1. Introduction
Teleconnection is an important and common phenomenon in large-scale atmospheric circulation motion. Atmospheric teleconnection patterns have prominent influences on global climate variability (Lau and Nath 1996; Alexander et al. 2002; Liu and Alexander 2007; Wu et al. 2009). Since the 1980s, many studies have employed various statistical methods to determine the dominant modes of atmospheric variability. Wallace and Gutzler (1981) identified five preferred patterns in the Northern Hemisphere (NH) winter 500-hPa height. Blackmon et al. (1984a,b) examined different time scale fluctuations. The long time scale patterns are similar to results in Wallace and Gutzler’s (1981), while the intermediate-scale 10–30-day fluctuations involve zonal wave trains along the westerly jet. The structure and energetics of these patterns were further investigated by Nakamura et al. (1987). Variations of 700-hPa height have also attracted attention (e.g., Chen 1982; Esbensen 1984; Van den Dool and Livezy 1984; Barnston and Livezey 1987). The Pacific–North America (PNA) pattern and zonally oriented waves along the westerly jet are prominent features. In addition, many researchers worked on circulation variability in the Southern Hemisphere (SH) (e.g., Mo and White 1985; Karoly 1989, 1990; Berbery et al. 1992; Mo and Higgins 1998; Kidson 1999). The Antarctic Oscillation (Rogers and van Loon 1982; Gong and Wang 1999), the zonal wavenumber-3–5 pattern at middle latitudes (Mo and White 1985; Karoly 1990), and the Pacific–South America pattern (PSA; Karoly 1989; Mo and Higgins 1998) were identified.
Boreal winter patterns are generally ENSO-related (Trenberth et al. 1998). Several teleconnection patterns in the NH summer associated with the summer monsoon have also been found, including the Pacific–Japan (PJ) and East Asian–Pacific (Nitta 1987, 1989; Huang and Lu 1989; Huang and Sun 1992) and Indo-Asian–Pacific (J. Li et al. 2013) patterns in convective activity, the “silk road” pattern in the 200-hPa meridional velocity (Lu et al. 2002; Enomoto et al. 2003), and the circumglobal teleconnection (CGT) pattern (Ding and Wang 2005; Ding et al. 2011). Teleconnection patterns are thought of as stationary waves emanating from a source region. These patterns, in general, are either zonally or meridionally oriented. The zonally oriented patterns, such as the Eurasian, the silk road, and the CGT patterns, develop along the westerly jet, which acts as a waveguide (Hoskins and Ambrizzi 1993, hereafter HA93), while the meridionally oriented patterns (e.g., PNA, PJ, and PSA) result from the arcing path of the meridional propagation of two-dimensional spherical Rossby waves (Hoskins and Karoly 1981). Hence, the study of Rossby wave propagation is vital to understand the variations of atmospheric circulation.
Rossby wave theory is based on the concepts of dispersion and group velocity (Rossby 1945; Yeh 1949). Disturbances are usually defined theoretically in terms of the limiting case of a linear perturbation on a basic state. Therefore, the features of the waves obtained depend on the fixed basic state. Rossby (1945) and Yeh (1949) set the basic state to be uniform and used the ß-plane approximation to study the one-dimensional motion. Longuet-Higgins (1964, 1965), Hoskins et al. (1977), and Hoskins and Karoly (1981) extended the theory to two-dimensional wave propagation on a sphere in a latitudinally varying medium. The “great circle” ray path is suggested as the preferred trajectory of stationary wave energy dispersion from the tropics to the extratropics. However, this meridional propagation is limited to westerly flow. Stationary wave energy is absorbed at the critical latitudes where the wavelength becomes very large and amplitude tends to zero as a result of the zonal wind approaching zero.
These results are based on zonally symmetric flow, which is far from the real situation. Modeling studies by Simmons (1982), Webster and Holton (1982), and Branstator (1983) emphasize the longitudinal variation of the zonal basic flow and suggest the existence of a “westerly duct” for cross-equatorial waves. Atmospheric circulation in the NH and SH interacts through the Hadley cell or the cross-equatorial flows. Cross-equatorial teleconnection was found over the tropical east Pacific and Atlantic during the NH winter in the upper troposphere (Hsu and Lin 1992; Tomas and Webster 1994). This is termed as Rossby wave propagation from the NH to SH via the westerly window (HA93). However, some wave train patterns associated with boreal summer monsoon have been identified across tropical easterly belts (e.g., Nitta 1987; Krishnamurti et al. 1997; Lin 2009; Y. Li et al. 2013). He (1990) stated the significant interactions between the atmospheric circulations in the NH and SH in boreal summer related to the large-scale monsoon systems. Recent modeling works by Lee et al. (2013) and Liu and Wang (2013) suggest that the NH summer monsoon can influence the SH circulation anomalies through barotropic responses, in which the meridional background wind plays an important role. So far, there are two different ways of illustrating the cross-easterly responses. One is the meridional propagation of stationary Rossby waves directly from the forcing to the other hemisphere, obtained by adding a mean meridional flow in the nondivergent vorticity equation and shallow water equations (Schneider and Watterson 1984; Farrell and Watterson 1985; Watterson and Schneider 1987; Esler et al. 2000; Kraucunas and Hartmann 2007). The other is the advection of the vorticity by perturbation divergent flow, which can transmit the tropical heating in the easterly to subtropical westerly jet and then make Rossby waves effectively. This way is proved by Sardeshmukh and Hoskins (1988) using a linearized barotropic vorticity equation with divergence and decomposing the wind into rotational and divergent components. Even though the two illustrations are still far from the real atmosphere (Held et al. 2002), they are landmarks in the effort made by meteorology researchers to understand the complicated reality.
