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  • View in gallery

    Composite zonal wind averaged from lag −15 to lag −5 days and over the region from 90° to 30°W for the strong (solid) and weak (dashed) jet NAO+ events.

  • View in gallery

    Composites of daily 500-hPa geopotential height (gpm; contours) for European blocking events, surface air temperature anomalies (red and blue), and precipitation area (>3 mm only; green) for (a) weak and (b) strong jet NAO+ events. The temperature anomaly regions above the 95% confidence level for a two-sided Student’s t test are plotted. Red (blue) color represents a positive (negative) temperature anomaly.

  • View in gallery

    The SJN-minus-WJN difference of the (a) time-mean SAT with precipitation areas (green) and (b) its variation ∂T′/∂t associated with blocking events averaged from lag −2 to lag 2 days between the strong and weak jet NAO+ events, where lag 0 denotes the day that the blocking amplitude is strongest. Red (blue) color denotes the positive (negative) temperature differences, and green areas represent regions with positive precipitation difference. Only regions with temperature anomalies and positive precipitation anomalies above the 95% confidence level based on a two-sided Student’s t test are plotted.

  • View in gallery

    The SJN-minus-WJN difference of the time-mean 850-hPa transient eddy temperature advection term Aeddy averaged from lag −2 to lag 2 day for transient eddies with three time scales of (a) 2.5–6, (b) 7–12, and (c) 7–31 days. Red (blue) color denotes the positive (negative) temperature difference region above the 95% confidence level for a two-sided Student’s t test.

  • View in gallery

    Composites of daily 500-hPa geopotential height anomalies (m) of European blocking events for the (a) weak and (b) strong jet NAO+ events, as shown in Fig. 2. The dark and light gray shading denotes the region above the 95% confidence level based on a two-sided Student’s t test. (c),(d) The solid (dashed) line denotes the intensity of the NAO+ (EB) dipole anomaly for the (c) weak and (d) strong jet NAO+ events. The dashed rectangle at lag 0 in (a),(b) denotes the region of the EB dipole.

  • View in gallery

    Spatial location of the maximum anticyclonic center (lag 0) of the EB events associated with the 23 SJN (circles) and 14 WJN (black triangles) NAO+ events during 1950–2013 winter based on the NCEP–NCAR reanalysis data. The red circle represents the location of three overlapping EB events for the SJN case. The blue circle (green triangle) denotes the mean position of the anticyclonic center at lag 0 for the EB events associated with SJN (WJN) events.

  • View in gallery

    Instantaneous fields of the composite daily geostrophic zonal wind anomalies (m s−1) for (a) weak and (b) strong jet NAO+ events. The dark and light gray shading denotes the region above the 95% confidence level for a two-sided Student’s t test. The dashed rectangle at lag 0 represents the region of the EB dipole for weak and strong jet NAO+ events.

  • View in gallery

    Zonal winds averaged from lag −5 to lag +5 days and over the (a) Atlantic basin (90°–30°W) and (b) European continent (0°–40°E), where the lag 0 day denotes the day that the European blocking is strongest. The solid (dashed) line represents the SJN (WJN) events.

  • View in gallery

    Meridional distribution of the prescribed jet uJ at x = xc = 0 for three cases: Δu = 0 and ac = 0.1 (dashed line); Δu = 0.1 and ac = 0.1 (solid line); and Δu = 0.1 and ac = 0.2 (dotted–dashed line). The units along the axes for u and y are 10 m s−1 and 1000 km, respectively.

  • View in gallery

    The nondimensional barotropic streamfunction of the planetary-scale flow ψP of an NAO+ event from the extended NMI model for (a) weak (Δu = 0) and (b) strong (Δu = 0.1) jets. The contour interval (CI) is 0.15. The North Atlantic is roughly defined as a region from x = −4.74 to x = 1, and the European continent ranges from x = 1 to x = 5.74; the regions marked by A and E, respectively.

  • View in gallery

    As in Fig. 10, but for the planetary-scale anomaly field ψNAO (CI = 0.2).

  • View in gallery

    Fields of ΨT (CI = 0.3) of an NAO+ event obtained from the extended NMI model for the (a) weak and (b) strong jet cases. The label H (L) denotes the ridge or anticyclone (trough or cyclone). The definitions of North Atlantic and European continent are as in Fig. 10.

  • View in gallery

    Time variation of (a) the zonal position, denoted by x, and (b) the phase speed (10 m s−1) of the EB obtained from the extended NMI model for weaker (dashed) and stronger (solid) mean zonal winds.

  • View in gallery

    Evolution of time-dependent geostrophic zonal wind anomalies (CI = 0.2 × 10 m s−1) corresponding to the NAO+ event shown in Fig. 10 under (a) weak and (b) strong jet background states. The definitions of North Atlantic and European continent are as in Fig. 10.

  • View in gallery

    Schematic diagram of NW–SE and NE–SW tilting of (left) the NAO+ and (right) EB dipole anomalies under (a) weak and (b) strong jet background conditions. The resulting dipole pattern influenced by the zonal wind distribution is on the right, and the case without the influence of the zonal wind distribution is on the left. The plus (minus) sign denotes the positive (negative) height anomaly. The red solid (dashed) line represents the meridional distribution of the zonal wind over the North Atlantic basin (European continent).

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The Positive North Atlantic Oscillation with Downstream Blocking and Middle East Snowstorms: Impacts of the North Atlantic Jet

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  • 1 Key Laboratory of Regional Climate-Environment for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
  • | 2 Key Laboratory of Regional Climate-Environment for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, and Qingdao Collaborative Innovation Center of Marine Science and Technology, Physical Oceanography Laboratory, Ocean University of China, Qingdao, China
  • | 3 Department of Atmospheric and Environmental Sciences, University at Albany, State University of New York, Albany, New York, and National Center for Atmospheric Research, Boulder, Colorado
  • | 4 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
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Abstract

A recent study revealed that cold winter outbreaks over the Middle East and southeastern Europe are caused mainly by the northeast–southwest (NE–SW) tilting of European blocking (EB) associated with the positive-phase North Atlantic Oscillation (NAO+). Here, the North Atlantic conditions are examined that determine the EB tilting direction, defined as being perpendicular to the dipole anomaly orientation. Using daily reanalysis data, the NAO+ events are classified into strong (SJN) and weak (WJN) North Atlantic jet types. A composite analysis shows that the EB is generally stronger and located more westward and southward during SJN events than during WJN events. During SJN events, the NAO+ and EB dipoles exhibit NE–SW tilting, which leads to strong cold advection and large negative temperature anomalies over the Middle East and southeastern Europe. In contrast, northwest–southeast (NW–SE) tilting without strong negative temperature anomalies over the Middle East is seen during WJN events.

A nonlinear multiscale interaction model is modified to investigate the physical mechanism through which the North Atlantic jet (NAJ) affects EB with the NAO+ event. It is shown that, when the NAJ is stronger, an amplified EB event forms because of enhanced NAO+ energy dispersion. For a strong (weak) NAJ, the EB tends to occur in a relatively low-latitude (high latitude) region because of the suppressive (favorable) role of intensified (reduced) zonal wind in high latitudes. It exhibits NE–SW (NW–SE) tilting because the blocking region corresponds to negative-over-positive (opposite) zonal wind anomalies. The results suggest that the NAJ can modulate the tilting direction of EB, leading to different effects over the Middle East.

Corresponding author address: Dr. Dehai Luo, RCE-TEA, Institute of Atmospheric Physics, Chinese Academy of Sciences, Mailbox 9804, Huayanli 40, Chaoyang District, Beijing 100029, China. E-mail: ldh@mail.iap.ac.cn

Abstract

A recent study revealed that cold winter outbreaks over the Middle East and southeastern Europe are caused mainly by the northeast–southwest (NE–SW) tilting of European blocking (EB) associated with the positive-phase North Atlantic Oscillation (NAO+). Here, the North Atlantic conditions are examined that determine the EB tilting direction, defined as being perpendicular to the dipole anomaly orientation. Using daily reanalysis data, the NAO+ events are classified into strong (SJN) and weak (WJN) North Atlantic jet types. A composite analysis shows that the EB is generally stronger and located more westward and southward during SJN events than during WJN events. During SJN events, the NAO+ and EB dipoles exhibit NE–SW tilting, which leads to strong cold advection and large negative temperature anomalies over the Middle East and southeastern Europe. In contrast, northwest–southeast (NW–SE) tilting without strong negative temperature anomalies over the Middle East is seen during WJN events.

