1. Introduction
The South Asia high (SAH), sometimes called the Tibetan high, is the strongest high pressure system in the upper troposphere (e.g., 200 hPa) during the boreal summer season, covering the entire Eastern Hemisphere from North Africa to the date line in the subtropics (Mason and Anderson 1963; Tao and Zhu 1964; Qian et al. 2002; Webster 2006). As a prominent circulation system of the Asian summer monsoon, it has been found that its formation and activity are closely associated with the weather and climate in China and surrounding regions since the 1960s (Tao and Zhu 1964; Yeh et al. 1979; Tao and Ding 1981; Zhang et al. 2005; Wang et al. 2008; Liu et al. 2012; G. Wu et al. 2015). The SAH extends eastward over the western North Pacific, the most active basin on earth for tropical cyclone activity (Gray 1968; Wu and Wang 2008). The high is also juxtaposed with the tropical upper tropospheric trough (TUTT) to its east (Sadler 1976). The strong westerly vertical wind shear associated with the TUTT generally limits the eastward extension of the tropical cyclone activity in the western North Pacific basin (Kelley and Mock 1982; Fitzpatrick et al. 1995; L. Wu et al. 2015). Zhang et al. (2005) found that the stronger SAH was correlated with the weaker TUTT on the interannual time scale. Therefore, the climate change in the SAH has profound implications for tropical cyclone activity over the western North Pacific, as well as Asian weather and climate (e.g., Liu et al. 2013; Choi et al. 2016).
Many studies have suggested that the formation of the SAH is due to the strong summertime continental heating, mainly in the form of surface sensible heat flux and the latent heat release in connection with the Asian monsoon (Flohn 1957, 1960; Mason and Anderson 1963; Tao and Zhu 1964; Luo et al. 1982; Zhang et al. 2002; Wu and Liu 2003; Liu et al. 2004; Zhang et al. 2016; Wu et al. 2016). It has long been recognized that the Tibetan Plateau acts as an elevated heat source in summer (Flohn 1957; Yeh et al. 1957; Yanai et al. 1992). The atmospheric response to the heat source generates the cyclonic and anticyclonic circulation in the lower and upper troposphere, respectively. The formation of the summertime SAH can be understood as a result of the air pump driven by the sensible heat flux associated with the Tibetan Plateau (Wu et al. 2007; G. Wu et al. 2015). It is argued that the summertime SAH becomes the strongest circulation system in the upper troposphere due to the thermal forcing of the Tibetan Plateau and the Eurasia continent, as well as the effect of the strong latent heat release associated with the eastern Asian summer monsoon (Wu et al. 1999; Liu et al. 1999, 2001). It is clear that changes in the thermal status of the Tibetan Plateau can affect the activity of the SAH.
Increasing evidence indicates that the Tibetan Plateau is warming faster than the rest of the world (e.g., Liu and Chen 2000; Duan et al. 2006; Wang et al. 2008; Liu et al. 2012; Duan et al. 2015). As a direct result of the amplified warming over the plateau, most of the glaciers have retreated (Qiu 2008; Duan et al. 2006). Wang et al. (2008) conducted numerical experiments to understand the influence of the Tibetan Plateau warming on precipitation changes in the East Asia. In their experiments, the Tibetan Plateau warming was realized by reducing the surface albedo in the ECHAM4 climate model. Wang et al. (2008) found that the plateau warming can enhance the East Asian subtropical frontal rainfall, which is consistent with observations (Gong and Ho 2002; Hu et al. 2003; Wang et al. 2008; Zhang et al. 2013; Song et al. 2014).