Results in the barotropic model (Schneider and Watterson 1984; Esler et al. 2000; Kraucunas and Hartmann 2007), baroclinic model (Lee et al. 2013), and even the intermediate model (Liu and Wang 2013; Ji et al. 2014) have suggested the importance of the former way in the interhemispheric teleconnection. However, the fundamental equation in the theory is linearized on a zonal mean state, neglecting the longitudinal variation, which is remarkable in the meridional wind particularly. Unlike the zonal wind, the meridional wind features a notable regional structure. These longitude-dependent structures must have different effects on the stationary wave propagation. Hence, we present the interhemispheric stationary wave propagation theory based on a latitudinally and longitudinally varying flow (herein referred to as a horizontally nonuniform flow) in this study as an extension of previous studies (Karoly 1983; Schneider and Watterson 1984).
The dispersion relation and ray equations for Rossby waves based on a horizontally nonuniform flow were derived by Karoly (1983). Although this more realistic flow complicates the wave theory and may undermine the validity of the Wentzel–Kramers–Brillouin (WKB) approximation, more realistic atmospheric responses could be understood qualitatively. Shaman and Tziperman (2005, 2007) used two-dimensional ray trajectories through low-pass filtered climatological wind fields to illustrate the ENSO-teleconnection influences on the South Asian monsoon. Additionally, the propagating behavior of nonzero frequency waves differs from stationary waves (Karoly 1983; Yang and Hoskins 1996; Li and Nathan 1994, 1997) and is not discussed here.
Li (1991) analyzed the global characteristics of the 30–60-day oscillation and found cross-equatorial correlation centers over the middle Pacific at 500 hPa. Ambrizzi et al. (1995) examined the global teleconnection patterns of the 10–30-day variability in the 200-hPa austral winter streamfunction for the period 1979–89. However, the cross-equatorial pattern in their work is unclear. The different results may indicate that the cross-equatorial teleconnection patterns depend on time scale. We attempt to further examine the interhemispheric teleconnections in the boreal summer mean streamfunction field.
The paper is organized as follows. In section 2, the data, methodology, and the model used in this work are introduced. Teleconnection patterns, especially those across the equator, in the June–August (JJA)-mean streamfunction field are analyzed in section 3 using more recent and longer time series than that in Ambrizzi et al. (1995). In section 4, the fundamentals of two-dimensional spherical Rossby wave theory over horizontally nonuniform flow are reviewed, and the possibility of interhemispheric propagation of stationary waves is discussed theoretically. Then, both the wave theory and barotropic model are applied to investigate the interhemispheric stationary wave propagation in idealized and realistic flows. Results from wave theory are shown in section 5 and from the barotropic model in section 6. Conclusions and dynamical implications are discussed in section 7.
2. Data, methodology, and model
a. Data and methodology
The 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data from 1958 to 2001 (Uppala et al. 2005) are used in this study. The data are obtained from a global spectral model with T159 truncation over a 320 × 160 global grid. The JJA-mean streamfunction is used in the teleconnectivity analysis, and the climatological JJA and December–February (DJF) flows are employed to study the interhemispheric propagation of stationary waves.
The WKB approximation used in Rossby wave theory requires the variation of the perturbation to be much smaller than that of the basic state. For this reason, a two-dimensional Fourier expansion truncated at zonal and meridional wavenumber 5 is used to smooth the climatological flows. The smoothed flows preserve most of the large-scale signals and approximate the desired slowly varying media in which the Rossby waves propagate. Details of this method are given in Sun and Li (2012).
