J. Meteor. Res.  2017, Vol. 31 Issue (1): 61-72 PDF
http://dx.doi.org/10.1007/s13351-016-6046-6
The Chinese Meteorological Society
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#### Article Information

ZHAO Liang, WANG Jingsong, LIU Haiwen, XIAO Ziniu . 2017.
Amplification of the Solar Signal in the Summer Monsoon Rainband in China by Synergistic Actions of Different Dynamical Responses. 2017.
J. Meteor. Res., 31(1): 61-72
http://dx.doi.org/10.1007/s13351-016-6046-6

### Article History

in final form August 29, 2016
Amplification of the Solar Signal in the Summer Monsoon Rainband in China by Synergistic Actions of Different Dynamical Responses
Liang ZHAO1,2, Jingsong WANG3, Haiwen LIU4, Ziniu XIAO1
1. State Key Laboratory of Numerical Modeling for Atmosphere Sciences and GeophysicalFluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;
2. National Climate Center, China Meteorological Administration, Beijing 100081;
3. China National Center for Space Weather, Beijing 100081;
4. Department of Aviation Meteorology, Civil Aviation University of China, Tianjin 300300
ABSTRACT: A rainband meridional shift index (RMSI) is defined and used to statistically prove that the East Asian summer monsoon rainband is usually significantly more northward in the early summer of solar maximum years than that of solar minimum years. By applying continuous wavelet transform, cross wavelet transform, and wavelet coherence, it is found that throughout most of the 20th century, the significant decadal oscillations of sunspot number (SSN) and the RMSI are phase-locked and since the 1960s, the SSN has led the RMSI slightly by approximately 1.4 yr. Wind and Eliassen–Palm (EP) flux analysis shows that the decadal meridional oscillation of the June rainband likely re-sults from both a stronger or earlier onset of the tropical monsoon and poleward shift of the subtropical westerly jet in high-solar months of May and June. The dynamical responses of the lower tropical monsoon and the upper subtropical westerly jet to the 11-yr solar cycle transmit bottom-up and top-down solar signals, respectively, and the synergistic actions between the monsoon and the jet likely amplify the solar signal at the northern boundary of the monsoon to some extent.
Key words: solar cycle     rainband     East Asian summer monsoon     decadal variability     EP flux     precipitation
1 Introduction

From the third to the fifth assessment reports (AR5) of the Intergovernmental Panel on Climate Change (IPCC), the uncertainties in climate change projection and climate modeling have not been reduced despite extensive studies using proxy data, historical instrumental observations, and model simulations (Zhou and Chen, 2015). An apparent hiatus in the increase in global mean surface temperature during the past 15 years (1999–2013) adds to the uncertainty. AR5 (IPCC, 2013) states that the warming rate over the past 15 years is 0.05°C (10 yr)–1, which is much lower than the rate calculated since 1951 [0.12°C (10 yr)–1]. Furthermore, AR5 (IPCC, 2013) indicates that the hiatus in warming of the past 15 years may be attributable to some combination of climate inner variability, incorrect radiative forcing, and model response deviation. This suggests that on the decadal timescale, solar radiation forcing likely plays a non-negligible role in climate change. In fact, many studies have exhibited correlations between the sun and climate (e.g.,Hoyt and Schatten, 1997;Herman and Richard, 2005), although the relationship has long been controversial (Rind, 2002;Li et al., 2003;Lean, 2010;Wang et al., 2010).

Some significant decadal variations in rainfall in China have been found and studied (e.g.,Huang et al., 1999;Zhai et al., 1999,2005;Ding et al., 2007,2009), and the cause of the variation in rainbands in China is usually attributed to the variation in the land–sea thermal contrast, resulting in variation in the strength of the East Asian summer monsoon (EASM). However, the fundamental cause of the decadal variation in the EASM and the land–sea thermal contrast is not very clear, and little attention has been given to solar activity. A fingerprint of the sunspot cycle in rainfall or atmospheric patterns is considered possible, and the relationship is valuable to long-range predictions of rainfall and the detection and attribution of modern and past climate change (Bhattacharyya and Narasimha, 2007;Liu et al., 2014;Ratnam et al., 2014). Since Herschel (1801) investigated and found the relationship between sunspots and land surface rainfall, many scientists have attempted to find and explain the linkage between the sun and terrestrial climate (Zhao et al., 2011;Xiao et al., 2013). Some studies have found that the responses of the tropical monsoon and low-level jet and sea–air interaction to the 11-yr solar cycle cause the decadal variation in rainfall or other factors, which is associated with the so-called “bottom-up” mechanism (e.g.,van Loon et al., 2004;Meehl et al., 2008,2009;van Loon and Meehl, 2012). Other studies, associated with the “top-down” mechanism，show that upper-level temperature and zonal wind anomalies induced by ozone increase during peaks in the 11-yr solar cycle and can influence the tropospheric circulation and the monsoon through the propagation of planetary waves and dynamical coupling between the stratosphere and troposphere (e.g.,Haigh, 1994;Kodera and Shibata, 2006).

