Abstract

This study investigates the dynamical linkage between the meridional mass circulation and cold air outbreaks using the ERA-Interim data covering the period 1979–2011. It is found that the onset date of continental-scale cold air outbreaks coincides well with the peak time of stronger meridional mass circulation events, when the net mass transport across 60°N in the warm or cold air branch exceeds ~88 × 109 kg s−1. During weaker mass circulation events when the net mass transport across 60°N is below ~71.6 × 109 kg s−1, most areas of the midlatitudes are generally in mild conditions except the northern part of western Europe. Composite patterns of circulation anomalies during stronger mass circulation events greatly resemble that of the winter mean, with the two main routes of anomalous cold air outbreaks being along the climatological routes of polar cold air: namely, via East Asia and North America. The Siberian high shifts westward during stronger mass circulation events, opening up a third route of cold air outbreaks through eastern Europe, where lies the poleward warm air route in the winter-mean condition. The strengthening of the Icelandic low and Azores high during stronger mass circulation events acts to close off the climatological-mean cold air route via western Europe; this is responsible for the comparatively normal temperature there. The composite pattern for weaker mass circulation events is generally reversed, where the weakening of the Icelandic low and Azores high, corresponding to the negative phase of the North Atlantic Oscillation (NAO), leads to the reopening and strengthening of the equatorward cold air route through western Europe, which is responsible for the cold anomalies there.

1. Introduction

Various anomalous synoptic- and planetary-scale patterns have been identified as precursor signals for cold air outbreaks over different regions (e.g., Wexler 1951; Colucci and Davenport 1987; Walsh et al. 2001; Konrad 1996). For instance, cold air outbreaks over North America have been found to be closely related to positive sea level pressure anomalies along the Alaska–Yukon border (Walsh et al. 2001) or the coexistence of a ridge over the Arctic and a trough over the Great Lakes region (Konrad 1996). Elsewhere, in East Asia, the intensification and expansion of the Siberian high are known to be the triggering mechanism for cold air surges (Ding 1990; Zhang et al. 1997; Gong and Ho 2004; Takaya and Nakamura 2005). Palmer (2014) pointed out that intensifying Rossby waves within the jet stream, excited by the latent heat release over the warming tropical west Pacific may have contributed to the extremely cold 2013–14 winter in the United States.

There is also ample evidence indicating a robust relationship between continental-scale cold air outbreaks and the leading oscillation modes in the winter extratropics. It is well recognized that the negative phase of the North Atlantic Oscillation (NAO) coincides with cold anomalies over Europe and warming in the northwest Atlantic (Rogers and van Loon 1979; Hurrell and van Loon 1997). The studies by Walsh et al. (2001) and Cellitti et al. (2006) show that the NAO tends to be in its negative phase 3–6 days prior to cold air outbreaks over different regions of the United States and Europe. Luo et al. (2014) related the cold air outbreak event in January–February 2012 to a positive-to-negative phase transition of NAO. As a broader anomaly pattern than the NAO, the Arctic Oscillation (AO), or the tropospheric northern annular mode (NAM), also tends to be in its negative phase when there are more frequent strong cold air outbreaks in the midlatitudes of Eurasia and North America (Thompson and Wallace 1998, 2001; Wettstein and Mearns 2002; Cohen et al. 2010). Accompanying these leading modes is the oscillation of extratropical zonal mean zonal wind in the troposphere, which was termed the “index cycle” to link variations of the westerly jet to cold air outbreaks in the pioneering work of Namias (1950).

Several promising precursors to winter cold air outbreaks have also been found in the stratosphere. The works of Baldwin and Dunkerton (1999), Wallace (2000), and Thompson et al. (2002) indicate that cold air outbreaks tend to occur more frequently over the midlatitudes in the period of 1–2 months after a weak stratospheric polar vortex event. Cai (2003) found that cold surface temperature anomalies tend to take place underneath the intrusion zone of high isentropic potential vorticity (IPV) into the troposphere from the stratosphere. Kolstad et al. (2010) found that cold temperature anomalies over the southeastern United States tend to appear within 1–2 weeks after the peak dates of weak vortex events, whereas the cold anomalies over Eurasia seem to appear at the inception of weak vortex events. In addition, continental-scale cold temperature anomalies are correlated with the easterly phase of the equatorial stratospheric quasi-biannual oscillation (e.g., Thompson et al. 2002; Cai 2003).

The pioneering work of Johnson (1989) and many subsequent studies [e.g., Cai and Shin (2014) and references therein] established a hemisphere-wide single-cell model for meridional mass circulation. The mass circulation is a thermally direct circulation that connects the tropical heating source to the polar heating sink via a poleward warm air branch in the upper troposphere (and also the stratosphere in the winter hemisphere) and an equatorward cold branch in the lower troposphere.1 Cold air outbreaks can be directly related to an anomalous strong meridional mass circulation, with more cold air discharged from the northern polar region into the lower latitudes within the cold air branch. The strengthening of the cold air branch is connected with the strengthening of the warm air branch in the upper atmosphere and is driven by the amplification of large-scale waves in the midlatitudes. Therefore, the meridional mass circulation perspective not only allows us to capture the preferred routes of cold air outbreaks directly but also can help us to investigate the precursory changes in various circulation fields for cold air outbreaks.

Iwasaki and Mochizuki (2012) and Iwasaki et al. (2014) identified two major routes of cold air from the northern polar region to lower latitudes: namely, the “East Asian stream” and the “North American stream.” Shoji et al. (2014) conducted a comprehensive isentropic diagnosis of East Asian cold air outbreaks within the cold air branch of the meridional mass circulation. Yu et al. (2015) constructed a mass circulation index (denoted as WB60N) to measure the intensity of the warm air branch of the meridional mass circulation and showed that changes of the index can be a precursor for the cold air outbreaks in midlatitudes. They also showed that there exist two dominant geographical patterns of temperature anomalies during the cold air discharge period (or 1–10 days after a stronger mass circulation across 60°N). One represents cold anomalies mainly in the midlatitudes of both North America and Eurasia, and the other represents cold anomalies mainly over only one of the two continents accompanied with abnormal warmth over the other continent. Yu et al. (2015) mainly focus on statistical evidence of the robust relation between the strengthening of meridional mass circulation across 60°N and cold air outbreaks in the midlatitudes but do not examine the spatiotemporal patterns of anomalous meridional mass circulation and their linkages to the anomalous changes in synoptic circulation systems that are directly connected with cold air outbreaks. The primary objective of this study is to examine the dominant spatiotemporal circulation patterns of the meridional mass circulation and indicate their roles in setting up the preferred routes for cold air outbreaks in the midlatitudes during anomalous mass circulation events.

