1. Introduction

Two occasional features of the wintertime extratropical atmospheric circulation over the Northern Hemisphere, blocking flows in the troposphere and sudden warmings in the stratosphere, are each characterized by a reversal of the normal zonal flow from westerly to easterly. In the case of blocking, the reversal is local, in the middle to upper troposphere over middle latitudes, while during stratospheric sudden warmings (SSWs) the reversal is in the high-latitude, stratospheric zonal-mean flow. Both phenomena can affect tropospheric weather. It has been known for some time [e.g., Carrera et al. (2004) and references therein] that tropospheric blocking can disrupt the normal eastward motion of weather systems, leading to locally persistent, anomalous weather. It is also known (Baldwin and Dunkerton 1999) that anomalously weakened westerly flow in the stratosphere can propagate downward into the troposphere, potentially leading to reduced tropospheric westerly flow resembling that during blocking. Anomalously weakened stratospheric vortices can also precede or coincide with anomalous cold-air outbreaks in the troposphere (Kolstad et al. 2010).

That there may be a connection between blocking and SSWs has been suspected at least since the observation by Quiroz (1986) that tropospheric blocking can precede an SSW. More recently, Martius et al. (2009) have shown that most SSWs in their climatological study are preceded within 0–10 days by tropospheric blocking, but only a small percentage of blocking events are each followed by an SSW. In other words, SSWs are relatively rare, occurring in the Northern Hemisphere on average every 1–2 years, while blocking events may occur several times each year (Martius et al. 2009). A dynamical explanation for the blocking–SSW connection is that tropospheric blocking features project strongly onto planetary waves that can propagate upward into the stratosphere, thereby breaking and leading to a weakening of the westerly flow (e.g., Polvani and Waugh 2004; Peters et al. 2007).

These observations raise some interesting questions. Namely, what distinguishes blocking events that are each followed by an SSW from those that are not? Also, why are so few SSWs not preceded by blocking? The purpose of this contribution is to address the first question and, through the results of that investigation, provide some insight concerning the second question. These issues are addressed through a diagnostic comparison of Northern Hemisphere blocking cases composited during SSW events with those composited during the absence of an SSW, as identified in the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) Reanalysis Project (NNRP) data (Kalnay et al. 1996). Diagnoses of four particular blocking events are presented to illustrate the contrast between SSW and non-SSW cases. Each of these particular blocking events occurred during the same time of the calendar year, from mid- to late January, in the years of 1987, 1996, 2000, and 2009. The onset of the 1987 and 2009 cases occurred 11 and 5 days, respectively, prior to the onset of an SSW, while neither the 1996 case nor the 2000 case was associated with an SSW. Specifically, the nearest SSW was 2 months (years) following the onset of the 2000 (1996) blocking case.

The upward wave activity fluxes thought to connect tropospheric blocking with stratospheric vortex weakening are associated with poleward eddy heat fluxes in the upper troposphere and lower stratosphere. Sjoberg and Birner (2012) showed that composited SSW events in reanalysis data were preceded in time by persistently anomalous poleward eddy heat fluxes at 200 hPa, averaged over a circumpolar ring (45°–75°N). A similar distinction was found between our SSW– and non-SSW–blocking composites, with SSW–blocking events characterized by significantly larger heat flux anomalies than the non-SSW blocks.

Further insight emerges from our examination of the spatial distribution of the heat flux anomalies, which are found to be significantly larger inside the stratospheric polar vortex in the SSW–blocking composites than in the non-SSW–blocking events near the block-onset time. Thermally forced stratospheric geopotential height rises are also significantly larger inside the polar vortex in the SSW–blocking composites than in the non-SSW–blocking events, consistent with weakening stratospheric westerlies during the SSW events. These distinctions suggest that the location of poleward heat fluxes, in addition to their persistence and magnitude, determine whether a blocking event coincides with an SSW. Furthermore, this distinction suggests a hypothetical scenario for an SSW to occur in the absence of blocking.

