• ADVANCES IN ATMOSPHERIC SCIENCES, 2018, 35(9): 1114-1128
    doi: 10.1007/s00376-017-7231-y
    Varying Rossby Wave Trains from the Developing to Decaying Period of the Upper Atmospheric Heat Source over the Tibetan Plateau in Boreal Summer
    Chuandong ZHU1,3, Rongcai REN1,2,, Guoxiong WU1,3

    Abstract:

    This study demonstrates the two different Rossby wave train (RWT) patterns related to the developing/decaying upper atmospheric heat source over the Tibetan Plateau (TPUHS) in boreal summer. The results show that the summer TPUHS is dominated by quasi-biweekly variability, particularly from late July to mid-August when the subtropical jet steadily stays to the north of the TP. During the developing period of TPUHS events, the intensifying TPUHS corresponds to an anomalous upper-tropospheric high over the TP, which acts as the main source of a RWT that extends northeastward, via North China, the central Pacific and Alaska, to the northeastern Pacific region. This RWT breaks up while the anomalous high is temporarily replaced by an anomalous low due to the further deepened convective heating around the TPUHS peak. However, this anomalous low, though existing for only three to four days due to the counteracting dynamical effects of the persisting upper/lower divergence/convergence over the TP, acts as a new wave source to connect to an anomalous dynamical high over the Baikal region. Whilst the anomalous low is diminishing rapidly, this Baikal high becomes the main source of a new RWT, which develops eastward over the North Pacific region till around eight days after the TPUHS peak. Nevertheless, the anomaly centers along this decaying-TPUHS-related RWT mostly appear much weaker than those along the previous RWT. Therefore, their impacts on circulation and weather differ considerably from the developing to the decaying period of TPUHS events.

    Key words: Tibetan Plateau; upper atmospheric heat source; Rossby wave train; circulation and weather;
    摘要: 本研究论证了与北半球夏季青藏高原上空发展/衰亡的高层大气热源相关的两种不同的Rossby波列. 结果表明, 夏季青藏高原上空高层大气热源(TPUHS)由准双周变率主导, 尤其是在七月下旬至八月中旬(副热带急流稳定位于青藏高原以北). 在TPUHS事件的发展阶段, 对应增强的TPUHS是青藏高原上空的异常高压, 它是由青藏高原向东北方向延伸波列(经华北, 中太平洋, 阿拉斯加, 到达东北太平洋地区)的主要波源. 在TPUHS的峰值位相附近, 由于进一步加深的对流加热, 青藏高原上空的异常高压被异常低压替代, 此波列破碎. 尽管在青藏高原上空持续高层(低层)辐散(辐合)的动力抵消作用下, 这个异常低压仅维持三到四天, 但它是连接贝加尔湖异常高压的新波源. 当此异常低压快速减弱时, 贝加尔湖高压成为新波列的主要波源. 从TPUHS的峰值到峰值后的8天左右, 此波列一直在北太平洋地区向东发展. 然而, 沿着与衰减TPUSH相关联的波列的中心, 大部分比沿着以前波列的中心要更弱. 因此, 从TPUSH事件的发展至衰减阶段, 它们对环流和天气的影响有相当大地不同.
    关键词: 青藏高原 ; 高层大气热源 ; Rossby波列 ; 环流和天气

    1. Introduction

    As a huge heat source of the atmosphere in summer, the thermal influence of the Tibetan Plateau (TP) is known to be crucial for the formation of the atmospheric circulation patterns and climate anomalies not only within the Asian region but also across the globe (Ye and Wu, 1998; Duan et al., 2012). The highly elevated surface sensible heat over the TP can drive strong vertical motion in summer, which can act as a powerful "air pump" to pump the lower air upwards and result in divergence and anticyclonic circulation in the upper troposphere (Ye and Gao, 1979; Wu et al., 1997). Other observational evidence (Flohn, 1960; Reiter and Gao, 1982; Yanai et al., 1992) and an early numerical experiment (Krishnamurti et al., 1973) have also confirmed that it is the diabatic heating over the summer TP that generates the South Asian high (SAH)——an important circulation system in the upper troposphere in summer (Mason and Anderson, 1963). In particular, it is the inhomogeneous spatial distribution of the diabatic heating over the TP and eastern Asia that determines the locations of the SAH and the northwestern Pacific subtropical high (NWPSH) (Wu and Liu, 2000; Liu et al., 2001a; Liu et al., 2004; Wu et al., 2015).

    Although the land-sea thermal contrast is known to be the main driver of monsoonal circulation (Murakami and Ding, 1982; Luo and Yanai, 1983, 1984; Chen et al., 1991), the strong heat source over the TP has been recognized as one of the most important factors modulating the onset and intensity of the Asian summer monsoon (ASM) (e.g. Yanai and Wu, 2006; Wu et al., 2007; Romatschke and Houze, 2011). For example, the sensible heating over the TP originated in spring can lead to an earlier reversal of the meridional gradient of the atmospheric temperature over the east side of the TP, which leads to the first onset of the ASM in the northeastern part of the Bay of Bengal (Wu and Zhang, 1998). When the sensible heating over the TP is anomalously strong in spring, the seasonal reversal of the vertical shear of both the zonal and meridional wind in the East Asian monsoon region is anomalously early, which marks an earlier onset of the East Asian summer monsoon (EASM) (Duan et al., 2013). In particular, recent evidence based on data analysis and numerical experiments provided by (Wu et al., 2012) further proved that the variability of the EASM, as well as the eastern part of the South Asian summer monsoon, can indeed be attributed to the thermal forcing anomalies over the TP.