However, precisely how the small 11-yr solar cycle signal is amplified in the climate system is poorly understood. Moreover, the apparent regional differences in the climate response to the solar cycle seems to make the sun–climate issue even more complex. Although the significant response in the monsoon boundary indicated by Wang and Zhao (2012) and Zhao and Wang (2014) can help understand the cause of the different responses in monsoon and non-monsoon regions, it cannot explain how the small solar cycle signal is amplified or transmitted in or out of the monsoon system to modify the monsoon domain area. In the present study, through defining a standardized index of rainband position according to the regional response difference in precipitation, the relationship between the 11-yr solar cycle and June rainband variability in China is investigated and verified; and the earlier responses of the tropical monsoon and the subtropical westerly jet to the solar forcing in May are stu-died in an effort to discuss the propagation and amplification of the solar signals.

2 Data

To define the position of the rainband, two high-reso-lution gridded monthly global land surface precipitation datasets for the 20th century are used in this study. One is the updated CRU TS3.23 dataset, at a resolution of 0.5°, from 1901 to 2014, from the University of East Anglia Climatic Research Unit (CRU) (Harris et al., 2014). In addition to updating the dataset with 2014 data, some new stations have been added for precipitation in CRU TS3.23. The other is the Global Precipitation Climatology Centre (GPCC) full data reanalysis, version 7.0, at a resolution of 0.5°, which is used to compare with the CRU TS3.23 dataset so as to test the results. The GPCC data were generated by using the complete GPCC monthly rainfall station database covering the period from 1901 to 2013 (Schneider et al., 2015). The CRU and GPCC products are freely available from http://www.cru.uea.ac.uk/ and http://gpcc.dwd.de, respectively. Both of these two independent datasets are produced based on long-term in-situ rain-gauge observations and are long enough to study decadal and interdecadal precipitation variations during the past 100 years.

The relative sunspot number (SSN) data in this paper are from the Sunspot Index and Long-term Solar Observations (SILSO) data/images, Royal Observatory of Belgium, Brussels (http://sidc.oma.be/silso/datafiles).

Wind and temperature data are from the US National Oceanic and Atmospheric Administration-Cooperative Institute for Research in Environmental Sciences (NOAA-CIRES) 20th century reanalysis, version 2, from 1871 to 2012, with a 2.0° spatial resolution for 1000 to 10 hPa (Compo et al., 2011).

The ozone data are from the ERA 20th century (ERA-20C) product of the ECMWF (Poli et al., 2013). ERA-20C is a 10-member reanalysis of the 20th century (1899–2010), only assimilating surface pressure, mean sea level pressure, and marine wind observations from the International Surface Pressure Databank and the International Comprehensive Ocean–Atmosphere Dataset. Its atmospheric data are available on the native 91 model levels and 37 pressure levels (as in ERA-Interim).

3 Quantification of rainband meridional shift

To test for possible connections between the sunspot cycle and rainfall during the EASM onset, a good approach is to select two kinds of maximum and minimum SSN years (denoted as MAX and MIN, respectively), thus allowing the difference to be as obvious as possible. Thus, according to MAX and MIN in the solar cycles from 1901 to 2014, we choose 11 MAX and MIN samples, respectively, in the composite analysis.

It is found that the climatological-mean East Asian Meiyu season (22 May–13 July) is the period with the strongest response to the 11-yr solar cycle (Zhao and Wang, 2014), which includes June. As shown in Fig. 1a, in June, there is a remarkable difference in rainfall in MAX and MIN over the monsoon regions of China. Both the positive difference and correlations are mainly located over the Huaihe River basin (HRB) (correlation:r = 0.33), and both the negative difference and correlations are mainly located in the south of the mid–lower reaches of Yangtze River basin (MLRYRB) (correlation:r = –0.30). The result suggests a possible difference in the EASM monsoon onset and evolution in MAX and MIN. Thus, June precipitation in the HRB (31°–34°N, 105°–122°E) and the MLRYRB (26°–29°N, 105°–122°E) (denoted by the two rectangles in Fig. 1a) are chosen to be studied.