This paper is organized as follows. Section 2 describes the dataset and indices used in this study and outlines the analysis procedures. In section 3, we examine the life cycle of anomalous WB60N events and the related temporal evolution of surface temperature anomalies. Section 4 presents the temporal and spatial patterns of various circulation anomalies associated with anomalous WB60N events, including the adiabatic and diabatic components of mass transport anomalies, the preferred routes of cold air outbreaks, the anomalies in surface synoptic systems, and tropospheric wave activities. Conclusions are provided in section 5.

2. Data and analysis procedures

The data fields used in this study include the temperature (Ts), pressure (Ps), and meridional wind (υs) at the surface, and the three-dimensional air temperature (T), geopotential height (z), and meridional wind (υ), which are derived from the daily ERA-Interim data for the 32 winters from 1 November 1979 to 28 February 2011 (ECMWF 2012; Simmons et al. 2006; Dee et al. 2011). The data fields are on 1.5° latitude × 1.5° longitude grids and on 37 pressure levels spanning from 1000 to 1 hPa. Three-dimensional and surface potential temperature ( and ) fields are obtained from the temperature fields at pressure levels. Total diabatic heating fields ( and ) are calculated from 6-hourly three-dimensional and surface temperature, wind, and vertical motion fields.

Other variables and indices used in this study are calculated from variables available in daily ERA-Interim data following the corresponding references listed in Table 1. Each of the 32 winters lasts for 120 days from 1 November of the current year to 28 February of the next year. The daily climatological-mean fields are obtained by averaging the data across the 32 years (1979–2011) for each calendar day from 1 November to 28 February. Daily anomalies are obtained by removing the daily climatology from the total fields. Next, the physical meaning of each of the calculated variables and indices is briefly introduced.

Table 1.

A list of the derived indices and variables.

A list of the derived indices and variables.
A list of the derived indices and variables.

We have used the same methods in Yu et al. (2015) [also see Pauluis et al. (2008) and Cai and Shin (2014)] to calculate variables associated with mass circulation (including air mass, mass tendency, and meridional and vertical mass fluxes in isentropic layers) from daily fields. We have preselected 13 potential temperature surfaces (n: 1–13): 260, 270, 280, 290, 300, 315, 330, 350, 370, 400, 450, 550, and 650 K. Vertical mass fluxes are defined at all that satisfy , where is the surface potential temperature varying with location and time (note that the mass flux across is always zero, since we only consider dry air mass in this study). All other variables are defined in the 12 layers between and surfaces plus two additional layers: one is the surface layer, which accounts for all mass between the ground and the minimum of that satisfies , and the other is the top layer, which accounts for all air mass above 650 K. We use the bottom surface of each layer (, for the surface layer) in referencing the variables defined in these isentropic layers.

We denote a zonally integrated field using angle brackets. For example, the zonally integrated meridional mass flux (MF) is denoted as 〈MF〉 which is a function of , , and t. Positive values of 〈MF〉 correspond to poleward mass transport on day t across the latitude within the two adjacent isentropic surfaces ( and ), and negative values of 〈MF〉 correspond to equatorward transport. On average, negative values of 〈MF〉 mainly appear in the lower troposphere within the equatorward cold air branch of the meridional mass circulation, while positive values mainly appear in upper layers within the poleward warm air branch (see Fig. 1a in Cai and Shin 2014). For the zonally integrated vertical mass fluxes (VF), denoted as 〈VF〉, positive values correspond to upward mass fluxes across the isentropic surface because of diabatic heating, and negative values correspond to downward mass fluxes because of diabatic cooling. Positive values of 〈VF〉 are observed mainly in the tropics and the surface layer in the extratropics; whereas negative values are found outside of the tropics above the surface layer (see Fig. 1b in Cai and Shin 2014). Combining the vertical and meridional mass flux fields, we obtain the isentropic meridional mass circulation as a function of latitude and isentropic surface level at each day. The net mass change due to convergence of meridional and vertical mass fluxes is measured by the daily tendency of the total mass between two adjacent isentropic surfaces ( and ) within each latitude band .

Following Iwasaki et al. (2014), we adopt the cold mass intensity (CMI), which was termed as negative heat content in Iwasaki et al. (2014), to measure the degree of coldness of the air mass within the cold air branch. To obtain the total cold mass intensity within the cold branch, we first calculate the product of the air mass in each isentropic layer in this grid box and the departure of its potential temperature from 280 K and then sum them up from the surface layer to the layer of 280 K, which roughly corresponds to the layer that separates the warm and cold branches of the mass circulation in the extratropics (Iwasaki et al. 2014; Cai and Shin 2014). The absolute value of the sum is defined as the CMI as a function of time. In general, the larger the CMI is, the colder the air is in the cold air branch.

The level that separates the warm and cold branches at latitude and at each day t is identified by searching for the isentropic level such that the vertical sum of 〈MF〉 for all n < or reaches its maximum negative value. Generally, decreases with latitude, which reflects the latitudinal variation of stratification in the troposphere. The value of mainly lies between 270 and 290 K. Following Yu et al. (2015), the WB60N index is constructed to measure the intensity of the poleward warm air branch crossing 60°N at a given time according to

 
formula

The overbar with the superscript denotes a 7-day running mean centered at time t. The curly braces the time average over the 32 winters from 1979 to 2011 for each calendar day between 1 November and 28 February, which produces a 120-day time series of winter-season daily climatology of total mass transport crossing 60°N into the polar region in the poleward warm air branch. The quantity SDW = 16.4 × 109 kg s−1, represents the standard deviations of the time series of . Based on the analysis of the WB60N index in Yu et al. (2015), variations of the anomalous mass transport into the polar region by the warm air branch, as well as that out of the polar region by the cold air branch, can be represented by this index because of the synchronization of the two branches in terms of their timing and intensity.

The mass circulation index is defined at 60°N because the cold polar air mainly resides north of 60°N inside the polar region (Iwasaki et al. 2014). We have also tested the choices of latitudes from 50° to 70°N and always found a similar seesaw pattern between mid- and high latitudes in the regressed surface temperature anomalies against the mass circulation index. However, the choice of 60°N yields the largest amplitude of temperature anomalies in such a seesaw pattern.

