Physical mechanisms for the dominant summertime high-latitude atmospheric teleconnection pattern and the related Northern Eurasian climates

Summertime atmospheric teleconnection patterns over Eurasia have a significant influence on regional weather and climate. Despite extensive studies on the subtropical patterns, the high-latitude counterpart has received relatively less attention. This study proposes physical mechanisms for the formation and maintenance of the dominant high-latitude teleconnection pattern. The formation of the pattern is associated with variability in synoptic-scale eddy activity due to the meridional gradient of sea surface temperature anomalies in the vicinity of the Gulf Stream, causing a meridional shift of the central axis of storm track at the exit of Atlantic jet. The resultant convergence of transient vorticity fluxes to the west of the British Isles induces low-frequency cyclonic circulation anomalies and continued propagation of Rossby waves downstream along northern Eurasia. Once these circulation anomalies are formed, the subsequent latent heat-related diabatic anomalies over the northern Eurasian landmass act as another source of Rossby waves to maintain the teleconnection pattern. Regional temperature and precipitation variability is closely linked to the wave pattern along a route through northern Eurasia, and even precipitation over the East Asian summer monsoon region is influenced by the teleconnection pattern.


Introduction
In recent decades, severe heat waves, characterized by anomalous high temperatures resulting from highpressure anomalies lasting at least two weeks in Europe or Russia, have more frequently occurred.In particular, heat waves in Eurasia occurred in the summers of 2003, 2010, and 2020 (figure 1), causing enormous socio-economic impacts and human and ecological damages in these regions.The 2003 European heat wave, the hottest summer recorded in Europe since 1540, resulted in the deaths of more than 70 000 people across Europe and damaged grain crops in southern Europe (figure 1(a)) (Robi et al 2008).In addition, the 2010 heat wave that affected the northern hemisphere recorded a maximum temperature of 53 • C in Eastern Europe (Ukraine, Kazakhstan, Belarus, and Georgia) and Russia, causing more than 55 000 deaths in Russia and about $500 billion in damage in northern hemisphere (figure 1(b)) (UNDRR, CRED 2020).Meanwhile, due to the Siberia heat wave that occurred in June 2020, the Arctic Circle recorded the highest temperature of 38 • C in the northeastern region of Siberia, resulting in ecosystem changes such as many wildfires, pest infestations, and melting permafrost (figure 1(c)) (Overland and Wang 2021).Previous studies have suggested that the wellknown large-scale teleconnection patterns in summer, such as the silk road pattern (SRP) and circumglobal teleconnection along upper-atmosphere subtropical jets, may be responsible for persistent extreme weather conditions (Zhu and Li 2016, Li et al 2021).However, the extreme weather-related teleconnection patterns mentioned in figure 1 tend to be confined and propagate along the higher latitudes of the Eurasian continent, where the polar front jet (PFJ) is located.The summer PFJ waveguide in the higher latitudes has not been receiving much attention compared to the summer subtropical jet waveguide (Nakamura andFukamachi 2004, Iwao andTakahashi 2008).However, the maximum variance of total wavenumber K (K s ), indicating a favorable region for propagation of barotropic quasi-stationary Rossby waves, appears to have a large value not only over the low latitude where the subtropical jet locates but also over the northern Eurasian region (figure S1 in the supporting information).This suggests two distinctive pathways for Rossby wave teleconnection on the Eurasian continent in summer.Also, several studies proposed that the meridional gradient of potential vorticity (PV) is much more important (in other words, stretching vorticity is more important) than the meridional gradient of absolute vorticity for the Rossby wave propagation over the northern Eurasian continent in summer (figure 2(b)) (Hoskins et al 1985, Iwao and Takahashi 2008, Wirth 2020, Woollings et al 2023).
