Editorial Type:
Article
Article Type:
Research Article

Intraseasonal Variations of the British–Baikal Corridor Pattern

Peiqiang Xu Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, and College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China

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Lin Wang Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, and College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China

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https://orcid.org/0000-0002-3557-1853
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Wen Chen Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, and College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China

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Guosen Chen Earth System Modeling Center, Nanjing University of Information Science and Technology, Nanjing, China

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In-Sik Kang Indian Ocean Operational Oceanographic Research Center, State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou, China

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Online Publication:
01 Feb 2020
Print Publication:
15 Mar 2020
DOI:
https://doi.org/10.1175/JCLI-D-19-0458.1
Page(s):
2183–2200
Free access

Abstract

The British–Baikal Corridor (BBC) pattern is the dominant waveguide mode trapped along the summertime polar front jet over northern Eurasia. It consists of four geographically fixed centers over the west of the British Isles, the Baltic Sea, western Siberia, and Lake Baikal, respectively. Its intraseasonal variations and dynamics are investigated based on reanalysis datasets. The BBC pattern has a life cycle of about two weeks. Its precursor could be traced back to an upstream wave packet propagating along the Atlantic jet 10 days before its peak, and its life cycle resembles the evolution of a quasi-stationary Rossby wave train. Diagnosis of the streamfunction tendency equation suggests that the growth and decay of the BBC pattern are primarily driven by the nonlinear processes, whereas the quasi-stationary feature of the BBC pattern arises from the cancellation among the linear processes. Energetics analysis indicates that the energy cycle with the transient eddies (TEs) plays an essential role in the growth and decay of the BBC pattern. The BBC pattern first feeds on the barotropic energy provided by the TEs and then returns the energy to TEs in the form of baroclinic energy. It is this nonlinear interaction with the TEs that poses a tough challenge to the current state-of-the-art models to capture the BBC pattern reasonably.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Lin Wang, wanglin@mail.iap.ac.cn

Abstract

The British–Baikal Corridor (BBC) pattern is the dominant waveguide mode trapped along the summertime polar front jet over northern Eurasia. It consists of four geographically fixed centers over the west of the British Isles, the Baltic Sea, western Siberia, and Lake Baikal, respectively. Its intraseasonal variations and dynamics are investigated based on reanalysis datasets. The BBC pattern has a life cycle of about two weeks. Its precursor could be traced back to an upstream wave packet propagating along the Atlantic jet 10 days before its peak, and its life cycle resembles the evolution of a quasi-stationary Rossby wave train. Diagnosis of the streamfunction tendency equation suggests that the growth and decay of the BBC pattern are primarily driven by the nonlinear processes, whereas the quasi-stationary feature of the BBC pattern arises from the cancellation among the linear processes. Energetics analysis indicates that the energy cycle with the transient eddies (TEs) plays an essential role in the growth and decay of the BBC pattern. The BBC pattern first feeds on the barotropic energy provided by the TEs and then returns the energy to TEs in the form of baroclinic energy. It is this nonlinear interaction with the TEs that poses a tough challenge to the current state-of-the-art models to capture the BBC pattern reasonably.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Lin Wang, wanglin@mail.iap.ac.cn
Keywords: Atmospheric circulation; Dynamics; Rossby waves; Teleconnections; Budgets; Intraseasonal variability

1. Introduction

Atmospheric teleconnection patterns refer to a few recurring patterns that link weather and climate anomalies over vast distances across the globe (Feldstein and Franzke 2017). In contrast to well-known teleconnection patterns such as the North Atlantic Oscillation (NAO) and the Pacific–North America (PNA) pattern whose structures are prominently meridionally oriented (Wallace and Gutzler 1981; Barnston and Livezey 1987), there exists a class of teleconnection patterns whose structures are mainly zonally oriented and confined in a limited latitude band (Branstator 2002; Petoukhov et al. 2013). These zonally oriented teleconnection patterns often propagate along the tropospheric jet streams into very distant regions (Ding and Wang 2005, 2007; Ding et al. 2011; Branstator and Teng 2017), exerting influences on climate over broad areas (Wakabayashi and Kawamura 2004; Iwasaki and Nii 2006; Saeed et al. 2014; Wang et al. 2017).

The formation mechanism of these zonally oriented teleconnection patterns can be well understood in the context of stationary Rossby wave theory. Similar to Snell’s law in optics, the ray paths of Rossby waves in the atmosphere are always reflected toward the region with larger refractive index (Matsuno 1970; Hoskins et al. 1977; Hoskins and Karoly 1981) and trapped in the latitudes of the local maximum refractive index where the tropospheric jet generally resides (Hoskins and Ambrizzi 1993). In other words, the time-mean tropospheric jet can act as a waveguide to allow the zonal propagation of Rossby waves. Observational studies have confirmed the existence of the jet-trapped teleconnection patterns over the Northern Hemisphere both in boreal winter (Hsu and Lin 1992; Branstator 2002; Hu et al. 2017) and boreal summer (Lu et al. 2002; Enomoto et al. 2003; Ding and Wang 2005; Kosaka et al. 2009; Chen and Huang 2012; Chen et al. 2013; Wang et al. 2017; Chowdary et al. 2019). These jet-trapped patterns are generally weaker and located farther north in boreal summer than in winter, in good agreement with Ambrizzi et al. (1995).

Compared with comprehensive literature concerning the waveguide teleconnection patterns trapped by the subtropical jet mentioned above, the trapped teleconnection patterns along the polar front jet have been less discussed (Xu et al. 2019, hereinafter XWC). One reason is that the polar front jet is weaker than the subtropical jet and that it cannot be well separated from the latter in many regions during most of the year. However, in contrast to their inseparable character in spring, autumn, and winter, these two jets have a well-defined geographical boundary around 65°N in the boreal summer over Eurasia (Fig. 1a). Besides, although the meridional gradient of absolute vorticity along the polar front jet is weak, the meridional gradient of potential vorticity along the polar front jet is strong due to the large meridional gradient of stratification over northern Eurasia (Iwao and Takahashi 2008). These facts indicate that the summertime polar front jet over Eurasia can act as an independent waveguide to trap Rossby wave activity.

Fig. 1.
Fig. 1.

