1. Introduction

During the past several decades, amplified Arctic warming is one of the most remarkable phenomena regarding global temperature change (Stouffer and Manabe 2017; Xie et al. 2019). Meanwhile, remarkable regional cooling on decadal or multidecadal scales occurs in the context of overall global warming, such as the Eurasian cooling (Easterling and Wehner 2009; Cohen et al. 2014; Shepherd 2016). This kind of decadal variability is generally blamed for internal climate variability (Trenberth 2015; Steinman et al. 2015). On the one hand, the dominant role of internal climate variability associated with Atlantic and Pacific Oceans on multidecadal variability of temperature has been proposed by previous studies (Held 2013; Kosaka and Xie 2013; Steinman et al. 2015; Dai et al. 2015; Huang et al. 2017; Luo et al. 2017a). On the other hand, as directly observed in Fig. 1, Arctic warming is one of the strongest signatures during the past several decades (1979–2017), which overwhelms the signals of internal climate variability directly reflected by the temperature change over the Atlantic and Pacific Oceans. Recently, more and more studies have put their efforts into investigating the relative or joint effect of the warm Arctic and internal climate variability on the cold Eurasian pattern. Specific attention was paid to the internal climate variability of the upstream region (i.e., North Atlantic) (e.g., Luo et al. 2016, 2017a; Sung et al. 2018; Yang et al. 2018; B. Luo et al. 2019). An exact attribution relies on the model simulation such as the fingerprint method (Ding et al. 2019), while intermodel discrepancies make a robust attribution far from realizing (Cohen et al. 2018; Smith et al. 2019).

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(a) Near-surface air temperature change (K) (linear trend multiplied by the time span) for the period of 1979–2017 during boreal winter. The results are based on GISTEMP. The gray dots indicate that the linear trend is significant at the 99% confidence level based on a two-tailed Student’s t test. (b) Time series of near-surface air temperature anomalies (relative to 1951–80) averaged over the region of 40°–70°N, 50°–130°E, outlined by the rectangle in (a). The raw series is the gray line, and the orange line and the blue and red line indicate the long-term trend (IMF6 from EEMD) and decadal/multidecadal variability (sum of IMFs 3–5), respectively. The dashed black line indicates the trend line of the raw series from 1979 to 2017.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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Apart from a full attribution, this paper focuses on the general dynamics that could link the Arctic warming with Eurasian cooling. Regarding dynamics, there are extensive works published. Here, a detailed review of all the previous works is not necessary because some excellent reviews are already available, such as those of Cohen et al. (2014, 2018), Overland et al. (2016), Coumou et al. (2018), and Screen et al. (2018). Previous works suggest many possible pathways linking the Arctic and the midlatitude. The main pathways include Rossby waves (Francis and Vavrus 2012; Sung et al. 2018; Li et al. 2019), meandering of the jet stream (Screen and Simmonds 2013, 2014; Francis and Vavrus 2015; Di Capua and Coumou 2016), the Arctic Oscillation (Yang et al. 2016), the North Atlantic Oscillation (Yang et al. 2018; B. Luo et al. 2019), polar vortices (Cohen et al. 2014), the Siberian high (Ye et al. 2018; Sung et al. 2018), atmospheric blocking (Yao et al. 2017; Luo et al. 2017b, 2018; B. Luo et al. 2019; D. Luo et al. 2019; Wegmann et al. 2018), stratospheric anomalies (Zhang et al. 2018), and eddy energy propagation (Gu et al. 2018).