A nonlinear multiscale interaction model is modified to investigate the physical mechanism through which the North Atlantic jet (NAJ) affects EB with the NAO+ event. It is shown that, when the NAJ is stronger, an amplified EB event forms because of enhanced NAO+ energy dispersion. For a strong (weak) NAJ, the EB tends to occur in a relatively low-latitude (high latitude) region because of the suppressive (favorable) role of intensified (reduced) zonal wind in high latitudes. It exhibits NE–SW (NW–SE) tilting because the blocking region corresponds to negative-over-positive (opposite) zonal wind anomalies. The results suggest that the NAJ can modulate the tilting direction of EB, leading to different effects over the Middle East.

Corresponding author address: Dr. Dehai Luo, RCE-TEA, Institute of Atmospheric Physics, Chinese Academy of Sciences, Mailbox 9804, Huayanli 40, Chaoyang District, Beijing 100029, China. E-mail: ldh@mail.iap.ac.cn

1. Introduction

In recent decades, the frequency of extreme rainfall and snowstorm events during the winter over the Mediterranean Sea, southeastern Europe, and the Middle East was found to have increased (Zolina et al. 2009; Krichak et al. 2012). Many studies have revealed that the frequency of extreme precipitation events over southern Europe is closely related to atmospheric teleconnection patterns in the Euro-Atlantic sector (Eshel and Farrell 2000, 2001; Krichak et al. 2002; Krichak and Alpert 2005a,b; Feldstein and Dayan 2008; Black 2012; Krichak et al. 2014). In these teleconnection patterns, the North Atlantic Oscillation [NAO; the positive (negative) phase of which is referred to as the NAO+ (NAO) here], was found to be a very important factor affecting European weather and climate (Hurrell 1995; Yiou and Nogaj 2004; Scaife et al. 2008; Croci-Maspoli and Davies 2009; Cattiaux et al. 2010; Seager et al. 2010; Black 2012; Luo et al. 2014; Yao and Luo 2014; Diao et al. 2015).

The winter snowstorm that occurred over the Middle East during 9–15 December 2013 is a particularly severe extreme precipitation event. Although the precipitation over southern Europe or the Middle East is modulated by the phase of the NAO and the East Atlantic/Western Russia (EA/WR) pattern (Feldstein and Dayan 2008; Black 2012; Krichak et al. 2014), the physical mechanism of the outbreak of the December 2013 Middle East snowstorm event is not yet clear. In Luo et al. (2015, hereafter L15), we examined the large-scale conditions of the outbreak of this snowstorm event. It was shown that the combination of the NAO+ and European blocking (EB) patterns played an important role in the outbreak of this extreme event. In particular, the northeast–southwest (NE–SW) tilting1 of the southward-displaced EB dipole pattern in the geopotential height anomaly (with a positive anomaly over southern Scandinavia and a negative anomaly over the eastern Mediterranean Sea on 12 and 13 December, as shown in Fig. 3 of L15) associated with an NAO+ event is crucial for the outbreak of the Middle East snowstorm in December 2013. The location of the cold temperature anomalies is more sensitive to the tilting direction of the EB dipole than the amplitude of the blocking anticyclone, although the latter does influence the intensity and persistence of the cold event over Europe. An interesting question raised here is what factors affect the strength of the EB dipole and its meridional tilting. This is investigated in this paper as a follow-up study of L15. Here, we first classify the NAO+ events with concurring EB events into two different types: one with a strong and the other with a weak North Atlantic jet. We then perform a composite analysis to examine which type of NAO+ event and what factors contribute to low temperatures over the Middle East and southeastern Europe. Finally, we modify a nonlinear multiscale interaction (NMI) model of the NAO events developed by Luo et al. (2007a,b, 2010a,b) and Luo and Cha (2012) to include the North Atlantic jet distribution to further investigate the above questions.

This paper is organized as follows: The data and method are described in section 2, which also describes the classification of the NAO+ events. In section 3, the results from a diagnostic analysis using reanalysis data are presented. We describe the extension of the NMI model to include a jetlike background flow in section 4. The model results are presented in section 5. The conclusions and a discussion are presented in section 6.

2. Data and method

We used the daily multilevel geopotential height, wind, and air temperature from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis dataset (http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html) for the winters [December–February (DJF)] from December 1950 to February 2014. Daily precipitation data were obtained from the European Climate Assessment and Dataset (http://eca.knmi.nl/download/ensembles/download.php) on a 0.5° × 0.5° grid for the same period. The daily NAO index was obtained from the National Oceanic and Atmospheric Administration (NOAA)/Climate Prediction Center (CPC) (ftp://ftp.cpc.ncep.noaa.gov/cwlinks/), which was derived from a rotated principal component analysis (RPCA). An NAO event is defined to have taken place when the normalized daily NAO index exceeds one standard deviation for at least three consecutive days. As in L15, the index of Tibaldi and Molteni (1990, hereafter TM), which is defined based on the reversal of the 500-hPa geopotential height gradient, is used to identify EB events associated with NAO+ events. Also, the anomalies at each grid point were calculated as the deviation from their climatological (1950–2004) mean for each day of the winter.

As shown in L15, 37 NAO+ events in DJF from December 1950 to February 2014 are followed by EB events. Here, we only consider these 37 NAO+ events with concurring EB events. Moreover, the time-mean 500-hPa zonal wind averaged from lag −15 to −5 days is defined as the mean zonal wind prior to the NAO onset, and it is referred to as the background zonal wind of each NAO+ event at a longitude λ and a latitude ϕ, where τ denotes the time from lag −15 to −5 days, and lag 0 day denotes the day that the NAO+ event has its largest amplitude. Such a definition is approximately valid because the amplitude of the NAO+ event is relatively small from lag −15 to −5 days.

In this paper, we define the zonal mean of the time-mean 500-hPa zonal wind in the Atlantic basin averaged from 90° to 30°W for each NAO event as . Then, we further define the latitude-averaged 500-hPa zonal wind averaged from 25° latitude south to 25° latitude north of the jet core latitude as the strength of the North Atlantic jet. A strong (weak) North Atlantic jet is also defined to have occurred if the value of Um for an NAO+ event is greater (less) than the mean value of Um for all 37 NAO+ events. The strong and weak jet NAO+ events are referred to as SJN and WJN events, respectively. Of the 37 NAO+ events, there are 23 SJN and 14 WJN events. Based on this classification, we compute 500-hPa geopotential height composite anomalies for EB events associated with the SJN and WJN events and their associated temperature and precipitation anomalies. Our tests showed that the results are similar if the strength of the North Atlantic jet is defined in terms of the maximum value of the zonal wind at the jet core latitude averaged from lag −15 to −5 days and from 90° to 30°W for an NAO+ event (results not shown).

3. Results from reanalysis data

a. Temperature and precipitation anomaly patterns associated with weak and strong jet NAO+ events

Based on the above classification of the WJN and SJN events, we show the composite U(ϕ) fields for the WJN and SJN events in Fig. 1. It can be seen that the mean zonal wind exhibits a jetlike meridional distribution centered around 45°N. As expected from the definition, the maximum composite U(ϕ) is larger for SJN events than for WJN events. The composite 500-hPa geopotential height, surface air temperature (SAT) anomaly, and areas with precipitation (the area of precipitation exceeding 3 mm) from lag −2 to lag +2 days during EB episodes are shown in Fig. 2 for the SJN and WJN cases, where lag 0 day denotes the day that the EB is strongest. As shown in Fig. 2, the composite height field exhibits an Ω-type pattern for the SJN events, but a diffluent (weak dipole) flow pattern for the WJN events. As we can see from the composite anomaly field discussed in section 3c, the EB is stronger during its growing phase for the SJN events than for the WJN events (cf. Figs. 5a,b before lag 0). Besides the difference of the EB strength between SJN and WJN cases, there is a significant difference between their trough locations. For the SJN case, a trough is located on the downstream side of the EB over the Middle East (for lag 0; Fig. 2b), whereas for the WJN case, the corresponding trough occurs over southwestern Europe (for lag 0; Fig. 2a).

Fig. 1.
Fig. 1.

Composite zonal wind averaged from lag −15 to lag −5 days and over the region from 90° to 30°W for the strong (solid) and weak (dashed) jet NAO+ events.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

Fig. 2.
Fig. 2.