    Owing to the high elevation and vast area of the TP heating, its influence can be passed to remote regions outside Asia. Coupled with the SAH and strong upward motion over the TP, compensative downward motion always prevails over the vast surrounding regions (Ye and Wu, 1998). The downward motion to the east of the TP can be as far away as the central North Pacific, and that to the west——over Afghanistan, Iran, and Saudi Arabia——is largely responsible for the dry climate and deserts in these regions (Yang et al., 1992; Rodwell and Hoskins, 1996; Ye and Wu, 1998; Wu et al., 2009). In the meridional direction, the divergent flow over the TP may extend southwards across the equator and induce downward motion in the southern subtropics, thus forming the well-known Hadley-monsoonal meridional circulation (Ye and Wu, 1998). It may also extend northwards and then descend to the north of the TP, corresponding to the Taklimakan and Dzungaria deserts (Ye and Gao, 1979). On the other hand, the influence of the TP may also be passed to remote regions via a Rossby wave train (RWT). The modeling results of (Hoskins and Karoly, 1981) and (Huang and Gambo, 1981) suggested that the atmospheric responses to mechanical and thermal forcing of large-scale topographies may exhibit Rossby wave patterns. Two southeastward-propagating RWTs can be identified in summer across the Northern Hemisphere, one of which is generated from the Rocky Mountains and the other from the TP (Grose and Hoskins, 1979). (Huang, 1985) also indicated that the propagation of Rossby waves forced by a strong TP thermal forcing may result in anticyclonic circulation at 300 hPa over the TP, Sea of Okhotsk, and the northern part of North America, and cyclonic circulation over the west of Lake Baikal and the Aleutian region. In particular, modeling studies by (Wu et al., 1997) and (Ye and Wu, 1998) emphasized that the elevated surface sensible heating over the TP can excite an RWT pattern across the globe. The RWT splits over the North Pacific, with its southern branch bending southward along the westerlies at the bottom of the tropical upper-tropospheric trough (TUTT); and its northern branch propagating further eastward to Alaska and Baffin Bay, and then bending southward over the North Atlantic to the north of Cape Verde, where the axis of the subtropical high lies. A similar RWT pattern emanating from the TP was also identified by (Liu et al., 2002) and (Wu et al., 2002). These results indicated a clear pathway for the remote influences of TP surface heating on the atmospheric circulation and climate from the subtropics to the high latitudes.

    However, the TP heat source in summer tends to be dominated by convective condensation heating in the upper troposphere, especially over the eastern TP region (Chen et al., 1985; Jiang et al., 2016), although the surface sensible heating is known to be the primary driver of the related vertical motion over the TP (Wu et al., 2002). This implies a further elevated atmospheric heat source over the TP, which may excite RWTs that are different from those excited by the surface sensible heat source. In addition, on top of the interannual variabilities of the TP heat source upon which most previous studies have focused (Krishnamurti et al., 1973; Reiter and Gao, 1982; Wu et al., 1997; Ye and Wu, 1998; Zhao and Chen, 2001; Ueda et al., 2003; Duan et al., 2005, 2013; Liu et al., 2007a; Zhang et al., 2009), significant intraseasonal timescale (10-30 days) variations have been identified for the column-integrated apparent heat source, especially over the eastern TP (Nitta, 1983). (Wang and Duan, 2015) further indicated the dominance of a quasi-biweekly (10-20 days) oscillation mode of the precipitation, diabatic heating and tropospheric circulation over the TP. In terms of the origin of this quasi-biweekly oscillation over the TP, agreement is still lacking as to whether it originates locally or is influenced by circulation in the tropics or in the middle and high latitudes (Wang and Duan, 2015). Consistent with the quasi-biweekly oscillation of the heat source over the TP, the SAH, particularly its longitudinal position, seems also to exhibit quasi-biweekly variation in boreal summer (Tao and Zhu, 1964; Liu et al., 2007b; Ren et al., 2007). This longitudinal shifting of the SAH has been found to be closely related to an opposing longitudinal shift of the NWPSH in the lower and mid troposphere (Tao and Zhu, 1964; Ren et al., 2007), which in turn is closely related with extreme changes in monsoonal rainfall over the East Asian region. The present study focuses on the daily variations of the upper-tropospheric heat source over the TP, and investigates the RWT related to this TP heat source in boreal summer.

    In particular, we examine the dynamic and thermodynamic processes related to the daily variations of the upper atmospheric heat source over the Tibetan Plateau (TPUHS) and the associated RWT, and demonstrate the possible climatic impacts of the RWT on the atmospheric circulation and weather anomalies in summer in the northern extratropics. The aim in carrying out this work is to help improve our understanding of the climatic effects of TP heating, on multiple timescales, as well as the remote influence of the TP on the northern extratropics in summer.

    Following this introduction, section 2 introduces the data and method; section 3 demonstrates the seasonal evolution of the TPUHS in summer and its dominant sub-monthly variability; section 4 illustrates the different RWTs related to the TPUHS from its developing to decaying period; section 5 explores the possible effects of the TP-related RWTs on the climatological circulation systems and weather anomalies in the northern extratropics; and section 6 provides a summary and discussion.

    2. Data and method
    2.1. Data

    The daily atmospheric circulation fields are from the National Centers for Environmental Prediction and National Center for Atmospheric Research (NCEP-NCAR) reanalysis dataset (Kalnay et al., 1996), which covers the period from 1 January 1979 to 31 December 2014, and has a horizontal resolution of 2.5° latitude × 2.5° longitude and 17 pressure levels spanning from 1000 to 10 hPa. The daily surface sensible heat flux fields from NCEP-NCAR covers the same period as the atmospheric circulation fields, and are interpolated from Gaussian grids to 2.5° latitude × 2.5° longitude grids before analysis. The daily precipitation fields are from the Global Precipitation Climatology Project (GPCP), version 1.2, 1° Daily Precipitation Dataset (Bolvin et al., 2009), covering the period from 1 January 1997 to 31 December 2014. We first calculate the daily annual cycle of all variables by taking an average of them across the 36 years for each calendar day, and then we remove the daily annual cycle from the respective original fields to obtain the daily anomaly fields. The reliability of the NCEP-NCAR reanalysis in representing the diabatic heating over the TP and its variabilities has already been validated in many previous studies (e.g., Nigam et al., 2000; Rodwell and Hoskins, 2001; Duan, 2003; Wang et al., 2011). We also confirmed the general consistency of the NCEP-NCAR reanalysis with other datasets (e.g., JRA-55) in representing the TP heat source and the related RWTs.