In order to examine the relationship between the summer monsoon rainband in China and the SSN, it is necessary to quantitatively depict the extent of the shift in the rainband by defining an index. In the present paper, the difference in precipitation between the HRB and the MLRYRB is used for this purpose, and its standardized time series is defined as the rainband meridional shift index (RMSI):

 ${\rm{RMSI}} = {\rm st\;\!\!d}\left( {{R_{{\rm{HRB}}}} - {R_{{\rm{YRB}}}}} \right),$

where R is regional mean precipitation, and std is stan-dardization. For sample data with a mean $\overline x$ and standard deviation s, the standardization of a value x is $\frac{{x - \overline x }}{s}$ . If RMSI in a period is bigger (smaller) than 1 (–1), the precipitation in the HRB is obviously more (less) than that in the MLRYRB in the period, which indicates that the rainband has shifted northward (southward).

Figure 1b shows two time series of the June RMSI of China by using the CRU TS3.23 and GPCC datasets. The correlation between the two RMSI time series is 0.93. Therefore, the indication is that the influence resulting from the datasets should be minor.Figure 1c shows the correlation coefficients between the RMSI (calculated by using the CRU dataset—the same below) and June precipitation in China. It is found that the Yangtze River is an important divide, which also indicates that the RMSI index can clearly reflect the meridional variation of the rainband.

 Fig. 1 (a) Difference (contours) between composites of June precipi-tation in MAX and MIN and significant correlations (color shading) between the June SSN and precipitation in China during 1901–2014. The rectangles outline the HRB and MLRYRB, respectively. The Monte Carlo approach is used in the significance tests. The interval of the contours is 20 mm month–1, and positive and negative differences are represented by solid and dashed contours, respectively. (b) Time series of the June RMSI of China using the CRU TS3.23 (blue) and GPCC (red) datasets. (c) Significant correlation coefficients between the June RMSI and precipitation in China.
4 Verification of the shift in the rainband modulated by the sunspot period 4.1 Evidence for a significant difference in rainband position between MAX and MIN

Raw data contain signals of various timescales, so the prominent periods of precipitation and the sun are likely to be different. This asymmetry means that it is easy for the 11-yr solar-cycle signals in precipitation to be inundated by high-frequency signals that probably originate from earth, not the sun. Thus, it is difficult to obtain a credible relationship between the 11-yr solar cycle and precipitation through use of raw data. Therefore, to remove the influence of the higher-frequency components [e.g., ENSO, with a different period (< 8 yr) from that of the sun], the signals in precipitation with periods of less than 8 yr are filtered out using a fast Fourier transform. The correlations between the annual SSN and raw or filtered monthly (annual) precipitation or RMSI are listed in Tables 13. Due to different degrees of freedom between filtered and unfiltered time series, the Monte Carlo approach is applied to test the statistical signifi-cance more vigorously (Zhao et al., 2012). The results demonstrate that most of the maximum values of correlation coefficients occur in June at the confidence level greater than 90%; after low-pass filtering, the correlations mostly increase. The correlation in June is the highest among all summer half-year months, at the 95% confidence level. The correlation between the filtered RMSI and SSN in June even reaches 0.45 at the 98% confidence level.

Table 1 Correlation coefficients between the SSN and precipitation over 31°–34°N, 105°–122°E for 1901–2014
 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Whole year Raw 0.21 –0.01 0.13 –0.07 –0.01 0.22 0.03 0.12 0.12 –0.08 0.05 0.09 0.16 Filtered 0.33 0.01 0.29 –0.17 –0.14 0.33 0.03 0.17 0.14 –0.10 0.08 0.15 0.28 Note: 0.16 and 0.31 denote the 90% confidence level for 112 unfiltered and 8-yr low-pass filtered samples, respectively; SSN, sunspot number.
Table 2 Correlation coefficients between the SSN and precipitation over 26°–29°N, 105°–122°E for 1901–2014
 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Whole year Raw 0.19 0.14 0.21 –0.01 0.15 –0.19 –0.12 0.06 0.01 –0.14 –0.09 –0.09 –0.01 Filtered 0.37 0.31 0.34 0.01 0.25 –0.32 –0.23 0.04 –0.04 –0.24 –0.16 –0.20 –0.02 Note: 0.16 and 0.31 denote the 90% confidence level for 112 unfiltered and 8-yr low-pass filtered samples, respectively.
Table 3 Correlation coefficients between the SSN and RMSI for 1901–2014
 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Whole year Raw –0.10 –0.15 –0.14 0.03 –0.14 0.25 0.08 0.05 0.09 0.07 0.14 0.17 0.12 Filtered –0.26 –0.28 –0.21 –0.13 –0.28 0.45 0.17 0.12 0.16 0.16 0.27 0.32 0.22 Note: 0.16 and 0.31 denote the 90% confidence level for 112 unfiltered and 8-yr low-pass filtered samples, respectively.