2. Data and methodology

a. Definitions

The NNRP data from winters (November–March) of 1980/81–2011/12 over the Northern Hemisphere were searched for blocking and SSW events. Each of the blocking cases satisfied a wave-breaking definition of blocking, adapted to isobaric surfaces from the isentropic potential vorticity (PV) wave-breaking definition of Pelly and Hoskins (2003). Specifically, blocking is defined by a persistent, spatially coherent reversal of the meridional gradient in isobaric PV at 250 hPa, where PV or Π, is defined, as in Bresky and Colucci (1996), by

In Eq. (1), g is gravity; η is absolute vorticity; u and υ are eastward (x) and northward (y) analyzed wind components, respectively; P is pressure; and θ is potential temperature. Spatial coherence requires that the meridional PV reversal, over 15° of latitude within 30° of latitude centered on the climatological jet stream, span at least 20° of longitude, while persistence requires that this spatially coherent reversal last at least three consecutive 0000 UTC analysis times. The block onset date for each case is the first 0000 UTC time at which the blocking definition was satisfied, while blocking decay is the last consecutive 0000 UTC time at which the definition was satisfied. Blocking duration is the difference in days between block onset and decay.

A blocking event was associated with an SSW if at least 1 day during the block’s duration occurred within 20 days centered on an SSW central date, defined as the first day within November–March when the zonal-mean zonal wind at 60°N and 10 hPa became negative or easterly [e.g., Charlton and Polvani (2007) and references therein]. After the zonal-mean zonal wind at 60°N and 10 hPa returned to westerly, it must have remained westerly for at least 20 days before another reversal to easterly winds could be counted as a separate SSW event. Otherwise, it was counted as part of the first SSW event. All other blocking events—that is, those whose durations did not each include at least 1 day within 20 days centered on an SSW central date—were classified as non-SSW–blocking events. Details about the SSW cases and the blocking events that were associated with them are summarized in Table 1. Notice that some SSW cases were associated with more than one blocking event, such that during the period of investigation there were 17 SSW cases and 25 associated blocking events. By contrast, there were 155 non-SSW–blocking events during the period of investigation (see appendix A).

Table 1.

Blocking events coinciding with SSWs, showing SSW central (onset) date, blocking onset and decay dates, blocking duration, and blocking location. All dates are formatted as YYYY–MM–DD.

b. Diagnostics

In a frictionless, quasigeostrophic atmosphere, the zonal-mean zonal wind obeys

where

is the divergence of the wave activity flux F, with P as the vertical coordinate, and

is the diabatic residual-mean meridional wind. Here is a constant air density, u_g and υ_g are the eastward and northward geostrophic wind components, f₀ is a constant Coriolis parameter, R is the dry gas constant, is the isobarically constant static stability parameter, T is temperature, the overbar represents a zonal average, and the prime denotes a departure from zonal average or eddy. See appendix B for a derivation of Eqs. (2)–(4).

Attention here will be focused on the role of the wave activity flux divergence in temporal changes of the zonal-mean zonal wind during the blocking composites. The vertical component of this flux divergence [second term on the right-hand side of Eq. (2)] includes the meridional eddy heat flux , which, when evaluated in the upper troposphere or lower stratosphere, can be used to represent the upward wave activity flux from the troposphere to the stratosphere (e.g., Polvani and Waugh 2004; Sjoberg and Birner 2012). Following the procedure of Sjoberg and Birner (2012), these heat fluxes, calculated from the NNRP data, were averaged around the 45°–75°N zonal ring at 200 hPa, then shown as anomalies, or departures from heat fluxes calculated from long-term (1981–2010) daily mean data. These anomalies were further averaged in time over 20-day periods, smoothing high-frequency variations but retaining submonthly variability. Note that here we use the analyzed, rather than geostrophic, υ component of the wind, although the difference between the heat fluxes calculated with analyzed versus geostrophic υ components is negligible when they are area and time averaged.

We calculated 12-h analyzed geopotential height tendencies and their anomalies were also calculated from the NNRP data, then averaged over consecutive 10-day periods. The possible role by the heat fluxes (temperature advection) in forcing these height tendencies was investigated with a simple quasigeostrophic diagnosis as follows. Conservation of quasigeostrophic potential vorticity q following the geostrophic wind V_g requires that

where

for geopotential height Z and static stability σ. Combining Eqs. (5) and (6) and using hydrostatic balance yields

(e.g., Holton 2004). The first term on the right-hand side of Eq. (7) is proportional to vorticity advection, while the second term is related to temperature advection or thermal forcing. Focusing only on this second term, Eq. (7) can be rewritten as

where χ_T is the height tendency associated with temperature advection.