Composites of daily 500-hPa geopotential height (gpm; contours) for European blocking events, surface air temperature anomalies (red and blue), and precipitation area (>3 mm only; green) for (a) weak and (b) strong jet NAO+ events. The temperature anomaly regions above the 95% confidence level for a two-sided Student’s t test are plotted. Red (blue) color represents a positive (negative) temperature anomaly.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

Previous studies (Hurrell 1995; Seager et al. 2010) have revealed that the negative (positive) NAO phase corresponds to negative temperature anomalies over northern (southern) Europe for the seasonal mean climate. Figure 2 shows that, during the NAO+ events followed by EB, the spatial pattern and magnitude of the SAT anomalies actually depend on the strength of the mean westerly wind in the Atlantic basin as a North Atlantic jet prior to the NAO+ event. Specifically, during these NAO+ events, large negative SAT anomalies are seen over southeastern Europe, the Middle East, northwestern Africa, and from northeastern Canada to southwestern Greenland during the SJN events (Fig. 2b), whereas only weak negative SAT anomalies are seen over parts of northwestern Africa and southwestern Europe during the WJN events (Fig. 2a). Furthermore, the positive SAT anomalies over northern Europe extend slightly farther to the south in the SJN case than the WJN case. The SJN-minus-WJN time-mean SAT difference averaged from lag −2 to 2 days is shown in Fig. 3a, which shows a lower SAT during SJN events than during WJN cases from northeastern Canada to western Greenland, southeastern Europe and parts of the Middle East and northern Africa, and northwestern Russia, but a higher SAT during SJN events than during WJN events over northern Europe and the high-latitude North Atlantic. The significant decrease in the SAT over southeastern Europe in the SJN case may be explained by the negative ∂T′/∂t [Eq. (1)] induced by the intense Ω-type EB during the SJN events (Fig. 3b), although the maximum SAT decrease does not correspond to the largest negative ∂T′/∂t region for the difference of the time mean between SJN and WJN.

Fig. 3.
Fig. 3.

The SJN-minus-WJN difference of the (a) time-mean SAT with precipitation areas (green) and (b) its variation ∂T′/∂t associated with blocking events averaged from lag −2 to lag 2 days between the strong and weak jet NAO+ events, where lag 0 denotes the day that the blocking amplitude is strongest. Red (blue) color denotes the positive (negative) temperature differences, and green areas represent regions with positive precipitation difference. Only regions with temperature anomalies and positive precipitation anomalies above the 95% confidence level based on a two-sided Student’s t test are plotted.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

As shown below, the large negative SAT anomalies over the Middle East and southeastern Europe are, to a large extent, caused by the enhanced high- and low-frequency transient advection of cold air from northern Europe because of the enhanced European blocking circulation and its NE–SW tilting. As shown in L15, the NE–SW tilting of the EB dipole is crucial for the negative SAT anomalies over the Middle East and southeastern Europe. Below, we will demonstrate that the NE–SW tilting of the EB dipole is closely related to the presence of a strong North Atlantic jet.

We further see from Fig. 2 that the precipitation has almost the same pattern for the two types of NAO+ events. Even so, snowfall does not occur over the Middle East during the WJN events because the SAT is relatively high in those regions (Fig. 2a). Thus, we conclude that the SJN events are more likely to cause cold temperatures and snowfall over the Middle East than the WJN events (Fig. 2b).

b. Roles of low- and high-frequency transient eddies in the temperature decline

In middle-to-high latitudes, the temperature variation induced by the blocking flow is associated with the changes in the blocking position and amplitude. Because our focus is placed on the contribution of temperature advection by the blocking flow, we may neglect the vertical temperature advection term. If we decompose temperature and wind velocity into monthly mean and transient eddy parts, after neglecting the vertical advection term, the equation for the temperature change becomes (Diao et al. 2015)
e1
where the overbar denotes the monthly mean and the prime represents the deviation from the monthly mean, referred to as the transient eddy contribution. The variable (T′) is the monthly mean (transient eddy) temperature anomaly, and [v′ = (u′, υ′)] represents the monthly mean (transient eddy) horizontal velocity vector.

If the transient eddies are separated into high-pass (2.5–6 days) and low-pass (7–31 days) contributions, the role of high- and low-frequency transient eddies in the temperature change associated with the blocking events can be diagnosed from Eq. (1). We show the SJN-minus-WJN time-mean temperature advection Aeddy difference at 850 hPa averaged from lag −2 to 2 days in Fig. 4 for transient eddies at three different time bands of 2.5–6, 7–12, and 7–31 days.

Fig. 4.
Fig. 4.

The SJN-minus-WJN difference of the time-mean 850-hPa transient eddy temperature advection term Aeddy averaged from lag −2 to lag 2 day for transient eddies with three time scales of (a) 2.5–6, (b) 7–12, and (c) 7–31 days. Red (blue) color denotes the positive (negative) temperature difference region above the 95% confidence level for a two-sided Student’s t test.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

It is seen that, for transient eddies with 2.5–6 (Fig. 4a), 7–12 (Fig. 4b), and 7–31 days (Fig. 4c), the SJN-minus-WJN time-mean 850-hPa Aeddy difference shows a large negative value over southeastern Europe and the Middle East. This demonstrates that high- and low-frequency transient eddies associated with the Ω-type EB play comparable roles in contributing to the stronger temperature decreased over southeastern Europe and the Middle East for SJN compared to WJN events, while the contribution of 7–12-day transient eddies is slightly weaker than that of the 7–31-day time band. As we show below, the NAO+-related EB is stronger and located farther westward and southward during the SJN events than during the WJN events. As a result, the southward high- and low-frequency transports of cold air are enhanced on the eastern side of the growing blocking anticyclone during the SJN events. This process induces enhanced cold advection, allowing the cold air to intrude into the lower latitudes, leading to the sharp decline in temperature over the Middle East and southeastern Europe. This indicates that the SJN events are important for generating negative temperature anomalies over the Middle East and southeastern Europe.

c. Strength and pattern of EB anomalies and their relationship with NAO+ events

Figure 5 shows the anomaly fields of the composite daily 500-hPa geopotential height for the WJN and SJN events, in contrast to the total height field shown in Fig. 2. It is clear that the composite blocking anomaly over Europe is more intense for the SJN events than the WJN events (for lag 0; Fig. 5b). For the SJN (WJN) events, the intensified blocking anomaly originates from the local amplification of an anticyclonic anomaly over the upstream (downstream) side of the European continent (at lag −2 days; Fig. 5). During the growth stage (from lag −3 to lag 0 days) the intensified blocking anticyclonic anomaly retrogrades (i.e., moves westward) for the WJN events (Fig. 5a), while the eastward movement of the EB anticyclone is seen during the decay phase (from lag 1 to lag 3 days in Fig. 5a; not shown for lag 3 days) for the WJN events. But the EB anticyclone shifts eastward for the SJN events (Fig. 5b). This eastward (westward) shift of the growing EB anticyclone for the SJN (WJN) event may be related to the stronger (weaker) North Atlantic jet prior to the NAO onset (Fig. 1). During the mature phase (from lag −1 to +1 days; Fig. 5), the blocking anomaly over Europe exhibits a dipole structure with a strong anticyclonic circulation to the north of a weak low. Moreover, both the blocking and NAO+ dipole anomalies are distributed along the NE–SW [northwest–southeast (NW–SE)] direction for the WJN (SJN) events (see Fig. 15 below) so that the weak cyclonic anomaly of the EB dipole is located on the upstream (downstream) side of Europe (for lag 0; Fig. 5). According to the definition of the dipole tilting, which is the direction perpendicular to the actual orientation of the anomaly dipole (L15), the blocking and NAO+ dipole anomalies exhibit NW–SE (NE–SW) tilting for the WJN (SJN) events. For SJN events, the combination of the NAO+ and EB dipole anomalies at lag −2 days forms a clear arching wave train from North America to Europe through the Atlantic basin. But the anticyclonic center associated with the NAO+ is split into two centers over North America and the eastern North Atlantic. For the EB dipole, the zonal position of the weak cyclonic anomaly plays a crucial role for the location of negative temperature anomalies over southern Europe and the Middle East, while the intensity of the blocking anticyclone affects in part the magnitude of the negative temperature anomalies for the SJN or WJN events (Figs. 7 and 11 in L15).

Fig. 5.
Fig. 5.

