Can the effects of changes in the stratospheric polar vortex on troposphere blockages over the Atlantic Ocean region be predicted? Why do tropical and humid high-pressure vortices always form from the Atlantic Ocean regions? What is the role of atmospheric rivers in high-pressure hurricanes and dangerous wind gusts in Florida, USA?

Impacts of stratospheric polar vortex changes on tropospheric blockings over the Atlantic region

In recent years, extreme weather events associated with atmospheric blocking in the northern extratropics have become more frequent. This study has revealed the impacts of the stratospheric polar vortex on the blockings over the North Atlantic sector, using both reanalysis data and large-ensemble experiments performed by general circulation model. It is found that a weak stratospheric polar vortex (WPV) can cause more blockings to be generated over Greenland and move more westward than normal, while a strong stratospheric polar vortex (SPV) can cause more blockings to be generated over the south of Greenland and Western Europe. The stratospheric polar vortex could influence blocking anomalies by modulating both synoptic-scale eddy and planetary wave activities. Under WPV conditions, the generation of synoptic-scale eddies is suppressed due to decreased upper-troposphere background baroclinicity, which is favorable for positive geopotential height anomalies and more blockings over Greenland. Additionally, WPV can suppress the planetary wave train that is accompanied with lower pressure center over Greenland, further contributing to the positive geopotential height anomalies and more blockings over Greenland. The abovementioned processes under SPV conditions are nearly opposite to those under WPV conditions.

1 Introduction

Blocking is recognized to be a persistent and quasi-stationary system in the middle to upper troposphere and its notable impacts have been observed for decades. Blockings can redirect air mass below and amplify meridional heat and moist exchanges, resulting in frequent extreme weather events such as heavy rainfall, droughts, and cold spells during winter (e.g., Sillmann et al. 2009; Matthias et al. 2020; Chen et al. 2021). In the Atlantic–European region, blocking events are typically associated with cold and dry spells over central to Eastern Europe, and anomalous warming over Greenland and Iceland (Buehler et al. 2011). The presence of Greenland blocking can significantly influence weather upstream and downstream. For example, strong cooling may occur over North America when the Greenland blocking moves westward, while strong cooling can appear over North Europe and eastern Asia when quasi-stationary Greenland blocking develops (Chen et al. 2017). The persistent Ural Blockings have been linked to more frequent cold events over mid-latitude Eurasia (Luo et al. 2016; He et al. 2017; Yao et al. 2022). Furthermore, blockings may also influence Arctic climate and weather. Ionita et al. (2016) reported that increased Greenland blockings since the 1960s have resulted in the accumulation of sea ice in the Arctic and weakened the Atlantic Meridional Overturning Circulation. An increase in blocking frequency over the Barents Sea sector during winter could also lead to warming over the Arctic region and amplify the sea ice reductions (Gong et al. 2017; Yao et al. 2018; Tyrlis et al. 2019; You et al. 2022), ultimately contributing to the warm Arctic and cold Eurasia pattern (Kim et al. 2022). Therefore, it is crucial to understand the underlying mechanism responsible for the formation and evolution of blockings.

It has been suggested that the formation and maintenance of atmospheric blockings are dynamically connected with the amplification of planetary waves and transient eddy activities (Lejenas 1992; Lupo 1997; Edouard 1997). Both internal atmospheric variability and external forcing can influence blockings by modulating planetary waves or baroclinic wave activities. For instance, positive sea surface temperature anomalies over Indonesia can increase the frequency of Pacific blockings during winter through the Pacific–North-American (PNA)-like wave trains (Huang et al. 2002). Additionally, during the cold phase of El Niño

Southern Oscillation (ENSO) events, the frequency of winter blockings in the North Pacific region may increase due to anomalous quasi-stationary waves (Hinton et al. 2009; Henderson et al. 2016). Over the Euro-Atlantic sector, the strong baroclinicity of atmospheric background state and the convergence of synoptic-scale baroclinic eddies are found to play a crucial role in blocking formation (Hoskins et al. 1983; Michelangeli et al. 1998; Barriopedro et al. 2022; Zhang et al. 2022). Cassou (2008) suggested that the Madden–Julian Oscillation could trigger a low-frequency wave train and lead to the positive phase of North Atlantic Oscillation (NAO), favorable for European blockings. The Gulf Stream SST front can also increase the frequency of European blockings by enhancing meridional eddy heat transport in the lower troposphere (O'Reilly et al. 2016). In addition, Kwon et al. (2020) found that following the warm phase of the Atlantic multi-decadal variability, the weakened meridional gradient of air temperature could result in an enhanced blocking over Greenland.