Recent studies provide support for the importance of high-latitude teleconnection patterns on the northern Eurasian continent during the summer season.Xie and Kosaka (2016) analyzed the second empirical orthogonal function (EOF) mode using 300 hPa meridional wind data over this region and suggested a relationship with the development of the Okhotsk high-pressure system.However, this study did not offer insights into the formation mechanisms, nor did it provide information on the antecedent conditions that may have led to their development.Li and Ruan (2018) proposed an Atlantic-Eurasian high-latitude teleconnection pattern with five centers of action linked to tropical and subtropical diabatic forcing through idealized model experiments.Meanwhile, Xu et al (2019) identified that vorticity forcing in the North Atlantic (NA) region can be the primary driver of the dominant summertime highlatitude teleconnection pattern (BBC pattern) using the reanalysis data.However, their follow-up work (Xu et al 2022) using the linear baroclinic model does not simulate this teleconnection pattern well, particularly in the downstream region.Despite the recent advances in identifying highlatitude teleconnection patterns, a comprehensive understanding of the precise mechanisms governing the formation and maintenance of the patterns is still lacking.In this study, our primary goal is to demonstrate the detailed physical mechanisms, with a causal relationship focus, governing the formation and maintenance of the dominant summertime highlatitude atmospheric teleconnection pattern.To support our findings, we employ a nonlinear stationary model (SWM) and quantitatively identify the potential for high-latitude Rossby wave propagation through a ray tracing technique.In addition, we illustrate how this pattern relates the climate of both the northern Eurasian region and the East Asian region.These approaches will contribute to better our understanding of the summertime high-latitude teleconnection pattern over the northern Eurasian continent.

Data and methods
The data used includes the following: (1) The monthly mean atmospheric reanalysis data with a horizontal resolution of 1.25 • × 1.25 • from Japanese 55 year Reanalysis (JRA-55) data provided by the Japanese Meteorological Agency (Kobayashi et al 2015).(2) The monthly precipitation data from the Global Precipitation Climatology Project (GPCP) version 2.3 dataset provided by NOAA/OAR/ESRL PSD with 2.5 • × 2.5 • latitude-longitude resolution (Adler et al 2003).Only boreal summer, from June to August (JJA), is considered for the period of 1979-2019.
An EOF analysis is employed to extract the dominant atmospheric teleconnection mode on the northern Eurasian continent.In order to understand the associated spatial patterns, a composite analysis is conducted using the obtained EOF principal component (PC) time series.A 2-6 day Lanczos bandpass filter is applied to obtain signals associated with synoptic-scale disturbances (Duchon 1979).The three-dimensional (3D) wave activity flux (WAF) is calculated to represent the propagation of Rossby wave packets (Takaya and Nakamura 2001).Also, to identify the evolution of wave activity, a ray tracing analysis is performed to the horizontally nonuniform flow by using the divergent barotropic Rossby wave theory (Hoskins andKaroly 1981, Hoskins andAmbrizzi 1993).The ray path of the Rossby wave activity, which is determined by group velocity (c gx and c gy ), is computed by using a fourth-order Runge-Kutta method (Press et al 2007, Seo et al 2012, 2016, 2017): where ω is frequency (ω = 0, for stationary Rossby wave), ūM and vM represent the basic zonal and meridional flow on a Mercator projection, (the total wavenumber), with k and l being zonal and meridional wavenumbers, (the Rossby radius of deformation), with g, H and f 0 being the gravitational acceleration, scale height, and Coriolis parameter, respectively.The zonal and meridional gradients of quasigeostrophic PV qx and qy take the form qx = To simulate the atmospheric teleconnection pattern and examine the dominant forcing mechanism of stationary Rossby waves, we use a SWM (Ting and Yu 1998).This SWM is a fully nonlinear baroclinic model with a dry dynamical core.For damping, Rayleigh friction and Newtonian cooling terms are included in the momentum and temperature equations.In this study, we use rhomboidal truncation at wavenumber 15 in the horizontal space (R30) with 24 vertical sigma (σ) levels.For further details of the model, see Ting and Yu (1998) and Simpson et al (2016).