Overall, more and more light is being shed on the dynamics of the Arctic and midlatitude linkages. As seen above, the complexity of the connections increased at the same time. And some pathways are tightly connected, such as the North Atlantic Oscillation and atmospheric blocking (Yang et al. 2018; B. Luo et al. 2019). Thus, this study examines the general dynamic and thermodynamic features of atmospheric circulation without preference as to the aforementioned specific pathways. To achieve this objective, we do the investigation using potential vorticity (PV) dynamics. We use PV dynamics because PV inherently depicts seamless coupling between dynamic and thermodynamic aspects (Ertel 1942; Yeh and Chu 1958; Charney and Stern 1962). In other words, any observed circulation and temperature change can, on a fundamental level, be attributed to PV. In this paper, piecewise PV inversion and the PV equation are used (Davis and Emanuel 1991; Hartley et al. 1998; Zhao et al. 2007; Egger 2008; Spengler and Egger 2012; Egger et al. 2017). Piecewise PV inversion (PPVI) quantitatively tells the effects of arbitrary PV change on the entire atmosphere, while the PV equation tells how the PV change occurred. Importantly, we show that PV inversion can also be used in the climate change realm, although it is commonly used in synoptic cases.

This paper focuses directly on the persistent change of the mean state from 1979 to 2017 rather than weather or interannual variability. The remainder of this paper is arranged as six parts. Section 2 describes all the data and methods used in this paper. Essential characteristics (e.g., the spatial pattern and vertical structure) of Eurasian cooling and Arctic warming are presented in section 3. Section 4 addresses the concept of PV adaptation based on the ideal case. Sections 5 and 6 address the vertical coupling among different levels and horizontal coupling among different locations, respectively. Concluding remarks are provided in section 7.

2. Data and method

3. Appearance and structure of Eurasian cooling and Arctic warming

As shown in Fig. 1, the most apparent feature of wintertime temperature change from 1979 to 2017 is the amplified Arctic warming, also known as Arctic amplification (Stouffer and Manabe 2017). Meanwhile, the contrasting characteristic is cooling to various degrees over many regions globally, especially Eurasian cooling in the midlatitude regions. To better understand the Eurasian cooling, a series of temperature evolution averaged over the area of 40°–70°N, 50°–130°E is shown in Fig. 1b. EEMD (see section 2d) is used to identify the variability of temperature on various time scales. First, the overall change is a rise in temperature, namely, long-term warming. Besides, large interannual variability is involved, which is common in the high latitudes due to large internal atmospheric circulation variability (Wallace et al. 2012). Meanwhile, the decadal variability is indeed remarkable. Such a large magnitude of decadal variability will accelerate or decelerate warming by favoring or offsetting long-term warming trends. Taken together, the Eurasian cooling is mainly associated with the observed downward-trending decadal variability. However, the underlying mechanisms of this downward-trending decadal variability in temperature from 1979 to 2017 need to be explored further.

To get a global view, the vertical structure of Eurasian cooling and Arctic warming is examined further. Figure 2 shows a vertical–latitudinal cross section of the changes in temperature and geopotential height averaged over 60°–120°E. Eurasian cooling occurs not only at the surface but also throughout almost the entire troposphere (Fig. 2a). The strongest cooling in the troposphere presents at about 500 hPa. Meanwhile, the Arctic warming also occurs throughout the whole troposphere. The strongest Arctic warming occurs at the surface, which is also suggested by Screen and Simmonds (2010) and Cohen et al. (2014). There is also remarkable cooling or warming occurring in the stratosphere, and we will examine the stratospheric influences on troposphere in section 5.

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(a) Vertical–latitudinal cross section of temperature changes (linear trend multiplied by the time span) for the period of 1979–2017 averaged over the region of 60°–120°E during boreal winter. The gray contour line indicates the corresponding climatology for the period of 1979–2017. (b) As in (a), but for geopotential.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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Under geostrophic approximation, circulation could be represented by geopotential height in pressure coordinates. In pressure coordinates, the hydrostatic relation is ∂Φ/∂p = −(R/p)T, and the relation is applicable for both the mean state and change in the pressure coordinates. Thus, the temperature change should be proportional to the vertical gradient of geopotential change at the arbitrary pressure level. The relation is confirmed by the results in Fig. 2. The results show that the absolute changes in the vertical gradient of geopotential are larger in areas where the absolute value of temperature changes is larger for the same pressure level. Thus, the tight connections between atmospheric circulation change and regional temperature change are evident.