Note that the net meridional mass transport in a given layer crossing a given latitudinal circle in the extratropics is always a residual between the equatorward mass transport of cold air behind the trough and the poleward mass transport of warm air in front of the trough, because the extratropical portion of the meridional circulation is driven by large-scale westward-tilted baroclinic waves (Johnson 1989). To investigate the preferred pathways of the equatorward and poleward airmass transport within the cold branch, we also calculate the 7-day running-mean meridional mass transport at longitude λ and across latitude ϕ, denoted as MFCB, according to

 
formula

By definition, the zonal summation of is equal to the net equatorward mass transport crossing latitude ϕ within the cold branch. The anomaly fields of MFCB can be obtained by removing its climatological annual cycle. Positive anomalies of MFCB represent either a reduction in the equatorward cold airmass transport or an increase in the poleward warm airmass transport crossing a specific latitude ϕ through a 1.5° longitude sector centered at λ in the lower troposphere. The opposite is true for negative anomalies of MFCB.

As in Yu et al. (2015), warm and cold temperature area indices are defined to measure the spatial extent or the percentage of area occupied by warm or cold anomalies that exceed the 0.5 local standard deviation. The cold area index for midlatitude (25°–60°N) is denoted as CM, and that for high latitude is denoted as CH. The corresponding warm area indices are WH and WM, respectively.

3. Composite anomalous WB60N events and the associated surface air temperature anomalies

There are a total of 157 episodes of strong mass circulation in the 32 winter seasons that have peak values of WB60N exceeding 0.5 or a poleward mass transport into the upper polar region exceeding half a standard deviation above its climatological value for more than three days. For ease of reference, we refer to these as WB60N+ events. There are a total of 161 episodes of weak mass circulation that have minimum values of WB60N below 0.5 or a poleward mass transport into the upper polar region below the climatological value by half a standard deviation, and these are referred to as WB60N events. The black curves in Fig. 1 depict the temporal evolutions of these individual WB60N+ and WB60N events, and the red curves are the averages of these WB60N+ (Fig. 1a) and WB60N (Fig. 1b) events, referred to as the composite WB60N+ and WB60N events, respectively. It is found that the duration of both WB60N+ and WB60N events has a relatively wide range, from 3 days up to 2–3 weeks. On average, it takes about 5 days for a WB60N+ event to reach its peak value from the climatological-mean circulation intensity (i.e., the value of 0) and another 5 days to return to 0 from the peak intensity. The same can be said for a WB60N event. Therefore, the average time scale of both WB60N+ and WB60N events is about 10 days. The mean peak intensity of WB60N+ events is close to 1.5 standard deviations (one standard deviation corresponds to poleward mass transport into the polar atmosphere in the warm air branch at a rate of 16.4 × 109 kg s−1) above the climatology (about 79.8 × 109 kg s−1), and the mean peak intensity of WB60N events is also close to 1.5 standard deviations below the climatology. It should be noted that, though the composite temporal evolutions of WB60N+ and WB60N events are very similar to each other, individual events exhibit some noticeable asymmetries between WB60N+ and WB60N events. Specifically, the time span of the circulation strengthening period before the peak times of WB60N+ events seems to be shorter than the weakening period after, while the time span of the circulation weakening period before the peak times of WB60N events is also relatively longer; the duration of WB60N+ is generally shorter than WB60N; and the peak intensity of WB60N+ events tends to be stronger than that of WB60N events.

Fig. 1.

Temporal evolutions of (a) 157 WB60N+ and (b) 161 WB60N events centered at their peak times (black curves). Note that these black curves only cover the temporal spans during which the WB60N index is continuously above zero (for WB60N+) or below zero (for WB60N). The red curves correspond to their composite means. The ordinate represents the value of the WB60N index, and the abscissa is the lag days from the time of peak amplitude.

Fig. 1.

Temporal evolutions of (a) 157 WB60N+ and (b) 161 WB60N events centered at their peak times (black curves). Note that these black curves only cover the temporal spans during which the WB60N index is continuously above zero (for WB60N+) or below zero (for WB60N). The red curves correspond to their composite means. The ordinate represents the value of the WB60N index, and the abscissa is the lag days from the time of peak amplitude.

In the remainder of the paper, we report composite temporal evolutions of temperature area indices and circulation anomalies according to the timeline in the range from −7 days to 7 days relative to the positive and negative peak dates of individual WB60N+ (157) and WB60N (161) events. The choice of [−7, 7] days is made because it is slightly longer than the average time scale of individual anomalous WB60N events. The period from −7 to 7 days relative to the peak times of anomalous WB60N events can cover the temporal span of the majority of individual anomalous WB60N events (black curves in Fig. 1). Below, we will plot these composite fields sequentially from [−7, 7] days relative to the peak dates of WB60N+ events to [−7, 7] days relative to the peak dates of WB60N events. But it should be noted that (i) the duration of individual WB60N+ or WB60N events varies as indicated in Fig. 1; (ii) displaying the composite WB60N+ events sequentially together with the composite WB60N events does not necessarily mean that the actual evolution from the WB60N+ to the WB60N takes place in around 30 days; and (iii) the composite evolution may include some overlapping between the WB60N+ and the WB60N events when the actual transition between them is very abrupt and their duration is shorter than 15 days.

Displayed in Figs. 2a and 2b are the temporal evolutions of composite-mean daily tendencies of the temperature area indices CH (solid blue), CM (dashed blue), WH (solid red), and WM (dashed red) in the period from −7 to 7 days, relative to the peak dates of WB60N+ (Fig. 2a) and WB60N (Fig. 2b) events. The tendencies of WH and CM evolve highly in phase with WB60N, exhibiting their positive maximums at the peak dates of WB60N+ and their negative maximums at the peak dates of WB60N, while the tendencies of CH and WM are generally out-of-phase with WB60N. The positive peak of the tendency of CM and the negative peak of the tendency of WM correspond to the timing of the onset of cold air outbreaks in the midlatitudes, which themselves coincide with the peak dates of WB60N+ events. By the same token, the negative peak of the tendency of CM and the positive peak of the tendency of WM correspond to the timing of the demise of the cold period in the midlatitudes, coinciding with the peak dates of WB60N events. Physically speaking, stronger meridional mass circulation is associated with more cold airmass transport from the polar region to the midlatitudes, which is responsible for an increase in the area occupied by cold surface air temperature anomalies in the midlatitudes and a decrease in the area occupied by warm surface air temperature anomalies. The reverse is true when the meridional circulation is weaker. The continuous cooling tendency during the strengthening of the meridional mass circulation results in the maximum of CM and minimum of WM at ~5 days after the WB60N+ peak dates, and vice versa after the WB60N peak dates (Figs. 2c,d). The dates with maximums of the percentage area indices for CM and WH and minimums of CH and WM are referred to as the mature dates of cold air outbreaks. The mature dates of the percentage area indices for the midlatitudes (CM and WM) appear to be 1–2 days earlier than those (CH and WH) for the high latitudes.

