipitation locates in Northeast China, which are mainly attributed to the cyclonic and anticyclonic wind anomalies in North Pacific though their intensities are relatively weak and insignificant. During the decaying stage of positive PDO phase (Fig. 4b), due to the significantly weakened EASM that is caused by the strong cyclonic wind anomaly in North Pacific, an obvious meridional tripole pattern of precipitation anomalies occurs in eastern China, with much more precipitation in middle and lower reaches of Yangtze River valley and much less precipitation in Huanghuai River valley and South China, which is quite similar to the PDO impact on summer precipitation in eastern China in its positive phase (Fig. 2e). Differences of precipitation and low-level wind between decaying and developing stages in positive PDO phase show remarkable precipitation increase in Yangtze River valley accompanied by the strengthened cyclonic wind anomalies in North Pacific from developing stage to decaying stage (Fig. 4c), and they are well consistent with the intensified SST anomalies in both North Pacific and tropical ocean regions (Fig. 3c), further confirming the dominant contribution of PDO impact on summer precipitation in eastern China during decaying stage of positive PDO phase to that in the whole positive PDO phase.
Compared with those in positive PDO phase (Fig. 4a-c), the precipitation and 850 hPa wind anomalies during developing and decaying stages of negative PDO phase and their differences basically have the opposite patterns ( Fig. 4d-f), except that during the decaying stage of negative PDO phase, the decreased precipitation anomalies in Yangtze River valley and anticyclonic wind anomalies in North Pacific have larger amplitudes and shift a little southward, forming a meridional dipole pattern of "South Drought North Flood" in eastern China (Fig. 4e). Nevertheless, PDO impact on summer precipitation in eastern China during the decaying stage of negative PDO phase also dominates the whole negative PDO phase.

Large-scale atmospheric circulations
To understand how the PDO-related SST anomalies exert impacts on summer precipitation in eastern China, the related large-scale atmospheric circulations are further investigated from the aspects of both tropical and extratropical dynamical processes.

a Tropical dynamical process
Firstly, the tropical 200 hPa velocity potential together with its associated divergent wind anomalies in PDO four evolutionary stages and their differences are shown in Fig. 5. During the developing stage of positive PDO phase (Fig. 5a), there are four centers of anomalous 200 hPa velocity potential in the tropical region, consisting of two divergent centers and two convergent centers in the upper troposphere. The divergent centers corresponding to upward motion (Fig. 6a) are located in the eastern tropical Pacific and the western tropical Pacific, respectively, whereas the convergent centers corresponding to downward motion   . 6a) are located in the central tropical Pacific and western Indian Ocean, respectively, which have similar spatial pattern with that in the whole positive PDO phase (Fig. 2d) but with much weaker amplitudes in the eastern tropical Pacific and western tropical Indian Ocean. Compared to the developing stage, there is an obvious transition from four tropical divergent anomaly centers to two during the decaying stage, indicating the enhanced tropical zonal atmospheric circulations and their associated influences on the climate over East Asia due to the increased tropical SST forcing.
Specifically, the significant upper-level divergence anomaly with strong upward motion in eastern tropical Pacific and convergence anomaly with strong downward motion in western tropical Indian Ocean are the major features during the decaying stage of positive PDO phase (Figs. 5b, 6b). Thus, a larger-scale Walker circulation anomaly forms in the whole tropical region (Fig. 6b), and it is generally similar to the difference of decaying and developing stages (Fig. 5c), consistent with the strengthened SST anomalies in the tropical ocean regions from developing to decaying stages (Fig. 3a-c). And at the same time, during the decaying stage of positive PDO phase, significant divergent wind anomalies together with upward motion in eastern tropical Pacific lead to the convergent wind anomalies and downward motion in western tropical Pacific (Figs. 5b, 6b), suppressing the local convective activities (Fig. 4b) and causing a meridional wave train like EAP pattern over East Asia (Huang and Sun 1992;Sun et al. 2019a, b), which favors the cyclonic wind anomalies in western North Pacific and the meridional tripole pattern of precipitation anomalies in eastern China as well ( Fig. 4b; Sun et al. 2019a, b).