4. Concept of PV adaptation based on the ideal case

In the PV view, the seamless dynamic and thermodynamic coupling are straightforwardly indicated by Eq. (2), in which any change in geopotential Φ′ could induce the changes in both circulation [represented by vorticity term (1/f₀)∇²Φ′] and temperature [represented by static stability term $\left(\partial /\partial p\right)\left[\left(f_0/\overline{S}\right)\left(\partial {\mathrm{\Phi }}^{\prime }/\partial p\right)\right]$ and supported by results shown in Fig. 2]. The classic Ertel PV conservation picture concisely and vividly depicts the inherent dynamic and thermodynamic coupling as shown in Fig. 3a. The corresponding pseudo-PV conservation picture is shown in Fig. 3b, which is similar to Fig. 3a but replacing the isentropic surface with the isobaric surface. PV conservation picture is shown in a Lagrangian view rather than an Eulerian view, which is generally adopted in climate change. In an Eulerian view, as indicated by Eq. (4), local PV conservation is very hard to satisfy because advection of PV widely exists and will change local PV even for the absence of diabatic heating and friction.

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Schematic views of (top) PV conservation for (a) EPV (Ertel PV) and (b) pseudo-PV (PPV) and (bottom) PV adaptation (c) under constant PPV but anomalous surface thermal conditions and (d) under anomalous PPV but constant surface thermal conditions. PV adaptation means the adaptation of PV (PV change) to forcing and coherent dynamic–thermodynamic adaptation to PV change. All the variables have the same meaning as described in section 2. Subscript T indicates the top of the atmosphere. The gray parallelogram indicates Earth’s surface. The visual illustration in (c) and (d) is similar to the traditional PV conservation illustration in (b) but with a fixed top and bottom.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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However, the picture of PV conservation still helps to get insights. Here, two ideal cases extended from the PV conservation picture are used for some instructive discussions. Two specific questions emerged when applying PV dynamic to climate change: 1) What is the effect of PV change? and 2) Why did the PV change? As already addressed in the introduction section, PV inversion and the PV equation can answer the two questions. However, a more fundamental question that has no direct help to solve the practical question but that helpful to conceptual understanding is this: “Why should the PV change?”.

Here let us take the effect of diabatic heating in generating PV as an example, which has a simple mathematical expression as $\partial q/\partial t\propto -f_0\left(\partial Q/\partial p\right)$. Thus, diabatic heating generates positive, negative, and zero PV change when Q is increased, decreased, or unchanged with height, respectively. Here, an ideal case extended from the PV conservation is shown in Fig. 3c. In this ideal case, at first, there is temperature change present at the surface. Then, the atmosphere strongly adapts to the surface temperature change so that the diabatic heating of atmosphere (induced by the surface temperature change and corresponding vertical motion of atmosphere) is even in the vertical direction (i.e., ∂Q/∂p = 0). In such a case, the surface temperature change induces no PV change, but geopotential greatly changes, and the balance relation is ${\nabla }^2{\mathrm{\Phi }}^{\prime }=\left(\partial /\partial p\right)\left[\left(f_0^2/\overline{S}\right){\alpha }^{\prime }\right]$ according to Eq. (2), where the hydrostatic relation, ∂Φ′/∂p = −α′, is introduced.

In practice, the ideal case in Fig. 3c can be quantified by using PPVI according to the superposition principle, which needs to keep only the change in surface thermal condition in the PPVI, as shown in Fig. 4b. The ideal case (Fig. 4b) with surface heating change but keeping a constant PV will make the geopotential change of atmosphere much stronger than the real case (Fig. 4a). In other words, changed PV in response to surface diabatic heating makes the change in motion of atmosphere more moderate. This conclusion also holds for the friction as demonstrated in section 2c. Therefore, PV change works as a stabilizer of the atmosphere in a fundamental understanding. This is an answer to “Why should the PV change?”.