Besides, from the polar coordinate plots of filtered monthly precipitation in the HRB and MLRYRB and the RMSI in MAX and MIN (Fig. 2), it is clearly apparent that there are different patterns in precipitation in both the two regions between MAX and MIN, and the difference in June is maximum. The averaged June precipitation in the HRB (MLRYRB) in MAX and MIN is 141 (229 ) mm and 117 (253) mm, respectively, with the value in MAX being 21% (10%) higher (lower) than that in MIN. Using the Student's t-test for the difference between MAX and MIN, the p-values are 0.05–0.10. For the RMSI, the mean values for June in MAX and MIN are –1.02 and –1.80, respectively, with a significant difference (p < 0.01), which testifies that the position of the June rainband in MAX is significantly different from that in MIN.

 Fig. 2 Composite polar coordinate plots of 8-yr low-pass filtered monthly (a) HRB and (b) MLRYRB precipitation, and (c) RMSI, using 11-yr data in MAX (red) and MIN (blue), respectively. The radius denotes the value. One circle denotes one year due to one month per 30 degrees.
4.2 Evidence for solar-cycle signals in monsoon rainband variation

Wavelet analysis is a tool for analyzing localized variations of power within a time series. It decomposes a time series into time-frequency space. Both the domi-nant modes of variability and how those modes vary in time can be determined (Torrence and Compo, 1998). When using wavelets for feature extraction, Morlet's wavelet is a suitable choice because it provides a good balance between time and frequency localization (Grinsted et al., 2004). If a vertical slice through a wavelet plot is a measure of the local wavelet spectrum, the average over all the local wavelet spectra is called the global wavelet spectrum (Torrence and Compo, 1998).Figure 3 shows the time series and the global wavelet power spectra of the RMSI before and after filtering. The evolution of the RMSI is coincident with that of the SSN, with correlation coefficients of 0.25 and 0.45 before and after filtering, respectively (Figs. 3a and 3c). The Monte Carlo test shows that the two correlations (0.25 and 0.45) are both significant at the greater than 99.9% confidence level, suggesting that a solar cycle signal in the RMSI is likely. As shown in Fig. 3b, before filtering, the peaks of the global wavelet spectrum of the RMSI appear approxi-mately at 3, 5, 11, and 28 yr, but only the 3- and 5-yr peaks are at a confidence level greater than 95%. However, after filtering, the global wavelet spectra of the residual show a quasi-11-yr period (Fig. 3d). Therefore, these results preliminarily indicate that, during EASM onset, the movement of the position of the rainband has a quasi-11-yr period, similar to that of SSN.

 Fig. 3 (a, c) Standardized time series of the SSN and RMSI in June for 1901–2014 and (b, d) their global wavelet spectra using Morlet's wavelet as the mother wavelet: (a, b) raw RMSI and (c, d) 8-yr low-pass filtered RMSI. The test lines at the 95% confidence level are plotted in (b, d).
 Fig. 4 The (a) continuous wavelet transforms, (b) cross wavelet transform, and (c) wavelet coherence of the SSN and RMSI in June (with in-phase pointing right, anti-phase pointing left, and the SSN leading the RMSI by 90° pointing straight down).

If the position of the rainband is physically related with the sunspot cycle, their common power and a consistent or small phase lag should be detectable. Herein, the continuous wavelet transform (CWT), cross wavelet transform (XWT), and wavelet coherence (WTC) are used to detect the possible physical connections. The CWT is a common tool for analyzing localized intermittent oscillations in a time series. The XWT of two time series X and Y, with CWTs WX and WY, is defined as WXY=WXWY*, where* denotes complex conjugation (Torrence and Compo, 1998). The XWT constructed from two CWTs will demonstrate their common power and relative phase shift. The WTC of two time series is defined as the absolute value squared of the smoothed XWT, normalized by the smoothed wavelet power spectra (Torrence and Webster, 1998). The WTC, which can be thought of as the local correlation between two CWTs, will reveal any locally phase-locked oscillation (Torrence and Compo, 1998;Grinsted, 2004).

The CWTs of the SSN and RMSI are shown in Fig. 4a. The significant wavelet power of the SSN is concentrated near the 11-yr band. Those of the RMSI appear in different positions, such as the 9–13-yr band for the sunspot cycle around the 1930s and 1960s, an approximate 5-yr band for ENSO around the 1950s and 1970s, and an approximate 30-yr band from the 1950s to 1960s, which seems to hint that the RMSI is primarily dominated by the sunspot cycle and ENSO, alternately. However, the similarity of them in the 11-yr band between the SSN and RMSI is so low that it is hard to tell if the relationship between the SSN and RMSI in June is merely a coincidence.