Fig. 2.

Composites of temporal tendencies of temperature area indices (% day−1) during (a) WB60N+ events and (b) WB60N events, and temperature indices (%) during (c) WB60N+ events and (d) WB60N events in the period from −7 to +7 days from the peak dates of anomalous WB60N events. Solid (dashed) blue curves are for CH (CM); and solid (dashed) red curves are for WH (WM). Dots denote composites that are statistically significant above the 95% confidence level.

Fig. 2.

Composites of temporal tendencies of temperature area indices (% day−1) during (a) WB60N+ events and (b) WB60N events, and temperature indices (%) during (c) WB60N+ events and (d) WB60N events in the period from −7 to +7 days from the peak dates of anomalous WB60N events. Solid (dashed) blue curves are for CH (CM); and solid (dashed) red curves are for WH (WM). Dots denote composites that are statistically significant above the 95% confidence level.

Shown in Figs. 3a–f are composite maps of surface air temperature anomalies in different phases of WB60N+ events (maps along the right half of the circle around Fig. 3g, which shows the stationary wave component of the climatological-winter-mean surface air temperature field) and WB60N events (maps along the left half). These composite maps compliment the results shown in Fig. 2 with information on both the temporal evolution and the geographical pattern of surface air temperature anomalies. The quadrature relation of surface air temperature anomalies with the WB60N index revealed in Fig. 2 can be seen vividly in the temporal evolution of the geographical pattern of surface air temperature anomalies during different phases of anomalous WB60N events. The reversal of the opposite sign of surface air temperature anomalies between the polar region and the midlatitudes takes place around the peak dates of WB60N+ events (Fig. 3a vs Fig. 3c) and WB60N events (Fig. 3d vs Fig. 3f). Prior to the peak dates of WB60N+ events, warm anomalies are still prevalent over the midlatitudes of Eurasia and North America, while cold anomalies are present over the polar region. At the peak time of WB60N+, when the equatorward mass transport across the polar circle is strongest, cold surface temperature anomalies begin to move southward, while warm anomalies begin to appear over the Nordic seas and Bering Sea (Fig. 3b). During the week after the peak dates of WB60N+ events, cold surface temperature anomalies intensify and gradually spread over the entire midlatitudes, with the coldest centers over the two continents. Meanwhile, warm temperature anomalies also intensify and spread over the polar region, although the warmest centers are still over the Nordic seas and Bering Sea. Conversely, during the week before the peak dates of WB60N events, warm temperature anomalies over the Nordic seas and Bering Sea, as well as cold temperature anomalies over the two continents, begin to gradually diminish. On the peak dates of WB60N events, the midlatitudes of East Asia and the northwest Pacific Ocean are occupied by warm temperature anomalies, while part of the polar region north of Eurasia becomes anomalously cold (Fig. 3e). During the week after the peak dates of WB60N events, the entire midlatitudes are dominated by warm temperature anomalies, with the warm centers over the two continents, whereas cold surface temperature anomalies return to the polar region. The week after the peak dates of WB60N events can be referred to as the “cold air charge period,” and the week after the peak dates of WB60N+ events corresponds to the “cold air discharge period,” as in Yu et al. (2015).

Fig. 3.

Composite surface air temperature anomalies (K) in various phases of anomalous WB60N events in the domain of 25°–90°N clockwise from top right: (a) −7 to −2, (b) −1 to 1, and (c) 2 to 7 days from the peak dates of WB60N+ events; and (d)–(f) as in (a)–(c), but for WB60N events. Slashed areas denote the composites are statistically significant above the 95% confidence level. (g) The stationary wave component of the 32-yr-, November–February (NDJF)-mean surface air temperature field. The contours for (a)–(f) are shown in the color bar in the bottom left, and those for (g) are in the bottom right.

Fig. 3.

Composite surface air temperature anomalies (K) in various phases of anomalous WB60N events in the domain of 25°–90°N clockwise from top right: (a) −7 to −2, (b) −1 to 1, and (c) 2 to 7 days from the peak dates of WB60N+ events; and (d)–(f) as in (a)–(c), but for WB60N events. Slashed areas denote the composites are statistically significant above the 95% confidence level. (g) The stationary wave component of the 32-yr-, November–February (NDJF)-mean surface air temperature field. The contours for (a)–(f) are shown in the color bar in the bottom left, and those for (g) are in the bottom right.

4. Circulation anomalies associated with anomalous WB60N events

In this section, the temporal evolutions of the spatial patterns of circulation anomalies in various fields associated with anomalous WB60N events are examined. The identification of the spatial patterns of circulation anomalies that evolve with the anomalous WB60N events helps to provide a more physics-based explanation as to why the onset dates of cold air outbreaks in the midlatitudes coincides with the peak dates of WB60N+ events, and the mature phase of cold air outbreaks tends to appear a week after the peak dates of WB60N+ events.

a. Meridional mass circulation anomalies

Figure 4 shows the composite anomalies of the zonally integrated mass fluxes (vectors), the mass tendency (contours), and the zonally integrated mass itself (shading) during the WB60N+ and WB60N events. Note that the total meridional mass fluxes always tend to be poleward (positive values in the Northern Hemisphere) in the upper atmosphere within the warm air branch and equatorward (negative values in the Northern Hemisphere) near the surface within the cold air branch. Therefore, positive–negative meridional mass flux anomalies in upper levels imply stronger–weaker poleward mass transport, whereas, in lower levels, negative–positive mass flux anomalies are indicative of stronger–weaker equatorward mass transport.

Fig. 4.

Composite anomalies of zonally integrated mass fluxes (vectors), mass (shading), and mass tendency (contours) in different phases of anomalous WB60N events as a function of latitude (abscissa) and isentropic level (ordinate): (a)–(e) WB60N+ events and (f)–(j) WB60N events. The length of the reference vector corresponds to 10 × 109 kg s−1; the contours for the shading are in 1014 kg; and the mass tendency contour interval is 0.2 (109 kg s−1), with solid contours for positive values and dashed contours for negative values. Composites not exceeding the 95% confidence level in terms of statistical significance are omitted for the mass and mass flux anomalies, and displayed as thin contours for the mass tendency anomalies.

Fig. 4.