Composites of daily 500-hPa geopotential height anomalies (m) of European blocking events for the (a) weak and (b) strong jet NAO+ events, as shown in Fig. 2. The dark and light gray shading denotes the region above the 95% confidence level based on a two-sided Student’s t test. (c),(d) The solid (dashed) line denotes the intensity of the NAO+ (EB) dipole anomaly for the (c) weak and (d) strong jet NAO+ events. The dashed rectangle at lag 0 in (a),(b) denotes the region of the EB dipole.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

To see the relationship between the NAO+ and EB dipole anomalies, the difference of the 500-hPa geopotential height anomaly averaged over 90°–30°W between 35° and 65°N is defined as the intensity index of the NAO+ anomaly, while its value averaged over 0°–60°E is defined as the EB intensity. The results are shown in Figs. 5c and 5d for the SJN and WJN events. It is found that the EB event lags the NAO+ event by about 1 day for the WJN events, whereas this lag is 2–3 days for the SJN events. These lags are consistent with the theoretical study of Luo et al. (2007a), who found that the EB lags the NAO+ because it results from the decay of the NAO+ event.

The EB dipole anomaly is also found to be located farther southward during the SJN events than during the WJN events (for lag 0; Fig. 5). This can be seen from the latitudinal position of the maximum anticyclonic center of the EB dipole at lag 0 (Fig. 6; the red circle denotes the location of three overlapping blocking events). Figure 6 shows that, on average, the anticyclonic center of the EB is located more westward and southward for the SJN events than for the WJN events. Their location difference is about 5° latitude and 10° longitude in the meridional and longitudinal directions, respectively. A Monte Carlo test is used to examine the statistical significance of the position difference. It is found that both the latitude and longitude differences between SJN and WJN events are statistically significant at the 95% confidence level. The main reason for this difference is that the EB dipoles have different origins for the SJN and WJN events. As can be seen in Figs. 5a and 5b, the EB for WJN events originates in eastern Europe (lag −2 days; Fig. 5a) and exhibits a westward shift from lag −2 to lag 0 days. In contrast, the EB for SJN events originates in western Europe (lag −2 days; Fig. 5b) and shows an eastward shift from lag −2 to lag +2 days. An interesting feature is that for the NAO+ dipole anomaly, its cyclonic center shifts eastward (westward) for WJN (SJN) events (Fig. 5), opposite to the zonal movement of the anticyclonic center of the EB dipole. This slower (faster) eastward movement of the anticyclone (cyclone) of the EB dipole in higher (lower) latitudes leads to the NE–SW tilting of the EB dipole for the SJN events (see Fig. 7 below), even though the EB anticyclone shifts eastward. The opposite is seen for the WJN events (Fig. 5a). In particular, because the EB dipole is located in western Europe for the SJN events (Fig. 6), its NE–SW tilting leads to a strong trough over southeastern Europe and the Middle East, thus favoring the cold air outbreak over the Middle East and its adjacent region.

Fig. 6.
Fig. 6.

Spatial location of the maximum anticyclonic center (lag 0) of the EB events associated with the 23 SJN (circles) and 14 WJN (black triangles) NAO+ events during 1950–2013 winter based on the NCEP–NCAR reanalysis data. The red circle represents the location of three overlapping EB events for the SJN case. The blue circle (green triangle) denotes the mean position of the anticyclonic center at lag 0 for the EB events associated with SJN (WJN) events.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

Fig. 7.
Fig. 7.

Instantaneous fields of the composite daily geostrophic zonal wind anomalies (m s−1) for (a) weak and (b) strong jet NAO+ events. The dark and light gray shading denotes the region above the 95% confidence level for a two-sided Student’s t test. The dashed rectangle at lag 0 represents the region of the EB dipole for weak and strong jet NAO+ events.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

Our previous study has revealed that the spatial distribution of the geostrophic zonal wind can approximately reflect the position and tilting direction of the EB and NAO dipole anomalies (Luo et al. 2010b, their Fig. 3). Figure 7 shows the corresponding geostrophic zonal wind anomalies for the composite 500-hPa geopotential height anomalies shown in Fig. 5 for the SJN and WJN events. Over the North Atlantic basin, it is seen that the zonal wind exhibits a positive anomaly over the region from 45° to 65°N and negative anomalies on its two flanks. An opposite wind anomaly pattern is seen over Europe. The zonal wind anomalies are stronger for the SJN events (for lag 0; Fig. 7b) than for the WJN events (for lag 0; Fig. 7a). It is well known that the location of the EB event can be crudely estimated as corresponding to the weak zonal-mean zonal wind region (Kaas and Branstator 1993). As shown in Fig. 8, the zonal-mean zonal wind over Europe is weaker at a relatively low latitude south of 55°N for the SJN events than the WJN events, while it is stronger in high-latitude Europe. For the SJN events, because a large portion of the anticyclonic circulation of the EB dipole is located farther southward, where the zonal wind is weaker than the winds for the location of the negative anomaly center, it is inevitable that the EB dipole for these events exhibits NE–SW tilting (for lag 0; Fig. 5b), as the steering winds for the northern part of the dipole (i.e., the anticyclonic center) move more slowly toward the east than do those for its southern counterpart (i.e., the negative anomaly center) (Fig. 7b). We also see the same tilting for the NAO+ dipole anomaly related to the SJN events (for lag 0; Fig. 5b). The opposite tilting of the EB and NAO+ dipole anomalies is seen for the WJN events, because the EB (NAO+) dipole anomaly corresponds to the positive-over-negative zonal wind anomaly region (for lag 0; Fig. 7a).

Fig. 8.
Fig. 8.

Zonal winds averaged from lag −5 to lag +5 days and over the (a) Atlantic basin (90°–30°W) and (b) European continent (0°–40°E), where the lag 0 day denotes the day that the European blocking is strongest. The solid (dashed) line represents the SJN (WJN) events.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

A comparison between Figs. 5a and 5b shows that the EB dipole anomalies are stronger and located more westward and in lower latitudes for SJN events than for WJN events. In the next section, we will extend the NMI model of NAO events developed by Luo et al. (2007a,b) and Luo and Cha (2012) to investigate the factors that determine the occurrence and zonal movement of strong blocking over the European continent under SJN conditions. On this basis, although the extended NMI model is highly idealized, we will try to explain why both the NAO+ and EB dipole anomalies exhibit NE–SW (NW–SE) tilting during SJN (WJN) events by placing the dipole anomalies in the latitudinal band.

4. An extended weakly NMI model of NAO events and its analytical solution

In recent years, Luo and his coauthors developed an NMI model for describing the life cycle (growth, maintenance, and decay) of eddy-driven NAO events (Luo et al. 2007a,b; Luo and Cha 2012). They extended the blocking model of Luo (2000, 2005) based upon a scale separation assumption between the blocking and synoptic-scale eddies. This model can tell us how the duration, strength, and position of an NAO event depend upon atmospheric background conditions, such as the strength of the mean zonal wind, Atlantic storm track intensity (the maximum eddy kinetic energy), and so on, although additional damping terms are not involved in it. Furthermore, this model can describe the mutual relationship between the EB and NAO+ events. Although the NMI model was obtained previously based on a barotropic assumption, it was able to describe how the strength of the background westerly wind affects the EB associated with an NAO+ event (Luo and Cha 2012).