The XWT and WTC can help us further test and capture the physical correlation between them. The XWT of the SSN and RMSI is shown in Fig. 4b. Here, it is noticeable that there is significant continuous common power, especially in the approximate 9–13-yr band, suggesting that, in the 20th century, the decadal oscillations of the SSN and RMSI are generally phase-locked. It is also apparent from the relative phase relationship shown as vector arrows, that in the sectors with significant common power, the SSN has been in-phase with the RMSI or slightly led it by about 1.4 yr (i.e., approximately one-eighth of the 11-yr cycle), since the 1960s. This result is relatively consistent with historical records; that is, flooding often occurs in the current year or two subsequent years of MAX (MIN) in the HRB (MLRYRB), e.g., 1991 in the HRB and 1998 in the MLRYRB. In the areas of the greater than 13-yr band of Fig. 4b, the SSN is also predominantly in-phase with the RMSI or leads it slightly. The significant area near the 11-yr band of Fig. 4b is so large that this is unlikely to be by chance. Thus, it can be speculated that there is a physical link between the SSN and the RMSI. The WTC of the SSN and RMSI is displayed in Fig. 4c. Compared with the XWT, the sections not only near the 11-yr band, but also near the 30-yr band, stand out as being significant and show that the SSN is in-phase with the RMSI or somewhat ahead of it.

Therefore, on the decadal timescale, the meridional variation in the June rainband position in the HRB and MLRYRB of China, usually as a response to variation in regional climate systems, is very likely influenced by solar activity, which magnifies or diminishes the role of the EASM or other climate factors.

5 Discussion 5.1 Possible mechanisms and paths for the solar influence on the monsoon rainband in China

A key question is: why does the close relationship between solar variability and regional precipitation appear in early summer? Monsoon onset in early summer, providing warm and wet air, is likely an important factor. The variation in the westerlies providing cold and dry air may also play a crucial role. All the above evidence is based on statistics, which in itself cannot prove that there is a physical connection between the monsoon rainband and solar cycle. The solar signal near the summer monsoon boundary needs to be supported by the earlier dynamical variation in atmospheric circulation, including the monsoon and the westerlies on the decadal timescale. Since the period with the strongest response of the rainband to the 11-yr solar cycle begins from late May (Zhao and Wang, 2014), the upstream solar signal should appear in May or earlier.Figure 5 shows the correlation coefficients between the May SSN or the June RMSI and the June 850-hPa wind field for 1901–2012. We find that the distribution of the correlation coefficients between the May SSN and the June zonal wind (U) is similar to that between the June RMSI and U. Westerly anomalies (positive correlations) over tropical regions and 30°–35°N in China suggest a larger domain of influence in high-solar months of June than those in low-solar months of June, which is inclined to cause rain in the HRB in high-solar months of June. The westerly anomalies at 30°N and easterly anomalies (negative correlations) at 20°N constitute an anticyclonic anomaly, which suggests the western Pacific subtropical high (WPSH) is stronger over southern China and is not conducive to rain in southern China (e.g., the MLRYRB). Although the significant correlation area with the SSN (Fig. 5a) is smaller than that with the RMSI (Fig. 5b), there is always a steady north–south seesaw of correlation coefficients in the June U between 30° and 20°N in East Asia, and the strongest correlation is over the tropical ocean, which suggests that the solar signal in the lower troposphere likely propagates from the tropics to the subtro-pics. For the 850-hPa meridional wind (V), although there are some differences between Figs. 5c and 5d, the significant positive correlations over 30°N and the tropical Indian Ocean signify a stronger monsoonal flow in these regions in high-solar months of June, favoring precipitation in the more northern regions. Therefore, the low-level circulation field basically supports the decadal meridional oscillation of the monsoon rainband synchroni-zing the 11-yr solar cycle.

 Fig. 5 Correlation coefficients between the (a, c) May SSN or (b, d) June RMSI of China and (a, b) zonal (U) and (c, d) meridional (V) 850-hPa wind at each grid point in June for 1901–2012. Absolute values more than 0.16 (> 90% confidence level) are shown in shaded areas according to the legend.