Composite anomalies of zonally integrated mass fluxes (vectors), mass (shading), and mass tendency (contours) in different phases of anomalous WB60N events as a function of latitude (abscissa) and isentropic level (ordinate): (a)–(e) WB60N+ events and (f)–(j) WB60N events. The length of the reference vector corresponds to 10 × 109 kg s−1; the contours for the shading are in 1014 kg; and the mass tendency contour interval is 0.2 (109 kg s−1), with solid contours for positive values and dashed contours for negative values. Composites not exceeding the 95% confidence level in terms of statistical significance are omitted for the mass and mass flux anomalies, and displayed as thin contours for the mass tendency anomalies.

It is apparent that both the warm and cold branches of the meridional mass circulation begin to intensify a few days before the peak time of WB60N+ events, as indicated by the gradual decrease in negative meridional mass flux anomalies in upper levels and positive mass flux anomalies in lower levels in the extratropics (Figs. 4a,b). During this period, the mass tendency anomalies above 280 K change from negative to positive in the high latitudes and from positive to negative in the midlatitudes, but the opposite is found below 280 K. This is a result of the simultaneous strengthening of the poleward mass transport in the warm air branch and equatorward mass transport in the cold air branch. Since changes of mass anomalies must take place after changes in mass transport that cause mass tendency in the first place, mass anomalies north of 65°N are still negative above 280 K and positive below 280 K, and those south of 65°N are still positive above 280 K and negative below during the period of 2–7 days before the peak dates of WB60N+ events. The strengthening of the meridional mass circulation leads to a reversal of the pattern of the opposite signs of mass anomalies in the meridional and vertical directions shown on the peak dates (Fig. 4c). On the peak dates of WB60N+ events, the poleward mass flux anomalies in the upper layer are the strongest, extending to the North Pole, while the equatorward flux anomalies in the lower layer are also the strongest, extending southward up to 30°N. The strongest meridional mass circulation on the peak dates causes the largest positive (negative) mass anomalies above 280 K, and the largest negative (positive) anomalies below, in the high latitudes (midlatitudes) within a few days after the peak dates of WB60N+ events (Fig. 4d). This indicates that the strengthened meridional mass circulation has transported more warm air from the midlatitudes to the polar region in the upper layer (above 280 K) and more cold air from the polar region to the midlatitudes below. After the peak dates, anomalies of both the meridional mass flux and the mass tendency begin to weaken (Fig. 4d) and their signs become reversed at 5–7 days after the peak dates of WB60N+ events (Fig. 4e). The mass anomaly pattern, however, remains unchanged throughout the week after the peak dates because of the temporal delay of the mass field with respect to the mass transport. Moreover, the meridional extent and the intensity of the mass anomalies reach their maximums about 4–5 days after the peak dates.

Opposite patterns of meridional mass circulation, mass tendency, and mass anomalies are found during the negative half of anomalous WB60N events (Figs. 4f–j). Comparing Figs. 4a–e with Figs. 3a–e and Figs. 4f–j with Figs. 3f–j, it is evident that mass anomalies induced by equatorward mass transport anomalies in the lower-tropospheric layers are closely linked to surface temperature anomalies in the extratropics, in terms of both timing and intensity.

It should be noted that, following the strengthening or the weakening of the meridional mass transport in the extratropics, the vertical mass flux anomalies can also contribute to mass tendency and mass anomalies. During WB60N+ events, the strengthened meridional mass transport is followed by anomalous upward mass transport south of 60°N and anomalous downward mass transport in the north within the week after the peak time of WB60N+ events (see the vertical component of mass flux anomalies in Figs. 4c–e). This indicates that more meridional mass transport of the warm air into the upper polar region is accompanied by stronger radiative cooling there, while more transport of the cold polar air mass into the lower midlatitudes is associated with stronger diabatic heating from the ground. The opposite pattern of diabatic mass flux anomalies is found in the WB60N events. Although these anomalous cross-isentropic mass transports tend to cancel out part of the mass and its tendency anomalies induced by the anomalous meridional mass transport, the polarity of the mass and its tendency anomalies is still determined by the polarity of the anomalous meridional mass transport.

b. Anomalies of the CMI

To confirm the close relation between the mass anomalies in lower isentropic layers and surface temperature anomalies, we next examine (Fig. 5) the temporal evolution of the meridional profiles of anomalies of the vertically integrated mass in layers below 280 K and CMI (shading) and their daily tendencies (contours) in the period from −7 to 7 days, relative to the peak dates of WB60N+ and WB60N events. It can be seen that the temporal evolution and the latitudinal profile of the mass and mass tendency anomalies (Figs. 5a,b) are highly similar to their counterparts of the CMI and CMI tendency anomalies (Figs. 5c,d). The meridional dipole pattern of the cold airmass depletion tendency in the high latitudes and the cold airmass accumulation tendency in the midlatitudes reaches its peak amplitude as a WB60N+ event approaches the peak time, as does the meridional dipole pattern of the negative CMI tendency in the high latitudes and the positive CMI tendency in the midlatitudes. This clearly indicates that the increase of air mass in lower isentropic layers indeed corresponds to the increase of CMI, and vice versa. After the peak of WB60N+ events, positive anomalies of both cold air mass and CMI appear in the midlatitudes, and negative anomalies of cold air mass and CMI appear over the polar region, implying anomalously cold conditions in the midlatitudes and warm conditions in the high latitudes. The opposite situation can be seen in Figs. 5c and 5d for WB60N events: the weakening of the meridional circulation leads to a negative cold airmass and CMI anomalies in the midlatitudes, as well as a positive cold airmass and CMI anomalies in the high latitudes.

Fig. 5.

Composite anomalies of the zonally integrated mass under 280 K (shading; 1014 kg) and its tendency (contour interval: 0.5 × 109 K kg s−1) as a function of latitude (abscissa) and number of days from the peak time (ordinate) of (a) WB60N+ events and (b) WB60N events. (c),(d) As in (a),(b), but for the anomalies of the CMI (shading; 1014 K kg) and its tendency (contour interval: 10 × 109 K kg s−1). Composites not exceeding the 95% confidence level in terms of statistical significance are omitted for the anomalies represented by shading, and are plotted in thin contours for those indicated by contours.

Fig. 5.

