Planetary Wave Modulations Associated with the Eurasian Teleconnection Pattern

Abstract

This study analyzes the modulation of planetary waves associated with the Eurasian (EU) pattern—one of the dominant teleconnection patterns seen over northern Eurasia in the boreal winter—through composite analyses using the Japanese 55-year reanalysis dataset to reveal its dynamic mechanism, including wave-mean flow interaction.

From the viewpoint of deviation from climatological flow, the EU pattern is known as a stationary Rossby wave teleconnection type with an equivalent barotropic structure and action centers over northern Europe, mid-western Siberia, and Japan. However, from the viewpoint of deviation from the zonal average, the EU pattern modulates planetary wave activities, which include the East Asian winter monsoon as one component.

In the positive phase of the EU pattern, corresponding to the enhanced Asian monsoon, the upward and eastward propagation of the planetary wave from Central Eurasia to the North Pacific in the troposphere is enhanced, compared with that of the climatology. The baroclinic energy conversion from the zonal mean to the deviation from that over East Asia contributes to the amplified planetary wave. The enhanced upward and eastward propagating planetary wave converges in the upper troposphere, thereby causing anomalous extratropical direct circulation and cold outflow toward the lower mid-latitude troposphere. These results indicate that the EU pattern is one of the global dynamic modes related primarily to planetary wave activities.

1. Introduction

The Eurasian (EU) pattern is one of the dominant teleconnection patterns in the boreal winter. The EU pattern has action centers over northern Europe, midwestern Siberia, and Japan (Wallace and Gutzler 1981), indicating its significant impact on winter climate conditions over East Asia (Wang and Zhang 2015). Since the strong positive phase of the EU pattern often brings severe cold winters, associated with the enhanced East Asian winter monsoon (EAWM), improved monitoring and forecasting of the pattern has been an important issue for long-range forecasts of Japan's climate. However, there are few studies on the detailed structure of the EU pattern and related dynamics.

The horizontal structure of teleconnection patterns has two types: the north–south seesaw type and the wave train type. The EU pattern belongs to the latter (Nakamura et al. 1987), and a stationary Rossby wave propagating eastward from northern Europe to the Far East is considered a major part of its dynamics (Wang and Zhang 2015). The EU pattern generally has an equivalent barotropic anomalous structure, with its largest amplitude near the tropopause (Wang and Zhang 2015).

Using potential vorticity inversion analysis, Takaya and Nakamura (2005) showed that the upper-tropospheric amplified ridge in mid-western Siberia, which is enhanced due to the equivalent barotropic Rossby wave propagation from northern Europe, induces anomalous wind near the ground surface, resulting in cold air advection in front of the ridge and intensifying the Siberian high (Takaya and Nakamura 2005) and EAWM. This means that the vertical structure of the ridge changes from the equivalent barotropic to the westward tilting due to interaction with the surface thermal conditions. In other words, the planetary wave activities related to the Siberian high are enhanced compared with the climatological ones. The anomaly over mid-western Siberia is one of the crucial action centers of the EU pattern for the East Asian climate. When the ridge is strengthened in the positive phase of the EU pattern, the mechanism proposed by Takaya and Nakamura (2005) is expected to enhance the Siberian high and related planetary wave activities.

Iwasaki et al. (2014) analyzed the climatological outflow of cold air from the high- to mid-latitude in the Northern Hemisphere winter, using mass-weighted isentropic zonal mean (MIM). They showed that there are two mainstreams of cold air over East Asia and the east coast of North America. The East Asian cold stream flows southward in geostrophic balance with the eastward pressure gradient force from the Siberian high toward the Aleutian low. The southward-intruded cold air presses the upper-level isentropic surface westward as a reaction of the eastward pressure gradient force. This means that the westward angular momentum is converted from a southward cold airflow into the upward Eliassen-Palm (E-P) flux. In energetics terms, the cold stream along the down-gradient geopotential height releases considerable amounts of available potential energy (APE) and creates the eddy kinetic energy (Iwasaki et al. 2014). In the positive phase of the EU pattern, the East Asian cold stream, being stronger than the climatology, should contribute to the enhancement of the upward propagating planetary wave by this mechanism. The amplified planetary wave activities due to the EU pattern will affect the downstream mean flow through their wave-mean flow interaction.