Equation (8) was numerically solved for χ_T every 6 h and at every Northern Hemisphere grid point, at every pressure level from 850 to 30 hPa, with the right-hand side of Eq. (8) calculated from the reanalyses over the four-dimensional domains during the period under investigation. These calculations were repeated on the long-term daily mean data and subtracted from the χ_T calculated from the reanalyses to yield χ_T anomalies. These anomalies were then averaged over 10-day periods, a typical synoptic time scale, centered on different time lags relative to block onset.

3. Composite results

The diagnostic quantities described above were composited over the 25 blocking events associated with SSWs and compared with composites over the 155 blocking events not associated with SSWs. For example, zonal-ring (45°–75°N)-averaged, 200-hPa heat flux anomaly composites are contrasted in Fig. 1. Twenty-day-averaged heat flux anomalies were significantly larger in the SSW–blocking composites than in the non-SSW–blocking composites from prior to about day −10 through about day +20 relative to block onset. Statistical significance was assessed using a Student’s t test for unequal variances (Wilks 2011). Interestingly, the heat flux anomalies became significantly lower in the SSW than in the non-SSW–blocking cases prior to days 35–40, indicating a recovery of the stratospheric polar vortex in the former cases. Specifically, the zonal-mean zonal wind increased with time at 10 hPa during this period in the SSW composites, but not in the non-SSW composites (not shown).

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Eddy heat flux anomalies (K m s⁻¹) at 200 hPa, zonally averaged over 45°–75°N and temporally averaged over the preceding 20 days, as a function of day relative to block onset and composited over SSW–blocking events (red) and non-SSW–blocking events (black). Red dots indicate a statistically significant difference between the red and black curves at the 5% level.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

Composited analyzed geopotential height tendency anomalies at 30 hPa, averaged over the 10 days centered on the block onset dates, are presented in Fig. 2, overlain with composited analyzed 10-hPa geopotential heights. Not surprisingly, the height tendencies were significantly more positive at high latitudes in the SSW-associated blocking composite than in the non-SSW composite, consistent with weakening stratospheric westerly winds at 60°N in the SSW composite. Perhaps surprisingly, the positive height tendency anomalies in the SSW composite were not symmetrically distributed about the North Pole, but concentrated near 75°N, 90°W. This suggests that spatial asymmetries in the analyzed height tendency anomalies distinguish SSW-associated blocking events from non-SSW–blocking events.

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Analyzed 30-hPa geopotential height tendency anomalies [colors; m (12 h)⁻¹] averaged over the 10 days centered on block onset and 10-hPa geopotential height (contours; m) on the block onset date, composited over (left) the SSW–blocking events and (right) the non-SSW–blocking events. The thick dark contour encloses the area of statistically significant difference between the left and right panels at the 5% level.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

These asymmetries are also evident in the thermally forced height tendency anomalies at 30 hPa (Fig. 3), with significantly larger 30-hPa height rises near and poleward of the 10-hPa vortex center 10 days before (Fig. 3a) and 10 days after (Fig. 3c) block onset in the SSW composites than in the non-SSW composites. It is noteworthy that at these lag times there are also significantly greater thermally forced 30-hPa height falls equatorward of the 10-hPa vortex center, over Asia and the Pacific Ocean, respectively, in the SSW–blocking composites than in the non-SSW events. These asymmetric patterns are evident at the block onset date (Fig. 3b) but the 30-hPa thermally forced height tendency anomalies are weaker in magnitude and with smaller areas of significant difference between the SSW and non-SSW composites.

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As in Fig. 2, but for thermally forced height tendencies averaged over 10 days centered on days (a) −10, (b) 0, and (c) +10 relative to block onset.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

These asymmetries can be quantified by averaging the height tendency anomalies over the area enclosed by the polar vortex. Adapting the method of Baldwin and Holton (1988), we defined the polar vortex edge by the 150 potential vorticity unit (PVU; 1 PVU = 10⁻⁶ K kg⁻¹ m² s⁻¹) contour at 20 hPa, where. As an illustration, the climatological (1981–2010) December–February mean 10-hPa height field and the corresponding 150-PVU contour at 20 hPa are shown in Fig. 4. Grid points on and poleward of the vortex edge were defined to be inside the vortex, whereas those equatorward of the edge were considered to be outside the vortex.