On the other hand, it is argued that the amplified warming in the Tibetan Plateau does not enhance its thermal forcing. Duan and Wu (2008) and Liu et al. (2012) found a weakening trend in the thermal forcing of the Tibetan Plateau, which was characterized by decreased sensible heat flux in spring and summer over the last four decades. The reduced surface sensible heat flux results mainly from the faster weakening trend of surface wind speed than the plateau warming trend in magnitude, which may be associated with the ongoing global warming (Duan and Wu 2009). Liu et al. (2012) noticed that the plateau warming led to a strengthening of the subtropical high over the western North Pacific and an intensified southwesterly monsoon flow to the northwest of the subtropical high (Wang et al. 2008). Recent analysis indicates that little change has occurred to the intensity of the subtropical high since the late 1970s (Wu and Wang 2015; Huang et al. 2015). The southwesterly monsoon flow has actually weakened over the past several decades (Wang 2001; Xu et al. 2006; Ding et al. 2008; Zhou et al. 2009; Li et al. 2010). Liu et al. (2012) also conducted numerical experiments to understand the influence of the reduced thermal forcing over the Tibetan Plateau. Consistent with the air-pump theory (Wu et al. 2007), numerical results suggest a weakening of the SAH (G. Wu et al. 2015). Therefore, whether the SAH intensity has changed in the background of global warming is still an open question.
The climate change of the SAH intensity has been examined using the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis (NCEP-1; Kalnay et al. 1996), the NCEP–DOE AMIP-II reanalysis (NCEP-2), and the 40-yr European Center for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Uppala et al. 2005). Fu and Li (2012) found that the three reanalysis datasets underestimated the SAH intensity after comparing the reanalysis datasets with the observations based on stations within mainland China. Xue et al. (2015) also found considerable differences in the SAH intensity between NCEP-1 and ERA-40. Based on the radiosonde data at six stations in the SAH area, Xue et al. (2015) argued that the SAH has intensified since the mid-1980s. This is inconsistent with the influence of the weakening thermal forcing in the Tibetan Plateau (Duan and Wu 2008; Liu et al. 2012).
The modern reanalysis datasets have been produced not only with new model systems or updates to older systems but also with more observational and satellite data assimilated. It is meaningful to use the newest generation of reanalysis products to examine the climate change of the SAH intensity by focusing on the possible response of the SAH to the thermal condition changes in the Tibetan Plateau. Compared to the previous studies (Fu and Li 2012; Xue et al. 2015), the changes of the thermal conditions over the Tibetan Plateau in the modern reanalysis datasets are examined with the available station observations in this study. In addition, the global rise of pressure levels is considered in our analysis, because many studies indicated that the tropopause height and pressure levels have been elevated over the past several decades due to global warming (Highwood and Hoskins 1998; Randel et al. 2000; Seidel et al. 2001; Santer et al. 2003a,b; Wu and Wang 2015; He and Hu 2015).
2. Data and evaluation
The station observations are the monthly mean temperature from the National Climate Center of the China Meteorological Administration (CMA) to represent the observed state of the Tibetan Plateau. Figure 1 shows the locations of the 2-m air temperature at 123 stations with continuous data during the period 1979–2014, primarily in the eastern Tibetan Plateau and nearby regions. Four modern reanalysis datasets used in this study are the Modern-Era Retrospective Analysis for Research and Applications (MERRA) produced by National Aeronautics and Space Administration (NASA) with a horizontal resolution of 0.5° latitude × 0.667° longitude (Rienecker et al. 2011), MERRA version 2 (MERRA-2), with a horizontal resolution of 0.5° latitude × 0.625° longitude (Wargan and Coy 2016), the ECMWF interim reanalysis (ERA-Interim) with a horizontal resolution of 1.5° latitude × 1.5° longitude (Simmons et al. 2007), and the Japanese 55-year Reanalysis (JRA-55) with a horizontal resolution of 1.25° latitude × 1.25° longitude (Kobayashi et al. 2015).
Linear trends of the summer 2-m temperature (°C decade−1) at 123 stations over the eastern Tibetan Plateau and nearby regions in 1979–2014 with solid dots (increasing) indicating significance at the 95% confidence level. The large dashed rectangle shows the area for evaluating reanalysis datasets. Shading indicates the mean elevation.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
Our analysis mainly focuses on the period 1979–2015. Linear trends are calculated and statistical significance test is conducted using the nonparametric Mann–Kendall trend test with autocorrelation in the data being checked for the effective sample size (Kundzewicz and Robson 2000).