    2.2. Method

    2.2.1. Heat source index

    Based on the large-scale heat budget equation (Yanai et al., 1992): \begin{equation} \label{eq1} Q_1=c_p\left[\dfrac{\partial T_{\rm air}}{\partial t}+{V}\cdot\nabla T_{\rm air}+ \left(\frac{p}{p_0}\right)^\kappa\omega\dfrac{\partial\theta}{\partial p}\right] ,\ \ (1) \end{equation} where T air denotes air temperature; V is the horizontal wind vector; ω is the vertical velocity in pressure (p) coordinates; θ is the potential temperature; p0 equals 1000 hPa; and \(\kappa=R/c_p\), with R being the gas constant and cp the specific heat capacity of dry air at constant pressure, we first obtain the apparent heat source (Q1) fields at 19 pressure levels (1000, 925, 850, 700, 600, 550, 500, 450, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, and 10 hPa). Because the main focus of this study is the heat source in the upper troposphere, rather than the surface sensible heat source, we then vertically integrate Eq. (2) from the tropopause pressure level (p t=100 hPa) to the lowest pressure level (p b) that is about 100 hPa away from the surface to obtain the column-integrated atmospheric heat source \((\langle Q_1\rangle)\): \begin{equation} \label{eq2} \langle Q_1\rangle=\frac{1}{g}\int_{p_{\rm t}}^{p_{\rm b}}{Q_1dp} . \ \ (2)\end{equation} By averaging the \(\langle Q_1\rangle\) (the angle brackets denote column integration) over the TP region (25°-40°N, 70°-105°E) and above the altitude of 1500 m, we further define a daily TP apparent heat source index (THI).

    We also calculate the diabatic heating rate (K d-1) from dθ/dt (θ is the potential temperature) for each pressure level and the surface (Wu et al., 1999), to show the spatiotemporal evolution of the atmospheric heat source from the surface to the upper layer.

    2.2.2. Statistical significance test

    We apply the Student's t-test to assess the statistical significance of our results, where the effective sample size (N') is estimated using the method discussed in (Bretherton et al., 1999): \begin{equation} \label{eq3} N'=N\frac{1-r_1r_2}{1+r_1 r_2} , \ \ (3)\end{equation} where N is the original sample size, and r1 and r2 are the lag 1 auto-correlation coefficients of the two time series involved. As the lag 1 auto-correlation for the THI is 0.678, we have N'=0.37N, assuming that r1=r2, when we assess the statistical significance of the regressions against the THI.

    2.2.3. Wave activity flux

    To facilitate a subjective representation of Rossby waves, we adopt the three-dimensional wave activity flux in a spherical log-pressure coordinate, defined by (Plumb, 1985): \begin{equation} F_{\rm s}=\dfrac{p\cos\varphi}{p_0}\times\left( \begin{array}{c} v'^2-\dfrac{1}{2\Omega a\sin 2\varphi}\frac{\partial(v'\Phi')}{\partial\lambda}\\[2.5mm] -v'u'+\dfrac{1}{2\Omega a\sin 2\varphi}\frac{\partial(u'\Phi')}{\partial\lambda}\\[2.5mm] \dfrac{2\Omega\sin\varphi}{S_0}\left[v'T'_{\rm air}-\dfrac{1}{2\Omega a\sin 2\varphi} \dfrac{\partial(T'_{\rm air}\Phi')}{\partial\lambda}\right] \end{array} \right) , \ \ (4)\end{equation} where \begin{equation} \label{eq4} S_0=\frac{\partial\hat{T}_{\rm air}}{\partial z}+H ,\ \ (5) \end{equation} represents the static stability (the caret denotes an area average over the region north of 20°N), Φ is the geopotential, u and v are the zonal and meridional components of horizontal wind, the primes denote the deviations from zonal means, T air is the air temperature, H is the scale height, Λ is longitude, φ is latitude, a is Earth's radius (6378.388 km), and Ω is Earth's rotational angular velocity (7.2685× 10-5 rad s-1). The primes denote the deviations from zonal means. Because the wave activity flux is parallel to the local group velocity of Rossby waves, it can effectively indicate the propagating direction of the wave energy.

    3. Seasonal evolution of the TPUHS over the summer TP and its dominant quasi-biweekly variability
    3.1. Seasonal evolution of the TPUHS

    Figure 1a shows the seasonal evolution of the area-mean column-integrated (from 100 hPa to the pressure level that is about 100 hPa away from the surface) apparent heat source \((\langle Q_1\rangle)\) and the area-mean surface sensible heat flux (SH) over the TP region. It can be seen that the intensity of the atmospheric \(\langle Q_1\rangle\) has already become lager than the surface SH since May. Thereafter, while the atmospheric \(\langle Q_1\rangle\) keeps increasing after May and reaches 90-95 W m-2 in June-July, the surface SH shows a weaker increase and remains at around 50 W m-2 from May to October. This clearly indicates the dominance of strong latent condensation heating (LH) on the variation of the TP heat source in summer. After summer, both the SH and \(\langle Q_1\rangle\) decrease sharply from September, with the SH gradually becoming stronger than the \(\langle Q_1\rangle\) and beginning to dominate the TP heat source again.

    Fig. 1. Seasonal evolution (May-October) of (a) the area-mean surface sensible heat flux (blue; units: W m-2) and vertically accumulated apparent heat source (red; units: W m-2) over the TP (25°-40°N, 70°-105°E) above 1500 m, and (b) the 200-hPa zonal wind (units: m s-1) averaged from 70°E to 105°E. The horizontal black lines in (b) roughly mark the south and north boundaries of the TP, and the vertical blue lines indicate 18 July and 23 August, respectively.