Composite anomalies of the zonally integrated mass under 280 K (shading; 1014 kg) and its tendency (contour interval: 0.5 × 109 K kg s−1) as a function of latitude (abscissa) and number of days from the peak time (ordinate) of (a) WB60N+ events and (b) WB60N events. (c),(d) As in (a),(b), but for the anomalies of the CMI (shading; 1014 K kg) and its tendency (contour interval: 10 × 109 K kg s−1). Composites not exceeding the 95% confidence level in terms of statistical significance are omitted for the anomalies represented by shading, and are plotted in thin contours for those indicated by contours.

c. Anomalies in surface pressure systems and routes of the meridional mass transport near the surface

Figure 6 shows the meridional mass transport within the cold air across 60°N [i.e., , defined in Eq. (2)]. It is seen that, under winter-mean conditions (; Fig. 6a), the two main routes for the Arctic cold surface air to enter the midlatitudes are via East Asia and eastern North America, and the two main routes for warm surface air to enter the Arctic lie over the two oceans. A secondary route for the Arctic cold air lies in western Europe, which is paired with a secondary route over central Eurasia for the poleward transport of warm air. Because the equatorward mass transport is stronger than the poleward transport, the zonally integrated net mass transport within the cold air branch is always equatorward. Next, let us examine the composite anomalies of MFCB in various phases of the WB60N+ (Fig. 6b) and WB60N (Fig. 6c) events. It is seen that the simultaneous strengthening of the equatorward mass transport over East Asia and North America, and the poleward transport over the Pacific and Atlantic Oceans, takes place in the period from a few days before the peak time of WB60N+ events to several days after. The mass transport via the secondary winter-mean routes seems to be greatly weakened or even reversed during the week after the peak time of WB60N+ events. Specifically, the anomalous equatorward mass transport of Arctic cold air is via central Eurasia, and the anomalous poleward mass transport is via western Europe during the week after the peak time of WB60N+ events. The reverse pattern is found within the week after the peak time of WB60N events: i.e., the simultaneous weakening of the equatorward mass transport over East Asia and eastern North America and the poleward transport over the Pacific and Atlantic Oceans, as well as the strengthening or resumption of the secondary routes of Arctic cold air via western Europe and warm air via central Eurasia.

Fig. 6.

The longitudinal profile of the total meridional mass transport within the cold air branch at 60°N (109 kg s−1): (a) climatological winter (NDJF) mean and (b),(c) composite anomalies in the period from −7 to +7 days (ordinate) from the peak time of WB60N+ and WB60N events, respectively. Slashed areas denote the composites that are statistically significant above the 95% confidence level.

Fig. 6.

The longitudinal profile of the total meridional mass transport within the cold air branch at 60°N (109 kg s−1): (a) climatological winter (NDJF) mean and (b),(c) composite anomalies in the period from −7 to +7 days (ordinate) from the peak time of WB60N+ and WB60N events, respectively. Slashed areas denote the composites that are statistically significant above the 95% confidence level.

Next, we use the winter climatological-mean maps of the stationary wave fields of geopotential height at 1000 hPa (Fig. 7g) and meridional mass fluxes within the cold air branch (Fig. 8g) to reference the winter permanent surface pressure systems and climatological mean routes of winter cold outbreaks. The extratropical portion of the meridional mass circulation is driven by westward-tilted baroclinic Rossby waves (e.g., Johnson 1989). Accordingly, it is expected based on the geostrophic balance that, in the Northern Hemisphere, the equatorward portion of the winter climatological mean MFCB field will lie on the east side of the winter-mean surface high pressure centers or on the west side of the winter-mean surface low pressure centers, and vice versa for the poleward portion of the winter-mean MFCB field (Fig. 7g vs Fig. 8g). As in Fig. 6a, which is evaluated only at 60°N, Fig. 8g confirms that, on average, the polar cold air prefers to advance equatorward via the entire extratropical latitude span of East Asia and North America, with a secondary route via western Europe. Meanwhile, the poleward mass transport from the midlatitudes to the polar region favors the two main routes via the eastern half of the Pacific Ocean, the Atlantic Ocean, and a secondary route via central Eurasia. The main routes are well coupled with the four permanent surface systems—namely, the Siberian high, the North American high, the Aleutian low, and the Icelandic low—whereas the pair of the secondary routes is associated with the Siberian high and the Azores high.

Fig. 7.

As in Fig. 3, but for the wave fields of geopotential height at 1000 hPa (m).

Fig. 7.

As in Fig. 3, but for the wave fields of geopotential height at 1000 hPa (m).

Fig. 8.

As in Fig. 3, but for (a)–(f) the anomalies of the total meridional mass transport within the cold air branch (109 kg s−1) and (g) the corresponding winter climatological mean.

Fig. 8.

As in Fig. 3, but for (a)–(f) the anomalies of the total meridional mass transport within the cold air branch (109 kg s−1) and (g) the corresponding winter climatological mean.

Next, we discuss the composite wave fields of geopotential height anomalies at 1000 hPa () and the anomalies of meridional mass fluxes within the cold air branch () obtained by averaging from one week before to one week after the peak dates of all WB60N+ events (Figs. 7a–c and 8a–c) and WB60N events (Figs. 7d–f and 8d–f). The overall in-phase relationship between shown in Figs. 8b–c and in Fig. 8g is indicative of the strengthening of the winter-mean surface pressure system on the peak dates of WB60N+ events and during the week after. Specifically, positive anomalies of are found over Eurasia with maximums over northwestern portions of central Eurasia, which superpose the northwestern part of the winter-mean Siberian high. It follows that the Siberian high, which has been recognized as the key weather system initiating cold air surges over East Asia (e.g., Ding 1990; Zhang et al. 1997), is anomalously strong during peak dates of WB60N+ events. As reported in Walsh et al. (2001), positive sea level pressure anomalies over the Alaska–Yukon border are closely linked to cold air outbreaks in North America. Again, we see positive anomalies of over the Alaska–Yukon border around the peak time of WB60N+ events, though the amplitude is weaker than that over the Siberian high region. Meanwhile, the Aleutian low and the Icelandic low are anomalously deepened, as manifested by the negative there. Therefore, the strengthening of the permanent surface pressure systems in winter, which determine the climatological-mean routes of winter cold outbreaks, acts to bring more polar cold air equatorward on the east (high) side of high (low) pressure centers via the two main continental routes into the midlatitudes and to carry more warm air poleward on the west (east) side of high (low) pressure centers via oceanic routes into the polar region.