Compared with those in positive PDO phase (Fig. 5a-c), the anomalous tropical upper-level velocity potential and zonal-vertical circulation during the developing and decaying stages of negative PDO phase and their differences are also almost reversed (Fig. 5d-f). However, because of the remarkably intensified SST cooling in central tropical Pacific from developing to decaying stages in negative PDO phase (Fig. 3f), the differences of local upper-level convergent wind and downward motion anomalies are greatly enhanced (Figs. 5f, 6f). As a result, it in turn induces more prominent upward motion and upper-level divergent wind anomalies in tropical Indian Ocean through the anomalous Pacific-Indian Ocean Walker circulation (Figs. 5f, 6f). On the other hand, the greatly suppressed convective activities in central tropical Pacific can trigger stronger low-level anticyclonic wind anomalies in the western North Pacific (Fig. 4f) as Rossby wave response according to the Matsuno-Gill theory (Gill 1980), which helps to generate a meridional dipole pattern of precipitation anomalies in eastern China ( Fig. 4f; Sun et al. 2010).
In addition, considering the similar significant SST anomalies in both tropical Pacific and western tropical Indian Ocean but opposite local vertical circulation anomalies, it can be deduced that the SST anomalies in tropical Indian Ocean are mainly determined by the PDO-related tropical Pacific SST anomalies because warm (cool) SST anomalies are corresponded to the downward (upward) vertical motion ( Fig. 6; Wang et al. 2005;Dong et al. 2016;Xue et al. 2022). Nevertheless, though the tropical Indian Ocean plays a passive role in the tropical atmospheric circulation anomalies in the process of PDO evolution, the convection anomalies above induced remotely by SST anomalies in tropical Pacific can also have important contributions to the low-level cyclonic or anticyclonic wind anomalies over the western North Pacific via Kelvin wave response according to the Matsuno-Gill theory (Gill 1980;Sun et al. 2010;Xie et al. 2016), which in turn help to cause interdecadal summer precipitation anomalies in eastern China (Fig. 4).

b Extratropical dynamical process
Different from the Matsuno-Gill response to the direct thermal forcing of SST anomalies in tropical regions, atmospheric response of baroclinic instability owing to the meridional SST gradients is dominant in mid-to-high latitudes (Fang and Yang 2016;Tao et al. 2020). During the developing stage of positive PDO phase, because of the negative SST anomalies in mid-latitude westerncentral North Pacific (Fig. 3a), meridional SST gradients are increased and decreased on their southern and northern edges, respectively, and in turn, the local low-level atmospheric baroclinicity strengthens and weakens in the central North Pacific accordingly, demonstrating a southward shift of baroclinicity position (Fig. 7a), which favors local more and less active transient eddies above. Whereas, in the western North Pacific including the Sea of Japan, the lowlevel atmospheric baroclinicity is greatly increased (Fig. 7a). The atmospheric transient eddies can redistribute heat and momentum in the middle to upper troposphere, effectively influencing the large-scale atmospheric circulations. And according to the transient eddy-mean flow interaction (Lau and Holopainen 1984;Fang and Yang 2016;Tao et al. 2020), intensified transient eddy activities tend to induce convergence of anomalous transient eddy vorticity fluxes, causing increased upper-level westerly wind anomaly, and vice versa. In particular, following the anomalous low-level atmospheric baroclinicity indicated by the eddy growth rate, positive westerly anomaly center is located in the Sea of Japan while negative center is located in the Sea of Okhotsk (Fig. 8a), which is highly corresponding to the significant negative geopotential height center at 200 hPa over the Northeast China and its surrounding areas (Fig. 8a), favoring much more precipitation in Northeast China (Fig. 4a). At  The black isoline of 26 m/s indicates the climatological westerly jet core the same time, an obvious zonal wave train originated from the eastern North Atlantic dominates the mid-high latitude Eurasian continent, which serves as an important extratropical dynamical pathway to affect the climate over East Asia (Fig. 9a).