    The meridional location as well as the zonal structure of the upper-tropospheric westerly jet can affect the propagation speed, amplitude and phase of the Rossby waves excited by a tropospheric heat source (Hoskins and Karoly, 1981). By examining the successive seasonal shift of the East Asian upper-tropospheric westerly jet, (Lin and Lu, 2008) noted that it usually undergoes a significant northward shift around 20 July, and then stays stably to the north of 40°N, or to the north of the TP, for some time. To confirm this, we display the seasonal evolution of the 200-hPa westerly jet (>20 m s-1) over the TP region (70°-105°E) in Fig. 1b. It is apparent that the westerly jet shifts gradually northward from May to mid June and begins to be centered at 40°N; then, it exhibits a further northward shift around 18 July and remains steadily at ∼ 42.5°N until 23 August, after which it begins to retreat southward. To consider the possible RWTs associated with the intensive deep convection and strong TPUHS covering most of the TP region, we focus mainly on the period from 20 July to 20 August in the following investigation. Actually, for the TPUHS in summer and its synoptic variations, the related RWTs during this period are the most complete and strongest, compared with other time periods (data not shown).

    3.2. The dominant quasi-biweekly variability of the TPUHS

    To demonstrate the dominant variability of the TPUHS in boreal summer, we display in Fig. 2a the lead/lag regressions of the layer-by-layer area-mean diabatic heating rate anomalies over the TP against the THI (contours). It is apparent that, relative to the maximum values around the peak day of the THI, significant regression values for most layers decrease sharply with the increase in the lead/lag time, and consistently tend to approach zero until day 7. By referencing to the lead/lag auto-correlation of the THI time series and the corresponding e-folding time shown in Fig. 3, we can estimate that the lifetime of an anomalous THI event is about seven days, or the dominant variability of the THI (i.e., the upper-atmospheric heat source in the troposphere over the TP) is in a quasi-biweekly timescale. Spectral analysis confirms that the THI does exhibit significant quasi-biweekly (or 10-20 days) oscillation and the variance explained by the quasi-biweekly variability is up to 35.8% of the total variance (∼54.2) of the normalized THI timeseries (data not shown). As already mentioned in the introduction section, the quasi-biweekly oscillation is the dominant mode of the intraseasonal variations of the column-integrated apparent heat source (Wang and Duan, 2015). Consistent with this, (Yang et al., 2016) identified a quasi-biweekly mode of the intraseasonal oscillations in the eastern TP summer rainfall.

    Fig. 2. Lead/lag regressions against the THI (units: W m-2) of the area-mean diabatic heating rate anomalies (units: K d-1) over the TP (a) at each level (contour interval: 0.1; dashes for 0.05 and 0.15 are added) and (b) at the surface in boreal summer (20 July to 20 August). Stippling in (a) and dots in (b) indicate regressions above the 90% confidence based on the t-test. The abscissa is the lead time of the THI (units: d); the ordinate is the pressure level (units: hPa) in (a) and the amplitudes of the regression in (b).

    Fig. 3. Lead/lag auto-correlation of the THI (asterisks, left ordinate), and cross-correlation (right ordinate) between the THI and WTI1 (dots) and that between THI and WTI2 (circles). The thickened curve indicates the THI auto-correlation that is above 1/e. The horizontal solid, long-dashed and short-dashed lines denote the 99% confidence level for the THI auto-correlation, the THI-WTI1 cross-correlation, and the THI-WTI2 cross-correlation, respectively, based on t-test.

    Fig. 4. Regression of (a) column-integrated apparent heat source (units: W m-2) and (b) surface sensible heat flux (units: W m-2) against the THI. Stippling indicates regressions above the 95% confidence based on the t-test. Blue contours delineate the TP's topographic boundary of 1500 m.

    In addition, Fig. 2a also shows that the maximum regression center of the diabatic heating rate lies in the upper troposphere, and a maximum center appears in the further higher layer up to 150 hPa around the peak day of the THI [day(0)]. This clearly indicates the further vertical deepening of the convective LH with the maturing of TPUHS events. From the lead/lag regressions of the surface diabatic heating rate over the TP against the THI, it is easy to identify that the surface SH is always much weaker than the LH in the upper atmosphere throughout the entire period (Fig. 2b). This again confirms that the sub-monthly variations of the TP heat source are indeed dominated by condensation LH in the upper atmosphere.

    Figure 4 further shows the spatial regression patterns of the column-integrated heat source (Fig. 4a) and that of the surface sensible heat flux (Fig. 4b) in boreal summer. It can be seen that anomalous TPUHS events are characterized by significant anomalous \(\langle Q_1\rangle\) over most of the TP region, except its far western part (Fig. 4a). In contrast, significant SH anomalies are only found over the western TP and along the southern boundary area of the TP. This further confirms the overwhelming dominance of the upper-atmospheric LH source over the SH heat source in boreal summer.