To investigate the interaction between the NAO and synoptic-scale eddies, some assumptions were made in this NMI model. For example, the atmospheric flow is assumed to consist of a time-mean basic flow, an NAO anomaly, and synoptic-scale eddies (Luo 2005; Luo et al. 2007a). For the synoptic-scale eddies with a monopole meridional structure, the zonal wavenumber must be greater than 9 so as to have a period less than one week (synoptic scale), while the NAO anomaly is assumed to have both a zonal wavenumber 2 and a meridional dipole structure and to be quasi stationary. In this case, the NAO anomaly and synoptic-scale eddies are zonally separated. Under this scale separation assumption, two equations for the NAO anomaly and synoptic-scale eddies are obtained from a barotropic potential vorticity (PV) equation (Luo et al. 2007b). The eddy vorticity flux divergence as an eddy forcing term is included in the NAO anomaly equation [see Eq. (1a) of Luo et al. (2007b)], while the NAO–eddy interaction terms appear in the synoptic-scale eddy equation [see Eq. (1b) of Luo et al. (2007b)]. The two equations are solved separately on a β-plane channel with a rigid lateral boundary condition and a periodic condition in the zonal direction (Luo 2005) using a multiscale perturbation expansion technique (Luo 2005; Luo et al. 2007a,b). In the NMI model, the time-mean basic flow and synoptic-scale eddies are assumed to exist and are prespecified prior to the NAO onset. In solving these model equations, the time-mean basic flow is assumed to be uniform (i.e., a constant; Luo et al. 2007b; Luo and Cha 2012), or it is maintained by a specified large-scale stationary vorticity source, while the synoptic-scale eddies prior to the NAO onset (preexisting synoptic-scale eddies) are generated by a local synoptic-scale vorticity source (Luo 2005; Luo et al. 2007a,b) or a local eddy vorticity stirring, as in Barnes and Hartmann (2010). An important feature of our NMI model is that the prespecified basic flow subsequently becomes time dependent, and the preexisting synoptic-scale eddies are deformed as a result of the feedback by the time-varying NAO anomaly. For this case, the time-dependent basic flow and synoptic-scale eddies contain the amplitude of the NAO event, although the NAO event is forced by preexisting synoptic-scale eddies. The solution of the NMI model equations can help us better understand how the basic flow, NAO anomaly, and synoptic-scale eddies change during their interaction (Luo et al. 2007b). For a uniform basic flow prior to the NAO onset, the analytical solution of the NMI model for the variables describing the temporal variations of the NAO, synoptic-scale eddies, and the mean flow can be obtained as found in Luo et al. (2007b) and Luo and Cha (2012).

To obtain the analytical solution of this NMI model, different from the direct numerical solution of planetary waves embedded in a basic flow (e.g., Held et al. 2002), the NAO anomaly is assumed to be a wave of the form B exp(ikx) sin(my) with zonal and meridional wavenumbers k and m, respectively, during the NAO life cycle (Luo et al. 2007a,b; Luo and Cha 2012), where B = B(x, t) is the NAO amplitude and is a function of the slowly varying x and t. Such an assumption is reasonable in a mechanistic study, although the NAO amplitude varies slowly in time and in the zonal direction. The NAO amplitude B = B(x, t) satisfies a forced nonlinear Schrödinger (NLS) equation with topographic and eddy forcing terms [see Eq. (4) of Luo and Cha (2012)]. The solutions of the model variables, such as the NAO, synoptic-scale eddies, and mean flow contain only one unknown variable B, which is described by a forced NLS equation (Luo et al. 2007b; Luo and Cha 2012). In this case, all the solutions of the model variables are known if the solution of the NAO amplitude B(x, t) is known. For given initial condition B(x, 0) and preexisting synoptic-scale eddies, one can obtain the time-dependent solution of B by solving for its amplitude [see Eq. (A5) in the appendix] numerically using a finite-difference scheme (Luo 2005; Luo et al. 2007b; Luo and Cha 2012). Although the analytical solution of this NMI model is highly simplified, it resembles the numerical solution of the eddy-forced vorticity equation that is integrated forward in time from these initial conditions (Luo et al. 2010b). However, in contrast to the stationary state solution of a forced PV equation (e.g., Branstator and Opsteegh 1989; Held et al. 2002), our analytical solution can clearly identify how the basic flow, NAO, and synoptic-scale eddies evolve with time during the NAO life cycle (Luo et al. 2007a,b; Luo and Cha 2012).

Because our NMI model reflects the impact of the basic flow on the NAO event and subsequent downstream blocking (Luo and Cha 2012), in this paper we will extend the NMI model to examine how the strength of the North Atlantic jet affects the EB associated with the NAO+ event by considering an idealized basic flow prior to the NAO onset (see the appendix). As noted above, because the mean zonal wind prior to the NAO onset exhibits a jetlike distribution (Fig. 1), it is reasonable to assume that the idealized basic flow here has a jetlike profile in the meridional direction. Here we consider a weak jetlike flow , where is the streamfunction of the basic flow, with m = ±2π/Ly, θ > 0, and 0 < ε ≪ 1; as defined in Table 1, ac denotes the jet strength, xc is the zonal position of the jet center, u0 is the uniform westerly wind, and Ly is the width of the β-plane channel. In the following discussion, we choose m = 2π/Ly for the positive phase of the NAO. We notice that the NAO anomaly and preexisting synoptic-scale eddies interact with the basic flow ψc(εx, y) to produce additional terms, which are regarded as the modulation of the spatially varying basic flow on the NAO anomaly and the preexisting synoptic-scale eddies [see Eqs. (A4d) and (A4m) of the appendix].

Table 1.

The parameters and their values used in the extended NMI model.

Table 1.

If the nondimensional atmospheric streamfunction ΨT is decomposed into three parts, (where ψ and ψ′ correspond to the NAO and synoptic-scale eddy anomaly streamfunctions, respectively), the NAO anomaly and synoptic-scale eddy equations can be obtained from an equivalent barotropic PV equation under a scale separation assumption (see the appendix). Assuming u0 = uC + Δu, uC = β/(k2 + m2), and |Δu| ≪ uC (k is the zonal wavenumber of the NAO anomaly, and β is the nondimensional meridional gradient of the Coriolis parameter), the solutions of these equations and their parameters can be obtained, and they are described in the appendix.

Because the aim of this paper is to understand how the jet or mean zonal wind strength affects the EB associated with the NAO+ event, the NMI model must be able to reproduce the NAO+ event and concurrent EB pattern. Thus, we must fix the parameters listed in Table 1, except for the values of Δu (the strength of the mean westerly wind: 10 m s−1) and the jet peak strength ac. The sensitivity of the results to the parameters listed in Table 1 was also examined, and similar results were found (not shown). The model results on the impact of the jetlike basic flow on the EB associated with the NAO+ event are described below.

5. Model results

In this study, although the highly idealized jet distribution considered above does not strictly match the observed jet structure shown in Fig. 1, it does capture the main observed features. Moreover, because it cannot capture the asymmetry of the observed Atlantic jet, our extended NMI model cannot directly describe the horizontal tilting of the NAO+ dipole. While this is a drawback of our model, a merit of the NMI model is that it can describe how the Atlantic jet affects the EB following the development of the NAO+ pattern. Because the mean zonal wind is used in our extended NMI model, the meridionally averaged strength of the jet is . Thus, the value of Δu reflects the strength of North Atlantic jet. Here, we consider an NAO+ pattern (α = 1 and m = 2π/Ly in the appendix). At x = xc = 0, for ac = 0.1, the meridional profile of uJ is shown in Fig. 9 for Δu = 0 and Δu = 0.1 (0.1 × 10 m s−1 in dimensional form), respectively. The jet profile of Δu = 0.1 and ac = 0.2 is also depicted in Fig. 9.

Fig. 9.
Fig. 9.

Meridional distribution of the prescribed jet uJ at x = xc = 0 for three cases: Δu = 0 and ac = 0.1 (dashed line); Δu = 0.1 and ac = 0.1 (solid line); and Δu = 0.1 and ac = 0.2 (dotted–dashed line). The units along the axes for u and y are 10 m s−1 and 1000 km, respectively.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

The value of Δu reflects the magnitude of the mean zonal wind averaged in the Atlantic basin, while the value of ac indicates the strength of the peak jet speed. In fact, as shown in Fig. 1, a strong jet corresponds to a large regional-mean zonal wind. Thus, the strength of the regional-mean zonal wind in a jetlike basic flow may be crucial for the variation of EB. In this section, we will focus on examining how the different values of Δu affect the EB associated with the NAO+ event.

a. EB associated with the NAO+ event and its relationship with zonal wind strength

Here, we first consider two cases of the Atlantic jet with the same shape but with different strength. As revealed from the reanalysis data, the SJN (WJN) events possess stronger (weaker) mean westerly winds, thus corresponding to larger (smaller) values of Δu. For ac = 0.1 we show the planetary-scale component [ in Eq. (A4b) of the appendix] of the streamfunction of an NAO+ event with EB in Fig. 10 for Δu = 0 and Δu = 0.1, respectively. In our NMI model, the European continent is roughly defined as a region from x = 1 to x = 5.74, and the North Atlantic is crudely defined to range from x = −4.74 to x = 1, which are marked as E and A in Fig. 10 on day 0, respectively. It is found that a blocking flow occurs over the European continent as a result of downstream energy dispersion after the long time evolution of the NAO+ pattern. A further comparison between Figs. 11a and 11b below shows that the energy dispersion is stronger under a strong zonal wind condition because a more intense EB can occur (from day 33 to 48; Fig. 11b). For the strong jet (Δu = 0.1) case, the EB is more intense, as shown in Fig. 11 (for day 39) below. For this case with strong westerly winds, the westward movement of the intensified EB is suppressed so that its intensified low-pressure trough is located downstream of Europe (from day 33 to 48; Fig. 10b). That is to say, when the Atlantic mean zonal wind is relatively strong, as observed in Fig. 1b (solid line), the intensified EB originating from western Europe undergoes an eastward shift (Fig. 5b). The blocking pattern (from day 33 to 48; Fig. 10b) resembles the composite field of blocking events for the SJN events (from lag −2 to lag +2 days; Fig. 2b), although there are significant differences in the blocking pattern and time scale between reanalysis and theoretical results.