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Inverted geopotential changes (m² s⁻²) (linear trend multiplied by the time span) from PPVI with three pieces, at the 500-hPa level, during boreal winter from 1979 to 2017. The three pieces are (b) surface thermal condition change, surface and tropospheric PV change (not shown), and stratospheric total change (shown in Fig. 5f). (a) The sum of all the three pieces. Note that the ranges of the two color bars are different.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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Opposite to the ideal case in Fig. 3c, the other ideal case is shown in Fig. 3d, which prescribes a PV change at the surface but without surface thermal condition change {$\left(\partial /\partial p\right)\left[\left(f_0^2/\overline{S}\right){\alpha }^{\prime }\right]=0$ rather than a zero temperature change}. In Fig. 3d, the balance relation is ${\nabla }^2{\mathrm{\Phi }}^{\prime }=f_0{q}^{\prime }$. Thus, geopotential must have a negative change in response to a positive PV change (according to ${\mathrm{\Phi }}^{\prime }\propto -{\nabla }^2{\mathrm{\Phi }}^{\prime }$), and vice versa. Regarding the ideal case in Fig. 3c, for surface warming stronger at the surface than above, $\left(\partial /\partial p\right)\left[\left(f_0^2/\overline{S}\right){\alpha }^{\prime }\right]$ is positive under the current climatological $\overline{S}$. Therefore, geopotential change must be negative according to ${\nabla }^2{\mathrm{\Phi }}^{\prime }=\left(\partial /\partial p\right)\left[\left(f_0^2/\overline{S}\right){\alpha }^{\prime }\right]$, and vice versa.

The real case is the sum of Figs. 3c and 3d. Namely, for surface warming stronger at the surface than above, the balance in Fig. 3c tends to generate negative geopotential, while the stronger diabatic heating at the surface than above also induces negative PV, which tends to generate positive geopotential. Thus, the eventually observed geopotential change depends on the net effects after summing Figs. 3c and 3d together. In other words, the reality is the sum of one rule “warming is cyclonic and cooling is anticyclonic” and another rule “a positive PV change is cyclonic and a negative PV change is anticyclonic.” In short, from a “forcing” [i.e., diabatic heating and friction in Eq. (3)] to the final observed changes of atmosphere, two key adaptation processes are involved. One is the PV change as a direct adaptation to forcing [Eq. (3)]. The other is the commonly observed change of atmosphere (e.g., temperature and circulation) as an adaptation to PV change. Therefore, in brief, the adaptation of PV to forcing and coherent dynamic–thermodynamic adaptation to PV change is referred to as “PV adaptation.” The nature of PV adaptation is the seamless dynamic–thermodynamic coupling.

5. Vertical coupling among different levels

The previous section discusses the conceptual understanding of the “stabilizer” effect of PV change and introduces the concept of PV adaptation based on two ideal cases. In practice, the concept of PV adaptation can be quantified by using PPVI and further used to understand the vertical coupling between different levels. In a real case, the net influence of the surface on the atmosphere is determined by the surface total change (i.e., changes in both surface thermal condition and PV). Thus, a new three-piece PPVI scheme was performed based on this consideration. The three pieces are the surface total change, tropospheric PV change, and stratospheric total change.

Figure 5 shows the results of the new PPVI scheme. At 850 hPa, the geopotential change is dominated by surface total change (Fig. 5 left). The tropospheric PV change shows a tiny contribution to the geopotential change at 850 hPa (Fig. 5c), and even the 850-hPa level itself is located in the troposphere. The dominant surface contribution means that the change at 850 hPa is determined by the surface PV change via PV adaptation.

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Inverted geopotential changes (m² s⁻²) (linear trend multiplied by the time span) from PPVI with three pieces, at the (left) 850- and (right) 500-hPa levels, during the boreal winter from 1979 to 2017. The three pieces are (a),(b) surface total change, (c),(d) tropospheric PV change, and (e),(f) stratospheric total change. Note that the ranges of the two color bars are different.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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In sharp contrast, both surface total change and tropospheric PV change have great influences on the geopotential change at 500 hPa (Fig. 5, right). The positive geopotential change at 500 hPa corresponding to Arctic warming is determined by both surface total change and the tropospheric PV change. However, the negative geopotential change corresponding to Eurasian cooling (Figs. 1 and 2) is dominated by the tropospheric PV change (Fig. 5d), while surface total change shows negligible influence (Fig. 5b). The dominant contribution of tropospheric PV change means that enhanced Eurasian cooling at 500 hPa is mainly determined by tropospheric PV change via PV adaptation.