    3.3. Accompanying variations of the local circulation anomalies over the TP

    Figure 5 shows the lead/lag regressions of the local mean circulation anomalies over the TP region against the THI in boreal summer. As an anomalous TPUHS grows [before day(0)], anomalous convergence/divergence in the lower/ upper troposphere (shading) and anomalous ascent in the troposphere intensifies (contours), indicating the development of anomalous deep convection over the TP (Fig. 5a). And after the peak [day(0)] of the anomalous TPUHS, they begin to weaken and gradually diminish within about four days [day(+4)]. Because of the greatly deepened convection and the elevated strong LH release, the anomalous warm center that was originally located around 300 hPa before day(-4) is further elevated to about 150 hPa and above until the peak day [day(0)] (Fig. 5b). Although gradually weakening after day(+2), the warm center stays in this layer throughout the decaying period of the TPUHS. Owing to the much-elevated anomalous warm center, the anomalous geopotential high center that was originally centered at 300 hPa in the upper troposphere before day(-2) is temporarily replaced by negative height anomalies from the surface to the upper layer (up to 100 hPa) around day(0) (Fig. 5c). However, these negative height anomalies, resulting from the thermal effect of greatly elevated LH release in the upper troposphere, are relatively weaker above 200 hPa and only exist within two days around the peak day of the heat source. This is due to the counteracting dynamic effect of the persisting divergence/convergence in the upper/lower troposphere (Fig. 5a), which is always supporting an anomalous high/low in the upper/lower troposphere. Also associated with the greatly elevated heat source, the horizontal vorticity, originally characterized by positive/negative anomalies in the lower/upper troposphere, begins to be dominated by positive vorticity anomalies throughout the troposphere up to 50 hPa from day(-1) (Fig. 5d). These results clearly indicate that the strong thermal effect of the greatly elevated LH around the peak day of the TPUHS may temporarily offset the anomalous circulation pattern (anticyclonic circulation above cyclonic circulation) that prevails during the earlier developing period of the TPUHS.

    Fig. 5. Lead/lag regressions against the THI of the area-mean (a) horizontal divergence (shaded; units: 10-6 s-1) and vertical velocity (contours; units: 10-3 Pa s-1; only those statistically significant above the 90% confidence level are shown), (b) air temperature (units: °C), (c) geopotential height (units: gpm), and (d) relative vorticity (units: 10-6 s-1) in the atmospheric column over the TP. Stippling in all panels indicates regressions above the 90% confidence level based on the t-test. The abscissa is the lead time of the THI (units: d); the ordinate is the pressure level (units: hPa).

    4. Different RWT patterns during the developing/decaying period of anomalous TPUHS
    4.1. RWT patterns

    4.1.1. From vorticity anomalies

    Figure 6 shows the lead/lag regressions of the 200-hPa zonal wind (contours) and relative vorticity (shading) anomalies in the Northern Hemisphere against the THI during summer. Firstly, it is clear that, when the TPUHS or the convective LH anomaly is weak and begins to grow from day(-7) to day(-5) (Figs. 6a and b), significant negative vorticity anomalies dominate the TP, indicating an anomalous SAH related to the relatively weak and shallow TPUHS accompanied by minor surface SH over the summer TP. Meanwhile, positive vorticity anomalies exist in two areas from the Caspian region to Kazakhstan and from northeastern China to Japan. Correspondingly, positive zonal wind anomalies appear to the north of the TP and extend along the latitudinal band from the northwestern TP to southern Japan. Together with the negative zonal wind anomaly centers existing north of the positive vorticity anomaly centers mentioned above, the zonal wind anomalies favor a slightly weakening and southward-shifting of the subtropical westerly jet (SWJ) axis (thick dashed line) located just to the north of the TP (Fig. 6b). Along the SWJ axis, a clear teleconnection pattern of vorticity anomaly centers can be identified downstream as well as upstream of the TP during this time. Specifically, the downstream teleconnection pattern consists of five centers (marked "P", "Q", "R", "S" and "T") from the negative vorticity center ("P") over the TP to the negative vorticity center ("T") over the northeastern Pacific and west coast of North America; and the upstream teleconnection pattern includes four centers (marked "M", "N", "O" and "P") from "M" near the Baltic Sea to "P" over the TP (Fig. 6b). As the TPUHS continues to grow, the negative vorticity center over the TP gradually shifts southward from day(-4) to day(-3) (Figs. 6c and d). Accompanying this is the southward-shifting westerly anomaly center to its north, thus favoring a further southward shift of the SWJ axis. The negative vorticity center "R" tends to split and weakens and shifts westward, while the "Q" center becomes strengthened and shifts westward to North China. A new branch of the downstream teleconnection pattern seems to appear, from "Q" to "S" via the negative vorticity center "R1" over the central North Pacific (Fig. 6d). Also associated with the weakening and southward shifting of the SWJ axis, the upstream teleconnection pattern is significantly weakened until day(-3) (Fig. 6d).

    Fig. 6. Lead/lag regressions against the THI of the relative vorticity anomalies (shaded; units: 10-6 s-1) and the zonal wind anomalies (contours; units: m s-1; interval: 1; zero line omitted for clarity) at 200 hPa when the THI leads for (a) -7 days, (b) -5 days, (c) -4 days, (d) -3 days, (e) -1 day, (f) 0 days, (g) 2 days, (h) 4 days, (i) 6 days and (j) 8 days. Hatched and stippled areas denote the 90% confidence level for relative vorticity anomalies and for zonal wind anomalies, respectively. The thick dashed line denotes the climatological westerly jet axis (>20 m s-1) during the period from 20 July to 20 August. The numbers in the upper-left corner of each panel indicate the lead time of the THI. The blue letters mark the RWT and the anomaly centers along it.

    After, when the TPUHS is further intensified, the negative vorticity center "P" shifts further southward, away from the TP region, until day(-1) (Fig. 6e). A much stronger westerly anomaly center is then located just over the TP region, which corresponds to a maximum positive vorticity anomaly center to its north. Thereafter, a meridional tripole pattern of vorticity anomalies, as well as zonal wind anomalies, from the south to the north of the TP region, forms (Figs. 6e and f). The tripole pattern exists from day(-1) to day(+1) (data not shown), while the original teleconnection pattern downstream of the TP no longer exists during this time (Figs. 6e and f). This implies that the maturing of an anomalous TPUHS event can temporarily disrupt the teleconnection pattern that has developed during the developing period of the TPUHS, by offsetting the anomalous atmospheric circulation structure over the TP, as already shown in Fig. 5.