In addition to tropospheric processes, several studies have shown that the blocking is closely associated with stratospheric variability, particular during winter, when the stratosphere-troposphere two-way coupling is strongest (Hu et al. 2002; Baldwin 2007; Huang et al. 2017; He et al. 2021; Hu et al. 2021; Liu et al. 2021). Blocking has been demonstrated to be an important precursor of the sudden stratospheric warming (SSW) during winter (Martius et al. 2009; Woollings et al. 2010; Barriopedro et al. 2014). Castanheira et al. (2010) found that Euro-Atlantic blockings accompanied by enhanced planetary wave amplitude could result in displacement-type SSW events, whereas Pacific blockings could induce splitting-type SSW events. Peings et al. (2019) found that Ural blockings in November can drive polar stratospheric warming through upward propagation of planetary waves. In addition, some studies have reported on the occurrence of blocking anomalies under different states of stratospheric polar vortex. For instance, Davini et al. (2014) and Huang et al. (2017) found that blocking frequency is significantly different during weak (WPV) and strong (SPV) stratospheric polar vortex events. Chen et al. (2021) suggested that a WPV may enhance the westward movement of the pre-existed Ural blocking, which is unfavorable for its local maintenance. During the onset of SSW cases, anomalously stratospheric planetary wave reflection promotes the formation of Pacific blocking (Kodera et al. 2013). Therefore, blocking activities can exert a forcing on the stratospheric polar vortex, while the stratospheric polar vortex is not a passive receiver. Instead, it may also change the evolution of pre-existed blockings or influence the formation of new ones. Nevertheless, most of the studies mentioned above confirmed the correlation between blockings and stratospheric polar vortex. The direct impacts of stratospheric polar vortex changes on the formation and maintenance of blockings, as well as the underlying dynamic mechanisms, remain unclear. The present study aims to address these issues, focusing particularly on the blockings over the Atlantic-European region and the role of both planetary waves and transient eddies. The paper is organized as follows. Section 2introduces the data, method and numerical model used in our study. Section 3presents different features of blocking under WPV and SPV stratospheric polar vortex conditions based on reanalysis data and climate model simulations. In Sect. 4, the mechanisms responsible for the blocking anomalies are investigated. Finally, the results are summarized and discussed in Sect. 5.

2 D ata, methods and model simulations

2.1 Data

In this study, global 1° × 1° daily mean data during winters (December, January and February) from 1979 to 2019 are used. These data are obtained from the ERA5 data at 3-h intervals from the European Centre for Medium-Range Weather Forecasts (ECMWF; Bell et al. 2021). The dataset includes horizontal winds, temperature and geopotential height on 37 pressure levels extending from 1000 to 1 hPa.

2.2 Methods

To identify SPV and WPV events based on the ERA5 reanalysis data, a strength index of the stratospheric polar vortex is defined as area-weighted westerlies in latitudes from 55° N to 65° N at 100 hPa. Our results are not sensitive to the field (e. g., zonal wind, geopotential height and temperature) and averaged latitude of polar region used in the definition of the strength index. The day 0 of an SPV (WPV) event is identified when the strength index reaches its maximum (minimum) value and is greater than 0.5 (less than − 0.5) times the standard deviation of the daily strength index during winter. To ensure the independence of each event, the time span between day 0 of two adjacent events should exceed more than 20 days. Finally, 48 SPV events and 37 WPV events are identified, and the dates of these events are listed in Table 1.

Various objective methods have been developed to detect atmospheric blockings, with the Dole-Gordon (DG) type index (Dole et al. 1983) and the Tibaldi-Molteni (TM) type index (Tibaldi et al. 1990) being the most widely used and modified for better practicability. To identify a blocking event, both methods require a minimum spatial extension and a temporal duration criterion. The DG-type method identifies a blocking when 500-hPa geopotential height anomalies exceed a given threshold, while the TM-type method identifies a blocking when the meridional geopotential height difference in two reference latitudes exceeds a given value. In this study, we use the two-dimensional blocking index based on the TM-type method developed by Davini (2014). Blocking frequency on each grid point is further calculated as the blocking days divided by the total days during a period. In addition, to detect the trajectory of each blocking entity, a hybrid blocking index is also employed, which takes advantage of the DG-type and TM-type method. Following Dunn-Sigouin et al. (2013), this index is calculated as 500-hPa geopotential height anomalies z′ , which is defined as the daily deviation from its seasonal mean divided by the sine of the latitude. Same as the DG-type method, this index applies amplitude threshold (1 standard deviation for all grid point north of 30°N during winter), spatial scale (2.5 × 1 06 km), tracking over time (50% overlap in blocking areas within 2 days) and duration (at least 5 consecutive days). Meanwhile, the reversal of meridional gradient is also required for these events, following the TM-type method. The center of the identified blocking is calculated as the mean latitude and longitude weighted by area and geopotential height anomaly ( z′ ), which is used to obtain the trajectory of the blocking.

To investigate the potential impact of stratospheric polar vortex changes on baroclinic instability and therefore the synoptic eddy activity, daily Eady growth rate is calculated as described by Simmonds et al. (2009):

N where g, f, u and N denote the gravity acceleration, Coriolis parameter, westerlies, buoyancy frequency, respectively.