Dominant summertime teleconnection pattern in northern Eurasian continent
Previous observational analysis demonstrated several recurring and persistent patterns that can explain a considerable portion of the Northern Hemisphere low-frequency variability using statistical methods such as the temporal correlation approach, PC analysis (PCA), rotated PCA, and cluster analysis (Horel 1981 , Wallace and Gutzler 1981, Barnston and Livezey  1987, Johnson et al 2008).In this study, to extract the leading atmospheric teleconnection pattern in the NH mid-high latitudes, EOF analysis is applied to 250 hPa meridional wind anomalies over the region of 50 • W-150 • E, 50 • -80 • N. The selected region corresponds to the largest interannual variability of 250 hPa meridional winds at mid-high latitudes from the NA to the Eurasian continent (figure 2(a)).Using meridional wind anomalies for EOF to capture the wave patterns that have a shorter zonal scale is commonly used in previous studies (Xie and Kosaka 2016, Xu et al 2019, Li et al 2020).
Figure 2(c) shows the spatial pattern and temporal variation of the first EOF mode and this explains approximately 25% of the total interannual variability of atmospheric teleconnection patterns in the northern Eurasian continent during boreal summer.Based on the rule of thumb of North et al (1982), the first leading mode (EOF1) is well separated from other modes.The EOF1 shows four centers of action located in the eastern NA Ocean, Scandinavia, the Ural Mountains, and Lake Baikal.The positive EOF1 is indicative of cyclonic circulation anomalies at 250 hPa over the eastern NA Ocean and Ural Mountains, and anticyclonic circulation anomalies over Scandinavia and Lake Baikal (figure 2(d)).
To compare with the previously well-known atmospheric teleconnection patterns, we calculated the correlation coefficient for each pattern.As a result, the EOF1 time series shows a statistically significant relationship with the East Atlantic/West Russia (EA/WR) index (r = 0.56) at 99% confidence level, but when we see the details of its pressure anomaly pattern, some marked differences exist.In particular, over the NA region, EOF1 shows a NE [30 pattern, but EA/WR shows a horizontally elongated pattern (figure S2).Also, teleconnection pattern in the subtropics is not well separated for EA/WR pattern.This can make it difficult to accurately identify the mid-high latitude teleconnection pattern as its signals may overlap and interact with each other in complex ways.Therefore, to understand the characteristics of a mid-and high-latitude propagating teleconnection pattern that is independent of the subtropics, the EOF1 pattern is analyzed in this study.Note that since this dominant teleconnection pattern is highly correlated with the BBC pattern identified by Xu et al (2019), this mode is hereafter referred to as the BBC pattern.
When we see the vertical profile of the BBC pattern related to its center of action, it clearly shows the westward tilted equivalent-barotropic structure (figure 2(e)) in the lower-mid troposphere.This vertically tilted structure is associated with the baroclinic energy conversion that takes place through the eddy heat flux across the climatological temperature gradient, transferring available potential energy from the background field to the eddy field.The maximum values of omega are located in between the pressure centers, facilitating poleward transport of energy.The WAF plot provides insights into the origin and dissipation of waves, facilitating comprehension of the mechanics underlying the behavior of the large-scale Rossby wave.It is notable that low-level WAF over the NA region [60 • -10 • W] in BBC pattern shows the vertically propagating pattern, implying the possible source region of forcing (figure 2(e)).shading).This direction of wave energy propagation is demonstrated by Hoskins et al (1983) based on observational analysis using extended Eliassen-Palm vectors.In short, the synoptic eddies originate from low levels at the entrance of the storm track, propagate eastward along the central axis of the storm track, and then propagate equatorward at its end.