    With the decay of anomalous TPUHS events, and the weakening of the negative vorticity center south of the TP, both the strong westerly anomaly center over the TP and the associated meridional tripole pattern mentioned above quickly diminish from day(+2) to day(+4) (Figs. 6g and h). However, the negative vorticity center north of the TP that originally extended eastward, begins to develop near the Baikal region (denoted as "B"). Later, we show that this anomalous anticyclone center is dynamically forced and exhibits a deep barotropic structure. With the intensification of this "B" center and the associated strong easterly anomaly center to its south afterwards, the SWJ tends to be mainly weakened in the upstream region from the eastern Caspian Sea to the northern TP, whereas it mainly shifts southward over its exit region (Figs. 6g and h). Related to this, a new teleconnection pattern (B-C-D-E) seems to gradually form downstream along the SWJ axis. This new teleconnection pattern, with four vorticity anomaly centers (marked "B", "C", "D" and "E") from region "B" near Baikal to "E" over the northeastern Pacific, becomes the most apparent until day(+8), when the TPUHS event has largely decayed (Fig. 6j).

    4.1.2. From geopotential height and wave flux anomalies

    To confirm that the TPUHS-related teleconnection patterns identified above are RWTs, we similarly display in Fig. 7 the lead/lag regressions of geopotential height and horizontal Eliassen-Palm (EP) flux and its divergence anomalies. It is clear that the height anomaly centers exhibit teleconnection patterns similar to those of the vorticity anomaly centers in Fig. 6; plus, the significant anomalous EP flux flow that links the teleconnection centers clearly indicates that the teleconnection patterns are indeed RWTs. Specifically, for the teleconnection pattern downstream of the TP at day(-7) when the TPUHS is weak, the wave-flux flow is mainly in the midlatitudes along the zonal direction. Subsequently, the teleconnection anomaly centers during this time are seen mainly to be linked by this midlatitude wave-flux flow from the Baikal region, while the wave-flux flow from the TP region is still relatively trivial (Fig. 7a). With the growth of the TPUHS and the southward shifting of the SWJ later on, the midlatitude wave-flux flow gradually weakens, while that originating from the TP region increases and gradually becomes the main wave-flux flow linking the anomaly centers (P-Q-R1-S-T) (Figs. 7b-d). This suggests that, during the developing period of the TPUHS, the TP-related wave-flux flow can strongly modulate the RWT pattern in the extratropics, and is mainly responsible for a significant RWT pattern that extends from the TP to the northeastern Pacific and western coastal region of North America.

    Fig. 7. Lead/lag regressions against the THI of the geopotential height anomalies (contours; units: gpm; interval: 4), the wave activity flux anomalies (vectors; units: 10-2 m2 s-2; amplitudes larger than 0.6 are shown) calculated from the lead/lag regressions of stream function, and the wave activity flux divergence anomalies (shaded; units: 10-5 m s-2) at 200 hPa when the THI leads for (a) -7 days, (b) -5 days, (c) -4 days, (d) -3 days, (e) -1 day, (f) 0 days, (g) 2 days, (h) 4 days, (i) 6 days and (j) 8 days. Stippling denotes the 90% confidence level for geopotential height anomalies, and the blue lines in (c), (d) and (j) delineate the Rossby wave rays. The numbers in the upper-left corner of each panel indicate the lead time of the THI. The blue letters and rays mark the RWT and the anomaly centers along it.

    However, it should be noted that the wave-flux direction accompanying the upstream teleconnection pattern is southeastward rather than northwestward, indicating that this RWT is not originated from the TP region but from the North Atlantic region. Based on the climatological mean wave flux pattern (data not shown), we know that this RWT is a recurrent teleconnection pattern that plays an important role in linking the climate anomalies over the North Atlantic region to those over the Asian region (Chang et al., 2001; Buermann et al., 2005; Ren and Hu, 2014). Nevertheless, this recurrent RWT pattern largely diminishes and breaks up around the TPUHS peak from day(-1) (Figs. 7e and f), as also shown in Fig. 6.

    Around the TPUHS peak from day(-1), the anomalous high over the TP during the developing period is gradually replaced by an anomalous low, as already shown in Fig. 5. This displacement of the geopotential anomaly center over the TP also results in the break-up of the downstream RWT (P-Q-R1-S-T) due to the displacement of the wave flux source (Figs. 7e and f). Furthermore, the anomalous low over the TP (especially its western part) in turn seems to act as a new wave source, which points to the Baikal region and corresponds to significant intensification of an anomalous high center over the Baikal region from day(+1) (data not shown) to day(+4) (Figs. 7g and h). Although the anomalous TP low weakens quickly after day(+1), the wave-flux flow from the western TP to the Baikal region is persistently clear (Figs. 7g-i). This implies a clear linkage between the anomalous TP low and the anomalous Baikal high (center "B"), despite the zonal wave-flux flow in the midlatitudes seeming also to contribute to the intensification of center "B" during this time. After, center "B" becomes the main wave-flux divergence center for a new RWT that extends eastward, and a continuous eastward wave-flux flow from "B" to "E" becomes clear until day(+8) (Figs. 7j).

    4.2. Barotropic structure of the RWTs

    After showing the different RWT patterns from the developing to the decaying period of the TPUHS, next we diagnose the vertical structure of the anomaly centers along the RWTs. To do this, we choose day(-3) and day(+8), when the RWTs are the most pronounced, and show in Fig. 8 the vertical cross sections of the regressed geopotential height anomalies along the RWTs. It can be seen that the geopotential height anomaly centers along both RWTs consistently exhibit an equivalent barotropic structure. The exception is the anomaly center "P" over the TP at day(-3), which is anomalously positive/negative above/below 500 hPa and shows a general baroclinic structure. This demonstrates that these anomaly centers are indeed forced by dynamical processes associated with the RWTs; meanwhile, center "P" over the TP, which acts as the main wave source of the RWT P-Q-R1-S-T from day(-5) to day(-3) during the developing period of the TPUHS, is primarily thermally forced.