To diagnose local synoptic eddy activities and their influence on the low-frequency westerlies, the daily extended Eliassen-Palm (EP) flux (Hoskins et al. 1983) is calculated as:

E=[21(v2 −u2),−uv] (2) where uand v denote the zonal and meridional components of wind, respectively. The prime represents the synopticscale component (period of 2–10 days) using Lanczos filter and the overbar denotes the time mean. The divergence of EP flux indicates that the synoptic-scale eddies could accelerate the low-frequency westerly and induce anticyclonic (cyclonic) anomaly to its south (north) (Chen et al. 2018; Liu and He 2020).

In the upper troposphere, the direct effect of synoptic eddies on the geopotential height tendency is mainly determined by the convergence or divergence of eddy vorticity flux (Lau et al. 1984; Lau 1988), which can be diagnosed based on:

𝜕h 𝜕t (3) where 𝜁′corresponds to synoptic-scale eddy vorticity, and V′ is the synoptic-scale horizontal winds.

To study the potential impact of stratospheric polar vortex on the propagation of planetary wave, refractive index squared n2 is calculated based on the background state (Andrews et al. 1987):

📷n2(y,z) = 📷f2 cosN22𝜙)[qu𝜙 −(ak)2 −(f📷2cosNH𝜙)2] (4)

where a, H , k, q𝜙 and urepresent the radius of earth, scale height, zonal wave number, daily meridional gradient of zonal mean quasi-geostrophic potential vorticity (PV) and zonal mean zonal wind, respectively. Waves tend to propagate toward the region with larger value of n2 and be refracted away from the region with negative value of n2 (Holton et al. 1976; Hoskins and Ambrizzi 1993). Therefore, we use the frequency of the negative refractive index squared (Li et al. 2007; Zhang et al. 2019) to diagnose the environment of wave propagation.

Furthermore, daily zonal and vertical component of planetary wave flux are calculated as described by Plumb (1985):

(5) where pdenotes the pressure divided by 1000 hPa, denotes rotation speed and 𝜓′ denotes the zonal deviation of lowpass filtered (period of 10 days and longer) stream function.

2.3 Model simulations

The Whole Atmosphere Community Climate Model

(WACCM) is utilized to validate the direct influences of the stratospheric polar vortex on blockings. This model adopts the finite-element dynamic core with a horizontal resolution of 1.9° × 2.5° and a pressure-terrain hybrid vertical coordinate with 66 levels from the surface to approximately 140 km so that the stratosphere-troposphere coupling can be well described.

A 70-yr control experiment and two 70-member ensemble sensitive experiments are conducted with the same annual cycle of external forcings in 2000 (e.g., sea ice concentration, sea surface temperature, stratospheric ozone and other chemistry species, greenhouse gas, aerosols, solar radiation). The control experiment is in free-run mode, and its 70 instantaneous outputs on each November 1 are used as the initial conditions to initialize the two sensitive experiments (R1 and R2). In the first 25 days of sensitive experiments, artificial and zonally symmetric heating (cooling) is imposed in the stratospheric polar region in the R1 (R2) run (White et al. 2020):

where 𝜑 and p denote the latitude and pressure, respectively. Q is 2 K/day in the R1 run, corresponding to WPV forcing, and is − 2 K/day in the R2 run, corresponding to SPV forcing. We chose a forcing duration of 25 days because continuous anomalies persist for 20–30 days before day 0 (Fig. 1a and b). As stratospheric variabilities are mainly controlled by the longwave cooling and shortwave heating due to stratospheric ozone change (e.g. Liu et al. 2022; Hu et al. 2022) and the dynamical heating due to the converge of eddy heat flux, thermal forcing could be used to stimulate these processes and separate the direct effect of stratospheric polar vortex on the troposphere from climate variability.

After the 25-day artificial forcing and 5-day spin-up period, the tropospheric blocking responses in the following month (December) are analyzed. Due to the long memory of the stratosphere, the WPV (SPV) persists in December for the R1 (R2) run (Fig. 1e and f). Therefore, we derived all diagnostic fields based on the output during December in the R1 (R2) run and compared them with those during WPV (SPV) events based on ERA5 reanalysis data. The blockings are also detected during December in the R1 (R2) run. In addition, we conducted experiments (R3 and R4) in which the duration of thermal forcing is shortened to 5 days and Q equals to 5 K/day and −5 K/ day for WPV and SPV experiments, respectively, in order to simulate the rapid amplification of westerly anomalies since day −5 derived from reanalysis data (Fig. 1a and b). We further performed two additional experiments (R5 and R6) in which stratospheric thermal forcings are halved (Q = 1 K/day and −1 K/day for WPV and SPV experiments, respectively) for a period of 25 days. R3 -R6 are used to investigate the impacts of stratospheric heating forcings with different duration (T) and magnitude (Q) on the tropospheric blockings. For more details on the simulation configurations, please refer to Table 2. Fig. 1 Time-pressure cross sections of anomalies of zonal mean westerlies (shading; units: m/s) averaged over 55°–65° N around a WPV and b SPV events derived from ERA5 reanalysis data. Pressure-latitude cross sections of anomalies of zonal mean westerlies at day 0 of all c WPV events and d SPV events, derived from ERA5 reanalysis data. e and f are the same as c and d but derived from e R1 and f R2 run, respectively. The differences over the dotted regions are statistically significant at the 95% confidence level according to the Student’s t test