The Tibetan Plateau is the most prominent orographic feature in the world with a mean elevation of more than 4000 m above the sea level, covering the region 25°–40°N, 70°–105°E (Fig. 1). In summer the thermal forcing of the Tibetan Plateau plays a profound role in affecting the atmospheric circulations on the regional and global scales (Yanai and Wu 2006; Wang et al. 2008; Liu et al. 2012; G. Wu et al. 2015). It is essential that the thermal conditions of the Tibetan Plateau should be well represented in the reanalysis datasets.
First, we use the station observations from the National Climate Center of the CMA to evaluate the modern high-resolution reanalysis datasets. As shown in Fig. 1, there are increasing trends in the 2-m air temperature at most of the stations over the Tibetan Plateau. Figure 2a shows the change of the 2-m air temperature with elevation at the 123 stations. The 2-m air temperature in the four modern reanalysis datasets exhibits a linear decreasing trend with altitude in Fig. 3, in agreement with the observations as shown in Fig. 1. The decreasing rate in the JRA-55 dataset (−4.5°C km−1) is the same as the observations (−4.5°C km−1), while the other three reanalysis datasets show larger decreasing rates (−4.7°C km−1 in the MERRA data, −4.8°C km−1 in the MERRA-2 data, and −4.6°C km−1 in the ERA-Interim data) with altitude. The decreasing trends with altitude are statistically significant at the 95% confidence level in the observations and the four reanalysis datasets.
Changes of (a) the 2-m air temperature (°C) and (b) its trend (°C decade−1) with altitude (km) of station observations. The red lines show the linear fit of the observations.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
Changes of the 2-m air temperature (°C) with altitude over the selected region in the four reanalysis datasets. The red lines show the linear fit of the reanalysis datasets.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
As mentioned in the introduction, the Tibetan Plateau is warming faster than the rest of the world (e.g., Liu and Chen 2000; Duan et al. 2006; Wang et al. 2008; Liu et al. 2012; Duan et al. 2015). Moreover, the warming rate is amplified with elevation, suggesting that high-mountain environments experience more rapid change in temperature than those at lower elevations (Pepin et al. 2015). Figure 2b also shows the elevation dependence of the warming rate in the observations. The observed warming rate shows an increasing trend with the increasing elevation (0.033°C decade−1 km−1). As shown in Fig. 4, the change of the warming rate with altitude is 0.052°C decade−1 km−1 in MERRA, 0.018°C decade−1 km−1 in MERRA-2, 0.004°C decade−1 km−1 in ERA-Interim, and 0.027°C decade−1 km−1 in JRA-55. In general, the modern reanalysis datasets also show an increasing elevation-dependent warming rate, although the warming rates with altitude differ from the observed one in magnitude. Note that the linear trends of the warming rates with altitude in Figs. 2b and 4 are not statistically significant at the 95% confidence level.
As in Fig. 3, but for the 2-m air temperature trend (°C decade−1). The red lines show the linear fit (°C decade−1 km−1).
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
Following Liu et al. (2012), the changes of the thermal condition over the Tibetan Plateau in the reanalysis datasets are further examined with changes in the 2-m temperature and surface wind speed. As shown in Fig. 5, all of the four datasets can capture the general warming trends over the Tibetan Plateau, especially in the MERRA-2, ERA-Interim, and JRA-55 datasets. In the MERRA data, weak cooling trends can be found in the northern part of the plateau. We also examined the trends relative to that of the mean trend over the Northern Hemisphere (figure not shown). Faster warming rates are found in the ERA-Interim and JRA-55 datasets but not in MERRA and MERRA-2. Figure 6 shows the linear trends in the 10-m wind speed. Except in the ERA-Interim dataset, the surface wind speed trended downward in the other three datasets although the detailed patterns are different. It is suggested that the warming trends in the 2-m air temperature and the weakening trends in the surface wind speed over the Tibetan Plateau can be captured at least in three of the modern reanalysis datasets.