To further investigate the upstream signals associated with the low-level circulation pattern resulting in the decadal variation in the monsoon rainband, we analyze the correlations between U, temperature (T) or ozone (O3) variation, and the SSN or RMSI in the troposphere and stratosphere in East Asia (Fig. 6).Figure 6 shows that the correlation pattern between the SSN and U below 100 hPa is roughly similar to that between RMSI and U, which is a “+ – +” distribution and leans poleward. We call the correlation pattern associated with the SSN and RMSI the “SR teleconnection”. Besides, only near the East Asian westerly jet (EAWJ) are the SSN-T and RMSI-T correlations consistent, as are the SSN-O3 and RMSI-O3 correlations. In the tropics, they are inconsistent. This result suggests that in the troposphere and lower stratosphere, atmospheric dynamic, thermodynamic, and photochemical changes related to the solar cycle and the monsoon rainband are consistent or similar, and the region near the EAWJ is a likely key region. That is, the meridional SR teleconnection with positive and negative correlations in the north and south, respectively, of the climatological EAWJ, is likely modulated by the 11-yr solar cycle and associated with a poleward shift of the EAWJ in high-solar June. Under this zonal wind ano-maly background, the WPSH can easily control southern China and the monsoonal flow can transport more to the north.

 Fig. 6 Latitude–pressure vertical cross-sections of significant correlation coefficients between the June (a) SSN or (b) RMSI and zonal wind (U; color shading), temperature (T; black contours) for 1901–2012 or ozone (O3; green contours) for 1901–2010 along 115°E, respectively. Areas where the absolute values for U are more than 0.19 and 0.16 (> 95% and > 90% confidence levels) are shown by the color shading according to the legend. The contours (correlation:r = 0.19) for T and O3 are shown. The pink contours (labelled “JET”) are the 25-m s–1 mean zonal wind velocity in June, representing the EAWJ.

The above results confirm that the SR atmospheric meridional teleconnection related with the 11-yr solar cycle is directly responsible for the decadal variation of the RMSI. However, it is important to establish how the SR teleconnection pattern forms and whether the “top-down” mechanism, “bottom-up” mechanism, or both, work. In Fig. 6a, a very strong positive correlation in the midlatitude stratosphere extends downward and toward the north of the EAWJ, but in Fig. 6b, only a very weak significant positive correlation appears near the tropopause in the north of the EAWJ. This difference suggests that the solar influence related with the SR teleconnection at least partly originates from the stratosphere and that the “top-down” mechanism works.

In order to further verify this point, an index represen-ting the SR teleconnection, which is the meridional synergetic variation pattern in U near the tropopause, is defined by the 200-hPa U at 15°, 30°, and 45°N along 115°E:

 ${\rm{SRI}} = \left( {{U_{15^\circ {\rm{N}}}} - {U_{30^\circ {\rm{N}}}} + {U_{45^\circ {\rm{N}}}}} \right)/3.$

Then, a lower-level southerly area index (GNS;Wang and Zhao, 2012) in East Asia is used, indicating the EASM area to a certain extent. A large GNS signifies a large monsoon area, which easily results in a northward shift of the rainband. A high correlation between the SRI and GNS (r = 0.54) for 1901–2012 suggests a relationship between atmospheric variation near the tropopause and the lower-tropospheric monsoonal flow. Moreover, the monsoon area can significantly influence the monsoon rainband (GNS-RMSI correlation: 0.22). This re-sult further suggests that the “top-down” mechanism likely works. The possible pathway is SSN→SR and EAWJ→GNS (EASM area)→RMSI.

On the other hand, since the solar signals in the rainband (RMSI), EASM area (GNS), and the SR teleconnection appear in June when the monsoon has usually just begun, it is logical to investigate whether a “bottom-up” mechanism, including the response and influence of Asian monsoon onset and SST, also plays an important role in the relationship between the sun and the rainband. To detect the likely intermediate factors originating from the surface or low levels, a WPSH area index (WPSHI;Xu and Yang, 1993) and a South Asian monsoon index (SAMI;Li and Zeng, 2002) are employed. The WPSHI is the sum of grid points exceeding 5880 gpm at 500 hPa across 10°–90°N, 110°E–180°. The SAMI is defined as an area-averaged dynamical normalized seasonality at 850 hPa within the South Asian domain (5°–22.5°N, 35°–97.5°E).