Table 2 Description for model experiment configurations

3 B locking anomalies under WPV and SPV conditions

Figure 1a and b illustrate the evolution of anomalies of zonal mean westerlies during WPV and SPV events derived from ERA5 reanalysis data. Since day − 30 of the WPV (SPV) events, there are significant negative (positive) westerly anomalies centered in the upper stratosphere (about 5 hPa) and extending downward. On day 0, the significant westerly anomalies in the lower stratosphere reach peak values and extend down to the surface. After day 0, the negative (positive) westerly anomalies during the WPV (SPV) events in the upper stratosphere are weakened and reverse their sign, which are related to intraseasonal stratospheric vacillation (Holton et al. 1976). While in the lower stratosphere, significantly negative (positive) westerly anomalies can persist until around day 30. Rupp et al. (2021) has demonstrated that the tropospheric response is more sensitive to the changes of westerlies in the lower stratosphere than in the middle and upper stratosphere. Figure 1c and d show the vertical profile of zonal mean westerlies at day 0 of WPV and SPV events, respectively. For WPV (SPV) events, there are negative (positive) westerly anomalies centered in the upper stratosphere at 60°–75°N latitude band. Around day − 5, the westerly anomalies at 100 hPa in this latitudes band increase rapidly (Fig. 1a and b), reaching about − 5 to − 8 (5–8) m/s. In the R1 and R2 run (Fig. 1e and f), the vertical structure of stratospheric westerly anomalies can be well reproduced, with 100-hPa westerly anomalies at 60°–75° N latitude band approximately ranging from − 5 to − 8 (5–8) m/s for R1 (R2) run. Therefore, the amplitude of thermal forcing in the R1 and R2 run is reasonable to reproduce the real stratospheric westerly anomalies around day 0 during WPV and SPV events, respectively. In the R5 and R6 run, the amplitude of thermal forcing is weaker than the R1 and R2 run, and the monthly stratospheric westerly anomalies closely resemble that in day 5 to day 20 during WPV (SPV) events, respectively.

Figure 2 depicts the temporal evolution of blocking frequency in two latitude bands (55°–75° N and 40°–55° N) over Atlantic sector during WPV and SPV events, respectively. In the northern region of 55° N, there are significant positive anomalies of blocking frequency over Greenland (0°–60° W, 55°–75° N) during WPV events, peaking from day − 8 to day 8, coinciding with the time when westerly anomalies in the lower stratosphere are strongest (Fig. 1a). Notably, the second center of anomalies of blocking frequency appears around day − 16 of WPV events. This may be because tropospheric blocking is a crucial precursor of upward propagation of planetary waves and weakened stratospheric polar vortex (Kim et al. 2014), suggesting that it is difficult to clarify the cause-and-effect relationships between changes in stratospheric polar vortex and blocking based on reanalysis data only. In addition, there are significant positive anomalies of blocking frequency over Ural region (0°–90° E, 55°–75° N) centered around day − 16 of WPV events, consistent with the fact that Ural blockings are a significant driver of WPV (Peings et al. 2019). However, negative anomalies of blocking frequency over Ural region appear after day 0 of WPV event. Chen et al. (2021) have demonstrated that the WPV would reduce tropospheric zonal wind, which is unfavorable for the local persistence of Ural blockings. Therefore, the stratospheric polar vortex may have negative feedback on the Ural blocking. For the SPV events, the evolution of blocking frequency shows opposite features in the same latitude band of 55°–75°N (Fig. 2b): There are lasting negative anomalies of blocking frequency over the Greenland region from day − 30 to day 30, and the Ural blocking frequency is anomalously lower before day 0 and anomalously higher afterward. In the latitude band of 40°–55°N, it can be found that the blocking frequency around 0° is anomalously lower (higher) during the WPV (SPV) events from day − 30 to day 30. Therefore, the stratospheric polar vortex may have a significant coupling with the Atlantic blockings. The direct influence of stratospheric polar vortex on tropospheric blockings can be further separated based on the sensitive runs forced by WPV and SPV conditions.