Fig. 10.
Fig. 10.

The nondimensional barotropic streamfunction of the planetary-scale flow ψP of an NAO+ event from the extended NMI model for (a) weak (Δu = 0) and (b) strong (Δu = 0.1) jets. The contour interval (CI) is 0.15. The North Atlantic is roughly defined as a region from x = −4.74 to x = 1, and the European continent ranges from x = 1 to x = 5.74; the regions marked by A and E, respectively.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for the planetary-scale anomaly field ψNAO (CI = 0.2).

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

For the weak jet (Δu = 0) case, however, the intensified EB pattern moves westward so that the intensified low-pressure trough downstream of the EB ridge is also shifted westward (from day 21 to 48; Fig. 10a). As revealed in Fig. 5a (for lag −2 days), the EB anticyclone originates over the eastern side of the European continent for WJN events, and the weak mean zonal wind in Fig. 1 (dashed line) favors the westward displacement of the intensifying EB dipole. For this case, the ideal blocking structure in Fig. 10a is similar to the composite pattern of the blocking event for the WJN events (from lag −2 to +2 days; Fig. 2a). The large difference between reanalysis and theoretical results may be due to the exclusion of other parameters, such as baroclinicity, in our NMI model. For Δu = 0.2, the EB becomes more intense, and the suppression of its westward shift is more apparent so that the EB dipole undergoes a clear eastward shift (not shown). This may explain why the intensified EB dipole exhibits an eastward (westward) displacement for a strong (weak) Atlantic jet, as observed in Fig. 5. The sensitivity of the results to the different values of ac was also addressed. It was found that the result is not sensitive to the choice of ac (not shown).

b. Southward intrusion of cold air under different jet strengths

Figure 12 shows the total streamfunction field (ΨT = ψP + ψ′) of an NAO+ event for the same parameters as in Fig. 10. Figure 12 shows that an EB circulation occurs after the long time evolution from day 21 to 48 (from day 27 to 51) of an NAO+ flow for a weak (strong) North Atlantic jet. The deepening of the cyclones associated with the intrusion of cold air with low pressure from high latitudes is more evident in the strong jet case than in the weak jet case. This model result further confirms that, under an SJN condition, the cold air from high latitudes can intrude more easily into southeastern Europe and even the Middle East. This result occurs only for the EB dipole without tilting.

Fig. 12.
Fig. 12.

Fields of ΨT (CI = 0.3) of an NAO+ event obtained from the extended NMI model for the (a) weak and (b) strong jet cases. The label H (L) denotes the ridge or anticyclone (trough or cyclone). The definitions of North Atlantic and European continent are as in Fig. 10.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

c. Anomaly relationship between the EB and NAO+

Figure 11 shows the streamfunction of the planetary-scale NAO anomaly ψNAO, as defined in Eq. (A4c) of the appendix, of an NAO+ event. It is seen that, for a weak (strong) jet, the NAO+ anomaly exhibits two peaks at days 9 and 27 (9 and 30). The EB anomaly during its mature phase is stronger in the strong jet case than in the weak jet case. This is related to the greater energy dispersion associated with the NAO+ anomaly under the strong jet condition. For a weak jet, the blocking anomaly has its largest amplitude at day 33, about 6 days after the NAO+ anomaly reaches its second peak (Fig. 11a). In contrast, for the strong jet, the largest amplitude of the blocking anomaly is at day 40, 10 days after the second peak of the NAO+ (Fig. 11b). This implies that the EB needs a longer time to reach its largest amplitude in the strong jet case than in the weak jet case. This is qualitatively consistent with the composite result shown in Fig. 5.

To describe the location and movement of the EB dipole, we define the zonal position x of the anticyclonic center of the EB dipole anomaly ψNAO as the blocking location and its time variation (cp = ∂x/∂t) as the phase speed of the EB. The time evolution of the zonal position and phase speed of the EB are shown in Fig. 13 after day 20 because the EB occurs after day 20. It is seen that the EB dipole is located farther westward for weaker than for stronger mean zonal winds (Fig. 13a). As can be seen in Fig. 12, the time period when a relatively strong EB occurs is from day 21 to 45 (from day 33 to 45) for weaker (stronger) mean zonal winds. It is shown from Fig. 13b that, during the strong EB period, the time-mean phase speed is more negative for the weaker than for the stronger mean zonal winds. Thus, the blocking anomaly moves westward during the period from day 21 to 48 under the weak jet condition (Fig. 11a). However, such a westward shift is suppressed under the strong jet condition (Fig. 11b).

Fig. 13.
Fig. 13.

Time variation of (a) the zonal position, denoted by x, and (b) the phase speed (10 m s−1) of the EB obtained from the extended NMI model for weaker (dashed) and stronger (solid) mean zonal winds.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

The EB drifts eastward because of the enhanced westerly wind in the middle-to-high latitude region once the feedback of the NAO+ anomaly on the mean zonal wind is involved (Luo et al. 2007b). This feedback is not present in our NMI model because the NAO-induced mean zonal wind variation is regarded as a second-order small term. But this problem can be crudely solved by increasing the positive value of Δu. Below, we will construct a schematic diagram to explain why the NAO+ and EB dipole anomalies exhibit NE–SW (NW–SE) tilt for a strong (weak) jet state in terms of different zonal wind anomalies in different latitudes and longitudes.

d. Why do the NAO+ and blocking dipole anomalies exhibit NE–SW or NW–SE tilting?

As revealed above, the results from our NMI model cannot explain the meridional tilting of the EB dipole, because the NAO and EB dipole anomalies are assumed to be antisymmetric in the meridional direction. However, this issue can be solved by assuming that the NAO+ and EB dipole anomalies are located in different latitudinal and zonal regions. The spatial tilting of the dipole anomaly can be explained in terms of its existing position where the anomaly center moves faster (slower) in the positive (negative) zonal wind anomaly region. Thus, it is helpful to examine whether the zonal wind anomaly obtained from the NMI model exhibits a spatial distribution consistent with observed anomaly zonal wind structure before a theoretical explanation about the horizontal tilting of the NAO+ and EB dipole anomalies is presented.

Here we show the time-dependent zonal wind anomaly of an NAO+ event in Fig. 14 for weak and strong jet flows. It is found that the zonal wind anomaly over the North Atlantic basin (region A for day 0 in Fig. 14a) has a negative–positive–negative structure: a positive anomaly near the channel center and negative anomalies on its two sides. But the opposite zonal wind anomaly pattern is seen over the European continent (region E for day 0 in Fig. 14a). This zonal wind anomaly pattern can cause meridional tilting of the NAO+ and EB dipole patterns when the NAO+ and EB dipoles are located in a different latitudinal band of the channel model. The zonal wind anomaly has a similar pattern for both the weak and strong jet background states, while its strength is greater for the strong jet case (Figs. 14a,b). Here, the 50 (−50) gpm contour line is defined as the boundary of the NAO positive (negative) anomaly center (Fig. 5). As shown in Fig. 5a for lag 0, for WJN events, the NAO+ dipole is located in a lower-latitude band than the EB dipole, and the NAO+ dipole is located at higher latitudes for the SJN events (for lag 0; Fig. 5b). Because the NAO+ (EB) dipole corresponds to a positive-over-negative zonal wind anomaly at lower (higher) latitudes of the North Atlantic (European continent) for the WJN events (from lag −1 to lag +1 days in Fig. 7a and from day 27 to 39 in Fig. 14a), this forms the NW–SE tilting in the NAO+ and EB dipole patterns. In contrast, the NE–SW tilting of the NAO+ and EB dipole patterns is formed for the SJN events as the NAO+ (EB) dipole corresponds to a negative-over-positive zonal wind anomaly at higher (lower) latitudes of the North Atlantic (European continent) (Figs. 7b and 14b). Based on our theoretical result, we present a schematic diagram of the spatial tilting of the NAO+ and EB dipoles under the impact of the spatial distribution of zonal wind anomalies in the Euro-Atlantic region by placing the NAO+ and EB dipoles in different latitudes for the WJN and SJN events (Fig. 15, right-hand side). For a strong Atlantic jet or SJN event, the zonal westerly wind is strong (for day 36; Fig. 14b) over northern Europe, which inhibits the development of the EB dipole over higher latitudes (for lag 0; Fig. 5b). In this case, the EB occurs at lower latitudes, in contrast to the weak Atlantic jet case, which allows the EB to occur in higher latitudes. As a result, the EB dipole associated with the SJN event tends to distribute along the NW–SE direction (Fig. 15b, right-hand side) because the positive (negative) height anomaly of the EB dipole is mainly located in the negative (positive) zonal wind anomaly region, thus showing NE–SW tilting. The NAO+ dipole shows a similar spatial tilting, as its negative (positive) height anomaly region corresponds to the negative (positive) zonal wind anomaly. The opposite spatial tilting is seen for a weak Atlantic jet case (Fig. 15a, right-hand side).