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Climatological (1981–2010) winter (December–February)-mean 10-hPa geopotential height (colors; m) and outer edge of the polar vortex (black contour; 150 PVU at 20 hPa).

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

The thermally forced height tendency anomalies at 30-hPa grid points inside the vortex were then averaged and compared with tendency anomalies averaged outside the vortex. The resulting time series, relative to block onset day, are shown in Fig. 5. The inside-vortex-averaged 30-hPa height tendency anomalies were significantly more positive near lags −10 and +10 relative to block onset, and more negative near lag +20, in the SSW–block composites than in the non-SSW events. Also consistent with the plan views of the anomalies in Figs. 3a and 3c, the outside-vortex-averaged anomalies were significantly more negative near lags –10 and +10 in the SSW composites than in the non-SSW composites.

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Thermally forced 30-hPa geopotential height tendency anomalies [m (12 h)⁻¹] temporally averaged over the 10 days centered on the indicated day relative to block onset, spatially averaged over the area inside (solid contours; left ordinate) and outside (dashed contours; right ordinate) the 20-hPa polar vortex and composited over SSW–blocking events (red) and non-SSW–blocking events (black). Red dots indicate a statistically significant difference between the red and black curves at the 5% level.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

The vortex-averaging procedure described above was repeated for the 200-hPa heat flux anomalies shown in Fig. 1. The resulting time series of inside vortex-averaged heat flux anomalies in Fig. 6 are qualitatively similar to the zonal-ring-averaged anomalies in Fig. 1. Specifically, they are significantly more positive in the SSW composites than in the non-SSW composites from about day −5 to day +10 relative to the block onset date. Interestingly, the outside-vortex-averaged heat flux anomalies are small but significantly greater in the SSW composites than in the non-SSW composites from about day −20 to day +20 relative to block onset, thus leading the significant inside-vortex difference.

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Eddy heat flux anomalies (K m s⁻¹) at 200 hPa averaged over the 20 days prior to and including the indicated day relative to block onset, spatially averaged over the area inside (solid contours) and outside (dashed contours) the polar vortex, and composited over SSW–blocking events (red) and non-SSW–blocking events (black). Red dots indicate a statistically significant difference between the red and black curves at the 5% level.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

4. Case studies

The composite results presented above will now be illustrated in four particular blocking cases. The representation of these cases in the 250-hPa geopotential height field at each of their onset times is shown in Fig. 7. In three of the cases (1987, 1996, and 2000), blocking was detected over the eastern Atlantic Ocean and Europe, while in the 2009 case it was detected over western North America. At the 1987 and 2000 block onset times over the eastern Atlantic and western Europe, there was a local reversal of the normal poleward decrease in geopotential height at 250 hPa—a feature that is typical of blocking patterns (Figs. 7a,c). In the 1996 and 2009 cases, there was an amplified geopotential height ridge at 250 hPa over Europe (Fig. 7b) and western North America (Fig. 7d), respectively, at the block-onset times.

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The 250-hPa geopotential height (m) at the onset times of the four selected blocking cases: (a) 12 Jan 1987, (b) 11 Jan 1996, (c) 17 Jan 2000, and (d) 20 Jan 2009.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

The zonal-mean zonal (u component) wind at 60°N and 10 hPa is shown as a function of time relative to block onset for the four cases in Fig. 8. This zonal-mean zonal wind reversed from positive (westerly) to negative (easterly), defining a major SSW, following block onset in the January 1987 and January 2009 cases, but not in the January 1996 and 2000 cases when it remained strongly positive. By contrast, this zonal-mean zonal wind experienced a nearly 100 m s⁻¹ decrease during a 3-week period in January 2009. Consequently, the SSW during that month has attracted considerable attention (e.g., Evers and Siegmund 2009; Harada et al. 2010; Hinssen and Ambaum 2010; Kim and Flatau 2010; Albers and Birner 2014; Taguchi 2014), while Manney et al. (2005) and Matthewman et al. (2009) have discussed the January 1987 case.

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Zonal-mean zonal wind at 10 hPa and 60°N as a function of day relative to blocking onset on 12 Jan 1987 (red), 11 Jan 1996 (green), 17 Jan 2000 (blue), and 20 Jan 2009 (orange).