Figure 3 presents the climatological blocking frequency over Atlantic sector and its anomalies under the SPV and WPV conditions. Both the reanalysis data and the control run show a maximum frequency of climatological blocking over Western Europe and Greenland during winter. Compared with the result from reanalysis data, the simulated climatological blocking frequency is relatively lower. Previous studies suggested that numerical models tend to underestimate the frequency of Euro-Atlantic blockings, which may be due to the coarse horizontal resolution (Dunn-Sigouin et al. 2013; Jiang et al. 2019). During the WPV events, the blocking frequency increases significantly over Greenland and eastern Canada but decreases over the western Europe and Ural region (Fig. 3c), consistent with Fig. 2. Conversely, during the SPV events, the blocking frequency anomalies show an opposite pattern (Fig. 3e). The R1 and R2 runs Fig. 2 Time-longitude cross sections of anomalies of blocking frequency (shading; units: %) averaged over 55°–65° N around a WPV and b SPV events derived from ERA5 reanalysis data. c and d is the same as a and b but for the blocking frequency averaged over 40°– 55° N. The differences over the hatched regions are statistically significant at the 95% confidence level according to the Student’s t test

can capture well the anomalous blocking frequency during WPV and SPV events, respectively, which verify the fact that the change in the intensity of the stratospheric polar vortex could influence the blocking over the Euro-Atlantic region. Furthermore, there are similar responses of blockings associated with WPV and SPV conditions in R3 and R4, and in R5 and R6 (Fig. 4). These analyses indicate that our findings are not sensitive to the amplitude and duration of forcing imposed in the stratosphere. For simplicity, in the following text, we only discuss the results derived from runs R1 and R2.

The tracks of each blocking from day − 10 to day 20 of WPV (SPV) events and R1 (R2) runs (Fig. 5) reveal more details regarding the impact of stratospheric polar vortex Fig. 3 Climatology of blocking frequency (shading; unit: %) during winter based on areanalysis data and b the control run. Composite blocking frequency anomalies during day − 10 to day 20 of c WPV and e SPV events derived from ERA5 data. Composite blocking frequency anomalies in the d R1 and f R2 run with respect to the control run, respectively. Stippled regions are for values statistically significant at the 95% confidence level

on blockings. Both reanalysis data and model simulations indicate that under the WPV condition, most blockings over Atlantic sector originate over the ocean basin and Western

Europe, and later lysis mainly occur over the main body of Europe and northeastern North America (Fig. 5a and b). Thereby, we divide the blocking cases into three groups: those blockings generated over Greenland, the south of Greenland and Western Europe. Over Greenland (Fig. 5c and d), there are more blocking entities generated under WPV conditions than that under SPV conditions (Table 3), though the number of SPV events is more than that of WPV events (Table 1). This suggests that the blockings over Greenland are more likely to survive under WPV conditions, consistent with Figs. 3 and 4. Additionally, compared to SPV conditions, blockings under WPV conditions are more likely to migrate westward and be lysed over northeastern North America. Over the south of Greenland, both reanalysis data and sensitive runs show that the blockings generated under SPV conditions are more than twice as many as those generated under WPV conditions (Table 3). Furthermore,

Fig. 4 Composite blocking frequency anomalies in the a R3, b) R4, c R5 and d R6 runs with respect to the control run. Stippled regions are for

values statistically significant at the 95% confidence level

blockings generated there under SPV condition tend to move eastward toward Western Europe (Fig. 5e and f). In contrast, blockings generated under WPV condition tend to be more short-lived and die out over the ocean basin. Over Western Europe, more blocking genesis is detected under SPV conditions than that under WPV conditions, consistent with Figs. 3 and 4. The blockings generated there under SPV conditions tend to move slowly, which may have a potential impact on local extreme weather.

4 M echanisms responsible for the blocking anomalies As the formation of blockings is closely related to the evolution of synoptic-scale eddies and planetary waves, their roles are further studied in the following sectors. Figure 6a and b show the impact of synoptic eddies on geopotential height over Atlantic sector under WPV and SPV conditions, respectively. During WPV events, synoptic eddy activities tend to induce anomalously low-frequency positive (negative) geopotential height to the north (south) of 55° N over the Atlantic sector. In contrast, during SPV events, eddy activities tend to induce opposite geopotential height anomalies (Fig. 6b). Note that the forcings of anomalous eddy activities on geopotential height are strongest for the period from day − 10 to day 10 of WPV (SPV) events, when the anomalous stratospheric westerlies are strongest (Fig. 1). Figure 6c–f show the spatial patterns of anomalous geopotential height tendency due to synoptic eddies in the upper troposphere from day − 10 to day 10 of WPV (SPV) conditions. Both reanalysis data and sensitive runs suggest that under WPV conditions, synoptic eddy activities tend to induce positive geopotential height anomalies over Greenland (Fig. 6c and e), favorable for the formation of Greenland blockings. However, over the south of Greenland and Western Europe, eddy activities under WPV conditions tend to induce negative geopotential height anomalies. As a result, blocking is more likely to be inhibited there. Under SPV conditions, the Fig. 5 Distributions of blocking genesis (solid dots) and lysis (hollow squares) under the WPV (red) and SPV (blue) conditions from a ERA5 reanalysis data and b R1 and R2 runs. Dashed lines denote the regions of Greenland (60°–10° W, 55°–70° N), the south of Greenland (60°–10° W, 40°–55° N) and western Europe (10° W –40° E, 40°–55° N). In c the solid dots, hollow squares and solid lines denote the genesis, lysis and trajectory of each blocking generated over Greenland from day − 10 to day 20 of WPV (red) and SPV (blue) event derived from ERA5 reanalysis data, respectively. d Is the same as c but for the blockings derived from the R1 (red) and R2 (blue) run. e and f are the same as c and d but for the blockings generated over the south of Greenland, respectively. gand h are the same as c and d but for the blockings generated over the western Europe, respectively

low-frequency geopotential height tendency due to anomalous synoptic eddies shows an opposite dipole (Fig. 6d and f), corresponding to a background state favoring of blocking generation over the south of Greenland and Western Europe. Therefore, the anomalous stratospheric state can influence Atlantic blockings through modulating the synoptic eddies activities in the upper troposphere, which are sensitive to the background baroclinicity.