During the decaying stage of positive PDO phase, the negative SST anomalies in the mid-latitude western North Pacific develop and expand southward, which encounter the growing SST warming in the subtropical western Pacific and form the dramatically enhanced meridional SST gradient over there (Fig. 3b). Accordingly, the low-level atmospheric baroclinicity is significantly increased to the south of its climatology, indicating the obviously southward shift of its position (Fig. 7b), so will be the associated transient eddy activities. Therefore, both the EASWJ (Fig. 8b) and the negative geopotential height center at 200 hPa ( Fig. 9b) are distinctly shifted southward compared to those during the developing stage of positive PDO phase (Figs. 8a, 9a). As a result, much more precipitation occurs in Yangtze River valley and less precipitation in North China ( Fig. 4b; Sun et al. 2019a, b). Such southward shifts of anomalous atmospheric circulations as well as low-level baroclinicity are more evident in the differences of decaying and developing stages (Figs. 7c, 8c and 9c), and they are all associated with the locally enhanced and southward shifted meridional SST gradient due to the fully developed "north cooling south warming" SST anomalies in subtropical western Pacific (Fig. 3c), greatly contributing to the increased precipitation anomalies in Yangtze River valley during the decaying stage of positive PDO phase (Fig. 4c). Moreover, different with those during the developing stage of positive PDO phase, the mid-high latitude wave train over Eurasian continent during the decaying stage is getting rather weaker (Fig. 9b, c). On the contrary, associated with the suppressed convection in the tropical western Pacific due to the enhanced tropical SST forcing (Figs. 3b,c,5b,c), a clear meridional wave train originated from the tropical western Pacific prevails over East Asia during the decaying stage of positive PDO phase (Fig. 9b, c).
Compared to those in positive PDO phase (Figs. 7a,b,8a,b,9a,b), the dynamical processes in mid-latitude North Pacific and anomalous atmospheric circulations are almost opposite for both developing and decaying stages in negative PDO phase (Figs. 7d,e,8d,e,9d,e), so are the differences between decaying and developing stages (Figs. 7c,f,8c,f,9c,f), which further confirms the important contributions of the extratropical dynamical process to the interdecadal summer precipitation anomalies in eastern China besides the tropical dynamical process.

Conclusions and discussions
As the most significant interdecadal signal in Pacific, PDO has been regarded as one of the important factors to explain the interdecadal variabilities of summer precipitation in eastern China (Zhu and Yang 2003b;Deng et al. 2009;Qian and Zhou 2014;Zhu et al. 2015;Si and Ding 2016;Zhang et al. 2018;Sun et al. 2019a, b;Chen and Zhang 2020;). However, recent studies noted that the SST anomalies and the interdecadal summer precipitation anomalies in eastern China cannot keep the constant pattern during the same positive or negative PDO phase (Zhu and Yang 2003a;Deng et al. 2009;Huang et al. 2011). One reason may be attributed to the joint influences of interdecadal SST anomalies in Pacific (PDO), Atlantic Ocean (Atlantic Multidecadal Oscillation, AMO) and Indian Ocean (Indian Ocean Basin Mode, IOBM) (Zhang et al. 2018), and another one may mainly rely on the evolution of PDO itself. By dividing the positive or negative PDO phase into developing and decaying stages, PDO impacts in the four evolutionary stages on interdecadal summer precipitation anomalies in eastern China are further investigated based on the corresponding composite analyses of SST, precipitation and atmospheric circulation anomalies. It is found that the PDO-related SST anomalies and their impacts in its positive or negative phase are always dominated by that during the decaying stage, which is due to both the tropical and extratropical dynamical processes in terms of the corresponding SST anomalies in tropical and mid-latitude North Pacific. The mechanism is summarized by a schematic diagram in Fig. 10.