Modifications of planetary waves by the EU pattern are discussed by Takaya and Nakamura (2013). They showed that the trough of planetary waves over the Far East region is modulated by the EU pattern. More specifically, in association with the EU pattern, the strengthened (weakened) planetary trough tends to be shifted southward (northward) in cold (warm) winter over the mid-latitude Far East. However, they mainly investigated the modifications of the upper-tropospheric planetary waves and did not discuss characteristics of the wave packet propagations and the vertical structure.

In this study, we focus on the modifications of planetary waves associated with the EU pattern, including the characteristics of the wave propagation, the vertical structure, and their influence on the zonal mean field, from the viewpoint of wave-mean flow interaction.

2. Data and method

In this study, we use the Japanese 55-year reanalysis dataset (JRA-55; Kobayashi et al. 2015) in mid-winter (January) from 1958 to 2019 to diagnose atmospheric circulation. “Climatological” circulation is defined as the 30-year average from 1981 to 2010. On the other hand, “eddy” is defined as deviation from the zonal mean in each January. From this definition, “eddy” corresponds to components of the “planetary waves”.

The EU index is derived using 500 hPa geopotential height field based on the definition supplied by Wallace and Gutzler (1981):   

where Z* represents the normalized 500 hPa geopotential height deviation from the climatology. Figure 1 shows the interannual time series of the EU index in January over 62 years, from 1958 to 2019. To examine the statistical characteristics of the EU pattern, we conduct a composite analysis of the atmospheric circulation using the EU index. The statistical significance is evaluated using t-test. In the composite analysis, we used the average of the 10 top EU index years (EU+) and the bottom 10 years (EU−) over the 62-year period, and the difference in composite between EU+ and EU− is defined as “anomaly”. The EU+ and EU− years are shown as follows, in descending and ascending order of their index value:

Fig. 1.

Interannual time series of the Eurasian (EU) index in January from 1958 to 2019.

• EU+: 1963, 1984, 2011, 1981, 1986, 1976, 2012, 1959, 2004, 1995,
• EU−: 1972, 1973, 1989, 1964, 2006, 1997, 1969, 1992, 1991, 1990.

To investigate wave-mean flow interaction associated with the EU pattern, we used the quasi-geostrophic three-dimensional wave-activity flux (WAF) of stationary Rossby waves Fs defined by Plumb (1985):   

where is the static stability, with the caret indicating an area average over the area north of 20°N, a is the Earth's radius, Ω is the angular velocity of the Earth's rotation, φ is the latitude, λ is the longitude, p = pressure/1000 hPa, z = −H lnp with the constant scale height H of 7 km, u is the zonal wind, v is the meridional wind, T is the temperature, and Φ is the geopotential. The prime denotes the eddy component. The WAF is derived from the monthly average, thus corresponding to the flux of planetary wave activities. To examine the wave-mean flow interaction on the zonal mean meridional plane, we used the MIM (Iwasaki 1989) and the E-P flux based on the MIM, which is defined by the Eq. (2.14) in Tanaka et al. (2004). The MIM framework can express the lower boundary condition appropriately in the ground surface vicinity. To assess the influence of the eddy variation associated with the EU pattern on the zonal mean circulation, we also used the Arctic Oscillation (AO) index defined by Thompson and Wallace (1998).