b. Barotropic model
3. Interhemispheric teleconnections in the JJA 300-hPa streamfunction
Figure 1 shows the teleconnectivity distribution for the 300-hPa streamfunction and eddy streamfunction (with zonal mean removed) fields. The significant cross-equatorial correlations in the tropics are the most prominent feature in the streamfunction field (Fig. 1a). This indicates that the circulations in the two hemispheric tropics are closely related. These patterns are mainly dipoles and are zonally symmetric on the one-point correlation maps of mostly base points (not shown), as seen in previous studies (Hsu and Lin 1992; Lau et al. 1994; Ambrizzi et al. 1995). They seem to be the symmetric responses to tropical heating. However, the correlation pattern over the Pacific sector has a wave train–like structure. This pattern is more clearly defined in the eddy streamfunction field but for two additional centers at high latitudes in the SH. The one-point correlation maps of the base points at 22.991°S, 204.75°E (Fig. 2c) and 12.897°N, 200.25°E (Fig. 2d) show the positive and negative centers distributed at intervals over the Pacific and Atlantic. The structure is PSA-like, but previous PSA studies have not mentioned the north tropical Pacific center. We refer to it as the North Pacific–South America (NPSA) pattern here to distinguish it from the traditional PSA. Figures 2a and 2b show another wave train pattern in the eddy streamfunction field with significant correlation centers over North Africa, South Africa, the south Indian Ocean, the Southern Ocean, and the Antarctic. This pattern, called the North Africa–Antarctic (NAA) pattern, has a wavenumber-2 structure in the SH. It indicates that climate variability over Africa and Antarctica may be related, a hypothesis that will require specific statistical and dynamical studies. In addition, the cross-equatorial correlations over the tropical Indian Ocean and equatorial South America are also distinct. Thus, it can be inferred that interhemispheric teleconnections are clearly evident in JJA in the upper troposphere.
Teleconnectivity maps for the JJA fields of (a) streamfunction and (b) eddy streamfunction (with zonal mean removed) at 300 hPa. Negative signs have been omitted and correlation coefficients multiplied by 100. The gray shading indicates regions where the value is >55. The easterly regions are filled in with red dots. Arrows connect centers of strongest teleconnectivity with the grid points. The calculation is based on the JJA-mean data from ECMWF for the period 1958–2001.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
One-point correlation maps of eddy streamfunction for the base points (a) 25.234°S, 15.75°E, (b) 29.719°N, 16.875°E, (c) 22.991°S, 204.75°E, and (d) 12.897°N, 200.25°E. The gray shading indicates areas significant at the 95% confidence level. The easterly regions are filled in with red dots. The red symbols “+” and “Δ” denote the location of the base point and the minimum negative correlation, respectively.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
In DJF, the interhemispheric teleconnection is found over the tropical east Pacific (Hsu and Lin 1992), where the westerly window is embedded in the tropical easterly belt (Fig. 3b). The spatial distribution of the stationary wavenumber (Fig. 3d; defined as
(a),(b) The climatological 300-hPa wind vectors (m s−1) and the meridional gradient of absolute vorticity Qy (color shading, 10−11 m−1 s−1); (c),(d) the total wavenumber of the stationary waves defined as (2.13) in HA93. (left) JJA and (right) DJF. The climatological flows are smoothed using a two-dimensional Fourier series truncated at zonal and meridional wavenumber 5.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
4. Interhemispheric propagation theory in a horizontally nonuniform flow
a. Fundamentals
b. The possibility of interhemispheric propagation
over regions where the ageostrophic flow cannot be neglected, such as the tropics. Here, β and γ are different, indicating inhomogeneity of the basic state;
for steeper waves that have a larger scale in the x direction than y. Here, tanα is large because of the structure of the waves themselves.
When
When
- When
It can be seen that ug has the same form in flows with and without υ, whereas the form of υg in the two flows is distinct. In the with-υ case, υg depends on the basic state, especially
When
5. Sensitivity of interhemispheric propagation to the meridional wind in idealized flows
Five experiments are designed to investigate the dependence of the meridional wave propagation on the meridional basic wind. The basic state in experiment Exp0 includes only zonal flow (see Fig. 4a), the without-υ case. Exp1–Exp4 are the with-υ cases, with different meridional wind structures in the tropics (briefly introduced in Table 1 with different y0 and V0; see Figs. 4b,c). Given E = 18 m s−1 and F = 14 m s−1, the zonal wind is symmetric about the equator: westerly at middle to high latitudes with a maximum of 26 m s−1 and easterly in the tropics with a maximum about 4 m s−1. The meridional wind in Exp1 (Exp2) is northerly (southerly) in the tropics, while that in Exp3 (Exp4) is antisymmetric about the equator, southerly (northerly) in the NH, and northerly (southerly) in the SH. They all have the same maximum value of 2 m s−1. The Exp1 (Exp2) meridional wind profile crudely represents the climatological cross-equatorial flows at the upper troposphere in JJA (DJF) and lower troposphere in DJF (JJA). Exp4 crudely describes the trade wind in the intertropical convergence zone. Exp3 denotes the situation observed at DJF 300 hPa over the tropical Indian Ocean and Indonesian islands. The role of the meridional background wind in the cross-equatorial stationary wave propagation is isolated by comparing the results in these experiments.
(a) Zonal wind profile and (b) meridional wind profiles in Exp1 (dashed line) and Exp2 (solid line), and (c) Exp3 (dashed line) and Exp4 (solid line).