Possible formation mechanisms and its impact on climate in northern Eurasia
The convergence of transient vorticity flux has a strong tendency to occur on the leftward side of the central axis of the storm track (Jin et al 2006a, 2006b, Kug and Jin 2009) and anomalous low-frequency circulation can be enhanced by eddy vorticity fluxes (Hoskins et al 1983, Lau and Holopainen 1984, Lau 1988).The following equation represents the relationship between the geopotential height tendency and the vorticity fluxes of high-frequency transient eddies: where f indicates the Coriolis parameter, g is the gravitational acceleration, V is the horizontal wind, ζ is  : 1979, 1980, 1985, 1987, 1992, 1997, 2001, 2002, 2015, and 2019; and seven negative years: 1981, 1987, 1989, 1993, 2004, 2012, and 2016.The simulated response closely resembles the observed geopotential anomalies in the upper troposphere, exhibiting a pattern correlation of approximately 0.61 (figures 2(d) and 5(a)).However, the simulated cyclonic (anticyclonic) circulation anomaly over the Ural Mountains (Scandinavia and Lake Baikal) displays a slightly different center of action and a rather smaller amplitude compared to the observed anomaly.These discrepancies in the simulated anomalous stationary waves may be attributed to factors such as an inaccurate dissipation parameterization or other unaccounted physical phenomena (Liu et al 1998, Ting et al 2001, Sobolowski et al 2011, Behera et al 2013).Nevertheless, there exists a strong concurrence among the ray path of Rossby wave activity (depicted by the blue line in figure 5(a)), the center of action response of the model simulation (figure 5(a)), and the large meridional gradient of PV area (figure 2(b)).However, even though the above eddy vorticity forcing is the primary driver for the downstream wave propagation, this does not produce large enough anomalies shown in the observationin particular, those over the Ural Mountains and Lake Baikal.
The anomalous Rossby wave propagating through northern Eurasia in the summertime basic state (figure S3, i.e. land-sea thermal contrast and lower stability in the midtroposphere) could be maintained for a longer period (Xu et al 2019, 2020, Li et al 2020).The Rossby waves from the NA towards the Eurasian continent can induce atmospheric disturbances that cause changes in temperature, moisture, and pressure.These changes can then lead to the generation of diabatic heating or cooling and this can act as a source of Rossby wave and influence the maintenance of the teleconnection pattern.The diabatic heating (cooling) anomalies associated with precipitation or temperature advection anomalies of the BBC pattern coincide with the center of the omega in the midtroposphere and are located about a 1/4 wavelength east of the center of the geopotential height anomalies (figure 4  simulated response to vertically integrated diabatic heating (cooling) forcing over the northern Eurasian continent, demonstrating a strong pattern correlation with the observed spatial pattern of the BBC (r = 0.78).Notably, this agreement is especially well represented over the Ural Mountains (cyclonic circulation anomaly) and Lake Baikal regions (anticyclonic circulation anomaly).The combined forcing simulation (transient vorticity flux forcing + diabatic forcing) of the nonlinear SWM exhibits the outstanding pattern correlation with the observed spatial pattern of the BBC (figure 5(c), r = 0.90).Results based on the observational analysis, model experiment, and theoretical approach all support the formation and maintenance mechanisms of high-latitude teleconnection patterns over the Eurasian continent.