    Furthermore, although the anomalously positive "P" center becomes relatively weaker with the growth of the TPUHS until day(-3), it is obvious that other anomaly centers along the RWT P-Q-R1-S-T are stronger and exhibit a much deeper vertical structure than those along the RWT B-C-D-E (Fig. 8a vs Fig. 8b). The significant anomalies along the former RWT can span vertically from the lower troposphere to the stratosphere up to 50 hPa (Fig. 8a), whereas those along the RWT B-C-D-E are mostly confined to below 100 hPa——except center "B", which also spans beyond 30 hPa. The vertically deep structure of the anomaly centers along the RWTs implies that the RWTs may have significant effects on the circulation systems in the northern extratropics.

    Fig. 8. Vertical cross sections of the regressed geopotential height anomalies (contours; units: gpm; interval: 2) (a) along the P-Q-R1-S-T RWT at day(-3), and (b) along the B-C-D-E RWT at day(+8). Shaded areas indicate the 90% confidence level of regression, based on the t-test.

    5. Effects of the RWTs on circulation and weather in the northern extratropics
    5.1. RWT indices

    To demonstrate the effects of the TPUHS-related RWTs on circulation and weather in the extratropics, we define two RWT indices to capture the synoptic variabilities of the RWTs more effectively than using the THI index. The indices are based mainly on the RWT patterns on day(-3) and day(+8), when the RWTs are the most pronounced and complete. For the RWT during the developing period of the TPUHS, we choose to define the index based on the P-Q-R1-S-T branch. Specifically, with this RWT as an example, we first calculate the weight coefficients (wi) for the five anomaly centers based on their relative intensities on day(-3), \begin{equation} \label{eq5} w_i=\frac{h_i}{\sum_{i={\rm P}}^{i={\rm T}}|h_i|} , \ \ (6)\end{equation} where hi is the maximum value of the geopotential height anomaly center i (P, Q, R1, S, T). We then use the wi to define the daily RWT index for the developing period of the TPUHS (denoted as WTI1) through \begin{equation} \label{eq6} {\rm WTI}_1=\sum_{i={\rm P}}^{i={\rm T}}{(w_iH_i)} , \ \ (7)\end{equation} where Hi is the daily normalized geopotential height anomaly time series for the anomaly centers. Similarly, the daily RWT index for the decaying period of the TPUHS (denoted as WTI2) is defined as \begin{equation} \label{eq7} {\rm WTI}_2=\sum_{j={\rm B}}^{j={\rm E}}(w_jH_j) . \ \ (8)\end{equation} Where wj is as same as wi, but for the geopotential height anomaly center j (B, C, D, E). Obviously, the values of the WTI1 and WTI2 daily indices fall within the range 0-1. As expected, Fig. 3 shows that the two defined wave indices are significantly correlated with the THI, and the maximum correlation appears on the day when WTI1 leads the THI by three days [day(-3)], and on the day when WTI2 lags the THI by seven days [day(+7)]. Below, based on these two wave indices, we diagnose the effects of the TPUHS-related RWTs on circulation and weather in the extratropics.

    5.2. Effects of the TPUHS-related RWT during the TPUHS developing period

    Figure 9 shows the regressed anomaly patterns of the geopotential height at 200 hPa and 500 hPa (shading in Figs. 9a and b), surface air temperature (T s, Fig. 9d), and 850 hPa wind and daily precipitation (Fig. 9c) anomalies, against the first RWT index (WTI1) defined above. Firstly, it is apparent that the geopotential height anomaly patterns in Figs. 9a and b are largely similar to that shown in Fig. 7d, because of the significant relationship between the THI and WTI1 shown in Fig. 3. From the circulation patterns of the summer climatology (contours in Figs. 9a and b), it is clear that the growth of the TPUHS can indeed exert a series of local and remote impacts on the circulation systems along the RWT in the troposphere. Specifically, the positive "P" over the southern TP and the stronger negative "Q" together yield a slightly stronger but southward-shifted SAH along with a southward shifting of the SWJ (Fig. 9a; also shown in Fig. 7d). This corresponds to an anomalously stronger and southward-shifted NWPSH at 500 hPa over southeastern China (Fig. 9b). On the other hand, the coexisting negative "Q" and downstream positive "R1" centers support an eastward extension of the SAH to the northwestern Pacific region (Fig. 9a), and a strengthening of the NWPSH below in the middle troposphere over that region, which in turn favors a pattern with a low to the west and a high to the east (or a "low-west-high-east" pattern) over the region from eastern China to the northwestern Pacific region (Fig. 9b). Therefore, we can see that the wave-train-related anomalous precipitation zone in East Asia is southwest-northeast oriented——from the southeastern TP, the middle and lower reaches of the Yangtze and Huaihe river valleys, to Japan——where the anomalous lower-tropospheric flow converges (Fig. 9c). Accompanying this is anomalously low T s over the region from East China to Japan (Fig. 9d). Meanwhile, negative precipitation and warm T s anomalies exist to the south and north of the positive precipitation anomaly zone, respectively (Figs. 9c and d).

    Fig. 9. The regressed (a) 200-hPa and (b) 500-hPa geopotential height anomalies (shaded; units: gpm), (c) daily rainfall and 850-hPa wind (vectors; units: m s-1) anomalies (shaded; units: mm), and (d) surface air temperature anomalies (shaded; units: °C) against the RWT index WTI1. Contours denote the corresponding summertime (20 July to 20 August) climatology (units: gpm; interval: 40). Stippling indicates the 90% confidence level of the regression, based on the t-test.