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
Sensitivity experiments with different meridional wind distributions.
a. WKB analysis
The meridional wavenumbers for zonal wavenumber 1, 3, and 6 in Exp0, Exp1, Exp2, and Exp3 are shown in Fig. 5. In Exp0, there are two real solutions of l with opposite signs in the westerly flow, indicating two branches of wave energy dispersion, one equatorward and the other poleward. However, there is no real solution in the easterly flow, indicating that wave energy dissipates quickly. Hence, the easterly region is known as the dead zone for stationary wave propagation. The zero-zonal-wind latitudes at about 10° are critical latitudes, where the meridional wavenumbers tend to infinity. The magnitude of the meridional wavenumber decreases with latitude. For the waves with zonal wavenumbers 1, 3, and 6, the meridional wavenumber becomes zero at 80°, 60°, and 30°, respectively. This means that long waves propagate farther than short waves and play an important role in tropic–extratropic interactions. These results are similar to those obtained in previous studies (e.g., Hoskins and Karoly 1981) but differ over the region of meridional flow in Exp1, Exp2, and Exp3. In Exp1, the positive branch of the meridional wavenumber tends to infinity at different latitudes for different waves: about 30° for k = 1, 20° for k = 3, and 18° for k = 6. The singularity in stationary wavenumber occurs at the latitude where 
The meridional wavenumber profiles for the without- and with-υ cases. (a)–(c) Exp1 (red) and Exp0 (gray) for zonal wavenumber k = 1, 3, and 6, respectively. (d)–(f),(g)–(i) As in (a)–(c), but for Exp2 and Exp0 and for Exp3 and Exp0, respectively.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
The field of meridional wavenumber shows the propagable and nonpropagable regions for stationary waves. Ray tracing results are presented in order to further understand how the wave energy disperses. Figure 6 shows the results from Exp0. Consistent with the meridional wavenumber field, one poleward and one equatorward ray are excited from wave sources at 30°N and 30°S, for each value of zonal wavenumbers 1–5. Both branches go eastward. The poleward branch of the wave with zonal wavenumber 1 reaches 80° after 8 days and then turns equatorward, while the other waves turn equatorward at lower latitudes. As they propagate, their wavelength first increases and then decreases after the waves reach the turning latitudes, with wavenumber 4–6 (6000–10 000 km) at 20°–45°, 0–3 (>10 000 km) at higher latitudes, and 7–9 or even larger (<5000 km) at lower latitudes until the equatorward propagation terminates at 10° as the zonal wind approaches zero. Results of Exp1–Exp4 are shown in Fig. 7. The notable differences in meridional propagation occur at the tropics, where the meridional winds are different. In Exp1, the tropics are dominated by easterly and northerly flow. Both the equatorward branch of waves triggered at 30°N and the reflected waves from the poleward branch propagate across the easterly flow, and continue propagating out of the tropical SH, then along the great circle with longer wavelength again. The equatorward waves triggered at 30°S and the reflected waves from the poleward branch, however, are reduced by the north wind near 15°S. The meridional flow in Exp2 is antisymmetric to that in Exp1. As a result, the propagation behaviors are antisymmetric to those in Exp1. Cross-equatorial propagation from the SH to NH is allowed, while that from the NH to SH is impeded by the southerly flow. In Exp3, the equatorward propagation in both the NH and SH disappears at about 15°, where the northerly flow in the NH and the southerly flow in the SH are strong. In Exp4, the equatorward waves propagate symmetrically to the equator and then turn westward. These results suggest that the basic meridional wind is important for the meridional propagation of stationary waves. The direction of meridional propagation is largely dependent on that of the meridional wind. Results of Exp1 and Exp2 indicate that cross-equatorial stationary wave propagation is made possible but limited to one direction by the cross-equatorial flow. In addition, the stationary waves tend to have a shorter wavelength when they propagate across the easterlies.
Ray paths (curves) and the evolution of total wavenumber (color) along the paths for k = 1–5 waves in the without-υ basic flow (Exp0). The red dots denote the wave sources at 30°N and 30°S. The propagation speed is indicated by the 2-day interval marked by black solid dots for k = 1, triangles for k = 2, square boxes for k = 3, crosses for k = 4, and circles for k = 5. The paths are terminated when the total wavenumber exceeds 40.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
As in Fig. 6, but for the with-υ flows: (a) Exp1, (b) Exp2, (c) Exp3, and (d) Exp4.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
b. Barotropic model results
The results of the WKB analysis are examined further using the barotropic model linearized on the idealized flow in Exp0–Exp4. The parameters controlling the source strength and width are set as (x0, y0) = (180°, 30°), xd = 12°, yd = 7°, and S0 = 1 × 10−10 s−2 as in Wang et al. (2005). Figure 8 shows the steady response of the streamfunction to the sources placed in the NH and SH. In Exp0, a negative streamfunction response occurs over the wave source. Positive and negative centers are distributed at intervals northeast of the local response, tracing out the great circle trajectory of energy dispersion. Cross-equatorial responses are not possible in this experiment with easterly flow in the tropics in the absence of meridional wind. In Exp1 where the north wind dominates, there are clear wave train responses in the SH to the NH source but almost no responses in the NH to the SH source. In contrast, in Exp2 where the south wind dominates, there are strong responses in the NH to the SH source but no response in the SH to the NH source. These results suggest that a meridional wind allows interhemispheric response in the same direction across the tropical easterlies. In addition, the spatial structures of the cross-equatorial responses in Exp1 (Exp2) are tilted SW–NE (SE–NW) and are of narrower spatial extent than those at middle to high latitudes. These features are consistent with the theoretical analysis and wave ray results. For Exp3 and Exp4, there are almost no responses to the sources in the other hemisphere. The streamfunction responses in Exp3 terminate at about 15°. These features are also similar to the results of the wave ray trajectories.