(a) Latitude–pressure cross sections of the climatological summer (JJA) zonal wind averaged over 0°–150°E [contour interval (CI) = 2 m s−1]. (b) As in (a), but for the variance of 10-day low-pass filtered meridional wind (CI = 10 m2 s−2). Negative contours in (a) are dashed.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Figure 1b shows the latitude–pressure cross section of the zonal mean variance of 10-day low-pass filtered meridional wind over Eurasia. Large variance can be observed along the subtropical jet. Moreover, an even larger variance can be found along the polar front jet, suggesting more frequent Rossby wave activities in the high latitudes. Recently, the dominant trapped pattern along the summertime polar front jet over Eurasia was analyzed on the interannual time scale by XWC and referred to as the British–Baikal Corridor (BBC) pattern. The BBC pattern consists of four equivalent-barotropic and geographically fixed centers of action over the west of the British Isles, the Baltic Sea, western Siberia, and Lake Baikal and features significant precipitation and surface air temperature anomalies along its path. Dynamical diagnoses indicate that the variability of the BBC pattern is primarily dominated by the internal dynamics. On the interannual time scale, the BBC pattern is excited by the active multiscale interactions among the climatological mean flow, the low-frequency flow, and the synoptic-scale transient eddies (TEs) in the exit region of the North Atlantic jet. Meanwhile, it is primarily maintained by the efficient baroclinic energy conversion with the mean flow and barotropic feedback from the high-frequency TEs. Despite these understandings from a climate perspective, most of the known atmospheric teleconnection patterns in the Northern Hemisphere have an e-folding time scale of approximately 7–10 days (Feldstein 2000). It means that it may be more fundamental to understand the dynamics and life cycle of the BBC patterns by analyzing its variability on the intraseasonal time scale. Hence, this issue will be addressed in this study as an extension of XWC. The organization of the remaining text is as follows. Section 2 describes the datasets and methods used in this study. Section 3 presents an overview of the temporal and spatial features of the BBC pattern on the intraseasonal time scale. Section 4 shows the evolutions of the BBC pattern and associated climate anomalies. Section 5 discusses the mechanism that governs the growth and decay of the BBC pattern. Finally, section 6 summarizes the main findings and discusses some open issues.

2. Data and methods

a. Data

Monthly and daily mean atmospheric reanalysis data are from the ERA-Interim dataset (Dee et al. 2011) provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). This dataset has 2.5° × 2.5° horizontal resolution on 37 pressure levels, beginning from 1979. The daily climatology of a particular day is calculated by averaging the corresponding daily-mean values over the 37 years. The intraseasonal time scale is concerned in this study, so the original data are filtered with a 6-day low-pass Lanczos filter to avoid the possible influence from the synoptic TEs unless otherwise stated (Duchon 1979). The boreal summer consists of 92 days in June, July, and August (JJA).

b. Identification of the intraseasonal BBC events

The BBC pattern is defined as the first empirical orthogonal function (EOF) of the summer mean 250-hPa meridional wind over the domain 50°–80°N, 20°W–150°E following XWC, and the daily BBC index is obtained by projecting the filtered daily 250-hPa meridional wind anomalies onto the summer mean BBC pattern. We also checked the BBC index that is obtained by performing EOF analysis directly with the daily data, like in Athanasiadis et al. (2010), Tan et al. (2015), and Cheng and Tan (2019). The correlation coefficient between the two indices is 0.85 for 3404 days. Therefore, it suggests that the BBC pattern on the intraseasonal time scale is robust and not sensitive to the specific defining method used.

After we get the normalized daily time series of the BBC pattern, the BBC pattern events are selected in the following way. First, the absolute value of the BBC index should exceed two standard deviations. Second, the peak day, referred to as day 0, is defined as the day on which the magnitude of the BBC index is larger than both the preceding day and the following day. According to this definition, 20 positive cases and 23 negative cases are selected from 1979 to 2015 and composited relative to day 0 to investigate the associated evolutions and dynamics. Since the criterion of two standard deviations is rather strict, the selected BBC pattern events are not sensitive to the procedure if we further limit the separating days between two adjacent events. Because the situations in the positive and negative events are rather symmetric, only the composite results for the positive events (corresponding to Fig. 3) are discussed in this paper. The two-tailed Student’s t test is used to evaluate the statistical significance of composite analysis.