The linear trends of the 2-m temperature (°C decade−1) over the Tibetan Plateau in the four reanalysis datasets. For clarity, the zero contour is not plotted and a 9-point smoothing approach is used. Crosses denote the gridpoint values at the 95% confidence level. The shaded area denotes the altitude higher than 2 km.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
As in Fig. 5, but for the linear trends (m s−1 decade−1) in the 10-m wind speed.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
Sensible heating flux data are only available in the MERRA and MERRA-2 datasets (Fig. 7). In agreement with previous studies (Duan and Wu 2008; Liu et al. 2012), the sensible heat flux generally trended downward over Tibetan Plateau in the MERRA-2 dataset, but only over the northern part of the plateau in the MERRA dataset. In Duan and Wu (2008) and Liu et al. (2012), we noted that the sensible heat flux was mainly calculated over the eastern part of the plateau because of a lack of observations in the western part. Figure 7 indicates a weakening trend in the thermal forcing of the Tibetan Plateau in MERRA-2.
The linear trends (W m−2 decade−1) in the sensible heat flux over the Tibetan Plateau in the (a) MERRA and (b) MERRA-2 datasets. Crosses denote the grids at the 95% confidence level. The contour denotes altitude higher than 2 km.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
3. Issues on analysis of the SAH intensity
a. Two centers of the SAH
The SAH is actually associated with the Tibetan Plateau and the Iranian Plateau although the latter is lower than the former in mean elevation, although of similar size (Wu et al. 2012). Tao and Zhu (1964) first noticed the east–west shift of the SAH center. Using the NCEP–NCAR reanalysis pentad mean data, Zhang et al. (2002) suggested that the SAH can be in two main modes in terms of its center shift in the east–west direction. The SAH is in the Tibetan (Iranian) mode when it is centered at about 90°E (60°E). Zhang et al. (2002) further found that the occurrence of the Tibetan mode is closely associated with the diabatic heating of the Tibetan Plateau, while the occurrence of the Iranian mode is mainly due to the adiabatic heating in the free atmosphere over the Iranian plateau, suggesting that different mechanisms are responsible for their formation and maintenance. Thus we should focus on the eastern part of the SAH for understanding of the influence of the thermal condition changes in the Tibetan Plateau.
The influences of the Tibetan Plateau and the Iranian Plateau can be seen by taking the SAH as a perturbation over the zonal mean flow in the four modern reanalysis datasets. Figure 8 shows the July–September 200-hPa wind field averaged over the period 1979–2015. The anticyclonic circulation extends from 20° to 150°E, covering the Eurasian continent and the western North Pacific. When the zonal-mean flows are removed from the wind field shown in Fig. 8, we can see two anticyclonic centers (Fig. 9). One is centered at about 35°N, 85°E over the Tibetan Plateau and the other is at about 40°N, 50°E over the Iranian Plateau. In previous studies (e.g., Zhang et al. 2000), the climate change of the SAH intensity is measured with the area index and intensity indices, which were calculated over a region (10°–50°N, 10°–130°E) that covers both the Tibetan Plateau and the Iranian Plateau. We argue that such indices may not be appropriate to represent the response of the SAH to the thermal condition change of the Tibetan Plateau.
The 200-hPa streamlines and the contour of 16 760 gpm Northern Hemisphere at 100 hPa for each decade in the four reanalysis datasets. The time periods are indicated by color: 1980–89 (green), 1990–99 (blue), 2000–09 (purple), and 2010–15 (red). The shaded area denotes altitude higher than 2 km. The letter A indicates the Tibetan center of the SAH.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
As in Fig. 8, but the zonal mean is removed and the contour is 100 gpm. The dashed rectangle shows the area for calculating the SAH intensity. The letter A indicates the Tibetan and Iranian centers of the SAH.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
b. Global rise of pressure levels
The extension and intensity of the SAH have been recently quantified with the geopotential height at 100 hPa (Qu and Huang 2012), 150 hPa (Liu et al. 2013), or 200 hPa (L. Wu et al. 2015; Ren et al. 2007). For example, the contour of 16 760 gpm at 100 hPa has been used to estimate the spatial coverage of the SAH (Qu and Huang 2012). Figure 8 also shows the decadal variations of the spatial coverage of the contour of 16 760 gpm at 100 hPa during 1979–2015. We can see that the contour of 16 760 gpm at 100 hPa extends eastward with time in the four reanalysis datasets. Recently, Choi et al. (2016) also found such an eastward expansion of the SAH and discussed its relationship with the summer rainfall variability over the Korea Peninsula.