Besides the strengthening of the winter surface pressure systems, the center of the winter high pressure system over Eurasia appears to shift westward during WB60N+ events. According to the composite-mean shown in Figs. 8b and 8c and the longitudinal profile of at 60°N shown in Fig. 6b, such a shift weakens the secondary winter-mean poleward route for warm air via central Eurasia, and even opens a new route for cold polar air to enter central Eurasia (Figs. 8b,c vs Fig. 8g and Fig. 6b vs Fig. 6a). This accounts for the coldest composite-mean surface temperature anomalies over central Eurasia in the period within one week after the peak dates of WB60N+ events (Figs. 3b,c). Previous studies have also indicated that central Eurasia is a critical region for trigging cold air surges over East Asia through eastward-propagating wave trains (Wu and Chan 1995; Ryoo et al. 2005; Hayasaki et al. 2006; Iwasaki and Mochizuki 2012; Iwasaki et al. 2014). The strengthening of the Icelandic low and Azores high, which begins during the week before the peak time of WB60N+ events and is indicative of the positive phase of the NAO, acts to weaken or possibly close off the climatological cold air route through western Europe, which is responsible for normal temperatures there during this period. The evidence provided above helps to explain physically why cold anomalies mainly appear over the midlatitude regions of Eurasian and North American continents, while warm anomalies in the polar region exhibit maximums over the northern sides of the Pacific and Atlantic oceans when the meridional mass circulation is anomalously strong, as conjectured in Yu et al. (2015).

According to Figs. 6b and 8a–c, the timing of the peak intensity of the anomalous equatorward mass fluxes through the three cold air routes and that of the anomalous poleward mass fluxes within the two warm routes are not exactly synchronized with one another. The equatorward over North America and that over East Asia reach their peak intensities during the peak dates of WB60N+ events and then weaken significantly afterward. The equatorward via the route of central Eurasia reaches its peak intensity a few days later, after the peak dates of WB60N+ events. The intensity of the poleward through two oceans also peaks a few days after the peak dates. Such a delay of the equatorward through central Eurasia, with respect to those through the other two main routes, explains why the strengthening of the cold anomalies over central Eurasia slightly lags that over East Asia and North America. In addition, the poleward via the Atlantic and Pacific Oceans slightly lags the equatorward via the two continents. This explains why the polar region continues to get warmer after the peak intensity of cold anomalies in the midlatitudes (see Figs. 2, 3).

During WB60N events, the four winter permanent surface pressure centers are weakened substantially, as indicated by the overall out-of-phase relationship between and (Figs. 7e,f vs Fig. 7g). The weakened surface pressure systems correspond to a weakened equatorward mass transport on the east side of the high pressure centers and the west side of the low pressure centers, responsible for anomalous warm conditions over the eastern parts of Asia and the United States during WB60N events, as shown in Figs. 8e and 8f and Fig. 6c. As the opposite case of WB60N+, the northwestern portion of the winter high pressure system over central Europe weakens substantially (Figs. 7e,f vs Fig. 7g). This causes the anomalous route for cold polar air to enter central Eurasia during WB60N+ events to become the route for warm air to enter the polar region as the climatological mean condition (Figs. 8e,f vs Fig. 8g and Fig. 6c vs Fig. 6a), which is responsible for the maximum warmth in eastern Europe during the week after the peak dates of WB60N events (Figs. 3e,f). The weakening of the Icelandic low and Azores high, corresponding to the negative phase of the NAO, begins as early as the end of WB60N+ events, or a week before the peak time of WB60N events. This helps to strengthen or reopen the secondary winter-mean cold air route via western Europe and its companion secondary climatological-mean poleward route for warm air via central Eurasia, as shown in Figs. 6a and 8g. This explains why temperature anomalies over western Europe are farther below normal during the week before the peak dates of WB60N events, while cold temperature anomalies over the rest of the two major continents gradually diminish. The weakening of the Icelandic low and Azores high is strongest around the peak dates of WB60N events and continues during the week after. However, the centers of the weakening gradually shift westward, away from western Europe (Figs. 7e,f vs Fig. 7d), which prevents the latitudinal span of the cold air route from farther extending to the southern latitudes of western Europe. As a result, only northern Europe still suffers from below-normal temperatures in this period (Figs. 3e,f). The corresponding patterns of (Figs. 7d–f) presents a westward shift of the center of the negative NAO mode, resembling the typical patterns identified in Walsh et al. (2001) for cold air outbreaks over western and northern Europe.

d. Anomalies in planetary wave activities

In this section, the temporal evolution of wave activities during the anomalous WB60N events is examined. Following Zhang et al. (2013) and Yu et al. (2014), we define a wave amplitude index (WAI) as a function of latitude, pressure level, and time to represent the meridional and vertical structure of wave amplitude at each time. At a given latitude, the WAI index is the standard deviation of the departure of (total) geopotential height from its zonal-mean value over the entire longitudinal span of the latitude. Shown in Fig. 9 are the temporal evolutions of the height–latitude structure of the WAI anomalies during the WB60N+ (Figs. 9a–e) and WB60N (Figs. 9f–j) events. The WAI anomalies in Fig. 9 have been normalized by their temporal standard deviation at each isobaric level. Thus, positive WAI anomalies represent higher zonal asymmetry of the geopotential height field or larger wave amplitude, and vice versa. Positive WAI anomalies in the extratropics first appear near the surface and in the low latitudes and then reach their maximum a few days after the peak time of WB60N+ with a poleward- and upward-propagation signal (Fig. 9c). This is well coupled with the strongest cold mass branch circulation in the troposphere in this period (Figs. 4c and 8b). Also, positive WAI anomalies gradually emerge in the stratosphere from the peak time to one week after. Note that the slightly lagged relation between the WAI anomalies in the troposphere and the WB60N index is probably as a result of the dependence of the net meridional mass transport not only on the amplitude, but also the westward-tilting angle of the waves. Further investigation is needed to prove this conjecture. The temporal evolution of WAI anomalies during WB60N events is similar, but with opposite sign. This confirms that it is the day-to-day variation of wave activities that drives the day-to-day intensity variation of the meridional mass circulation in the extratropics.

Fig. 9.

Composites of the normalized WAI anomaly in various phases of anomalous WB60N+ events as a function of latitude (abscissa) and isobaric surface level (ordinate): (a)–(e) WB60N+ events; (f)–(j) WB60N events. The normalization factor for the normalized WAI is the same for all latitudes at the same isobaric level, equaling the domain mean of the standard deviations of WAI at each isobaric level. Slashed areas denote composites that are statistically significant above the confidence level.

Fig. 9.

Composites of the normalized WAI anomaly in various phases of anomalous WB60N+ events as a function of latitude (abscissa) and isobaric surface level (ordinate): (a)–(e) WB60N+ events; (f)–(j) WB60N events. The normalization factor for the normalized WAI is the same for all latitudes at the same isobaric level, equaling the domain mean of the standard deviations of WAI at each isobaric level. Slashed areas denote composites that are statistically significant above the confidence level.