c. Diagnostic tools

To characterize the propagation of Rossby waves associated with the BBC pattern, we evaluate a particular form of wave-activity flux propose by Takaya and Nakamura (2001), which is defined as
W=p02|V¯|{u¯⁡(υ′2−ψ′υx′)+υ¯⁡(−u′υ′+ψ′ux′)u¯⁡(−u′υ′+ψ′ux′)+υ¯⁡(u′2+ψ′uy′)f0RN2H0 [u¯⁡(υ′T′−ψ′Tx′)+υ¯⁡(−u′T′−ψ′Ty′)]},
where ψ, R, f0, N, H0, and p0 denote the streamfunction, gas constant of dry air, Coriolis parameter at 60°N, buoyancy frequency, scale height, and pressure normalized by 1000 hPa, respectively. Also, V = (u, υ) is the horizontal wind velocity; subscripts x and y indicate partial derivatives in the zonal and meridional directions, and overbars and primes denote climatological quantities and perturbations associated with the BBC pattern, respectively. The Takaya–Nakamura wave activity flux is independent of wave phase and parallel to the local group velocity of stationary Rossby waves embedded in the zonally varying basic flow in the Wentzel–Kramers–Brillouin (WKB) sense.
To clarify the relative roles of various dynamical processes in the growth and decay stages of the BBC pattern, a vorticity budget decomposition framework is used to diagnose the low-frequency streamfunction (ψL) tendency equation (Cai and van den Dool 1994), which can be written as
∂ψL∂t=∑i=17ξi+Res.
Here the first seven terms on the right-hand side (rhs) are defined as follows:
ξ1=∇−2{−(υrL+υdL)1adfdθ},
ξ2=∇−2⁡(−[Vr¯]⋅∇ζL−VrL⋅∇[ζ¯])+∇−2⁡(−[Vd¯]⋅∇ζL−VdL⋅∇[ζ¯]),
ξ3=∇−2⁡(−Vr*¯⋅∇ζL−VrL⋅∇ζ*¯)+∇−2⁡(−Vd*¯⋅∇ζL−VdL⋅∇ζ*¯),
ξ4=∇−2{−(f+ζ=)∇⋅VdL}−ζL∇⋅Vd¯,
ξ5=∇−2⁡(−VrL⋅∇ζL)L+∇−2{−∇⋅(VdLζL)}L,
ξ6=∇−2⁡(−VrH⋅∇ζH)L+∇−2{−∇⋅(VdHζH)}L,
ξ7=∇−2⁡(−VrL⋅∇ζH)L+∇−2{−∇⋅(VdLζH)}L+∇−2⁡(−VrH⋅∇ζL)L+∇−2{−∇⋅(VdHζL)}L,
where a is Earth’s radius and ζ the relative vorticity. Res represents the residual term that includes neglected physical processes such as dissipation, lower boundary forcing, and a tilting term. The subscripts r and d denote the rotational and divergent parts of horizontal wind, and the superscripts L and H represent the low-frequency and high-frequency quantities which are separated at 10 days. Here it is somewhat arbitrary to use 10 days to separate high- and low-frequency fluctuations. Nevertheless, it has been well established that the spatial patterns of atmospheric TEs show distinct differences between the spectrums of high-frequency and low-frequency, and these differences are not sensitive to the particular choice to define them (e.g., Blackmon 1976; Blackmon et al. 1977; Lau et al. 1978). For a given variable, an overbar indicates the time mean, and the square brackets and asterisk denote the zonal mean and its deviation, respectively. The low-frequency tendency of streamfunction ∂ψL/∂t, which is calculated using the central difference upon time, can be measured by the summation on the rhs in the equation above. The physical interpretations of the processes associated with ξ1 to ξ7 are (i) the planetary vorticity advection by the meridional rotational wind and divergent wind that is equivalent to the beta effect, (ii) the interaction between the low-frequency anomalies and the zonally symmetric mean flow, (iii) the interaction between the low-frequency anomalies and the stationary wave, (iv) the convergence/divergence induced by the secondary circulation, (v) the self-interaction among the low-frequency anomalies, (vi) the self-interaction among the high-frequency anomalies, and (vii) the cross-frequency interactions. The first four terms on the rhs of Eq. (2) are designated as the linear terms, while the other three terms are defined as the nonlinear terms. By evaluating the relative importance of each term on the rhs, we can determine which physical mechanism plays the most essential role in the growth and decay of the BBC pattern. This diagnose framework has been used in many previous studies to investigate other low-frequency variabilities like the NAO and PNA pattern (e.g., Feldstein 2002, 2003).
We also attempt to understand the growth and decay of the BBC pattern from the perspective of energetics. The perturbed kinetic energy (KE) and available potential energy (APE) associated with the BBC pattern are defined following Kosaka and Nakamura (2006, 2010) as follows:
KE=12⁡ (u′2+υ′2),
APE=RT′22Sp,
where Sp is the static stability defined as ⁡(RT¯/CpP)−(∂T¯/∂p). The interactions between the mean flow and the perturbation that involve barotropic and baroclinic processes (Kosaka and Nakamura 2006, 2010) are formulated as
CKBF=υ′2−u′22⁡(∂u¯∂x−∂υ¯∂y)−u′υ′⁡(∂u¯∂x+∂υ¯∂y),
CPBF=−fS⁡(υ′T′∂u¯∂p−u′T′∂υ¯∂p),
where CKBF and CPBF denote the barotropic energy conversion and baroclinic energy conversion with the climatological-mean flow, respectively. Meanwhile, the feedback forcing from the TEs often plays an important role in maintaining the low-frequency variability (Shutts 1983; Lau 1988; Held et al. 1989; Branstator 1992, 1995), which is also observed for the BBC pattern in a seasonal-mean sense (XWC). To quantify this part of the contribution from TEs, the KE and APE extracted for the BBC pattern from TEs are evaluated following Tanaka et al. (2016):
CKHF=−u′[∂⁡(uH′′uH′′)′∂x+∂⁡(uH′′υH′′)′∂y]−υ′[∂⁡(uH′′υH′′)′∂x+∂⁡(υH′′υH′′)′∂y],
CPHF=−RT′pSp[∂⁡(uH′′TH′′)′∂x+∂⁡(υH′′TH′′)′∂y],
CKLF=−u′[∂⁡(uL′′uL′′)′∂x+∂⁡(uL′′υL′′)′∂y]−υ′[∂⁡(uL′′υL′′)′∂x+∂⁡(υL′′υL′′)′∂y],
CPLF=−RT′pSp[∂⁡(uL′′TL′′)′∂x+∂⁡(υL′′TL′′)′∂y],
CKCF=−u[∂⁡(uH′′uL′′)′∂x+∂⁡(uH′′υL′′)′∂y]−υ′[∂⁡(uH′′υL′′)′∂x+∂⁡(υH′′υL′′)′∂y]−u′[∂⁡(uL′′uH′′)′∂x+∂⁡(uL′′υH′′)′∂y]−υ′[∂⁡(uL′′υH′′)′∂x+∂⁡(υL′′υH′′)′∂y]
CPCF=−RT′pSp[∂⁡(uH′′TL′′)′∂x+∂⁡(υH′′TL′′)′∂y]−RT′pSp[∂⁡(uL′′TH′′)′∂x+∂⁡(υL′′TH′′)′∂y],
where the double prime denotes the transient quantities. Subscripts HF, LF, and CF indicate the energy conversion due to the high-frequency, low-frequency, and cross-frequency TEs, respectively. The sum of all the defined barotropic energy conversions and the baroclinic energy conversions with the TEs are referred to as the CKTE and CPTE, respectively. One can refer to Tanaka et al. (2016) for the relevant derivation of the energy gains due to the high-frequency TEs. The energy conversion equations for the low-frequency and cross-frequency TEs can be derived in a similar way.