Steady eddy streamfunction responses (thin contours, 106 m2 s−1) to the wave sources (thick lines, 10−11 s−2) for (top)–(bottom) Exp0–Exp4 with sources in the (a),(c),(e),(g),(i) NH and (b),(d),(f),(h),(j) SH. Contours are from −3 to 3 with an interval 0.6.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
The above analysis presents the sensitivity of the interhemispheric stationary wave propagation to the distribution of the basic meridional wind. Wang et al. (2005) examined the northern extratropical responses to tropical forcing through a southerly conveyor. Their results show that a stronger southerly wind contributes to stronger extratropical responses. Similarly, in order to further illustrate the effect of the basic meridional wind on the interhemispheric responses, we take Exp1 as the control experiment and perform another two sensitivity experiments in which the basic meridional wind has the same distribution but different strength. The parameters V0 in the experiments are set to be 1 and 4 m s−1, corresponding to the cases with weaker and stronger meridional wind, respectively. Figure 9 shows the steady streamfunction responses to the vorticity source located in the NH in these two experiments and their differences with respect to the result in Exp1. The SH responses in Exp1 are definitely weaker than those in the case with stronger meridional wind but stronger than those in the case with weaker meridional wind. This result indicates that the strength of the meridional wind affects the interhemispheric responses by modulating the energy dispersion velocity.
Dependence of the streamfunction responses to the NH source on the strength of the meridional wind: (a),(b) as in Fig. 8c, but for weaker and stronger meridional basic winds with V0 = 1 and 4 m s−1, respectively; (c) difference between the steady responses in the Exp1 flow with V0 = 1 and 2 m s−1; (d) as in (c), but for V0 = 4 and 2 m s−1. Contours in (a),(b) are from −3 to 3, with an interval 0.6, and in (c),(d), they are from −1 to 1 with an interval 0.2.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
6. Interhemispheric propagation of stationary waves in realistic flows
a. Wave ray results
In section 5, the sensitivity of the interhemispheric propagation of stationary waves to the basic meridional wind is examined, and the interhemispheric propagation behavior of stationary waves is shown to be strongly dependent on the meridional background wind. In this section, we apply the ray tracing method and the barotropic model to climatological flows. Cross-equatorial flow is observed in both the lower and upper troposphere. The climatological cross-equatorial flow in DJF is from the SH to NH in the upper troposphere and from the NH to SH in the lower troposphere. It is opposite in JJA. These seasonally and vertically opposite flows over the tropics would provide us good examples to compare the stationary wave propagation behaviors under them. Thus, we set the smoothed winter and summer climatological flows at 300 and 850 hPa as basic states to examine the possibility of stationary Rossby waves propagating through the tropical easterlies from one hemisphere to the other under these horizontally nonuniform flows.
Usually, the barotropic model is applied to one appropriate level. The upper troposphere is often used in many previous studies for the larger stationary wave component (e.g., Simmons 1982; HA93). Ting (1996) suggested that the barotropic model is able to describe the real atmosphere at the equivalent barotropic level and identified the equivalent barotropic level around 350 hPa in winter and 500 hPa in summer by comparing the rotational response of the barotropic linearized model with divergence at different vertical levels and that of the baroclinic model. However, the basic state in her work is zonal mean. The results would be changed when the horizontally nonuniform flow is taken into consideration. Therefore, the best choice of the vertical level for the barotropic model is still uncertain. The discussion about the extratropical responses to tropical heating by Held et al. (2002) indicates that the tentative work on the application of the barotropic model to the low level may be worthy. Hence, we involve the wave ray equations and the barotropic model to both the upper and lower troposphere.
A series of wave sources in the tropical NH and SH separately and the wave ray trajectories for each source are calculated. Since the wavenumber varies along the trajectory, the initial zonal wavenumber should be given before the calculation. We have compared the trajectories for the initial zonal wavenumber-1–6 waves. They have different behaviors over some regions, which seem to depend on the configuration of the basic state. For the interhemispheric propagation, they are generally similar. Here, we take zonal wavenumber 4 as an example, and derive the initial meridional wavenumber by solving the dispersion relation. Where there are three real solutions, the one with the smallest absolute value is chosen. Only waves with meridional wavenumber less than 40 (corresponding to wavelengths longer than 1000 km) are thought to propagate.