When discussing the climate change of the subtropical high over the western North Pacific, Wu and Wang (2015) revealed that the documented westward extension in previous studies was a result of the global rise of the 500-hPa pressure level due to global warming. They suggested that it is inappropriate to estimate the extension of the subtropical high with a contour (e.g., 5870 gpm) of geopotential height. For the same reason, we should not use the 16 760-gpm contour at 100 hPa to measure the eastward extension of the SAH. Following Wu and Wang (2015), we removed the rising trend of the whole pressure level by taking away the zonal mean geopotential height. Here we use the deviation of 100 gpm from the zonal mean to show the change of the SAH. Figure 9 indicates that little change occurred in the spatial coverage of the SAH over the past 15 years.
As we know, the SAH has a geopotential height higher than its surrounding areas at a pressure level in the upper troposphere. To reduce the influence of the global rise of geopotential height, we examine the seasonal variability of the geopotential height over the Tibetan Plateau (28°–38°N, 75°–102°E) by contrasting with the surrounding area (10°–60°N, 10°–150°E) at each pressure level (Fig. 10). The positive height anomaly can be found between 100 and 300 hPa, especially during July–September. The largest anomalies occur at 150 and 200 hPa. For this reason, our analysis focuses on the July–September change of the SAH over the Tibetan Plateau.
Seasonal evolution of the geopotential height (gpm) over the Tibetan Plateau (28°–38°N, 75°–102°E) compared to its surrounding area (10°–60°N, 10°–150°E) in the four reanalysis datasets. Various pressure levels are indicated.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
c. Shifts of the SAH center
Figures 11 and 12 depict the interannual shifts of the mean locations of the SAH centers in the meridional and zonal directions, respectively, which are identified from the July–September mean 200-hPa wind field after the zonal mean is removed. Note that the two SAH centers cannot always be identified in the reanalysis datasets. For example, there is only one center for 19 years in the JRA-55 dataset, with 12 years over the Tibetan Plateau and 7 years over the Iranian Plateau, respectively. It is interesting to note that the Tibetan center persistently shifted northward while the Iranian center shifted southward. For this reason, we calculate the parameters for measuring the SAH intensity in a rectangle centered at the Tibetan Plateau with a size of 15° latitude and 35° longitude. We also calculated the SAH intensity with a domain moving with the annual mean center and find that the results are very similar.
The shift of the centers over the Tibetan Plateau (red) and the Iranian Plateau (black) in the meridional directions, which are identified from the July–September mean 200-hPa wind field after the zonal mean is removed. Connections with dashed lines indicate years without identified centers and straight dashed lines show the corresponding linear trends.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
As in Fig. 11, but for the zonal direction.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
4. SAH intensity change over the Tibetan Plateau
In this study, the SAH intensity is measured with the July–September geopotential height, divergence, and relative vorticity averaged over its central area during the period 1979–2015. We first look at the geopotential height associated with the SAH. The time series at 100, 150, and 200 hPa exhibit an upward trend over the period 1979–2015 and the trend is statistically significant at the 95% confidence level (Fig. 13). As mentioned above, the SAH has a geopotential height higher than its surrounding areas at a pressure level in the upper troposphere. Here we select the mean height of the pressure levels over the Northern Hemisphere as the reference state. Figure 14 shows the time series of the deviation of geopotential height from the Northern Hemisphere mean. There are no significant trends in all of the four reanalysis datasets, suggesting that the upward trend in Fig. 13 resulted mainly from the global rise of the pressure levels.