3. Overview of the intraseasonal variation of the BBC pattern

This section examines the temporal features of the BBC pattern and its three-dimensional structure. Figure 2a presents the autocorrelations of the BBC index. To avoid the possible artificial influence from the filtering, the index used in Fig. 2a is obtained by projecting the unfiltered 250-hPa meridional wind anomalies onto the summer mean BBC pattern, while in the other parts of this paper the index is obtained by projecting the filtered anomalies to remove the possible influence from high-frequency TEs. The decorrelation time scale (i.e., the time scale over which the amplitude of the teleconnection pattern decays by a factor of e, indicated by the red dashed line in Fig. 2a) is around 4–5 days for the BBC pattern. This time scale is similar to the southern Levant (SL) pattern, which is the trapped waveguide mode along the subtropical jet (Feldstein and Dayan 2008). The 4–5-day decorrelation time scale found for the BBC pattern is significantly shorter than the NAO or PNA pattern, which are typically between 7 and 10 days. On the one hand, this difference in time scale may arise from the different seasons when the BBC and NAO/PNA patterns maximize. On the other hand, it implies different dynamics between the BBC pattern and the NAO/PNA patterns. The time scales for the NAO and PNA are likely dependent on the wave breaking and following mixing (Benedict et al. 2004; Franzke et al. 2004). In contrast, the time scale of the BBC pattern, as will be shown later, appears to depend on the group velocity of the wave packet and nonlinear interactions with the TEs (Robinson 1991; Yu and Hartmann 1993; Robinson 1996; Feldstein and Lee 1998; Hartmann and Lo 1998; Lorenz and Hartmann 2001; Nie et al. 2016).

Fig. 2.
Fig. 2.

(a) The autocorrelations of the unfiltered BBC index (blue line). The dashed red line represents the e-folding value. (b) Time evolution of the composited normalized PC time series for the positive BBC pattern events (red line) and negative BBC pattern events (blue line). 20 positive events and 23 negative events are selected to make the composite (see text for details about the definitions).

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Figure 2b presents the temporal evolutions of the composited normalized principal component (PC) time series for the selected BBC pattern events. Here, the red line and blue line indicate the composited PC time series for the positive and negative BBC events, which are roughly symmetric in their temporal evolutions. From day −10 to day −4 (a minus sign indicates the days preceding day 0), the composited PC values experience slow changes. The PC values develop rapidly from day −4 to day −1 and reach the peak on day 0. After day 0, the PC values decay rapidly before day +4 (a plus sign indicates the days after day 0) and experience slow decaying from day +4 to day +10. These results suggest that the BBC pattern events typically have a life cycle of about two weeks. In other words, its intrinsic dynamics should be subject to the atmospheric internal dynamics in the intraseasonal time scale. Hence, it is enough to look at the 21-day period to investigate its complete evolutions, which is the main subject in section 4.

We now present the three-dimensional structure of the BBC pattern on day 0, so one can get a basic idea about its overall feature. The upper and bottom panels of Fig. 3 respectively give the composited horizontal structure and the vertical structure along the major centers labeled A, B, C, D, E, and F in Fig. 3a. Only the geopotential height anomalies (black contour) and temperature anomalies (shading) that exceed 95% significance level are drawn. The spatial structure of the BBC pattern is broadly similar on both the intraseasonal and interannual time scales, both of which are characterized by a zonally oriented and meridionally confined wavelike structure with geographically fixed equivalent-barotropic centers. However, there exist two subtle differences. First, the spatial structure of the BBC pattern on the intraseasonal time scale is oriented more zonally than the arching-like feature on the interannual time scale. Second, the amplitude of the BBC pattern on the intraseasonal time scale is much stronger than its interannual counterpart. The structure of positive and negative BBC events is rather symmetric, except that the action center over northeast Asia in the negative phase is somewhat weaker (figure not shown).

Fig. 3.
Fig. 3.

(a) Composite map of 250-hPa geopotential height anomalies (black contour; CI = 40 gpm) and 925-hPa temperature anomalies [shading, shading interval (SI) = 1 K] for the positive BBC pattern at day 0. The 250-hPa total zonal wind is indicated as purple contours with interval 8 (16, 24, …; unit: m s−1). The major action centers, which are labeled with letters, are connected by the thick blue lines. (b) The vertical cross sections of the composite anomalies of geopotential height (contour; CI = 40 gpm) and temperature (shading; SI = 1 K) along the solid blue line in (a). Zero contours have been omitted, and negative contours are dashed. Only the anomalies that exceed 95% significance level are drawn based on a two-tailed Student’s t test.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

The BBC pattern shown in Fig. 3a looks quite similar to a recently identified Atlantic–Eurasian (AEA) pattern at first sight (Li and Ruan 2018), but it is different from the AEA pattern in several distinct aspects. First, the spatial structure of the BBC pattern is different from that of the AEA pattern. The BBC pattern has four primary action centers that oriented primarily in the east–west direction (Fig. 12 in XWC), whereas the AEA pattern has five main action centers that show a more distinct meridional component, especially over the North Atlantic (Fig. 3 in Li and Ruan 2018). All the action centers of the BBC pattern are located at higher latitudes than those of the AEA pattern except for the action center over Siberia. Second, the initiation regions of the two patterns are different. The BBC pattern is initiated at the exit region of the Atlantic jet in the middle latitudes (XWC), whereas the AEA pattern originates from the subtropics (Li and Ruan 2018). Third, the differences in the initiation region also imply their differences in the formation mechanism. The interannual variability of the BBC pattern is dominated by wave–mean flow interactions, and it is unrelated to any atmospheric external boundary forcing (XWC). In contrast, the AEA pattern is excited by the Atlantic sea surface temperature anomalies (Sun et al. 2015). The existence of these differences suggests that the BBC pattern and AEA pattern are two different atmospheric teleconnections although they share some similarities.

4. Evolution of the BBC pattern

This section examines the evolutions of the three-dimensional structure of the BBC pattern and associated climate impact. Figure 4 presents the composited evolutions of the 250-hPa geopotential height anomalies (black contour), associated wave activity flux (vector), and total zonal wind (purple contour). Early significant geopotential height anomalies can be detected back into day −10, when a preceding upstream wave packet propagates along the Atlantic jet (Fig. 4a). Once the geopotential anomalies propagate into the exit region of the Atlantic jet, the anomalies near Britain begin to amplify locally. Meanwhile, the action centers on the downstream side start to develop with continuous eastward propagation of wave activity fluxes (Figs. 4b–e). XWC suggested that the multiscale interaction between the climatological-mean flow, low-frequency flow, and high-frequency TEs near the exit of the Atlantic jet acts as a certain kind of natural selection to determine the region that upstream forcing takes place and thereby the geographical phase of the BBC pattern. The shape of action centers of the BBC pattern features a subtle northwest–southeast tilting in the upstream and northeast–southwest tilting in the downstream, indicating the Rossby wave reflection around the turning latitude due to the spherical effect (Hoskins et al. 1977). Nevertheless, the nearly zonal propagation of the BBC pattern along the latitude of 60°N is still apparent, suggesting its nature as a waveguide mode due to the large meridional gradient of the stratification over northern Eurasia in the boreal summer (Iwao and Takahashi 2008, XWC). The BBC pattern reaches its maximum intensity on day 0 (Fig. 4f) and decays quickly after that (Figs. 4g,h). The overall wavelike feature of the BBC pattern is obscured after day 6, but the action centers near central Siberia and northeast Asia could persist until day 10 (figure not shown) and affect the local climate persistently.