3. Results

3.1 Anomaly patterns related to the EU pattern

Figure 2 shows differences in the composites between EU+ and EU−, i.e., anomalies, and their 90 % confidence levels. The anomaly pattern is not so much different from the EU+ composite deviation from the climatology (figure is not shown). The geopotential height at 300 hPa shown in Fig. 2a indicates a wave train associated with the positive phase of the EU pattern, with positive anomalies over mid-western Siberia and negative anomalies over northern Europe and near Japan. Furthermore, significant anomalies are also seen over a wide area, such as from the North Pacific to North America, the North Atlantic, and the polar region. This is consistent with the results of previous studies (e.g., Nakamura et al. 1987; Ohhashi and Yamazaki 1999) suggesting that the EU pattern is not a phenomenon limited to Eurasia. The sea level pressure (SLP) shown in Fig. 2b indicates that both the Siberian high and the Aleutian low are stronger in the EU+ years, corresponding to the enhanced EAWM and the amplified planetary wave present there, in phase with the climatology (Held et al. 2002; Takaya and Nakamura 2013). In East Asia, the anomaly pattern of SLP shifts eastward compared with the anomalous 300 hPa geopotential height (Fig. 2a). The 850 hPa temperature shown in Fig. 2c exhibits a wide area of low-temperature anomalies in East Asia, corresponding to the enhanced winter monsoon.

Fig. 2.

Difference between EU+ and EU− in January of (a) geopotential height at 300 hPa, (b) sea level pressure, and (c) temperature at 850 hPa. Contour intervals are (a) 40 m, (b) 2 hPa, and (c) 1 K. Hatching indicates the area where the differences are statistically significant at the 90 % confidence level.

3.2 Modulated planetary wave structure related to the EU pattern

In the previous subsection, we indicated that the EU pattern is related to the activity of EAWM: the activity of EAWM is enhanced associated with the EU+. Takaya and Nakamura (2013) found that the interannual variability of EAWM accompanies modulations of planetary wave activities in the upper troposphere. As mentioned in the introduction, referring to Iwasaki et al. (2014), the East Asian cold stream related to EAWM generates an upward E-P flux. Therefore, the enhanced cold stream associated with the EU+ is expected to force more amplified planetary waves than the climatological one. To understand the modulation of the planetary wave associated with the EU pattern clearly, the eddies associated with the EU pattern are compared with the climatology through composite analysis.

Figure 3 shows geopotential height eddies at 300 hPa and 1000 hPa and horizontal components of WAFs at 300 hPa of the climatological fields, composite for EU+, and EU−. Vertical components of WAFs at 500 hPa are superimposed on the 300 hPa height eddies in Figs. 3a–c. As is well known (e.g., Held et al. 2002), the planetary wave is seen in the lower troposphere, with a high pressure over the Eurasian continent (the Siberian high) and a low pressure over the North Pacific (the Aleutian low) (Fig. 3d). The planetary wave tilts westward with height (Figs. 3a, d), exhibiting the baroclinic structure. Corresponding to the baroclinic structure, upward propagation of the planetary wave activity is clearly seen from midwestern Siberia to the North Pacific in the middle troposphere (Figs. 3a). The planetary wave indicates larger amplitude in the case of EU+ (Figs. 3b, e) compared with the climatology (Figs. 3a, d) and EU− (Figs. 3c, f). These results indicate that the amplified planetary wave and the upward propagation from mid-western Siberia to the North Pacific are crucial dynamic characteristics of the positive phase of the EU pattern.

Fig. 3.

Geopotential height distributions of the eddies (contour) and the horizontal component of 300 hPa WAF defined by Plumb (1985) (arrows; unit: m² s⁻²). (Left column) the climatological eddy, (middle column) composite maps for EU+, and (right column) those for EU− at (top row) 300 hPa and (bottom row) 1000 hPa. Contour intervals are 60 m for (a)–(c), and 30 m for (d)–(f), respectively. Color shading in (a)–(c) are vertical components of 500 hPa WAF (unit: Pa m s⁻²). Color and arrow scale are shown below in each panel.