Table 3 Counts of blocking events generated over Greenland, south of Greenland and Western Europe from day − 10 to day 20 of WPV, SPV events and under normal stratospheric polar vortex (NPV) state based on ERA5 reanalysis data

Counts of blocking events generated over the three regions derived from R1, R2 and control run (in December only) based on WACCM simula-

tions

Figure 7 shows the anomalous Eady growth rate in the upper troposphere under WPV and SPV conditions, which serves as an indicator of atmospheric baroclinicity. During WPV (SPV) events, the Eady growth rate in the Atlantic sector to the north of 50° N is anomalously lower (higher), with the maximum amplitude of anomalies occurring from day − 10 to day 10 of these events (Fig. 7a and b). In the upper troposphere, the negative (positive) anomalies of Eady growth rate during WPV (SPV) events are mainly located around 0° in longitude and north of 50° N. In the R1 (R2) runs, there are negative (positive) anomalies of Eady growth rate with similar pattern derived from reanalysis data, which verify that the stratospheric polar vortex can modulate the background baroclinicity in the upper troposphere. The stratospheric polar warming anomalies associated with the WPV can enhance the static stability and buoyancy frequency in the upper troposphere, while weaker stratospheric westerlies can weaken vertical wind shear, leading to weaker Eady growth rate and background baroclinicity in the high latitudes. Consequently, the eddies activities in the upper troposphere tend to be inhibited (enhanced) under WPV (SPV) conditions.

Figure 8 illustrates the anomalous extended EP flux for synoptic-scale eddies in the upper troposphere under the SPV and WPV conditions. Under the WPV condition (Fig. 8a and c), there are anomalously northward wave fluxes from the middle latitudes to the region around 50° N over the North Atlantic sector. This is due to a decrease in Eady growth rate and atmospheric baroclinicity in the tropospheric high latitudes during WPV conditions (Fig. 7), resulting in fewer baroclinic eddies being generated there and transported outward. As the eddy momentum flux is negatively correlated with the meridional component of EP flux (EQ.2), the eddy activities behave to transport momentum from 50° N to the south, weakening the westerlies from around 50°–60° N and enhancing the westerlies to the south. The convergence of EP flux around 50°–60° N and the divergence around 30°–50° N correspond well to the anomalous zonal wind induced by the WPV (contour lines), indicating that synoptic eddies play an important role in the stratospheric influence on the low-frequency pattern of eddy-driven jet. Therefore, the anticyclonic (cyclonic) circulation to the north (south) of the easterlies anomalies also enhances during WPV conditions. On the other hand, under the SPV condition (Fig. 8b and d), the anomalously southward EP fluxes from around 60° N toward lower latitudes result in wave flux divergence around 60° N and intensifies the westerlies. The SPV can enhance the baroclinicity to the north of 55° N (Fig. 7), resulting in more baroclinic eddies being generated and transported outside the baroclinic region, leading to stronger westerlies and anomalous cyclonic (anticyclonic) circulation to its north (south). In conclusion, the geopotential height anomalies and cyclonic anomalies associated with synoptic eddies correspond well with the blocking anomalies associated with stratospheric polar vortex changes.

To investigate how background flows associated with stratospheric polar vortex changes exert influences on planetary waves, Fig. 9displays the anomalous frequency of negative refractive index squared ( n2 ) for wavenumber one during WPV and SPV conditions. During WPV events, frequency of negative n2 in the latitude band of 50°–75° N from the middle (50 hPa) to the lowermost stratosphere (100–200 hPa) is anomalously higher, indicating that upward propagation of wave into the stratosphere tends to be suppressed, and the waves induced by tropospheric wave source are more likely to be confined below the tropopause. Conversely, during SPV events, frequency of negative n2 in the same region is anomalously lower, favoring the upward propagation of waves. The R1 (R2) run can reproduce the increased (decreased) frequency of negative wave n2 in the middle and lowermost stratosphere (Fig. 9c and d). Thus, the stratospheric polar vortex may also impact the Atlantic circulation and blockings through modulating the propagation of planetary waves, which is further analyzed in the following text.