Figure 10 shows the stationary wave ray paths and the associated total wavenumber based on the smoothed DJF 300- and 850-hPa climatological flows for sources in the tropical NH and SH. Under the 300-hPa flow, rays originating from the tropical NH mostly follow the great circle route: that is, poleward from the tropics and then reflecting equatorward. The wavenumber along these rays is about 4–9, which means they are synoptic scale (5000–10 000 km). At the entrance region of the African–Asian subtropical jet, the rays originating over North Africa and South Asia with a wavenumber of about 7–9 propagate eastward and northward and reflect equatorward at 45°N, where the wavenumber is larger. This is consistent with the waveguide effect of the westerly jet (HA93). At the exit region of the jet, the wave rays take diverse paths, some poleward reaching to 80°N and some equatorward across the equator to SH middle to high latitudes. The cross-equatorial rays appear over the east tropical Pacific, where the so-called westerly duct is embedded in the tropical easterlies. This is in agreement with previous work (Hsu and Lin 1992; HA93). The ray paths originating from the tropical SH to the middle to high latitudes exhibit a more remarkable great circle feature. The difference with respect to the rays originating in the NH is that the cross-equatorial propagation occurs not only in the westerly duct, but also in the easterly region over the Maritime Continent from the northeast of Australia to East Asia. Compared with the situation under 300-hPa flow, the propagation of steady waves based on 850-hPa flow is slower, and the scales are shorter, mainly as a result of the slower and less uniform climatological flow in the lower troposphere. The flow in the tropics is predominantly easterly. Stationary waves forced by the sources in the positions chosen here can only propagate very weakly in the traditional theory. However, in the horizontally nonuniform flow, waves with scales less than 4000 km can propagate westward and southward from the NH tropical easterlies across the embedded westerlies as far as 20°S. The cross-equatorial propagation from the NH to SH is evident over Africa, the Maritime Continent, and South America. The meridional basic wind over the northern tropics is predominantly northerly. Stationary wave propagation from the southern tropics to the NH seems to be prevented. Thus, to summarize, the interhemispheric propagation of stationary waves in DJF across the tropical easterlies tends to be restricted to one direction by the cross-equatorial flow, while that through the westerly duct in the upper troposphere is bidirectional.
Ray paths (curves) and the evolution of total wavenumber (colors) along the rays in the smoothed DJF (a),(b) 300- and (c),(d) 850-hPa flows (gray vectors), with sources in the (a),(c) NH and (b),(d) SH tropics. The light gray shading indicates the easterly wind regions. The initial zonal wavenumber is 4. The initial meridional wavenumber is derived from the dispersion relation. Where there are three solutions, the one with the largest wavelength is chosen. Propagation is terminated when the total wavenumber exceeds 40. Red points denote wave sources. The climatological flows are smoothed using a two-dimensional Fourier series truncated at zonal and meridional wavenumber 5.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
The interhemispheric stationary wave propagation behavior in JJA is shown in Fig. 11. At 300 hPa, the tropical easterlies occupy a belt at 10°S–20°N, while strong northerly cross-equatorial flows prevail over Africa, the Indian Ocean, the east Pacific, and the Atlantic. Wave rays initiated in the NH, especially over central Africa and the Asian monsoon region as well as the north and east of South America, propagate along these cross-equatorial flows and then reach middle and high latitudes in the SH. They propagate westward and southward in the easterly belt with wavelength smaller than 4000 km and then turn eastward with wavelength increasing to synoptic scale after entering the westerlies. The wave propagation initiated at the SH sources is predominantly poleward and eastward, along arc-like routes. There is no cross-equatorial propagation into the NH because of the impediment of the northerly. At the lower troposphere, significant cross-equatorial flow is observed from the south tropical Indian Ocean and Australia to South Asia and northward to East Asia. Guided by this flow, the stationary waves triggered over the south tropical Indian Ocean and north Australia propagate across the equator to South and East Asia. These waves are scaled 2000–4000 km (Fig. 11d). Additionally, evident meridional propagation of stationary waves across the easterly is found over the northwest Pacific and Atlantic, steered by the southwest flows of the subtropical highs (Fig. 11c). These eastward and northward trajectories of stationary waves will maintain an obvious meridional structure of the responses to the tropical convective heating. Meridional patterns over these two regions at low level have been observed (Nitta 1987; Kosaka and Nakamura 2006, 2010a,b). Since the cross-equatorial flow is from the SH to NH, the abovementioned meridional wave propagation is almost poleward, with negligible equatorward propagation. Consequently, it can be deduced that the interhemispheric propagation of stationary waves in JJA follows the direction of the cross-equatorial flow.