To further investigate the features of the planetary wave in the mid-latitude related to the EU pattern, longitude-height cross sections of geopotential height eddy and WAF, averaged from 40°N to 60°N, are shown in Figs. 4a–c. The westward tilting planetary wave with height and the associated upward propagation are clearly seen from mid-western Siberia to the North Pacific in the climatology. The planetary wave is more amplified further downstream in the case of EU+ (Fig. 4b) compared with that in the case of the climatology (Fig. 4a) and EU− (Fig. 4c). From Central Eurasia to the North Pacific, the convergence of WAF in the middle and upper troposphere is also stronger in the case of EU+ than that of the climatology and EU−.

Fig. 4.

Longitude–pressure cross section of (a) the climatological, (b) EU+, and (c) EU− composited geopotential height eddies (contour) and WAF defined by Plumb (1985) [arrows; unit: m² s⁻² (zonal), Pa m s⁻² (vertical)] averaged over 40°N to 60°N. Contour intervals are 60 m. Color shading denotes the divergence of WAF. The WAF and its divergence are shown above 850 hPa level. Color and arrow scale are shown below the figure.

3.3 Baroclinic energy conversion related to the EU pattern

From the viewpoint of energetics, we examined the modulation of planetary waves associated with the EU pattern. In energetics terms, the planetary wave can be developed by baroclinic energy conversion (CP) due to the conversion from the APE of the basic state to that of the eddy. Figure 5 shows the vertically integrated CP, from 950 to 300 hPa, in the Euler mean framework (Kosaka and Nakamura 2006) defined by   

where p represents pressure, f is the Coriolis parameter, and is the stability parameter, with the gas constant of dry air R and the specific heat of the air at the constant pressure C_p . The overbars and primes represent the zonal mean and the eddy, respectively. In the RHS of Eq. (3), the first term is dominant because of | ū | ≫ | v̅ | and v′T′ ≫ u′T′ over the strong baroclinic zone. CP is derived from the monthly average and is thus related to the planetary wave.

Fig. 5.

(a) Climatological, (b) EU+, and (c) EU− composites of baroclinic energy conversion CP vertically integrated from the 950 to 300 hPa level. Contour interval is 4 W m² s⁻¹ without the zero line. Hatching indicates the area where the differences of CP between the composite and the climatology are statistically significant at the 90 % confidence level.

The positive CP is seen in climatology over East Asia and to the west and east of North America, particularly over East Asia with the large amplitude (Fig. 5a). The case of EU+ shows significantly enhanced CP over East Asia (Fig. 5b) compared with the climatology and EU− (Fig. 5c). The time scale of the effective APE conversion is evaluated as where is the vertically integrated (from 950 hPa to 300 hPa) eddy APE and ⟨ ⟩ denotes areal average from East Asia to the western North Pacific (20–80°N, 60°E–180°). For EU+, EU−, and the climatology, τ_CP are 2.9, 5.5, and 3.5 days, respectively, indicating a more effective APE conversion in the case of EU+ compared with the climatology and EU−. These results show that the amplification of planetary waves due to the baroclinic energy conversion in East Asia is one of the important factors for the eastern parts of the EU pattern. The EU+ case also indicates enhanced CP not only in East Asia but also to the west coast of North America. Although it is interesting how the CP, which is far away from Eurasia, is related to the EU pattern, this is beyond the scope of this paper.

4. Discussion

4.1 Zonal mean anomalies related to the EU pattern

As shown in Fig. 4, from Central Eurasia to the North Pacific, the convergence of WAF in the middle and upper troposphere is stronger in the case of EU+ than that of the climatology, and there is no clear difference in other areas. Therefore, it is expected that the zonal mean westerly wind in the middle to upper troposphere is decelerated in the mid-latitude associated with the positive phase of the EU pattern compared with the climatology due to the wave-mean flow interaction. To examine the EU pattern's influence on the zonal mean circulation in the troposphere, we performed MIM diagnosis (Iwasaki 1989). As mentioned in Section 2, the MIM framework can express the wave-mean flow interaction in the lower troposphere appropriately, including the ground surface vicinity. In this subsection, we conducted composite analysis for the MIM.