Fig. 4.
Fig. 4.

Composite anomalies of the 250-hPa geopotential height (black contour; CI = 40 gpm), total zonal wind (purple contour; 16, 24, 32, …; unit: m s−1), and the wave activity flux (vectors; unit: m2 s−2) on days (a) −10, (b) −8, (c) −6, (d) −4, (e) −2, (f) 0, (g) 2, and (h) 6 of the positive BBC pattern. The light and dark shading indicate the 95% and 99% confidence levels based on a two-tailed Student’s t test, respectively.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Figure 5 shows the vertical cross section of the evolutions of the geopotential height anomalies (black contour) and associated wave activity fluxes along the major centers. The horizontal component of wave activity fluxes is calculated as the mean square of the zonal and meridional components of wave activity fluxes. The vertical component is multiplied by a factor of 25p in each pressure level for visual purposes. The main features here are overall similar to Fig. 3b in XWC, except that the evolutions of growth and decay of the BBC pattern are presented. The BBC pattern is characterized by several equivalent barotropic action centers that tilt westward with height in the lower troposphere. This feature matches the robust vertical propagation of wave activity fluxes and suggests the essential role of the baroclinic process in the development of the BBC pattern. The westward tilting is even more pronounced in the downstream centers C, D, and E, possibly due to the sharper meridional gradient of the climatological temperature over the continent (also see in Fig. 12b). This tilting gradually diminishes after the BBC pattern reaches its maximum intensity. Although each action centers show slight eastward movement during the whole life cycle, the stationary feature of the BBC pattern is rather noticeable. The growth and decay of the BBC pattern are highly similar to the life cycle of a quasi-stationary Rossby wave train, which can be seen more clearly in Fig. 6.

Fig. 5.
Fig. 5.

As in Fig. 4, but for the vertical cross sections of composite anomalies of geopotential height (contour; CI = 40 gpm) and wave activity flux (vector; unit: m2 s−2) along the blue solid line in Fig. 3a on days (a) −10, (b) −6, (c) −2, (d) 0, (e) 2, and (f) 6 of the positive BBC pattern. The horizontal component of wave activity flux is calculated as the mean square of the zonal and meridional component of wave activity flux. The vertical component has been multiplied by 25p (unit: hPa) for visual purposes. Zero contours are omitted, and negative contours are dashed. The light and dark shading indicate the 95% and 99% confidence levels based on a two-tailed Student’s t test, respectively.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Fig. 6.
Fig. 6.

The Hovmöller diagram of the composited geopotential height at 250 hPa (contour; CI = 40 gpm) and 925 hPa (shading; SI = 15 gpm) along the solid blue line in Fig. 3a. Only the anomalies that exceed the 90% significance level based on a two-tailed Student’s t test are drawn. Zero contours are omitted.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Figure 6 presents the Hovmöller diagram of composited anomalies of geopotential height at 250 hPa (black contours) and 925 hPa (shading). Only the geopotential height anomalies that exceed 90% significance level are drawn. If we only focus on the anomalies in the upper troposphere (black contours) and lower troposphere (shading) alone, the successive development of perturbations toward the downstream side of existing perturbations is apparent, indicating the so-called downstream development (Yeh 1949). Such behavior is typical to the wave packets that have an eastward group velocity (Chang 1993; Lee and Held 1993). A rough estimate of the group velocity according to the slope against the abscissa is about 10.7 m s−1. This speed is roughly consistent with the group velocity of a stationary zonal wavenumber-5 disturbance estimated from the classic Rossby wave theory (Hoskins and Karoly 1981). The near coincidence of the upper-tropospheric anomalies with the lower-tropospheric ones indicates the nearly barotropic character of the BBC pattern. However, a closer inspection reveals that the anomalies in the upper troposphere locate slightly at the western flank of the lower troposphere, consistent with the discussion of Fig. 5. This phase lag is more pronounced for the action centers C, D, and E, which are located over the continent. In particular, the vertical structure becomes fully baroclinic between D and E, where the positive geopotential anomalies in the upper troposphere correspond to the negative anomalies in the lower troposphere. This region also corresponds to the intense upward propagation of wave activity fluxes shown in Fig. 5, which indicates vigorous baroclinic interactions with the mean flow. This process is similar to the development of the Siberian high in boreal winter (Takaya and Nakamura 2005), where the equivalent barotropic wave train traveling in the upper troposphere is found to become baroclinic when it propagates into central Siberia and couples vertically with temperature anomalies in the lower troposphere (Hoskins et al. 1985). It is interesting to find that a similar process also takes place here when the background baroclinicity is considerably weaker in boreal summer. After day 0, the phase lag between the structures in the upper and lower troposphere is weakened, indicating that the intensity of the baroclinic interactions with the background flow declines.

Figure 7 presents the evolution of surface air temperature anomalies induced by the BBC pattern events. Warm anomalies are observed in central Siberia, and cold anomalies are observed in Europe and northeast Asia in the positive phase of the BBC pattern. These features are quite similar to those on the interannual time scale (e.g., Fig. 4d of XWC). XWC suggests that the BBC pattern causes local hot or cool weather primarily through the anomalous meridional advection of mean temperature. The temperature anomalies caused by the BBC pattern can generally persist for about one weak. In particular, the anomalies over the central Siberia, which are caused by the long-lived atmospheric circulation anomalies above (Fig. 4), can even maintain for about two weeks. The amplitude of induced temperature anomalies is quite remarkable, exceeding 6° over Siberia. The distinct BBC-related temperature anomalies indicate that the BBC pattern is an important teleconnection that should be understood in depth.

Fig. 7.
Fig. 7.