Figures 7a and 7b show the correlation coefficients between the SSN or RMSI, respectively, and SST in June in the western North Pacific and the north Indian Ocean. The common significant correlation appears over the southeast of Japan, which is usually located to the north of the WPSH. Therefore, a key SST index (KT) is defined as the area-averaged SST over the key region (25°–35°N, 150°–170°E) in the present study. The correlation between the KT and SRI is insignificant (r = 0.14,p = 0.12) for 1901–2012, which suggests that if the solar signal in the SST can modulate the monsoon rainband, the medium of the influence is likely not the upper-level SR teleconnection and the EAWJ. That is, the “bottom-up” and “top-down” mechanisms likely work independently before the solar signals in the two mecha-nisms transmit the north boundary of the EASM, respec-tively. According to a correlation analysis (Table 4), significant positive correlation exists between the KT and the WPSHI, GNS, or SAMI. In fact, this result implies that the KT is closely related to the Asian summer monsoon system. This is because in nature, the WPSHI, GNS, and SAMI all reflect variations in the Asian summer monsoon system. Herein, the WPSHI and GNS reflect the boundary and area variations in the WPSH and the EASM, respectively. Significant positive correlations also exist between the WPSHI and the GNS, and between the GNS and the SAMI or RMSI. These significant correlations suggest the response of the area or the north boundary of the EASM, i.e., the variation in the GNS, to solar forcing signals in the WPSH, can further influence the monsoon rainband (RMSI). Therefore, a possible “bottom-up” mechanism can be deduced; that is, SSN→key SST→WPSH→GNS (EASM area)→RMSI. In the mechanism, the response of the key SST and the relevant local climate systems (the Asian summer monsoon and the WPSH), and the transmission between them, play a crucial role in the meridional shift of the summer monsoon rainband.

 Fig. 7 As in Figs. 5a and 5b, but for SST.
Table 4 Correlation coefficients between the SSN, RMSI, and various atmospheric or sea indices in June
 SSN RMSI SRI GNS KT WPSHI SAMI 1901–2015 1901–2014 1901–2012 1901–2012 1901–2016 1901–2012 1948–2015 SSN 1 0.25*** 0.24** 0.14 0.25** 0.17* 0.06 RMSI 0.25*** 1 0.35*** 0.22** 0.19** –0.05 0.40*** SRI 0.24** 0.35*** 1 0.54*** 0.14 –0.01 0.03 GNS 0.14 0.22** 0.54*** 1 0.21** 0.22** 0.31*** KT 0.25** 0.19** 0.14 0.21** 1 0.34*** 0.23** WPSHI 0.17* –0.05 –0.01 0.22** 0.34** 1 –0.15 SAMI 0.06 0.40*** 0.03 0.31*** 0.23** –0.15 1 Note: *, **, and *** indicate the 90%, 95%, and 99.9% confidence levels, respectively; the time span is indicated below the name of each index; a common time span of two time series is selected to calculate the correlation coefficient between them.
5.2 Early solar signal and amplified dynamical response via synergistic action

The north–south seesaw of the June U anomalies in Figs. 5a and 5b over 30°N of the Yangtze River, and 20°N of southern China, actually reflects a variation in the WPSH; and the V anomaly over the tropical Indian ocean and the Yangtze River reflects a variation in monsoonal flow. The question now is: How do the wind ano-malies form? A north–south seesaw of convective acti-vity is also found over the Indian region during July and August, likely originating from the solar influence on the stratosphere (Kodera, 2004). In the present study, in order to further investigate the cause and earlier signal of the north–south seesaw of the June U anomalies (increase in the tropics and 30°N and decrease in southern China in high-solar months of June), correlation coefficients between the May SSN or June RMSI and the Eliassen–Palm (EP) flux and the EP-flux divergence in May or zonal wind tendency (ΔUJ–M, i.e.,U difference between June and May) are calculated (Fig. 8).Figure 8 shows that the two correlation fields with the May SSN and the June RMSI are very similar, suggesting that on the decadal timescale, solar activity is likely the major factor modulating the variation in the early-summer rainband in China. Positive correlation between the May SSN or the June RMSI and zonal wind tendency ΔUJ–M mainly exists near 30°N and to the north and beneath the EAWJ, and negative correlation exists to the south of 30°N and the westerly jet. These significant correlation regions with ΔUJ–M extend downward and equatorward to the lower troposphere across the monsoon boundary with the 0-m s–1 contour of southerly velocity. This suggests that in high-solar early summer, the westerly acce-leration in the area north of 30°N is greater than that in the south, and the EAWJ and the monsoon boundary in China are located more to the north. Further analysis using the EP flux shows a connection between the characteristics of the westerly acceleration from May to June and the divergence of the EP flux in May. In May, posi-tive correlation (corresponding to divergence) for the EP-flux divergence in the lower troposphere near 10°–15°N favors a westerly acceleration, suggesting a stronger or earlier onset of the tropical southwesterly monsoon (e.g., the monsoon over the South China Sea and Indochina Peninsula) in high-solar months of May than that in low-solar months of May. The other two divergence regions with positive correlation in May near 30°N and to the north of the EAWJ, respectively, favor an enhancement in the southwesterly monsoonal flow and a northward shift of the EAWJ from May to June, causing more precipitation in the HRB. Note that the divergent EP flux beneath the EAWJ transports equatorward and converges with the poleward EP flux originating from the tropical monsoon region near 20°N, causing a deceleration of southwesterly flow and less precipitation over southern China. This actually induces a cyclonic and anticyclonic zonal wind tendency to the south and north of 20°N, respectively, which is consistent with Kodera and Shibata (2006).