Figure 6 shows differences in the composite of E-P flux and its divergence (EPFD), mass stream function, temperature, and zonal wind between EU+ and EU−. Since the E-P flux is calculated from daily data, it includes the influence not only from stationary eddies but also transient eddies. In the positive phase of the EU pattern, the E-P flux anomalies (Fig. 6a) in the mid-latitude indicate upward propagation from the ground surface to the upper troposphere. The anomalously positive (negative) EPFD near the surface (in the upper troposphere) contributes to the acceleration (deceleration) of the westerly wind. These EPFD anomalies drive the meridional circulation, with southward flow in the lower troposphere and northward flow in the upper troposphere (Fig. 6b), indicating enhancement of the climatological extratropical direct (ETD) circulation (Iwasaki 1989). The southward flow anomalies in the lower troposphere in the mid-latitude correspond to the cold stream from the high latitude in the Northern Hemisphere (Iwasaki et al. 2014), indicating enhanced cold air outflow in the positive phase of the EU pattern compared with the climatology.

Fig. 6.

Difference between EU+ and EU− in January in the zonal mean composite of (a) the divergence of the E-P flux (contour interval 1.0 m s⁻¹ day⁻¹), (b) mass stream function (contour interval 0.5 × 10¹⁰ kg s⁻¹), (c) temperature (contour interval 0.5 K), (d) zonal wind (contour interval 1.0 m s⁻¹), (e) and (f) stationary component of (a) and (b), respectively, and (g) and (h) transient component of (a) and (b), respectively. Arrows in (a), (e), and (g) indicate E-P flux (unit: kg s⁻²). Gray contours denote the average of EU+. Color shadings indicate the area where the differences are statistically significant at the 90 % confidence level. The color bar shows the values of each difference.

Corresponding to the enhanced cold stream, anomalous low temperature is seen near the ground surface of 30–40°N. In contrast, an anomalous high temperature is seen in the lower to middle troposphere of 50–70°N, where the anomalous descent is associated with the ETD circulation (Fig. 6b). Consistent with the thermal wind balance, anomalous westerly and easterly winds are seen over 20–40°N and to its north, respectively (Figs. 6c, d).

To further investigate the wave-mean flow interaction, due to the planetary wave associated with the EU pattern, we divide the circulation into a stationary component defined by the monthly average and a transient component defined by the residuals (Kodama et al. 2010). The stationary component mainly corresponds to the planetary wave. The stationary component of the anomalous E-P flux, EPDF, and mass stream function in Figs. 6e and 6f are similar to the total component (Figs. 6a, b) over 30–50°N. The transient component (Figs. 6g, h), in contrast, shows opposite signs to the total and stationary component. These results indicate the stationary component's crucial contribution to the wave-mean flow interaction associated with the EU pattern, and the transient component acts to dump the variability associated with the stationary eddy.

4.2 EU pattern and cold air outbreaks in the Northern Hemisphere

The EU pattern is closely related to the East Asian cold stream's strength, which is one of the mainstreams of the cold outflow in the Northern Hemisphere (Iwasaki et al. 2014). Thus, the EU pattern is also expected to contribute to the zonal mean activity of the cold air outbreaks in the Northern Hemisphere. This relation is examined using the mass stream function at 45°N, 850 hPa (χ), where the climatological meridional circulation in boreal winter changes from downward to equatorward in the MIM diagnosis. As indicated by Iwasaki and Mochizuki (2012), χ is a good proxy for the cold outflow activity in the Northern Hemisphere. Figure 7a shows a scatter diagram of the EU index and χ. The relationship between them is statistically significant with the correlation coefficient of +0.48, indicating that the EU index accounts for approximately 25 % of the cold outflow variation in the Northern Hemisphere. Figures 7b–d show the differences in the composite between the 10 top and 10 bottom years for the values χ during the 62-year period. The differences between 500 hPa geopotential height, SLP, and 850 hPa temperature in Figs. 7b–d exhibit similar patterns to those of the EU anomalies shown in Fig. 2, indicating a close relationship between the EU pattern and the hemispheric activity of the cold outflow.