Figure 10 displays the anomalous vertical component of Plumb flux (Fz) at 100 hPa during WPV and SPV events. The evolution of Fz in the latitude band of 40°–55° N (Fig. 10c and d) is very similar to that in the latitude band of 55°–75° N (Fig. 10a and b) but with weaker amplitude. Before day 0 of WPV events, Fz is anomalously strong over

Fig. 6 Time-latitude cross sections of anomalies of 300-hPa geopotential height tendency due to synoptic eddies (shadings; units: gpm/day) averaged over 60° W − 30° E around a WPV and b SPV events derived from ERA5 reanalysis data. Composite anomalies of 300-hPa geopotential height tendency due to synoptic eddies (shadings; gpm/day) from day − 10 to day 10 of c WPV and d SPV events. c and f are the same as c and d but for e R1 and f R2 run, respectively. Stippled and hatched regions are for values statistically significant at the 95% confidence level

Fig. 7 The same as Fig. 6 but for the Eady growth rate (shadings; units: 1/day)

almost all longitudes (Fig. 10a and c), indicating strong upward propagation of waves forcing the stratosphere during this period, corresponding to the weakening of stratospheric westerlies (Fig. 1a). While after day 0 of WPV events, Fz decreases significantly, with anomalously weaker upward propagation of wave over the region around 0°and the east coast of Eurasian continent (from 90° E to 120° W). This indicates the feedback of WPV, which suppresses upward of waves through increasing the frequency of negative n2 (Fig. 9a). The climatological mean wave sources as well as upward propagation of planetary wave in the northern hemisphere are mainly located over the region around 0° in longitude and the east coast of Eurasian continent in the middle-to-high latitudes (Sun et al. 2013), corresponding to the strongest suppression of Fz there. Conversely, the evolution of 100-hPa Fz shows an opposite process during SPV events (Fig. 10b and d). Upward propagation of waves is anomalously weaker before day 0 of SPV events and becomes anomalously stronger afterwards, especially over the region around 0° and the east coast of Eurasian continent (around 90° E–120° W). Over the upstream of Atlantic region (around 120°–60° W), there are significantly negative anomalies of Fz after day 0 of SPV events, indicating enhanced downward propagation of planetary waves from the stratosphere, which may further contribute to changes in the Atlantic circulation.

Figure 11a and b show the climatology of meridional and vertical propagation of planetary wave over the latitude band 55°–75°N during winter, as derived from ERA5 reanalysis data and control run, respectively. The control run can capture well the vertical structure of climatological wavenumber 1 in the stratosphere, with the westward tilt of geopotential height deviation with heights. Note that there is upward propagation of planetary wave over the east

Fig. 8 Composite anomalies of 300-hPa extended EP flux (vectors; units: m2/s2) for synoptic eddies, its divergence (shadings; units: m/s/ day) and westerlies (contours at interval of 1 m/s; dashed contours denote negative values) from day − 10 to day 10 of a WPV and b SPV events derived from ERA5 reanalysis data. c and d are the same as a and b but derived from c R1 and (d) R2 run, respectively. The vectors less than 2 m 2/s2 are omitted. Stippled and hatched regions are for values statistically significant at the 95% confidence level

coast of Eurasian continent and downward reflection of planetary wave over North America (around 150°–60° W) at 100 hPa in the climatological mean. It implies that the stratospheric wave path is an important way to deliver wave energy out of the region of wave source over east coast of Eurasian continent and contribute to the climatological negative zonal deviation of tropospheric geopotential height over Greenland. While after day 0 of WPV events, the upward propagation of planetary wave is anomalously weak over east coast of Eurasian continent and anomalously strong over North America (Fig. 11c), consistent with Fig. 10a. Due to increased frequency of negative n2 in the lowermost stratosphere (Fig. 9a) under WPV condition, the waves induced by wave source over east coast of Eurasian continent tend to be confined below the tropopause and are less likely to propagate into the stratosphere. Therefore, the downward propagation of planetary wave flux from the stratosphere downstream is also weakened. As a result, the climatological negative deviation of tropospheric geopotential height over Greenland cannot be maintained, leading to significant positive anomalies and more blockings there (Figs. 3 and 4). The weakened stratospheric planetary wave train can be well captured by the R1 run (Fig. 11d). In contrast, after day 0 of SPV events, more waves propagate upward into the stratosphere over the east coast of Eurasian continent and are further propagate downward from the stratosphere over North America. Therefore, due to decreased frequency of negative n2 in the lowermost stratosphere (Fig. 9b), the enhanced stratospheric wave path would further lead to the negative deviation of geopotential height over Greenland, unfavoring the generation and maintenance of blocking there. Overall, it is demonstrated that the planetary waves also play a crucial role in the impact of stratosphere polar vortex on the Atlantic blockings.