As in Fig. 4, but for the 2-m air temperature anomalies (contour; CI = 1°C) on days (a) −10, (b) −6, (c) −2, (d) 0, (e) 2, and (f) 6.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

5. Dynamics of the BBC pattern

a. Streamfunction tendency equation analysis

The physical processes that are responsible for the growth and decay of the BBC pattern can be clarified explicitly by examining each term on the rhs of Eq. (2). This can be summarized by projecting each term on the rhs of Eq. (2) onto the composite anomalous streamfunction pattern on day 0. The projection for each ξi can be written as (Feldstein 2003)
Pi=∑λ,θξi⁡(λ,θ)ψM⁡(λ,θ) cos⁡θψM2⁡ cos⁡θ, i=1−7,
where ψM denotes the streamfunction pattern on day 0; λ and θ indicate the longitude and latitude, respectively. The projection procedure is performed over the region northward of 30°N. The above projection represents the influence of individual ξi on the time rate of change of ψL toward day 0. Figure 8 presents the time series of projection calculated at the level of 250 hPa, where the amplitude of circulation anomalies is maximum (Held 1983; Held et al. 1985).
Fig. 8.
Fig. 8.

Projections for the positive BBC pattern phase of various combinations of terms on the rhs of Eq. (2) onto the composited 250-hPa streamfunction anomalies at day 0: (a) ∂ψL/∂t (solid black line) and ∑i=17ξi (dashed black line). (b) ∑i=17ξi (dashed black line), linear terms ∑i=14ξi (red line), and nonlinear terms ∑i=57ξi (blue line). (c) Four linear terms: beta term ξ1 (dashed blue line), interactions with the zonal symmetric mean flow ξ2 (solid blue line), interactions with the stationary wave ξ3 (dashed red line), and divergence term ξ4 (solid red line).

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

We first examine to what extent the streamfunction tendency decomposition is reliable. Figure 8a shows the time series of the projection of ∂ψL/∂t (solid black line) and ∑i=17ξi (dashed line). The difference between these two lines is a measure of the degree to which these terms balance with each other. Although there are some mismatches at some lags, the balance is overall reasonably satisfied, especially for the time around day 0. The balance is reasonably good at all levels above 700 hPa in the troposphere, whereas it is not well satisfied below 850 hPa (figure not shown). The large errors in the lower troposphere are possibly due to the frictional process and boundary forcing, which are implicitly neglected in the budget analysis.

Figure 8b shows the projection of the linear processes ∑i=14ξi (red line), and the nonlinear processes ∑i=57ξi (blue line). The projection of ∑i=17ξi is also drawn for the sake of comparison (dashed black line). The nonlinear process dominates the life cycle of the BBC pattern, while the linear processes together act to impede the growth of the pattern weakly. This is in contrast to the PNA pattern whose life cycle is primarily controlled by the linear processes (Feldstein 2002). Further decomposition of the linear terms indicates that the full picture is complicated (Fig. 8c). The two dominant terms for the linear processes are ξ2 and ξ4. The term ξ2 (solid red line) that represents the interactions with the climatological mean flow varies nearly at the same pace as ∂ψL/∂t, indicating it favors both the growth and decay of the BBC pattern. This contribution is nearly damped out by the divergence term ξ4 (solid red line), which always acts to obstruct the evolutions of the BBC pattern. The term ξ1 (dashed blue line) continuously acts to dampen the pattern. The term ξ3 (dashed red line), which represents the interactions with the climatological stationary wave, is negligible, consistent with the weak activity of the stationary wave in the boreal summer. On the other hand, further decomposition of nonlinear processes shows that there is no one particular spectrum of TEs that contribute dominantly to the growth and decay of the BBC pattern (figure not shown). All frequencies act to favor the evolution at least at some stages of the life cycle. The importance of high-frequency TEs in the maintenance of the low-frequency variabilities in the atmosphere has been well recognized (Shutts 1983; Illari 1984; Lau and Holopainen 1984; Mullen 1987; Lau 1988; Held et al. 1989; Lau and Nath 1991; Branstator 1992), and the interactions among the low-frequency TEs possibly indicate an additional energy source for the longer low-frequency waves through the upscale energy cascade process (Cai and van den Dool 1994). Previous studies suggest that the cross-frequency interactions exhibit a spatially incoherent structure and act more like a random process (Cai and van den Dool 1994). In contrast, we find that this process also coherently contributes to the growth and decay of the BBC pattern, especially around day 0.

To obtain further insight into the dynamical processes contributing to the evolutions of the BBC pattern, we also examine the horizontal (Fig. 9) and vertical (Fig. 10) structures of various terms on the rhs of Eq. (2) and their combinations on day −3 and day 2 when the growth and decay rates of the BBC pattern reach maximum, respectively. Because the projection errors are nonnegligible below 850 hPa, only the vertical structure between 100 and 700 hPa is drawn (Fig. 10). It is not surprising that the zonally symmetric part of the climatological mean flow tends to shift the BBC pattern eastward (Figs. 9b,h and 10b,h), whereas the beta effect tends to shift the BBC pattern westward (Figs. 9a,g and 10a,g). As a stationary Rossby wave with a zonal wavenumber of 5, the dominance of the advection of relative vorticity by the mean flow over the beta effect is broadly consistent with the classical Rossby wave dynamics theory. In addition, the divergence effect plays a vital role in compensating the advection effect by the mean flow and acts to retard the eastward propagation of the wave pattern (Figs. 9c,i and 10c,i). As a result, although terms ξ1, ξ3, and ξ4 all tend to move the pattern toward downstream or upstream considerably, the large cancellation among them reduces the phase speed and thereby enables the stationary feature of the BBC pattern.

Fig. 9.
Fig. 9.

Spatial distribution of various combinations of terms at 250 hPa on the rhs of Eq. (2) on day −3 for the positive BBC pattern phase (contour; CI = 2 × 106 m2 s−2): (a) beta term ξ1, (b) interactions with the zonal symmetric mean flow ξ2, (c) divergence term ξ4, (d) linear terms ∑i=14ξi, (e) nonlinear terms ∑i=57ξi, and (f) all terms ∑i=17ξi. (g)–(l) As in (a)–(f), respectively, but on day 2. The overlaid shading represents the streamfunction anomalies at day 0.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Fig. 10.
Fig. 10.

As in Fig. 9, but for the vertical cross sections along the blue line in Fig. 3a (CI = 1 × 106 m2 s−2).