    Similarly, by supporting the formation of a low-west-high-east pattern over the west coast of North America, the negative "S" and downstream positive "T" centers are responsible for the positive precipitation anomaly center in that region, as well as the cold T s anomalies over a wider region of the North Pacific, Alaska and northeast of Kamchatka (Figs. 9a-d). Meanwhile, the positive geopotential height anomalies related to center "T" over the eastern North Pacific act to weaken the TUTT over the northern Pacific (Fig. 9a), which is another important circulation system in the upper troposphere in northern summer (Kelly and Mock, 1982). The weakening of the TUTT obviously weakens the southwesterly flow from the eastern North Pacific to the western part of the United States, which should prevail in boreal summer (Fig. 9a). This corresponds to the warm T s anomalies over the North America region (Fig. 9d), although no significant negative precipitation anomalies appear (Fig. 9c).

    5.3. Effects of the TPUHS-related RWT during the TPUHS decaying period

    Firstly, it can be seen from Fig. 10 that the precipitation and T s anomalies associated with the second TPUHS-related RWT are much weaker and largely scattered (Figs. 10c and d), due to the relatively weaker anomaly centers along the RWT (Figs. 10a and b). Since the SAH as well as the NWPSH show less significant changes during this time (Figs. 10a and b), the precipitation anomalies are largely scattered over most of East and South China, and the T s anomalies are only weakly negative over the region from East China to Japan (Figs. 10c and d). Nevertheless, it is clear that the positive "B" and negative "C" centers support a high-west-low-east pattern from the Baikal region to the east of Japan, responsible for the strong and warm T s anomalies over a wider region of Northeast Asia (Fig. 10d). Around the region between the negative "C" and downstream positive "D" center, significantly positive precipitation anomalies exist over the North Pacific to the east of the Japan region (Fig. 10c). In addition, the geopotential height anomalies associated with the positive "D", and downstream negative "E" centers, and the even weaker positive center southeast of center "E", contribute to deepen the TUTT (Fig. 10a); however, this only results in weak and cold T s anomalies over the northwest region of North America and over the northeastern North Pacific (Fig. 10d), due to the weak intensity of the centers along this RWT.

    Fig. 10. As in Fig. 9 but for the regression against the RWT index WTI2.

    6. Summary

    This study concerns the sub-monthly variability of the upper atmospheric heat source over the TP and the related RWTs in the northern extratropics in summer. To effectively capture the variability of the TPUHS over the entire TP region, our study mainly focuses on the period from 20 July to 20 August, when the climatological westerly jet resides just to the north of the TP. We first identify that the dominant variability of the TPUHS in summer (July-August) is quasi-biweekly; and with the intensive development of an anomalous TPUHS event, the further elevated LH heating may temporarily offset the anomalous atmospheric circulation structure (anticyclonic circulation above cyclonic circulation) that prevails during the earlier developing period of the TPUHS, temporarily resulting in a low anomaly center over the TP in the upper troposphere where the SAH usually exists. However, this thermally forced anomalous low center diminishes rapidly due to the counteracting dynamic effect of the persisting lower/upper convergence/divergence over the TP.

    During the developing period of a TPUHS event, an anomalous high corresponding to weak and shallow LH over the TP acts as the main wave source of a southern-branch RWT (P-Q-R1-S-T) along the SWJ from day(-5) to day(-3), which extends northeastward and eastward to the northeastern Pacific and west coast of North America. However, accompanying the southward shift of the anomalous TP high, and the replacement by an anomalous TP low around the TPUHS peak, this TPUHS-related RWT is broken up from day(-1). Nevertheless, the existing anomalous low during this time then temporarily acts as a wave source to connect to an anomalous high over the Baikal region. After the anomalous TP low quickly diminishes, this strong anomalous Baikal high becomes the main wave source of a new RWT during the decaying period of the TPUHS. This RWT extends eastward from the Baikal region to the northeastern Pacific around eight days after the TPUHS peak.

    Compared to that during the decaying period of the TPUHS, the RWT pattern during the developing period is stronger and presents a much deeper barotropic structure. Correspondingly, the significant extratropical influences of the earlier RWT during the developing period of the TPUHS are much stronger and more systematic than those of the later RWT during the decaying period of the TPUHS. By modulating the circulation systems in the northern extratropics, the earlier RWT is associated with an anomalous southwest-northeast-oriented precipitation band extending from the southern TP and the middle and lower reaches of the Yangtze and Huaihe river valleys to Japan, whereas the later RWT only yields a significant precipitation anomaly center over the North Pacific——mainly to the east of Japan. The T s anomalies associated with the earlier RWT are also generally stronger than those associated with the later one.

    This study demonstrates the varying RWT patterns from the developing to the decaying period of anomalous TPUHS events, and investigates the related thermodynamic processes and the remote climate effects of the TPUHS-related RWTs. The dynamic processes responsible for the linkage between the TPUHS variation and the changes in the RWT pattern are also illustrated. However, as already indicated in section 4, the RWT patterns identified in this study might be implicitly contributed by the midlatitude RWT prevailing in boreal summer, including the upstream RWT originated from the Atlantic. However, the possible effects of midlatitude circulation on the local circulation anomalies over the TP are subject to further investigations in the future. Nevertheless, the demonstrated RWT patterns are what we can always observe during the life cycle of anomalous TPUHS events. In our group's future work, we will also use general circulation models to simulate the RWT patterns that are purely excited by the anomalous TPUHS, and provide further evidence of the mechanisms, processes and the variations of the TPUHS-related RWTs.

    Acknowledgements. Thanks to the two anonymous reviewers for their constructive comments and suggestions. This work was jointly supported by the National Science Foundation of China (Grant Nos. 91437105, 41575041 and 41430533) and the China Meteorological Administration Special Public Welfare Research Fund (Grant No. GYHY201406001). We are grateful for the availability of the NCEP-NCAR reanalysis dataset via the website http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html, and the GPCP dataset via http://precip.gsfc.nasa.nov/.

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    Key words
    Tibetan Plateau
    upper atmospheric heat source
    Rossby wave train
    circulation and weather

    Authors
    Chuandong ZHU
    Rongcai REN
    Guoxiong WU