The July–September geopotential height (gpm) averaged over the Tibetan Plateau at 100, 150, and 200 hPa. The straight lines show the corresponding linear trends.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
As in Fig. 13, but the Northern Hemisphere mean is removed.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
The mean divergence and vorticity associated with the SAH are calculated, providing an additional measure for the SAH intensity (Figs. 15 and 16). As expected, the SAH is associated with divergence and negative relative vorticity. No statistically significant trends can be found in the divergence over the period 1979–2015 (Fig. 13). The magnitudes of relative vorticity are smaller at 100 hPa than those at 150 and 200 hPa. The relative vorticity generally decreased with time during the period 1979–2015 (Fig. 16), but there are no statistically significant trends at the 95% confidence level. Consistent with the geopotential height with the Northern Hemisphere mean being removed, the divergence and relative vorticity indicate that no significant change of the SAH intensity occurred during the period 1979–2015.
Time series of the July–September divergence (s−1) averaged over the Tibetan Plateau at 100, 150, and 200 hPa. The straight lines show the corresponding linear trends.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
As in Fig. 15, but for relative vorticity (s−1).
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
5. Conclusions and discussion
In this study, the possible response of the SAH intensity to the thermal condition change in the Tibetan Plateau is examined with the four modern reanalysis datasets. Despite the surface air warming in the four modern reanalysis datasets, reducing surface wind speed in three of the reanalysis datasets, and decreasing surface sensible heat flux in the MERRA-2 dataset, there is no statistically significant trend in the SAH intensity over the period 1979–2015, although the reanalysis products are always subjected to temporal inhomogeneity in input datasets.
Wang et al. (2008) reduced the surface albedo to simulate the effect of the Tibetan Plateau warming. In addition to the enhanced subtropical summer rainfall that results from the plateau warming, they also simulated an intensified SAH [see Fig. 2b in Wang et al. (2008)]. The Tibetan Plateau warming induces a Rossby wave train along the upper-level westerly jet stream, but the anomalous anticyclone was centered at about 40°N, 90°E, about 10° north of the SAH center. It is suggested that the strongest atmospheric response to the plateau warming is not collocated with the SAH center. We think that one of the possible reasons is that the atmospheric response to the thermal condition changes of the Tibetan Plateau occurs mainly in the upper-level westerly jet stream, which is far away from the Tibetan center of the SAH. Because of the mismatch of the atmospheric response to the thermal forcing, the SAH intensity is not much sensitive to the thermal condition change of the Tibetan Plateau.
Such a northward shift of the anomalous anticyclone can be also found in the four reanalysis datasets. Figure 17 shows the 200-hPa mean wind field and the trend of the geopotential height during the period 1979–2015. The anomalies of geopotential height are strongest in the region of the jet stream. The maximum positive trend of the geopotential height is centered at about 45°N, 105°E, making the observed SAH center move northward. This is consistent with the northward shifting trend in the Tibetan center of the SAH over the period 1979–2015 (Fig. 11). Meanwhile, the negative trends in the geopotential height shift the Iranian center southward. Because of the mismatch of the atmospheric response to the thermal forcing change, the SAH intensity is not greatly sensitive to the thermal condition change of the Tibetan Plateau.
The linear trends of the 200-hPa geopotential height (shading; gpm decade−1), 200-hPa mean winds (vectors; m s−1) with the zonal average being removed, and the mean u wind speed (contour) equal to and larger than 25 m s−1 indicating the subtropical jet stream. Gray shading denotes the altitude higher than 2 km. Letter A indicates the Tibetan and Iranian centers of the SAH and positive and negative signs denote the increasing and decreasing trends in geopotential height.
Citation: Journal of Climate 30, 8; 10.1175/JCLI-D-16-0359.1
It should be pointed out that quantitative evaluation of the thermal condition change in the Tibetan Plateau is currently impossible due to lack of observations, especially in the western part. This may lead to an underestimation of the response of the SAH intensity to the thermal condition change in the plateau.
Acknowledgments
This research was jointly supported by the National Basic Research Program of China (2013CB430103 and 2015CB452803), the National Natural Science Foundation of China (Grant 41275093), and the project of the specially appointed professorship of Jiangsu Province.
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