5. Conclusions

To identify the key physical and synoptic linkages between the intensity variability of the meridional mass circulation and surface cold air outbreaks in winter, we use daily ERA-Interim data (1979–2011) and investigate the spatiotemporal variations of various circulation anomalies associated with the meridional mass circulation intensity variability in winter (November–February). Following Yu et al. (2015), a daily mass circulation index, defined as the normalized zonally integrated poleward mass transport in upper isentropic layers across 60°N (denoted as WB60N), is used to represent the intensity of the meridional mass circulation as a function of time. The four temperature area indices developed in Yu et al. (2015) (CM, WM, CH, and WH) are used to measure the intensity and polarity of temperature anomalies in the midlatitudes (25°–60°N) and high latitudes (north of 60°N). It is found that the peak time of the positive tendency of CM and the negative tendency of WM coincide with the peak time of WB60N+ events, whereas the peak time of the negative tendency of CM and the positive tendency of WM coincide with the peak time of WB60N events. Moreover, maximum values of the CM index or minimum values of the WM index tend to occur in the period within one week after the peak dates of WB60N+ events, and vice versa within one week after the peak dates of WB60N events. Otherwise similar but opposite relationships are found for the CH and WH indices during anomalous WB60N events. The results further confirm the finding of Yu et al. (2015) that cold air outbreaks in the midlatitudes, as well as the out-of-phase relation between surface temperature anomalies over the high and midlatitudes, are closely linked to the day-to-day intensity variability of the meridional mass circulation.

The strengthening of the meridional mass circulation is accompanied by the intensification of atmospheric wave activities in the extratropics throughout the troposphere and the stratosphere. The wave activities become the strongest a few days after the peak time of WB60N+ events and exhibit a poleward and upward propagation. Intensification of wave activities is synchronized with a strengthening of the poleward mass transport in the upper troposphere within the warm air branch and the equatorward mass transport below within the cold air branch. In upper layers, the air mass transported adiabatically from midlatitudes to the polar region overwhelms that transported downward across isentropic surfaces because of diabatic cooling, leading to a net increase of warm air mass in the high latitudes. In the lower layers, the air mass transported out of the polar region by the strengthened equatorward cold air branch dominates over that transported in from the upper layers because of diabatic cooling, resulting in a net decrease of cold air mass in the high latitudes. The opposite situation is found in the midlatitudes. The strengthened equatorward cold air branch results in a net increase of cold air mass in the lower troposphere. Thus, the strengthened equatorward cold air branch is responsible for an anomalous increase of CMI and decrease of surface temperature in the midlatitudes but an anomalous decrease of CMI and increase of surface air temperature in the high latitudes. Consequently, within one week after the peak time of WB60N+ events, there are below-normal temperatures in the midlatitudes and above-normal temperatures in the high latitudes.

The (composite) mean surface circulation anomaly pattern associated with the strengthening of the meridional mass circulation generally resembles that of the winter-mean pattern, indicating a strengthening of the Siberian and North American highs and their westward shifts toward central Eurasia and the Alaska–Yukon region, as well as the deepening of the Aleutian and Icelandic lows. The strengthening of the permanent surface pressure systems, which determine the climatological mean routes of winter cold outbreaks, acts to bring more polar cold air mass equatorward on the east (west) side of high (low) pressure centers via continental routes into the midlatitudes, and to carry more warm air poleward on the west (east) side of high (low) pressure centers via oceanic routes into the polar region. The strengthening of the equatorward transport of polar cold air via these climatological routes is responsible for massive cold air outbreaks over East Asia and North America during the week after the peak time of WB60N+ events. The reverse is found during WB60N events.

In addition, the center of the winter high pressure system over Eurasia tends to shift westward during WB60N+ events. Such a shift results in an opening of an anomalous route for cold polar air to enter central Eurasia, which is responsible for the coldest composite mean surface temperature anomalies there in the period within one week after peak dates of WB60N+ events. The strengthening of the Icelandic low and Azores high acts to close off the climatological-mean cold air route through western Europe, which is responsible for the normal temperatures there. Following the end of WB60N+ events, or within a week before the peak dates of WB60N events, weakening of the Icelandic low and Azores high, which corresponds to the negative phase of the NAO, helps to strengthen or reopen the secondary winter-mean cold air route via western Europe. Accompanied is the strengthening of the secondary winter-mean warm air route via central Eurasia. This explains why temperatures over western Europe are farther below normal during the week before the peak dates of WB60N events, while negative temperature anomalies over the rest of the two major continents gradually diminish. The westward shift of the center of the negative NAO mode during and within the week after the peak dates of WB60N events limits the latitudinal span of the cold air route via western Europe. Consequently, only northern Europe still suffers from below-normal temperature in this period.

We wish to add that the results presented here do not change when we use an index that directly measures the cold air branch intensity, because the cold air branch is nearly perfectly synchronized with the warm branch aloft in terms of both timing and intensity. The simultaneous strengthening of both warm and cold air branches is accompanied with the strengthening of westward-tilted large-scale baroclinic waves. Therefore, the stronger warm air branch of the mass circulation is a robust indicator of a simultaneous strengthening, in the cold air branch, of both the poleward mass transport of the midlatitudes warm air into the polar region along the climatological routes over oceans and the equatorward mass transport of Arctic cold air along the climatological routes through lands, as shown in Figs. 6 and 8. This is the basis for the existence of the physical causal relationship between the mass circulation in the warm air branch and cold air outbreaks. Furthermore, the perspective from the warm air branch aloft would allow us to extend the causal information for cold air outbreaks to a longer lead time in our future studies, based on the poleward propagation signal of temperature anomalies within the warm air branch, as elicited in Cai and Ren (2007) and Ren and Cai (2007), which provides a direct linkage of the variability of the WB60N index to tropical forcing anomalies.

Acknowledgments

YYY and RRC are supported by a research grant from the National Science Foundation of China (41430533, 91437105). MC is supported by grants from the National Science Foundation (AGS-1262173 and AGS-1354834), the NOAA CPO/CPPA program (NA10OAR4310168), and the DOE Office of Science Regional and Global Climate Modeling (RGCM) program (DE-SC0004974).

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Footnotes

1

The poleward and equatorward branches of the meridional mass circulation are defined in terms of the zonally integrated mass fluxes. Since the zonally integrated mass fluxes are poleward in the upper isentropic layers and equatorward in lower isentropic layers, they are also referred to as the warm and cold air branches in the literature (e.g., Cai and Shin 2014). Within each of the two branches, there exist both poleward warm airmass fluxes in some longitudinal sectors and equatorward cold airmass fluxes in others. This is particularly true in the extratropics, where the meridional mass circulation is mainly driven by baroclinically amplifying waves.