Stationary waves can significantly shape the distributions of surface temperatures and moisture along the path of wave propagation and impact the trajectories of mid-latitude cyclones (Simpson et al 2016).Figures 4(b) and (c) show the composite difference map of precipitation anomaly and surface temperature (T_SFC) anomaly over the Eurasian continent during summertime related to the PC1.Along each center of high (low) pressure anomalies, positive (negative) temperature anomalies appear, and the precipitation region coincides with the location of maximum omega velocity in relation to the vertically westward tilted structure in the lower and middle troposphere over northern Eurasia.When the teleconnection pattern is positive, significant high T_SFC anomalies are observed in the Scandinavia, northeastern Russia, and Mongolia-north China; and low T_SFC anomalies are present over the western Russia (figure 4(c)).The teleconnection pattern accounts for 24%, 71%, 52%, and 24% of the total variance of areal average temperature variability over the Scandinavia, western Russia, northeastern Russia, and Mongolianorth China, respectively.Meanwhile, more precipitation occurs over northern Siberia and less over western and eastern Russia (figure 4(b)).In addition, negative precipitation anomalies appear over mid China and the Korean Peninsula, and positive precipitation anomalies appear over southern China and to the south of Korea.The teleconnection pattern accounts for 53%, 58%, 34%, 12% and 14% of the total variance of areal averaged precipitation variability over western Russia, northern Siberia, eastern Russia, mid China and the Korean peninsula, and south China and to the south of Korea, respectively.All values show statistically significant correlations at the 95% confidence level.These results suggest that the dominant teleconnection pattern in northern Eurasia has a strong connection with regional climate variability and can even affect precipitation in East Asia.

Conclusion and discussion
EOF analysis applied to summer 250 hPa meridional wind anomalies over the region of 50 • W-150 • E, 50 • -80 • N. The leading mode (BBC pattern) shows the zonally oriented and meridionally confined teleconnection pattern and consists of several geographically fixed centers along the upper-tropospheric PFJ from the eastern NA to northern Eurasia (figures 2(b), (d) and (e)).
We demonstrate that synoptic-scale eddy activity in the vicinity of the Gulf Stream associated with the meridional gradient of SSTAs plays a more decisive role in the formation of Rossby wave propagation originating from the NA than diabatic forcing in the tropical or subtropical regions does.The increase in eddy activity causes an eastward extension and southward shift of the central axis of the Atlantic storm track, generating the convergence of transient vorticity flux on the left side of the central axis (i.e. the west of the British Isles).This convergence can generate a low-frequency cyclonic circulation anomaly over the NA and can induce the propagation of the Rossby wave along northern Eurasia.The diabatic forcing in the northern Eurasia continent induced by the upstream transient vorticity flux forcing acts as another source of Rossby waves and plays a critical role in sustaining and generating the teleconnection pattern downstream regions.Our results have been supported by the stationary wave ray tracing method applied to horizontally nonuniform horizontal flow, WAF, and simulations using a nonlinear SWM.
The BBC pattern is significantly linked to the regional climate variations in northern Eurasia and East Asia.In the positive phase of the BBC pattern in summer, higher temperatures develop in Scandinavia and Lake Baikal, and lower temperatures in the Ural Mountains.The precipitation anomalies appear around a quarter of a wavelength downstream from the center of the temperature change.Meanwhile, negative precipitation anomaly occurs over mid-north China and the Korean peninsula and positive precipitation anomaly develops over south China and to the south of Korea.
This study allows the better understanding of northern Eurasian atmospheric teleconnection patterns and helps improve the northern Eurasian continent seasonal prediction skills in summer.The complex nature of the physical, dynamical, and nonlinear processes involved in the formation and maintenance mechanisms of atmospheric teleconnection patterns over the mid-high latitudes makes it difficult to clearly understand this phenomenon.Our model results show that diabatic heating or cooling tends to induce or intensify the circulation anomaly downstream (figure 5(b)).Our analysis and approach is similar to the well-known previous studies by Hoskins and Karoly (1981), Hoskins and Ambrizzi (1993), Wirth (2020), and Woolings et al (2023), where diabatic heating plays a forcing role in producing the mid-to high-latitude circulation response.However, more in-depth study will be needed to understand the role of diabatic forcing at high latitudes in summer.