Fig. 14.
Fig. 14.

Evolution of time-dependent geostrophic zonal wind anomalies (CI = 0.2 × 10 m s−1) corresponding to the NAO+ event shown in Fig. 10 under (a) weak and (b) strong jet background states. The definitions of North Atlantic and European continent are as in Fig. 10.

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

Fig. 15.
Fig. 15.

Schematic diagram of NW–SE and NE–SW tilting of (left) the NAO+ and (right) EB dipole anomalies under (a) weak and (b) strong jet background conditions. The resulting dipole pattern influenced by the zonal wind distribution is on the right, and the case without the influence of the zonal wind distribution is on the left. The plus (minus) sign denotes the positive (negative) height anomaly. The red solid (dashed) line represents the meridional distribution of the zonal wind over the North Atlantic basin (European continent).

Citation: Journal of Climate 29, 5; 10.1175/JCLI-D-15-0350.1

6. Conclusions and discussion

In this paper, we have examined the factors that affect the meridional tilting of the EB dipole pattern associated with NAO+ events in order to reveal the physical process that led to the Middle East snowstorm events during 1950–2013. The NAO+ events were first classified into strong jet (SJN) and weak jet (WJN) NAO+ events in terms of the mean zonal wind strength prior to the NAO onset. It was found that, for the SJN (WJN) events, the NAO+ and EB dipole patterns exhibit NE–SW (NW–SE) tilting, with the actual orientation of the dipole centers along the NW–SE (NE–SW) direction. This implies that the tilting direction of the NAO+ and EB dipoles is closely linked to the strength of the North Atlantic jet. Moreover, it is shown that the EB dipole arises from the eastward (westward) displacement of the intensifying blocking anticyclone originating from the western (eastern) side of the European continent for the SJN (WJN) events (Figs. 5a,b). The EB dipole is located farther westward and southward during the SJN events than during the WJN events because of the suppressing (favorable) influence of the strong (weak) westerly wind over north (central) Europe. Although the Atlantic jet is stronger, the EB dipole is located more westward for the SJN events than for the WJN events. The NE–SW (NW–SE) tilting of the EB dipole can be explained in terms of the latitudinal region of its positive and negative height anomalies. As illustrated in Fig. 15, the NE–SW (NW–SE) tilting of the EB dipole is associated with the different steering winds: the positive (negative) height anomaly of the EB dipole coincides with the negative (positive) zonal wind anomaly region shown in Fig. 7. The NE–SW-tilted EB dipole is related to a strong North Atlantic jet and favors large-scale southward cold advection, thus providing the large-scale conditions favorable for the widespread decline of surface temperature over the Middle East and southeastern Europe, as seen during December 2013.

Moreover, an idealized nonlinear multiscale interaction (NMI) model was modified to include a jetlike basic flow for examining the physical mechanism behind the movement and meridional tilting of the EB dipole. The model results show that, when the North Atlantic jet is strong, the EB dipole tends to be more intense and drift eastward. The southward intrusion of cold air caused by cyclones on the downstream side of the blocking region is also strong. At the same time, the zonal wind over high-latitude (midlatitude) Europe becomes stronger (weaker) (from day 36 to 45; Fig. 11b), which inhibits the development of the EB dipole at high latitudes. As a result, EB events occur over lower-latitude Europe when the North Atlantic jet is strong (Fig. 5b). The spatial tilting of the dipole height anomaly can be explained in terms of the different zonal speeds that steer its anticyclonic and cyclonic centers at different latitudes. If an anticyclonic center is located over a region with positive zonal wind anomalies, the steering zonal speed would be faster than that in the region with negative zonal wind anomalies. For this reason, the dipole anomaly inevitably exhibits spatial tilting during the dipole life cycle, because the difference of the movement speed between higher and lower latitudes is large. While the theory of Hoskins and Karoly (1981) is suitable for explaining the formation of stationary wave trains through energy dispersion, it is unable to describe the zonal movement of the NAO+ or EB dipole. Although the NAO+ or EB dipole is a strongly nonlinear phenomenon, its phase speed depending upon the mean zonal wind and the amplitude itself can be obtained under a weakly nonlinear framework (Luo et al. 2011). For fixed amplitude, the zonal movement speed of the NAO+ or EB dipole is determined by the zonal wind strength. Thus, it is inevitable that the different strength of zonal wind in higher and lower latitudes leads to the different movement speed of the NAO dipole in the meridional direction, thus leading to the spatial tilting of the NAO dipole (Luo et al. 2010a,b). Thus, this result can simply be explained by directly calculating the meridional distribution of zonal wind where the dipole anomaly is located, rather than using the linear energy dispersion theory of Hoskins and Karoly (1981).

As can be seen in Fig. 5b, the NAO+ dipole is located at relatively higher latitudes of the North Atlantic basin. Both the NAO+ and EB dipoles exhibit NE–SW tilting (Fig. 15b), because the cyclonic (anticyclonic) center of the NAO+ dipole as well as the positive (negative) anomaly of the EB dipole are located over the negative (positive) zonal wind anomaly region. The NE–SW tilting of the EB dipole results in an arcing wave train from North America to Europe across the North Atlantic basin, although the anticyclonic anomaly over North America is split into two centers: one over North America and another over the North Atlantic basin with the intensified EB dipole. For a weak North Atlantic jet, the NW–SE tilting of the NAO+ and EB dipoles as shown in Fig. 5a has a similar interpretation (Fig. 15a) according to the meridional distribution of the zonal wind anomaly in different latitudes. Thus, the strength of the North Atlantic jet can modulate the zonal wind and thus the tilting direction of the EB, leading to different effects over the Middle East.

The extended NMI model also shows that the EB events lag the NAO+ events, which is qualitatively consistent with the reanalysis results. However, the lag time is much longer than that seen in the reanalysis. This may be because several factors that affect the lifetime of NAO+ and EB events were excluded in our idealized NMI model. For example, atmospheric baroclinicity and stratification were neglected. These issues deserve further investigation.

Acknowledgments

The first two authors acknowledge the support from the National Science Foundation of China (Grants 41505075, 41430533, and 41375067). Dai acknowledges the funding support from the U.S. National Science Foundation (Grant AGS- 1353740), the U.S. Department of Energy’s Office of Science (Award DE-SC0012602), and the U.S. National Oceanic and Atmospheric Administration (Award NA15OAR4310086). Feldstein would like to offer his gratitude for support through National Science Foundation Grant AGS-1401220. The authors thank three anonymous reviewers for valuable comments that improved this paper.