Fig. 7.

(a) Scatter diagram of the EU index (horizontal axis) and mass stream function at 45°N, 850 hPa (χ) (vertical axis; unit: 10¹⁰ kg s⁻¹), and difference in the composite of the (b) geopotential height at 500 hPa, (c) sea level pressure, and (d) temperature at 850 hPa between the 10 top and 10 bottom years of mass stream function at 45°N, 850 hPa (χ) in January. Contour intervals are (b) 20 m, (c) 2 hPa, and (c) 1 K. Hatching indicates the area where the differences are statistically significant at the 90 % confidence level.

It is well known that the AO (Thompson and Wallace 1998) is also related to the hemispheric cold outflow. The relationship between χ and the AO index with the correlation coefficient of −0.23 is weaker than that between the χ and the EU index, although the correlation is significant with a confidence level of 90 %. Figure 8 shows the mass stream function differences in composite between the 10 top and 10 bottom years for the AO index during the 62-year period. Although the ETD circulation is enhanced in the negative phase of AO, the center of the anomalous circulation shifts northward compared with that associated with the EU pattern (Fig. 6b). Although the AO has a significant relationship to the EU pattern with a correlation coefficient between their indices (−0.38) at a confidence level of 99 %, it is closely related to cold air redistribution within the genesis regions in the high latitude, as suggested by Kanno et al. (2015), rather than the cold outflow toward the mid-latitude.

Fig. 8.

As in Fig. 6b, but the difference in composite of mass stream function between AO+ and AO− in January. AO+ years are 1993, 1989, 1973, 2007, 2017, 1962, 1975, 1992, 1981, and 2009. AO− years are 1977, 1969, 1960, 1963, 1966, 1959, 1970, 1979, 1980, and 1985.

5. Conclusions and remarks

In this study, we examined the planetary wave modifications associated with the EU pattern through composite analyses using JRA-55. In the positive phase of the EU pattern, corresponding to the enhanced EAWM, the upward and eastward propagation of planetary waves from Central Eurasia to the North Pacific in the troposphere is enhanced compared with that of the climatology. The baroclinic energy conversion from the zonal mean flow to eddies over East Asia contributes to the amplified planetary wave. The enhanced upward and eastward propagating planetary wave converges in the upper troposphere, thereby causing the enhanced ETD meridional circulation and cold outflow toward the lower mid-latitude troposphere. These results indicate that the EU pattern is one of the global dynamic modes related primarily to planetary wave activities.

In this study, the EU pattern's excitation mechanism is not investigated. Additionally, future work needs to focus on the relationship between the EU pattern and the Arctic sea ice, decadal climate change, and global warming to deepen understanding on the EU pattern.

The operational seasonal forecasting and climate system monitoring often focus on anomalous circulation factors. This study's results deepen our understanding of EU pattern dynamics by focusing on the modification of the planetary wave structure. Further, it is expected that this procedure will deepen our understanding of the dynamics of other teleconnection patterns and low-frequency variability, improving operational climate service activities.

Acknowledgments

We are grateful to Dr. Mio Matsueda and two anonymous reviewers for their constructive and helpful comments. S. Maeda especially thanks the late Prof. Gambo for teaching the dynamics of Rossby waves and teleconnection patterns through discussion and many letters over a course of more than 25 years. This study is supported in part by the Japanese Ministry of Education, Culture, Sports, Science, and Technology through Grant-in-Aid 15H02129 and 20H05171.