Therefore, in high-solar months of May, the stronger tropical monsoon or the earlier onset of the tropical monsoon and the more northward EAWJ together lead a convergence of the EP flux over southern China and a weakening and an enhancing of the southwesterly monsoonal flow in the areas south and north of 30°N, respectively. Note that the “bottom-up” dynamic response in the lower tropical monsoon to high-solar activity couples with the “top-down” dynamic response in the upper subtropical jet. Moreover, the joint role of the two mechanisms enhances the convergence of the EP flux over southern China. Therefore, these synergistic actions likely amplify solar signals in the EASM boundary region.

 Fig. 8 Latitude–pressure vertical cross-sections of correlation coefficients between the (a) May SSN or (b) June RMSI of China and the May EP flux (vectors) and May EP-flux divergence (color shading) or zonal wind tendency (ΔUJ–M; contours) along 115°E, respectively, for 1901–2012. Absolute values more than 0.19 and 0.16 (> 95% and > 90% confidence levels) are shown by deep and light coloring for EP-flux divergence or thick and thin contours for ΔUJ–M. Pink contours (labelled “JET”) are the 25-m s–1 mean zonal wind velocity in May (outer) and June (inner), respectively, representing the subtropical westerly jet, i.e., the EAWJ. The thick purple curves denote the 0-m s–1 meridional wind in June, representing the northern boundary of the EASM. Norms of vectors for correlation between the SSN and May EP flux greater than 0.3 are shown.
6 Conclusions

The present paper studies the relationship between the 11-yr solar cycle and the EASM rainband during the past 11 solar cycles and the dynamic mechanism of the decadal meridional oscillation of the rainband. The conclusions can be summarized as follows.

(1) It is statistically proven that the rainband is usually positioned more northward during early summer in MAX than in MIN. The low-frequency (> 8 yr) evolution of the rainband is markedly coincident with that of the SSN (correlation: 0.45). It is found that throughout most of the 20th century, the decadal oscillations of the SSN and the June RMSI in China are phase-locked, and since the 1960s, the SSN has led the RMSI slightly, by approximately 1.4 yr.

(2) The low-level wind field, with a north–south seesaw of the zonal wind anomaly, supports the decadal meridional oscillation of the monsoon rainband. A stronger monsoon and larger domain of influence in high-solar months of June than those in low-solar months of June favor the northward shift of the monsoon rainband.

(3) During the monsoon onset period in high-solar months of May, before the monsoon rainband response period (usually in June) to the solar cycle, the stronger lower tropical monsoon or earlier onset of the tropical monsoon and the more northward upper subtropical westerly jet together lead a convergence of the EP flux over southern China and a weakening and enhancing of the southwesterly monsoonal flow in the south and north of 30°N, respectively. The “bottom-up” dynamic response in the lower tropospheric tropical monsoon to high-solar activity and the “top-down” dynamic response in the upper tropospheric subtropical jet can together influence subtropical southern China. It is likely that the “bottom-up” mechanism or the “top-down” mechanism cannot cause alone such strong convergence of the EP flux over southern China. Therefore, their sy-nergistic actions likely amplify the solar signals in the monsoon boundary region.

(4) Further analysis shows that the possible pathway for the “top-down” mechanism is SSN→SR and EAWJ→GNS (EASM area)→RMSI. The SR atmospheric meridional teleconnection related to atmospheric dynamic, thermodynamic, and photochemical changes in the stratosphere and the troposphere, is modulated by the solar cycle and can influence the monsoon area, and is thus partly responsible for the decadal variation of the RMSI. A possible “bottom-up” mechanism also works; that is, SSN→key SST in the western North Pacific→WPSH→GNS (EASM area)→RMSI. In this mechanism, the solar signal in the key SST may influence the WPSH and transmit to the Asian summer monsoon.

Acknowledgments . We are grateful to the reviewers for their valuable comments and suggestions, and to the editors for helping us to improve this paper. We thank the CRU of the University of East Anglia and the GPCC for the precipitation datasets, SILSO for the SSN data, NCEP–NCAR for the wind and temperature data, and ECMWF for the ozone data. We also thank C. Torrence and G. Compo (http://paos.colorado.edu/research/wavelets), and A. Grinsted et al. (http://www.pol.ac.uk/home/ research/waveletcoherence) for wavelet analysis softwares.

References