APPENDIX

The Description of an Extended Nonlinear Multiscale Interaction Model and the Derivation of Its Solution

a. Model description

The nondimensional equivalent barotropic model in a β-plane channel with a width of Ly can be expressed as follows (Luo 2005):
ea1
where ΨT is the nondimensional barotropic total streamfunction (and is sometimes considered as a vertical average between 300 and 850 hPa for reanalysis data), Ff is a large-scale vorticity forcing, such as topography and diabatic heating, and is balanced by the climatological stationary state flow , ∇2ψS is a synoptic-scale wave maker that maintains synoptic-scale or high-frequency (~1000 km) eddies prior to NAO events. The square of the ratio of the characteristic length L with respect to the radius of Rossby deformation Rd is defined by F = (L/Rd)2; β = β0L2/U is the nondimensional meridional gradient of the Coriolis parameter; U is the characteristic horizontal velocity; J is the Jacobian operator; and the other notations are often used in meteorology (Luo 2005).
Here, we assume that ΨT of the atmospheric flow comprises three parts of (where ): the stationary mean flow for X = εx, a large-scale (~10 000 km) dipole anomaly ψ(x, y, t), and a synoptic-scale eddy anomaly ψ′(x, y, t). Moreover, the mean flow is assumed to exist before an initial weak NAO dipole anomaly is amplified, where ψC(X, y) is the climatological stationary streamfunction anomaly and represents a jetlike basic flow in Eq. (A1). As a result, Eq. (A1) yields
ea2
where has been used in the derivation of Eq. (A2) and satisfies the boundary conditions and .
In this paper, we assume that ψ(x, y, t) has a zonal scale of wavenumber 2 (~10 000 km) and the synoptic-scale eddies have a comparable scale to the Rossby deformation radius Rd (~1000 km). This allows us to make an assumption that there is a zonal-scale separation between the planetary-scale NAO anomaly with zonal wavenumber k and synoptic-scale eddies with zonal wavenumbers of (j = 1, 2, …). Under the scale separation assumption that the zonal wavenumbers of synoptic-scale eddies are much larger than that of the NAO anomaly (), as in Luo (2005), we may split J(ψ′, ∇2ψ′) = ∇ ⋅ (vq′) [where v′ = (−∂ψ′/∂y, ∂ψ′/∂x) and q′ = ∇2ψ′] into two parts, ∇ ⋅ (vq′)P and ∇ ⋅ (vq′)S, and assume J(ψ′, ∇2ψ + h)P ≈ 0 and J(ψ, ∇2ψ′)P ≈ 0. In this case, one obtains J(ψ′, ∇2ψ + h)SJ(ψ′, ∇2ψ + h) and J(ψ, ∇2ψ′)SJ(ψ, ∇2ψ′). Note that the subscript P denotes a large-scale component close to the zonal wavenumber of the NAO mode, while S represents the synoptic-scale component. Then, from Eq. (A2), the following equations of the interaction between planetary and synoptic scales can be obtained as
ea3a
ea3b
where the rigid lateral and periodic zonal conditions used for Eqs. (A3) are the same as in Luo (2005). Note that −J(ψ′, ∇2ψ′)P = −∇ ⋅ (vq′)P has been used in Eq. (A3a), and ∇ ⋅ (vq′)S is neglected in Eq. (A3b) because its zonal scale is much smaller than that of ψ′. It should be pointed out that Eqs. (A3) are the extended equations of the interaction between planetary and synoptic scales derived by Luo (2005) and Luo et al. (2007a,b). This extended version can describe the evolution of the eddy-driven NAO event [Eq. (A3a)] and its feedback on synoptic-scale eddies [Eq. (A3b)] in a basic flow.

Here, we consider a weak jetlike basic flow so that ψC(X, y) = ψWC(X) sin(my) and ψWC(X) = εac0 exp[−θ(X + εxc)2] can be assumed in the North Atlantic basin, where 0 < ε ≪ 1, θ > 0, and xc is the zonal position of the maximum wind. To specify that the basic flow u0 − ∂ψC/∂y is a jet, ac0 < 0 (ac0 > 0) is required for m < 0 (m > 0). Note that ac0 denotes the strength of the peak jet speed, while u0 represents the strength of its uniform part. For a fixed value of ac0, the large value of u0 represents a strong jetlike westerly wind. It should be pointed out that the prescribed basic state ψC(X, y) satisfies both and , where the bracket denotes a zonal average.

In Eqs. (A3), we assume u0 = uC + Δu and |Δu| ≪ uC, where uC = β/(k2 + m2) is the critical mean westerly wind for the dipole mode to be stationary. Similar to Luo et al. (2007b) and Luo and Cha (2012), we further assume that the preexisting synoptic-scale eddies comprise two synoptic-scale Rossby waves, both having a monopole meridional structure and zonal wavenumbers (j = 1, 2). For the detailed mathematical form of the preexisting synoptic-scale eddies, readers may refer to Luo (2005) and Luo et al. (2007a,b). In this case, one can show that the eddy vorticity forcing (EVF) −∇ ⋅ (vq′)P has both a dipole meridional structure and a zonal wavenumber of . When −∇ ⋅ (vq′)P matches the NAO anomaly or , the EVF reinforces and amplifies the NAO anomaly. Below, we will present the analytical solution of Eqs. (A3) using the same method as in Luo et al. (2007a,b) and Luo and Cha (2012).

b. Model solution

Using the multiscale perturbation expansion method (Luo et al. 2007a,b; Luo and Cha 2012), the analytical solution of the nondimensional atmospheric streamfunction ΨT of an eddy-driven NAO event with both zonal wavenumber 2 and dipole meridional structure, together with a wavenumber-2 topography, can be obtained as
ea4a
ea4b
ea4c
ea4d
ea4e
ea4f
ea4g
ea4h
ea4i
ea4j
ea4k
ea4l
ea4m
where hA = −[β/uC − (k2 + m2/4)]−1, , |B|2 = BB*, α1 = 1, α2 = α, α = ±1, u0 = uC + Δu, uC = β/(k2 + m2), |Δu| ≪ uC, hα = −[β/uC − (k2 + 9m2/4)]−1, hβ = −[β/uC − (k2 + m2/4)]−1, , and , and where Δu denotes the strength of the uniform westerly wind, ac = εac0 is the strength of the jet pulse, cc denotes the conjugate of its preceding term, and other coefficients can be found in Luo et al. (2007b) and Luo and Cha (2012).

In the solution of Eqs. (A4), ψNAO represents the NAO dipole anomaly, and ψCNAO is a jet-induced term due to the interaction between the NAO anomaly and the jetlike flow. Correspondingly, ψH is the wavenumber-2 topography-induced standing wave that is designed to model the climatological stationary wave anomaly observed in the Euro-Atlantic sector during the winter (Luo et al. 2007b, their Fig. 3), where ψCH is the interaction term between the jetlike flow and the topography. As was described in Luo et al. (2007b) and Luo and Cha (2012), ψm denotes the variation of the mean flow due to the evolution of the NAO anomaly and its interaction with the topographic wave ψH. Moreover, () denotes the preexisting (deformed) eddies during the NAO life cycle, while represents the interaction term between the preexisting synoptic eddies and jetlike flow.

It is interesting to see that, in the absence of a jetlike flow, the solution of Eqs. (A4) is reduced to that obtained by Luo et al. (2007b) and Luo and Cha (2012) because of the vanishing of ψCNAO, ψCH, and . Thus, the solution of Eqs. (A4) may be considered as an extension of the analytical solution of the NAO event derived by Luo and Cha (2012). Moreover, we notice that the solution of Eqs. (A4) contains the amplitude B of the NAO anomaly. Thus, all the solutions of the time-dependent mean flow, planetary-scale, and synoptic-scale components of an NAO event in Eqs. (A4) are known if the solution of B is obtained for a given initial condition and all the parameters.

The nonlinear evolution equation of the eddy-driven NAO anomaly amplitude B can be obtained as
ea5
where , , , and the other coefficients can be found in Luo and Cha (2012).

It is seen from Eq. (A5) that, when the jetlike basic flow vanishes, it is identical to that obtained by Luo et al. (2007b) and Luo and Cha (2012). Thus, Eq. (A5) is an extension of the previous forced nonlinear Schrödinger equation derived by Luo and Cha (2012). The time variation of B reflects the time evolution of the NAO+ and EB patterns. A finite-difference scheme similar to that used in Luo (2005) is used to solve Eq. (A5) numerically and obtain its numerical solution when both the initial amplitude of the NAO+ event and the model parameters are prescribed. The model results on the impact of the North Atlantic jet on the EB associated with the NAO+ event are described in section 5.

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1

As explained in L15, the EB dipole is defined to exhibit NE–SW (NW–SE) tilting if its positive and negative anomalies are located in the northwest and southeast (northeast and southwest) sides of the blocking region, respectively.

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