As in Fig. 10, but for the smoothed JJA flow.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
We examined the teleconnectivity of the JJA eddy streamfunction in section 2. The wave train NAA pattern is found (Figs. 1b, 2c,d). Here, we plot wave ray trajectories to determine whether this pattern results from energy dispersion by Rossby waves. Figure 12 shows the trajectories and energy dispersion speeds of stationary waves starting from 15°S, 150°E with different initial zonal wavenumbers. The supposed source is located in the region of easterlies. Based on the theory with only zonal wind in the basic-state, stationary waves from such a source cannot propagate through the easterly belt. This means that the circulation anomalies over North Africa cannot affect the SH circulation. However, the significant correlation centers in the SH suggest that there is, in reality, a close relationship between North African and SH circulation. Ray trajectories based on the horizontally nonuniform basic flow match the teleconnection pattern very well. The propagation behaviors of the different initial zonal wavenumber waves diverge south of 10°S. The wavenumber-1 wave propagates westward and poleward to 30°S, 34°W, and then turns eastward and propagates along about 27°S. The wavenumber-2–5 waves propagate along a similar trajectory, eastward and poleward until they arrive at polar regions. The trajectory connects the five correlation centers. Wavenumber-6–8 waves are reflected at lower latitudes. It seems that the conclusion that long waves propagate farther and faster than short waves is still satisfied, but it is not as strict as the situation in the zonally symmetric flow, since the zonal wavenumber varies along the ray in the horizontally nonuniform flow.
Ray paths (curves) of initial zonal wavenumber-1–8 waves (indicated by color) in the smoothed JJA 300-hPa flow with a source at 5°N, 20°E (large red dot). The markers on the rays indicate 2-day interval. Contours, shading, and filling by little red dots are as in Fig. 2b.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
b. Barotropic model results
In section 6a, wave ray tracing was employed to examine the possibility of interhemispheric propagation of stationary waves in nearly realistic climatological flows. Interhemispheric propagation across the tropical easterlies is mainly determined by the cross-equatorial flow. The westerly duct over the eastern tropical Pacific in DJF in the upper troposphere behaves as a two-way waveguide for stationary wave propagation between two hemispheres. In this section, we attempt to examine these results further using the barotropic model.
Figure 13 is the steady eddy streamfunction response to the tropical NH sources for the DJF 300-hPa flow. When the source is located in the entrance region of the North African–Asian jet, positive and negative centers occur at intervals over Eurasia and downstream. When the source is at 90°E, the downstream responses are stronger. The cross-equatorial signals can be detected over the east Pacific and are enhanced when the source moves to 150° and 210°E. The effect of the westerly duct on the waves propagating from the tropical NH to the SH is clear. In addition, the PNA-like pattern is clearly seen when the sources are at 90°, 150°, and 210°E. Figure 14 shows the eddy streamfunction responses to the SH tropical sources. The east tropical Pacific is still an important area for interhemispheric responses, but 100°–150°E is also key for cross-equatorial propagation from North Australia to Asia. This corresponds to the wave ray results in Fig. 10b. Note that the climatological flow over the Maritime Continent is easterly, while to its north the flow is southerly. This tends to favor the northward propagation of stationary waves and contributes to the interhemispheric responses. At 850 hPa, the interhemispheric responses are generally weak (figures not shown) and are effectively absent in the NH when the sources are in the tropical SH, but there are still some cross-equatorial signals when the sources are in the tropical NH.
Steady eddy streamfunction responses (thin contours, 106 m2 s−1) to the sources (thick lines, 10−10 s−2) located at (a) 15°N, 30°E, (b) 15°N, 90°E, (c) 15°N, 150°E, and (d) 15°N, 210°E in the smoothed DJF 300-hPa flow. Contour values and intervals are shown below each panel.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
As in Fig. 13, but for sources located at 15°S.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
The JJA results are shown as Figs. 15 and 16. At 300 hPa, the steady responses to sources at 20°N, 60°E and 20°N, 190°E exhibit a distinctive wave-train pattern in the SH. The forcing located over the Indian summer monsoon region can trigger a cyclonic and anticyclonic anomaly west and east of it, respectively, and then one branch of wave trains propagates northward to high latitudes in NH, one branch propagates southward into the subtropic SH. The anomalies centered over North Africa, South Africa, the south Indian Ocean, and the South Ocean, as well as the South Pole, agree with the NAA pattern indicated in Figs. 2a and 2b. The barotropic responses in subtropical SH in the model are more robust than the observation, and they have almost the same pattern with globally zonal wavenumber 3 when the forcing moves over the tropical Pacific. Compared with the NAA pattern, the meridional structure of the NPSA is less described by the barotropic model. When the source moved to the tropical SH, the zonal wavenumber-3 pattern is stronger, especially when the source is at the entrance region of the jet. However, the responses in the NH to the SH forcings are much weaker than those in the SH to the NH forcings. The interhemispheric responses only occur from the NH to the SH at the upper troposphere in JJA in the same direction as the cross-equatorial flow.