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

The negative projection of divergent term ξ4 suggests that the driving effects of the eddy transient fluxes dominate those of the baroclinic processes. This is because the transient eddy fluxes that project positively onto the BBC pattern will lead to horizontal divergence that projects negatively onto the BBC pattern under the thermal wind balance constraint. In contrast, the baroclinic growth that is accomplished by interactions with the mean flow can result in the divergence term that favors the growth of the BBC pattern (Holton 2004). This interpretation can be further confirmed by comparing the spatial patterns of Fig. 9e with Fig. 9f and of Fig. 10e with Fig. 10f, which indicate that ∂ψL/∂t is dominated by ∑i=57ξi. On the other hand, the effect of the TEs changes dramatically into a damping term to destroy the BBC pattern in the decaying phase (Figs. 9k and 10k). Together with the weaker damping effect of linear terms, this results in the rapid decay of the pattern after day 0 (Figs. 9l and 10l). The dramatically different behaviors of the transient eddy fluxes in the growing and decaying phase are essential in driving the BBC pattern. We will gain more insight into this issue from the perspective of energetics in the next section.

b. Energetics budget analysis

In addition to the above streamfunction tendency analysis, investigating the energetics may provide a complementary and possibly more essential view in understanding the life cycle of the low-frequency mode. We will use the energy conversion terms introduced in section 2 to investigate the energetics evolutions of the BBC pattern. First, we check the reliability of our energetics budget. Figure 11a shows the time series of eddy energy tendency ∂(KE + APE)/∂t (solid black line), and the sum of the energy conversion terms with basic flow (CKBF + CPBF) and TEs (CKTE + CPTE) (dashed black line). Here the calculated energy conversions are integrated horizontally northward of 30°N and vertically from the surface to 100 hPa. Although the sum of calculated energy conversion has larger value than the actual eddy energy evolutions due to the neglected physical processes such as friction and diabatic heating, these two curves are overall consistent with each other. This result suggests that the energy budget can reasonably capture the essential dynamics controlling the evolutions of the BBC pattern.

Fig. 11.
Fig. 11.

Time series of various energy conversion terms and their combinations (unit: 10−2 W m2): (a) tendency of the eddy energy [∂(KE + APE)/∂t, solid black line], and the sum of all defined energy conversion terms (CKBF + CPBF + CKTE + CPTE; dashed black line). (b) The sum of all defined energy conversion terms (dashed black line), sum of the interaction with the basic flow (CKBF + CPBF; red line), and the sum of the interaction with the TEs (CKTE + CPTE; blue line). (c) The barotropic energy conversion with the mean flow CKBF (dashed red line), the baroclinic energy conversion with the mean flow CPBF (solid red line), the barotropic energy conversion with the TEs CKTE (dashed blue line), and the baroclinic energy conversion with the TEs CPTE (solid blue line). The various energy terms are integrated horizontally northward of 30°N and then vertically from the surface to 100 hPa.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Figure 11b suggests that the interactions between the BBC pattern and the mean flow always act to strengthen the BBC pattern throughout the life cycle (red line). This contribution is primarily through the baroclinic process (solid red line in Fig. 11c). On the other hand, the tendency of the perturbed energy associated with the BBC pattern varies at the same pace with the interactions with TEs (blue line in Fig. 11b). This result is consistent with the discussions in section 5a that the nonlinear processes essentially drive the life cycle of BBC pattern. Besides, Fig. 11c reveals that TEs contribute to the growth and decay of the BBC pattern in a different way. In the growing stage, TEs lead to the growth of the BBC pattern primarily through the barotropic process (dashed blue line in Fig. 11c). In contrast, approximately one day before day 0, the baroclinic process of TEs weakens dramatically and turns into the dominant damping term to destruct the BBC pattern in the decaying stage (solid blue line in Fig. 11c). Meanwhile, the barotropic energy conversion also decreases rapidly and becomes a less efficient damping term. The interactions between TEs and the BBC pattern imply an energy cycle that the BBC pattern first feeds on the energy from TEs through the barotropic process, and then returns the energy back to TEs primarily through the baroclinic process. It is this energy cycle that drives the growth and decay of the BBC pattern.

More intuitive insights can be gained by examining the spatial pattern of various energy conversion terms. Figure 12 presents the vertically integrated barotropic energy conversion CKBF (upper panel) and baroclinic energy conversion CPBF (lower panel) on day 0, when the interactions between the BBC pattern with the basic flow maximize. Consistent with Fig. 11c, the mean flow primarily contributes to the growth of the BBC pattern through the CPBF, and the intensity of CKBF is negligible. The region with large positive CPBF also corresponds to the area with strong upward propagation of wave activity flux and distinct westward tilt of the vertical phase line (Fig. 5). Figure 13 shows the energy conversion with TEs on day −2 (left panel) and day 2 (right panel), when the energy conversion with the TEs has the largest positive and negative values (Fig. 11b), respectively. The barotropic energy conversion contributes primarily to the growth of the BBC pattern on day −2, and the intensity of baroclinic energy conversion on day −2 is very weak. In contrast, the baroclinic energy conversion dramatically turns into an overall negative pattern with large amplitude on day 2, indicating its efficient damping effect at this time. Meanwhile, the barotropic energy conversion also changes into a weak damping term to favor the decaying of the BBC pattern, broadly in agreement with the result of Fig. 11c.

Fig. 12.
Fig. 12.

The spatial distribution of energy conversion with the climatological mean state at day 0 (shading; SI = 2 × 10−1 W m−2): (a) barotropic energy conversion CKBF and (b) baroclinic energy conversion CPBF. Purple contours represent the 250-hPa zonal wind (16, 24, 32, …; unit: m s−1) in (a) and 400-hPa temperature (240, 244, 248, …; unit: K) in (b), respectively. The energy conversions are integrated vertically from the surface to 100 hPa.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

Fig. 13.
Fig. 13.

The spatial distribution of energy conversion with the TEs on day −2 (SI = 2 × 10−1 W m−2): (a) barotropic energy conversion CKTE and (b) baroclinic energy conversion CPTE. (c),(d) As in (a),(b), respectively, but on day 2.