In the new piecewise scheme, the tropospheric PV change piece covers a wide vertical range, which includes the 850- and 500-hPa target levels themselves. In this sense, we cannot determine the vertical coupling among different levels within the troposphere. To make the vertical coupling clearer, two additional schemes of PPVI with five pieces are performed. In the new piecewise schemes, the surface and stratospheric pieces are the same as those in Fig. 5, while the tropospheric PV change piece is divided into three pieces in two ways. Regarding the 850-hPa level, the three pieces of tropospheric PV change are 900 hPa and below, 875–825 hPa, and 800–250 hPa. Meanwhile, for 500-hPa level, the three pieces are 600 hPa and below, 550–450 hPa, and 400–250 hPa.

Figure 6 shows the results of the two new PPVI schemes. In Fig. 6, the two pieces 900 hPa and below and 875–825 hPa are merged for the 850-hPa level (Fig. 6a). Similarly, the two pieces 600 hPa and below and 550–450 hPa are merged together for 500 hPa (Fig. 6c). Because the contribution of the 900-hPa and below piece (not shown) is very tiny relative to the other two pieces, so does the 600-hPa and below piece (not shown). Thus, Figs. 6a and 6c represent the effects of a PV change within the vertical levels of 850 and 500 hPa, respectively. Meanwhile, the 800–250-hPa and 400–250-hPa pieces represent the influences from upper levels (relative to the 850- and 500-hPa levels, respectively). As shown in Fig. 6, the influences from the upper-level PV change are larger than those of local (vertical levels) PV change on geopotential change at both the 850- and 500-hPa levels. Simply put, in the vertical direction, the influences of tropospheric PV change on both the 850- and 500-hPa levels are mainly top-down.

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Inverted geopotential changes (m² s⁻²) (linear trend multiplied by the time span) from PPVI with five pieces, at the (top) 850- and (bottom) 500-hPa levels, during the boreal winter from 1979 to 2017. Two of the five pieces are surface and stratospheric total change. For 850 hPa, the remaining three pieces are tropospheric PV change from the surface to 900 hPa, 875–825 hPa, and (b) 800–250 hPa. For 500 hPa, the remaining three pieces are tropospheric PV change from the surface to 600 hPa, 550–450 hPa, and (d) 400–250 hPa. (a) The sum of two pieces (surface–900 hPa and 875–825 hPa) is shown, because the surface–900-hPa piece has a very small value. (c) As in (a), but the sum of two pieces is shown (surface–600 hPa and 550–450 hPa). Again, please notice the range of the color bar.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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Notably, the top-down influence of PV change on 850 hPa (Fig. 6b) is negligible (relative to the bottom-up influence shown in Fig. 5a). In contrast, the top-down influence of PV change on the 500-hPa geopotential change is as large as the influence of the surface total change (Figs. 5c and 6d). In particular, the negative geopotential change at 500 hPa over the Eurasian cooling region is almost completely generated by the top-down influence of PV change. Thus, enhanced Eurasian cooling at 500 hPa is mainly determined by the top-down influence of PV change via PV adaptation. According to Figs. 5e and 5f, stratospheric total change show tiny direct influence on both the 850- and 500-hPa levels. Nevertheless, the stratosphere may indirectly affect 850 and 500 hPa via a top-down mechanism, such as a gradual influence through the upper troposphere to 500 and 850 hPa. Therefore, the effect of stratospheric total change on troposphere should be reexamined.

To do so, the stratospheric influence on the 250-hPa level was examined, where the stratosphere is simply chosen as the range of 225–1 hPa. Figure 7 shows the geopotential change at 250 hPa from three-piece PPVI, the same as that in Fig. 5. As shown in Fig. 7, stratospheric total change show very little influence on the 250-hPa geopotential change relative to that of the tropospheric PV change. In addition, stratospheric influence mainly occurred over the Arctic rather than over the Eurasian cooling region (Fig. 7b). The stratospheric influence on tropospheric Eurasian cooling is negligible. Nevertheless, on the synoptic scale, the stratospheric influence on the troposphere may be crucial (Hartley et al. 1998; Cohen et al. 2014; Zhang et al. 2018). In summary, through PV adaptation, the bottom-up surface influence dominates the 850-hPa level, while both bottom-up surface and top-down upper-level (troposphere) influences control the 500-hPa level. However, enhanced Eurasian cooling at 500 hPa is solely determined by the top-down influence.