During the developing and decaying stages of positive PDO phase, similar to those in positive PDO phase, there are significant negative SST anomalies in the mid-latitude western-central North Pacific and positive SST anomalies in off-equator central-eastern Pacific. However, compared to the developing stage of positive PDO phase, the decaying stage of positive PDO phase is mainly manifested as the strengthened and westward expanded cooling in midlatitude western North Pacific and the enhanced warming in northeastern tropical Pacific and western tropical Pacific. Wherein, the SST warming in northeastern tropical Pacific are mainly responsible for a larger-scale Walker circulation anomaly in the whole tropical region (Wang et al. 2000), which suppresses the convective activities in western tropical Pacific and in turn causes a meridional wave train like EAP pattern over East Asia (Fig. 10b; Huang and Sun 1992;Sun et al. 2019a, b). On the other hand, in the western North Pacific, a meridional dipole pattern of "north cooling south warming" significantly increases the meridional SST gradient and the low-level atmospheric baroclinicity as well, conductive to the intensified and southward shifted EASWJ and an equivalent barotropic structure of "cold trough" (Tao et al. 2020), which is demonstrated by the prominent low geopotential height and cyclonic wind anomalies over the North Pacific and its surrounding areas, especially in south of Japan. Therefore, during the decaying stage of positive PDO, the intensified SST anomalies in tropical and midlatitude North Pacific both favor the meridional tripole pattern of summer precipitation anomalies in eastern China through tropical and extratropical dynamical processes. The PDO impact and associated dynamical processes are generally linearly reversed during the decaying stage of negative PDO phase.
It should be noted that in response to the off-equator central-eastern Pacific warming in positive PDO phase, the anomalous local upward motion as well as Walker circulation anomaly in Pacific is much more significant during the decaying stage than that during the developing stage (Figs. 5a-c, 6a-c). The possible reason is that along with the evolvement of PDO in its positive phase, the major warming center in off-equator central-eastern Pacific is Fig. 10 Schematic diagram of how the SST anomalies influence the interdecadal summer precipitation anomalies in eastern China through tropical and extratropical dynamical processes during (a) the developing and (b) the decaying stages of positive PDO phase. The red (blue) shaded area represents the warm (cold) SST anomalies. The green (yellow) shaded area in eastern China indicates increased (decreased) precipitation. The purple shaded area indicates the lowlevel atmospheric baroclinicity, and the arrow above indicates the anomalous westerly wind. The black circles with arrowheads are the anomalous low-level atmospheric circulations. In (a), the solid and dash circles with symbols "A" and "C" represent the mid-high latitude wave train over the Eurasian continent in upper troposphere, and the green arrow indicates the wave energy propagation direction. In (b), the tropical vertical cross-section indicates the anomalous Walker circulation Fig. 11 a The climatological means of summer SST (units: C, shaded) and precipitation (contour are 6 and 10 mm/day) during the period of 1979-2020 and b the relationships of SST and precipitation in the two centers (NETP: northeastern tropical Pacific 150°W-110°W, 10°N-25°N; SETP: southeastern tropical Pacific 120°W-90°W, 30°S-0°) shifted from southern hemisphere to northern hemisphere (Fig. 3a-c), and according to the relationships of local SST and precipitation in the two warming centers, i.e., northeastern tropical Pacific (NETP) and southeastern tropical Pacific (SETP) (Fig. 11b), precipitation response to the SST forcing in NTEP is much more sensitive than that in STEP, which is mainly due to the climatically northward shifts of both ITCZ and warmer SST in summer ( Fig. 11a; Hoerling et al. 1997;Kang et al. 2002).
With the same method, we have also examined the PDO impact by dividing one cycle of PDO into eight evolutionary stages, and the results are basically consistent with those during the four evolutionary stages presented in this study. Nevertheless, the PDO impact is quite stage-dependent, and it is more reasonable to understand and predict the interdecadal summer precipitation anomalies in eastern China based on the four PDO evolutionary stages, rather than simply taking the positive and negative PDO phases as the forcing factors of interdecadal climate variabilities. In this regard, this study reconciles the inconsistent interdecadal summer precipitation anomalies during the same PDO phases noted by previous studies (Deng et al. 2009;Huang et al. 2011). Moreover, the modulation of different evolutionary stages of PDO on interannual variabilities can be further considered in future study.