Citation: Journal of Climate 33, 6; 10.1175/JCLI-D-19-0458.1

6. Conclusions and discussion

a. Conclusions

Our previous work identified a new teleconnection pattern along the summertime polar front jet over northern Eurasia, referred to as the British–Baikal Corridor (BBC) pattern. In this study, we extend that study from the interannual time scale to the intraseasonal time scale. Based on filtered daily mean reanalysis data, 20 positive events and 23 negative events are composited to reveal the BBC pattern-related dynamics and climate anomalies. Because the main results for the positive and negative phases are roughly the same with opposite signs, only the positive phase is discussed in detail. Analysis indicates that the BBC pattern has a life cycle of approximately two weeks, which is much longer than the life cycle of typical midlatitude baroclinic wave packets that primarily fluctuate on subweekly time scales. This result indicates that the dynamics of the BBC pattern is subject to an intraseasonal phenomenon. Meanwhile, the e-folding time scale of the BBC pattern is around 4–5 days, considerably shorter than that of the NAO or PNA pattern. This result implies that the essential dynamics accounting for their evolutions are different. The life cycle of the NAO or PNA pattern mainly depends on the wave breaking and the following mixing (Benedict et al. 2004). In contrast, the life cycle of the BBC pattern primarily results from the wave packet dispersion and nonlinear interactions with TEs (sections 4 and 5).

The evolution of the BBC pattern resembles the life cycle of a quasi-stationary Rossby wave train with a wavenumber 5 and group velocity of approximately 10.7 m s−1. The precursor of the BBC pattern first appears as an upstream wave packet propagating along the Atlantic jet 10 days before the peak of the BBC pattern (i.e., day 0). The vertical structure of the BBC pattern indicates an equivalent-barotropic structure that tilts westward with height in the lower troposphere. This westward tilting is distinct for the action centers over the continent. It is more evident during the growing stage, but it gradually diminishes after day 0. The most distinct feature for the evolutions of the BBC pattern is the nearly zonal propagation throughout its life cycle, indicating its waveguide nature trapped along the polar front jet. This trapped effect arises from the strong meridional gradient of the stratification over northern Eurasia in the boreal summer (Iwao and Takahashi 2008; XWC), consistent with the baroclinic nature of the BBC pattern.

The growth and decay of the BBC pattern are dominated by nonlinear processes (i.e., the interactions between the BBC pattern and TEs). Although individual linear processes all have large values that favor the eastward or westward propagation of the BBC pattern, they cancel each other and hardly move the pattern, facilitating the quasi-stationary nature of the BBC pattern. In contrast, TEs contribute to growth and decay differently. In the growing stage, TEs drive the growth of the pattern primarily through the barotropic process. In the decay stage, they damp the pattern mainly in a baroclinic way. It is this energy cycle between the BBC pattern and the TEs that dominates the life cycle of the BBC pattern.

b. Discussion

Our results suggest that the linear terms act to dampen the BBC pattern in the streamfunction tendency equation, whereas they facilitate the growth of the BBC pattern in the energetics equation. This seeming contradictory conclusion arises from different definitions of the linear and nonlinear terms in the two equations. In the streamfunction tendency equation, the divergence term that is mathematically linear is defined as linear terms as in Cai and van den Dool (1994), Feldstein (2002), and Feldstein (2003). Because it is related to the secondary circulation and associated vertical motion in the quasigeostrophic framework, it can be caused by both the mean flow and TEs. In other words, the linear terms in the streamfunction tendency equation are not equal to the interactions between eddies with the mean flow. Hence, we can only conclude that the linear terms, not the mean flow itself, work together to retard the growth of the BBC pattern. However, we do not need to worry about this issue in the energetics equation, where the separation between the linear terms and nonlinear terms and the roles of mean flow and TEs are clear [e.g., Eq. (2)].

Nevertheless, the results of energetics analysis should be interpreted with care. The TEs tend to relax the anomalous temperature gradient associated with the BBC pattern through the downgradient heat flux transport (Lau and Holopainen 1984). Hence, they may act as a particular kind of weak thermal damping that destabilizes the external Rossby waves (Held et al. 1985, 1986; Robinson 1987). Held et al. (1986) suggested that a standard energy analysis that does not take into account the modulated eddy–mean flow interaction terms by the damping may to some extent underestimate the net contribution from TEs because the generation of APE due to the downgradient heat flux transportation by TEs outweighs the damped APE in the amplifying waves. Based on a quasigeostrophic three-layer model that captures the essential dynamical features of stationary external Rossby waves propagating along the tropospheric jet stream (Pedlosky 1987), Chen et al. (2013) demonstrated that adding weak thermal damping into a linear dynamical system, which can be viewed as a simple kind of parameterization scheme to represent the role of TEs, could induce the destabilization of the Silk Road pattern through modifying the vertical structure of the eddies. We speculate that a similar mechanism also works for the BBC pattern. Further studies with the same simple model are planned to gain more insight into this issue.

One question that remains unanswered is what mechanism initiates the upstream wave packet along the Atlantic jet on day −10. Zonal wind above North America is strengthened from day −10 to day −4 (Fig. 4). It is possible that the strengthened wind favors the wave packet activity by modulating the activities of TEs or causing barotropic instability. However, the mean flow is defined as the average of all summer days in this study, so the strengthening of the zonal wind may reflect the activities of the eddy itself. On the interannual time scale, the multiscale interaction among the mean flow, low-frequency flow, and high-frequency TEs is the primary initiation mechanism for the BBC pattern (XWC). On the intraseasonal time scale, we speculate that the instability of the jet stream or interactions between the jet stream and the TEs may also be crucial for the excitation of the BBC pattern.

Another question is how to interpret the physical picture behind the energetics analyses. The energy conversion from the mean flow to the BBC pattern can be regarded as the processes that the BBC pattern disturbs the zonal-mean circulation and induces anomalous momentum and heat fluxes. This process enables the BBC pattern to extract kinetic energy and potential energy from the mean flow. The barotropic strengthening and baroclinic dissipation by the TEs can be understood as the inverse life cycle of nonlinear unstable baroclinic waves discussed by Simmons and Hoskins (1978). The barotropic dissipation by the TEs is not as intuitive as the previous two processes. It may arise from the downscale cascade of the kinetic energy when the circulation associated with the BBC pattern is deformed and split into several smaller eddies. Further studies using simple models are needed to address this question in the future.

Acknowledgments

We appreciate the three anonymous reviewers for their insightful suggestions that helped us to improve the paper. Peiqiang Xu thanks Prof. Yihua Lin of IAP, Prof. Yang Zhang of Nanjing University, Dr. Christian Franzke of the University of Hamburg, Dr. Hao Fu of Stanford University, Prof. Geoffrey Vallis of the University of Exeter, and Dr. Zhenning Li of Sun Yat-sen University for their help. This work is supported by the National Key R&D Program of China (2016YFA0600604) and the National Natural Science Foundation of China (41721004, 41925020).

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