Additionally, the effects of global warming and climate change further complicate the examination of these mechanisms.There are several studies pointing out that wavier circulation anomaly pattern over mid-and high-latitude regions in summer is due to the Arctic amplification (AA) related to global warming (Petoukhov et al 2013a, Coumou et al 2014, 2018, Screen and Simmonds 2014).Moreover, due to climate change, the rate of increase in the surface temperature of the northern Eurasian continent in summer is higher than that of the Arctic, so it is expected that the Arctic PFJ is strengthened, and the storm track is extended eastward, increasing the possibility of enhancing the present EOF1 mode.These changes are closely related to the recent sustained heat waves and cold waves across Europe and Russia (Day andHodges 2018, Rousi et al 2022).Understanding the implications of these changes on the characteristics of high-latitude teleconnection in future climates requires further investigation.

Figure 1 .
Figure 1.The monthly mean 500 hPa geopotential height (contour; gpm) and surface temperature (shading; K) anomalies in (a) August 2003 (when a heat wave event occurred over western Europe), (b) July 2010 (when a heat wave event occurred over eastern Europe and western Russia), and (c) June 2020 (when a heat wave event occurred over Siberia), respectively.
Previous studies have suggested a link between teleconnection patterns propagating across the Eurasian continent and sea surface temperature anomalies (SSTAs) in the NA (Wu et al 2009, Sun et al 2015, Li and Ruan 2018).Figure 3(a) shows the tripolar SSTAs, with particularly strong negative anomalies to the west of the British Isles, yet the associated diabatic heating and cooling response in the tropical or subtropical regions is weak or insignificant.On the other hand, cold SSTAs around 40 • -60 • N and warm anomalies around 35 • N tend to strengthen the meridional gradient of SST around 40 • N (figures 3(a) and (b)).This SSTAs pattern may serve to continuously support the mid-latitude synoptic eddies (figure 3(c)), which play a significant role in the formation of the BBC-related teleconnection pattern.Figure 3(c) shows 700 hPa maximum Eady growth rate (EGR) related to the BBC pattern.The EGR is given by 0.3098 ( f N ) |∂U (z) /∂z|, where f is the Coriolis parameter, N the static stability, and U the zonal wind.The increase in synoptic eddy activity due to the low level baroclinicity associated with the positive EGR anomaly near the Gulf stream (70 • -20 • W, 40 • -50 • N) can shift the central axis of the storm track south-eastward (20 • -5 • W, 40 • -50 • N) compared to the climatological location (figure 3(d),

Figure 4 .
Figure 4. Composite difference maps of (a) geopotential height tendency induced by high-frequency transient eddies (shading; gpm day −1 ), and climatological 250 hPa summer mean zonal wind (black contour; m s −1 ), (b) Precipitation anomalies (shading; mm day −1 ) and vertically integrated diabatic heating (red contour; 95% confidence level), and (c) surface temperature anomalies (shading: K) from JJA using the PC1 time series for 1979-2019.Negative contours are dashed and hatching indicates the 90% confidence levels based on the two-tailed Student's t test.

Figure 5 .
Figure 5.The teleconnection pattern in the 250 hPa geopotential height anomalies (shading; gpm) from nonlinear stationary wave model simulations forced by (a) the idealized transient vorticity forcing (orange contour is at σ = 0.27 (3 × 10 −11 s −2 ), (b) the diabatic forcing (red contour is denoted at σ = 0.44 (10 −6 K s −1 ), and (c) the transient vorticity forcing + the vertically integrated diabatic forcings.Blue, green, red, and yellow lines denote the Rossby wave ray path for waves with the zonal wavenumber 3. (d) The vertical profile at the forcing center (vorticity; 10 −11 s −2 ) and the area-averaged vertical profiles (diabatic heating or cooling; 10 −5 K s −1 ) of stationary forcing prescribed to the nonlinear stationary wave model.The basic state is the summer mean climatology during 1979-2019 based on JRA-55 datasets.
Furthermore, several studies (Li and Zhang 2014, Huang et al 2015, Wu and Francis 2019, Li et al 2021, Xu et al 2021, Liu et al 2022, 2023) have demonstrated that summertime high-latitude teleconnection patterns associated with PFJs can exert a significant influence on the variability of northern Eurasian and East Asian climates.