As in Fig. 13, but for the JJA flow with sources at (a) 20°N, 60°E, (b) 20°N, 190°E, (c) 20°S, 60°E, and (d) 20°S, 210°E.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
As in Fig. 15, but for the 850-hPa flow with sources at (a) 15°N, 150°E, (b) 15°N, 300°E, (c) 15°S, 90°E, and (d) 15°S, 150°E.
Citation: Journal of the Atmospheric Sciences 72, 8; 10.1175/JAS-D-14-0239.1
At 850 hPa, a pattern remarkably similar to the PJ pattern can be seen when the source is at 15°N, 150°E, and another wave train pattern is found over North America in response to the source at 15°N, 300°E. The latter is in good agreement with the meridional teleconnection described by Kosaka and Nakamura (2010b). Nevertheless, few signals are found in the SH when sources are set in the NH. However, significant positive responses are found over South Asia to the north of the local anomalies triggered by the vorticity sources at 15°S, 90°E and 15°S, 150°E. When the source moves to other longitudes in the tropical SH, there is negligible cross-equatorial response. These longitude-dependent responses are attributed to the strong cross-equatorial flows from the SH to NH over the Australian–Asian monsoon region, which may transmit the wave energy across the easterlies in their directions.
7. Discussion and conclusions
In this study, we examined the interhemispheric propagation of stationary Rossby waves using statistical and theoretical analysis. Teleconnections of the JJA streamfunction field at 300 hPa were investigated using a correlation method (Wallace and Gutzler 1981). Significant correlations between the streamfunction in the NH and tropical SH were found. Two wave train patterns in the eddy streamfunction were identified: one over North Africa–Antarctica and another over the North Pacific–Atlantic sector. The former links the circulation anomalies over North Africa and the South Pole and is known as the NAA pattern. The latter is similar to the PSA pattern, but with an additional center located in the north tropical Pacific, and is referred to as the NPSA pattern. Both patterns straddle the tropical easterly belt. It is implied by our results that the direct propagation of stationary waves from one hemisphere to the other may be responsible for these interhemispheric teleconnections.
The possibility of interhemispheric propagation for stationary waves is presented based on two-dimensional spherical Rossby wave theory under the horizontally nonuniform basic state. The meridional group velocity at the traditional critical latitudes (where 
The paths of interhemispheric stationary wave propagation in the climatological upper- and lower-troposphere flows are investigated using the ray tracing method and barotropic model. In DJF, tunnels of interhemispheric stationary wave propagation are found in the upper troposphere over the east tropical Pacific and the Maritime Continent. The east Pacific tunnel is the westerly duct, which supports bidirectional propagation. However, propagation through the Maritime Continent is unidirectional because of the basic meridional wind. In JJA, the cross-equatorial propagation is from the NH to SH in the upper troposphere and from the SH to NH in the lower troposphere, consistent with the cross-equatorial flows. Because of the remarkable cross-equatorial flows, the Australian–Asian monsoon region is key for interhemispheric stationary wave propagation, which implies that the stationary waves may transmit the monsoonal heating far away from the monsoon region, even to the middle to high latitudes in the other hemisphere. Several modeling works recently suggest that stationary barotropic waves play an important role in the influence of summertime monsoon heating in the tropical NH on the circulations in the SH (Kraucunas and Hartmann 2007; Liu and Wang 2013; Lee et al. 2013). Therefore, this study provides an insight into global responses to the Asian monsoon (Lin 2009). Note that these results are based on a barotropic nondivergent model. How the tropical divergence will change the results needs to be investigated, and verification using a baroclinic model is desired in the future.
We emphasized the modulation by the meridional background wind of the interhemispheric propagation of stationary waves in the text. Since the zonal background wind is an order of magnitude larger than the meridional background wind at middle and high latitudes, the waveguide effect of the westerly jets may dominate the wave propagation (Naoe et al. 1997; Enomoto and Matsuda 1999; Müller and Ambrizzi 2007). Even so, our results suggest that the inclusion of the meridional background wind in the wave ray theory may better describe the actual teleconnection patterns along the jets. Shaman et al. (2012) extended the wave ray method to complex wavenumbers, but here we still consider real wavenumbers.
Previous studies (Dima et al. 2005; Kraucunas and Hartmann 2007) suggested the important role of the cross-equatorial momentum flux by the mean meridional circulation in accelerating the tropical easterly and the formation of the equatorial symmetric Rossby wave response to off-equatorial forcing. Hence, the transport of the momentum and energy by the interhemispheric propagating Rossby waves is an important and essential topic for understanding the general atmospheric circulation variations. An elaborate investigation would be worthwhile in the future.
Acknowledgments
The author Yanjie Li acknowledges useful discussions with David Karoly, Fred Kucharski, and In-Sik Kang during her visit to the Abdus Salam International Centre for Theoretical Physics (ICTP). We thank the European Centre for Medium-Range Weather Forecasts for providing the reanalysis data. This work is supported by the National Natural Science Foundation of China (Grants 41030961, 41205034, and 91437216).
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