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

Consistent with the composite heat flux anomalies (Fig. 1), the zonal-ring-averaged, 200-hPa heat flux anomalies were positive near the block onset times in the SSW–blocking cases (January 1987 and 2009) but negative or near zero in the non-SSW cases (January 1996 and 2000); results are not shown. Similarly, the thermally forced 30-hPa geopotential height tendency anomalies centered on the block-onset times were positive at and poleward of the 10-hPa vortex center in the SSW cases (Figs. 9a,d) but near zero or negative during the non-SSW cases (Figs. 9b,c), resembling the composite analyzed tendency anomalies in Fig. 2.

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Thermally forced 30-hPa geopotential height tendency anomalies [colors; m (12 h)⁻¹] averaged over the 10 days centered on the block onset dates on (a) 12 Jan 1987, (b) 11 Jan 1996, (c) 17 Jan 2000, and (d) 20 Jan 2009, and analyzed 10-hPa geopotential heights (contours; m) on those dates.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

5. Discussion

Recent findings have suggested that the location of tropospheric blocking and associated positive geopotential height anomalies determine whether these tropospheric features are associated with anomalous stratospheric flows. It is possible that anomalies in some locations may constructively or destructively interfere with the climatological stationary waves, as noted in studies by Garfinkel and Hartmann (2008), Smith et al. (2010), Fletcher and Kushner (2011), and Nishii et al. (2011). The geographical location of the upward wave activity forcing may also determine whether an SSW is a vortex-split or vortex-displacement type (Cohen and Jones 2012).

Specifically, anticyclonic anomalies in the troposphere over the Atlantic Ocean and Europe have been connected with stratospheric polar vortex weakenings (Garfinkel et al. 2010; Woollings et al. 2010; Nishii et al. 2011). However, Nishii et al. (2010) found that blocking anticyclones over the western Pacific Ocean are followed by stratospheric cooling because they coincide with a climatological trough and are associated with zonally averaged equatorward heat flux anomalies. This destructive interference of anomalies with the climatological stationary waves over the western Pacific was also noted by Woollings et al. (2010), who additionally found that blocking anticyclones over Greenland were out of phase with the stationary waves and associated with relatively weak upward wave activity fluxes. In general, Garfinkel et al. (2010) found that 500-hPa height anomalies in phase with climatological asymmetries were associated with a weakening of the stratospheric vortex. This included positive height anomalies over Europe and negative anomalies over the western Pacific.

The geographical distribution of blocking events during 1980–2012 (Fig. 10) reveals that while blocks not associated with SSWs were uniformly distributed with respect to longitude, there was an absence of blocks associated with SSWs over the western Pacific Ocean, from 120°E (240°W in Tables 1 and A1) eastward to about 150°W. It is noteworthy that this is the location of the climatological tropospheric trough and consistent with the results of previous works cited above. However, a similar absence of SSW-associated blocking is not evident near the climatological trough position over eastern North America. It therefore appears that the SSWs during the investigated time period were associated with tropospheric blocking from 150°W eastward to 120°E (240°W), but blocking events within this region were not necessarily followed by SSWs.

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Location of SSW (red)– and non-SSW (gray)–blocking events at the block onset time. Larger circles indicate multiple events at one location.

Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0160.1

6. Conclusions

Twenty-five objectively defined blocking events each occurring within 20 days centered on an SSW central date were diagnostically contrasted, in composites and case studies, with 155 blocking events each not temporally associated with an SSW. Consistent with previous findings, poleward eddy heat fluxes at 200 hPa were anomalously larger near the block onset time in the SSW–blocking composites than in the non-SSW–blocking events, viewed either as an average over a circumpolar ring (45°–75°N) or an average inside the polar vortex (150-PVU contour at 20 hPa). Thermally forced 30-hPa geopotential height tendency anomalies were also significantly larger inside the polar vortex in the SSW–blocking events than in the non-SSW blocks.

We therefore conclude that only those blocks associated with persistently anomalous upper-tropospheric poleward eddy heat fluxes and thermally forced stratospheric geopotential height rises, concentrated inside the stratospheric polar vortex, will coincide with a major weakening of that vortex. It may well be that the processes associated with these blocking events, not the blocking events themselves, are prerequisite for an SSW. This conjecture suggests that an SSW could occur in the absence of blocking given the necessary antecedent processes. The nature of these processes—namely, anomalous eddy heat fluxes—and their relationship with blocking and SSWs are being further investigated in our current research efforts.