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As in Fig. 5, but at the 250-hPa level.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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6. Horizontal coupling due to PV advection and adaptation

In the last section, we explored the vertical coupling among different levels. However, the vertical coupling is not enough to tell the whole story because the linkage between Eurasian cooling and Arctic warming must have a horizontal pathway. On the basis of vertical coupling, the horizontal coupling is explored. To access the horizontal coupling, we just need to determine whether the local PV change is contributed by horizontal PV advection.

Here, only horizontal PV advection at the levels 850 and 500 hPa is examined because the changes show equivalent barotropic structure (Fig. 2). Regarding climate change, the horizontal PV advection term is linearized as $-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}-{\overline{\mathbf{V}}}_g\cdot \nabla q^{\prime }$ according to Eq. (5). The PV change itself in the equilibrium PV equation is directly reflected in the horizontal advection term. This is very different from the synoptic case, in which the PV change is reflected in the local tendency term [∂q/∂t in Eq. (4)]. In terms of physical understanding, the nature of the difference between climate and the synoptic case is a complete or ongoing PV adaptation.

Figure 8 shows the PV climatology and change overlaid with the wind change and climatology for both 850 and 500 hPa. The combinations of wind change/PV climatology and wind climatology/PV change represent $-{\overline{\mathbf{V}}}_g^{\prime }\cdot \nabla \overline{q}$ and $-{\overline{\mathbf{V}}}_g^{\prime }\cdot \nabla q^{\prime }$, respectively. As shown in Fig. 8a, over the Eurasian cooling–Arctic warming region, the wind change flows across the isoline of climatological PV (with a large crossing angle). Thus, PV advection via wind change/PV climatology is vital. The situation at 500 hPa is similar (Fig. 8c).

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(a),(c) PV climatology (filled; 10⁻⁵ s⁻¹) and horizontal wind change (vectors; linear trend multiplied by the time span; m s⁻¹) during the boreal winter from 1979 to 2017. (b),(d) As in (a) and (b), but for PV change and horizontal wind climatology. Results are shown at the (top) 850- and (bottom) 500-hPa levels.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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Now, physical understanding of the relationship between horizontal PV advection change and PV change itself is a key to move forward. To make things clearer, we first examine an ideal case. According to Eq. (5), the balance relation is $-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}+{\overline{\mathbf{V}}}_g\cdot \nabla q^{\prime }=0$ when diabatic heating and friction are neglected. The situation at 500 hPa is closer to this ideal case than that at 850 hPa. Therefore, we use the featured values of wind and PV at 500 hPa. Symbolically, the domain is chosen as 0°–60°E, 40°–80°N, and the magnitudes of the variables in both climatology and change are roughly set according to the featured values in Fig. 8 (bottom). For simplicity, the climatological wind is pure zonal (uniformly 12 m s⁻¹), the wind change is pure meridional (with anticyclonic zonal shear of 5 to −5 m s⁻¹ from west to east, and northward is positive), and PV is zonally uniform but with a meridional gradient (1–8 × 10⁻⁵ s⁻¹ from south to north). This ideal case is shown in Fig. 9 (top), in which the overall patterns do not change with, although the magnitudes will change with, different values of selected parameters.