Fig. 9 Pressure-latitude cross sections of anomalous frequency of negative refractive index squared for planetary wave number 1 (shading, units: %) from day 0 to day 20 of a WPV and b SPV events derived from ERA5 reanalysis data. cand d is the same as a and b but derived from c R1 and d R2 run, respectively. Stippled regions are for values statistically significant at the 95% confidence level

5 Conclusions and discussion

Based on composite analysis, this study reveals significant differences in the tropospheric blockings over the North Atlantic sector between WPV and SPV condition. Specifically, under the WPV condition, blockings are more likely to occur over Greenland and move westward, while they are less likely to occur over the region south of Greenland, with a shorter track. Conversely, under the SPV condition, blockings are more likely to originate in the south of Greenland and move eastward (Figs. 3, 4, 5). The stratospheric polar vortex can affect the Atlantic blocking by modulating both synoptic eddies and planetary waves. Firstly, the SPV (WPV) can increase (decrease) the Fig. 10 Time-longitude cross sections of anomalies of vertical component of Plumb flux (Fz) at 100 hPa (units: m2/s2) averaged over 55° N–75° N around a WPV and b SPV events derived from ERA5 reanalysis data. c and d is the same as a and b but for the vertical component of Plumb flux averaged over 40° N–55° N. The differences over the hatched regions are statistically significant at the 95% confidence level according to the Student’s t test

background baroclinicity in the upper troposphere (Fig. 7), resulting in more synoptic eddies being generated there and transported outward (Fig. 8). The anomalous eddy activities lead to negative geopotential height anomalies over Greenland and positive anomalies over the south of Greenland and the Western Europe under SPV conditions, and vice versa under WPV conditions (Fig. 6). Secondly, the WPV (SPV) can increase (decrease) the frequency of negative refractive index squared for planetary waves in the lower stratosphere (Fig. 9), providing an unfavorable (favorable) condition for the upward propagation of planetary wave into the stratosphere. As a result, under WPV condition, planetary waves induced by climatological mean wave source over the east coast of Eurasian continent tend to be confined below the tropopause. The downward propagation of wave from the stratosphere downstream is also weakened, unfavorable for the maintenance of climatological negative zonal deviation of geopotential height over Greenland and favoring the blocking there. In contrast, under SPV condition, more planetary waves induced by climatological mean wave source could be transported into the stratosphere. The enhanced downward propagation from the stratosphere over North America could lead to negative geopotential height deviation over Greenland and unfavoring the blocking there (Figs. 10 and 11). The R1 (R2) run with zonally symmetric thermal heating (cooling) Fig. 11 Pressure-longitude cross sections of zonal deviation of climatological geopotential height (shading; units: gpm) and the zonal and vertical component of Plumb flux averaged over the latitude band 55°–75° N (vectors; units: m2/s2) during winter derived from a ERA5 reanalysis data and b WACCM control run, respectively. c and e is the same as a but for the composite anomalies from day 0 to day 20 of c WPV events and e SPV events, respectively. dand f is the same as c and e but for the composite anomalies derived from d R1 run and f R2 run, respectively. The vertical component of vectors above 100 hPa is scaled be a factor of 500. The doted regions are statistically significant at the 95% confidence level according to the Student’s t test

forcing over stratospheric polar region can effectively reproduce the responses of Atlantic blocking activity to stratospheric anomalies during WPV (SPV) conditions, verifying that Atlantic blockings can be influenced by stratospheric polar vortex. It is also found that the spatial patterns of blocking responses to the stratospheric polar vortex changes are not sensitive to the slight changes in the magnitude and duration of polar vortex forcings (Fig. 3).

We also note that the anomalies of planetary wave flux and zonally asymmetric response in the stratosphere in the R1 (R2) runs are stronger than that during day 0 to day 20 of WPV (SPV) events derived from the ERA5 reanalysis data (Fig. 11). This is partly due to the fact the amplitude of zonally mean westerly anomalies in the R1 (R2) runs are approximately twice as large as that during the period from day 5 to day 20 for WPV (SPV) events. In the R3 (R4) runs and R5 (R6) runs, the anomalies of wave flux and zonally asymmetric response are reduced greatly (Fig. S1c and S1d). Overall, the amplitude and duration of the thermal forcing, the simplification of the vertical structure of stratospheric anomalies, and the absence of chemical feedback in our idealized experiments may have some impact on the amplitude of zonally asymmetric response, which need further studies.

Based on reanalysis data, we found the significant and lasting blocking anomalies over the Atlantic region from day − 30 to day 30 around the stratospheric polar vortex events (Fig. 2). As anomalous tropospheric wave sources and the blockings over the Atlantic, Ural and Pacific sectors are widely reported to be the precursor of the WPV and SSW events (e.g., Castanheira et al. 2010; Peings et al. 2019), it is unclear if and how the stratospheric polar vortex could cause the blocking anomalies during the later stage of WPV (SPV) events directly. The present study attempts to separate the feedback of stratospheric polar vortex on tropospheric blockings from their two-way interactions through large-ensemble experiments with climate models forced by WPV (SPV) condition. Additionally, previous studies pointed out the significance of tropospheric synoptic waves in stratosphere-troposphere coupling (e.g. Polvani et al. 2002; Kushner et al. 2004; Wittman et al. 2004, 2007; Smy et al. 2009; Davini et al. 2014; Rupp et al. 2021), our study also highlight the role of feedback of planetary waves induced by climatological wave source in the zonally asymmetry response of tropospheric geopotential height and blockings to the anomalous stratospheric polar vortex.

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