References

•  Held,  I. M.,  M.  Ting, and  H.  Wang, 2002: Northern winter stationary waves: Theory and modeling. J. Climate, 15, 2125-2144.
•  Iwasaki,  T., 1989: A diagnostic formulation for wave-mean flow interactions and Lagrangian-mean circulation with a hybrid vertical coordinate of pressure and isentropes. J. Meteor. Soc. Japan, 67, 293-312.
•  Iwasaki,  T., and  Y.  Mochizuki, 2012: Mass-weighted isentropic zonal mean equatorward flow in the Northern Hemispheric winter. SOLA, 8, 115-118.
•  Iwasaki,  T.,  T.  Shoji,  Y.  Kanno,  M.  Sawada,  M.  Ujiie, and  K.  Takaya, 2014: Isentropic analysis of polar cold airmass streams in the Northern Hemispheric winter. J. Atmos. Sci., 71, 2230-2243.
•  Kanno,  Y.,  M. R.  Abdillah, and  T.  Iwasaki, 2015: Charge and discharge of polar cold air mass in Northern Hemispheric winter. Geophys. Res. Lett., 42, 7187-7193.
•  Kobayashi,  S.,  Y.  Ota,  Y.  Harada,  A.  Ebita,  M.  Moriya,  H.  Onoda,  K.  Onogi,  H.  Kamahori,  C.  Kobayashi,  H.  Endo,  K.  Miyaoka, and  K.  Takahashi, 2015: The JRA-55 reanalysis: General specifications and basic characteristics. J. Meteor. Soc. Japan, 93, 5-48.
•  Kodama,  C.,  Y.  Mochizuki,  S.  Hasegawa,  T.  Iwasaki, and  M.  Watanabe, 2010: Negative correlation between the interannual variabilities of the stationary and transient wave energy in the Northern Hemisphere. SOLA, 6, 37-40.
•  Kosaka,  Y., and  H.  Nakamura, 2006: Structure and dynamics of the summertime Pacific-Japan teleconnection pattern. Quart. J. Roy. Meteor. Soc., 132, 2009-2030.
•  Nakamura,  H.,  M.  Tanaka, and  J. M.  Wallace, 1987: Horizontal structure and energetics of Northern Hemisphere wintertime teleconnection patterns. J. Atmos. Sci., 44, 3377-3391.
•  Ohhashi,  Y., and  K.  Yamazaki, 1999: Variability of the Eurasian pattern and its interpretation by wave activity flux. J. Meteor. Soc. Japan, 77, 495-511.
•  Plumb,  R. A., 1985: On the three-dimensional propagation of stationary waves. J. Atmos. Sci., 42, 217-229.
•  Takaya,  K., and  H.  Nakamura, 2005: Mechanisms of intraseasonal amplification of the cold Siberian high. J. Atmos. Sci., 62, 4423-4440.
•  Takaya,  K. and  H.  Nakamura, 2013: Interannual variability of the East Asian winter monsoon and related modulations of the planetary waves. J. Climate, 26, 9445-9461.
•  Tanaka,  D.,  T.  Iwasaki,  S.  Uno,  M.  Ujiie, and  K.  Miyazaki, 2004: Eliassen-Palm flux diagnosis based on isentropic representation. J. Atmos. Sci., 61, 2370-2383.
•  Thompson,  D. W. J., and  J. M.  Wallace, 1998: The Arctic Oscillation signature in the wintertime geopotential height and temperature fields. Geophys. Res. Lett., 25, 1297-1300.
•  Wallace,  J. M., and  D. S.  Gutzler, 1981: Teleconnections in the geopotential height field during the Northern Hemisphere winter. Mon. Wea. Rev., 109, 784-812.
•  Wang,  N., and  Y.  Zhang, 2015: Evolution of Eurasian teleconnection pattern and its relationship to climate anomalies in China. Climate Dyn., 44, 1017-1028