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(top) An ideal case of zero net horizontal PV advection (i.e., ${\overline{\mathbf{V}}}^{\prime }\cdot \nabla \overline{q}+\overline{\mathbf{V}}\cdot \nabla q^{\prime }=0$), with prescribed climatology of PV $\left(\overline{q}\right)$ and wind $\left(\overline{\mathbf{V}}\right)$ and change of wind (V′). (top left) The prescribed $\overline{q}$ and ${\mathbf{V}}^{\prime }$ are shown as filled and blue arrows. Note that $\overline{q}$ is zonally uniform, and ${\mathbf{V}}^{\prime }$ is purely meridional (with a maximum value of 5 m s⁻¹); $\overline{\mathbf{V}}$ is a uniform zonal wind $\left(\overline{u}\right)$ of 12 m s⁻¹. These prescribed values approximately correspond to the situation at 500 hPa (Fig. 8, bottom, within the domain of approximately 40°–80°N, 0°–60°E). (top center) Distribution of $-{\mathbf{V}}^{\prime }\cdot \nabla \overline{q}$ (10⁻¹¹ s⁻²) under prescribed values. (top right) Distribution of q′ calculated from ${\mathbf{V}}^{\prime }\cdot \nabla \overline{q}+\overline{\mathbf{V}}\cdot \nabla q^{\prime }=0$, in which q′ at 0° longitude is prescribed as zero. (bottom) Schematic view of the evolution of horizontal PV advection under a situation with enhanced regional warming over the Arctic, a meridional PV gradient (larger to the north, brown dashed lines indicate isoline of PV), and purely westerly wind (gray arrow). The bottom row is based on results shown in the top row. As in the top row, the blue arrow indicates wind anomaly, “small” and “large” indicate the relative value of $\overline{q}$, and the minus and plus symbols indicate the sign of $-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}$. The filled symbol indicates a change in PV (q′).

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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Under the PV climatology in Fig. 9 (top left), the southward wind change has positive PV advection, whereas the opposite is true for the northward wind change. The PV advection change induced by $-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}$ for a given zonal shear value because of the wind change is shown in Fig. 9 (top center). Then, the term $-{\overline{\mathbf{V}}}_g\cdot \nabla q^{\prime }$ is balanced with $-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}$. After the balance relation is solved, the PV change is shown in Fig. 9 (top right), where the PV change at the western boundary is set as zero. The balance between $-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}$ and $-{\overline{\mathbf{V}}}_g\cdot \nabla q^{\prime }$ will eventually make the distribution of PV change induced by $-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}$ move downstream. Thus, the eventual PV change does not directly overlap with the PV advection change implied by the circulation change $\left(-{\mathbf{V}}_g^{\prime }\cdot \nabla \overline{q}\right)$.

With the help of the ideal case (Fig. 9, top), a real change at the 500-hPa level is not difficult to understand (Figs. 8c,d). The phenomenon that occurred around the Eurasian cooling region (Figs. 8c,d) is similar to the ideal case (Fig. 9, top). PV advection induced by the wind change upstream of the Eurasian cooling region (Fig. 8c) was advected by the climatological wind downstream (Fig. 8d). Eventually, the horizontal PV advection change generated a positive PV change over the Eurasian cooling region and a negative PV change over the upstream regions (Fig. 8d). In contrast, the situation at 850 hPa (Figs. 8a,b) seems different than that at 500 hPa and in the ideal case (Figs. 8c,d and 9, top). This discrepancy is expected because the diabatic heating effect is essential in the lower troposphere. Nevertheless, the general concept that PV advection induced by the upstream wind change will be advected by the climatological wind to downstream, that is, the compensation between $-{\mathbf{V}}^{\prime }\cdot \nabla \overline{q}$ and $-{\overline{\mathbf{V}}}_g\cdot \nabla q^{\prime }$, exists independent of whether force exists.

In extratropical regions, it is inevitable for an anticyclonic (or cyclonic) circulation change to cross the isoline of climatological PV because large PV gradients are widespread over the extratropical regions (e.g., Figs. 8a,c). Therefore, the anticyclonic circulation change induced by Arctic warming will extend southward via horizontal PV advection and PV adaptation. The schematic view in Fig. 9 (bottom) shows the extension of the Arctic warming–induced anticyclonic circulation change. As shown in Fig. 9 (bottom right), first the local anticyclonic circulation change induced by Arctic warming advects positive PV to the adjacent area to the southeast and negative PV to the adjacent area to the southwest. No PV advection is shown on the northern side of the anticyclonic circulation anomaly (Fig. 9, bottom) because the PV gradient is very small in very northern regions (Figs. 8a,c). Second, the PV change induced by meridional wind advection is advected by climatological wind downstream. As shown in Fig. 9 (top), after a temporal balance between meridional and zonal PV advection is achieved, the negative PV change on the southern side of the anticyclonic anomaly is enhanced. In turn, the enhanced PV change induces a northward extension of the anticyclonic circulation anomaly via PV adaptation. At the same time, PV advection by climatological wind induces positive PV change in the downstream regions (east of the anticyclonic circulation anomaly). The final balanced PV change is schematically shown in Fig. 9 (bottom right).

The illustration of the horizontal PV advection at 500 hPa (Fig. 8, bottom) is identical to the schematic view in Fig. 9 (bottom). In Fig. 8 (bottom), the negative PV change in the Arctic Ocean induced by Arctic warming, the northward extension of this negative PV change, and the positive PV change over the downstream Eurasian cooling region are all observed. As demonstrated in the last section, Eurasian cooling at 500 hPa is dominated by top-down influence. The situation of horizontal PV advection at levels higher than 500 hPa is similar to that at 500 hPa. Simply put, enhanced Eurasian cooling at 500 hPa is regulated by both horizontal coupling (with Arctic warming) at higher levels and top-down vertical coupling.

Based on the PV advection perspective, the horizontal coupling is further examined using PPVI. Figure 10 shows the results of a new PPVI scheme based on geographical piecewise. In the new scheme, there are three horizontal pieces, including 70°–90°N, 30°–70°N, and 10°–30°N. For each piece, the total change (changes in the thermal condition at the bottom and top boundaries and the PV for the entire atmosphere) is set to the observed values within the piece and is set to zero outside of each of the pieces. As shown in Fig. 10, the total change within each horizontal piece present evident influences on the circulation out of the piece. As shown in Fig. 10a, Arctic warming–related total change generates a clear influence on the circulation change over the adjacent area to the south (Europe). Similarly, total change over the midlatitude domain of 30°–70°N also has a clear influence on adjacent regions (Fig. 10b). The extended influences shown in Fig. 10 confirm the extension process of the PV change schematically shown in Fig. 9 (bottom). Specifically, Fig. 10 suggests that the local PV change can further advect PV to distant regions through its extended influences on circulation.

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Inverted 500-hPa geopotential changes (m² s⁻²) (linear trend multiplied the time span) from PPVI with three pieces, during the boreal winter from 1979 to 2017. The three pieces are total change over regions of (a) 70°–90°N and (b) 30°–70°N, as well as 10°–30°N (not shown). The purple dashed lines indicate the boundary of each piece. The lateral boundary conditions (geopotential change) at 90° and 10°N are observed and zero for the 70°–90°N piece, both zero for the 30°–70°N piece, and zero and observed for the 10°–30°N piece.

Citation: Journal of Climate 33, 7; 10.1175/JCLI-D-19-0073.1

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Actually, from a traditional wave view, the 500-hPa geopotential change associated with Eurasian cooling can be connected to the anomalous stationary wave that originated from upstream regions (e.g., Sung et al. 2018; Li et al. 2019). As shown in Fig. 11a, two wave trains pointed to the Eurasian cooling region. One is the western branch from Europe, and the other is the southeastern branch from the eastern coast of the Eurasian continent. Given the background of climatological eastward oriented stationary wave train (Fig. 11b), the upstream wave train means enhancement of the upstream influences the area from Europe to the Eurasian cooling region (Fig. 11a), while the downstream wave train means a reduction in the downstream influences from the Eurasian cooling region. Thus, the upstream wave train from Europe may contribute to the Eurasian cooling. However, the point is that the eddy streamfunction change over European regions connects with Arctic warming as demonstrated above. Such a wave view is a particular aspect of the PV view we proposed in Figs. 9 and 10 because anomalous wave depends on the existence of PV change (Hoskins et al. 1985; Plumb 1985, 1986).