Contrasting interannual impacts of European and Greenland blockings on the winter North Atlantic storm track

The daily atmospheric data, including the geopotential height, three-dimensional wind field, and air temperature, were obtained from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) global atmospheric reanalysis datasets (Kalnay et al 1996) with a time span from 1948 to 2018 and a horizontal resolution of 2.5° × 2.5°. Note that the use of the NCEP/NCAR reanalysis instead of the superior fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5; Hersbach et al 2020) is based on considerations of its long time span and the consistent interannual variation of WNAST among the different reanalyses (Chang and Yau 2016).

2.2.1. Atmospheric blocking detection

The present study uses the two-dimensional definition (Scherrer et al 2006, Davini et al 2012a) to detect instantaneous atmospheric blocking. More specifically, at each grid point, we calculate the daily meridional gradient of geopotential height at 500 hPa by the following formulas:

$$\begin{align*}{\text{GHGN}}\left( {\lambda ,\varphi } \right) = \frac{{Z\left( {\lambda ,{\varphi _{\text{N}}}} \right) - Z\left( {\lambda ,\varphi } \right)}}{{{\varphi _{\text{N}}} - \varphi }}\end{align*}$$

$$\begin{align*}{\text{GHGS}}\left( {\lambda ,\varphi } \right) = \frac{{Z\left( {\lambda ,\varphi } \right) - Z\left( {\lambda ,{\varphi _{\text{S}}}} \right)}}{{\varphi - {\varphi _{\text{S}}}}},\,{\text{and}}\end{align*}$$

$$\begin{align*}{\text{GHG}}{{\text{S}}_2}\left( {\lambda ,\varphi } \right) = \frac{{Z\left( {\lambda ,{\varphi _{\text{S}}}} \right) - Z\left( {\lambda ,{\varphi _{{\text{S}}2}}} \right)}}{{{\varphi _{\text{S}}} - {\varphi _{{\text{S}}2}}}},\end{align*}$$

where $Z$ denotes the daily geopotential height at 500 hPa, $\lambda$ represents the longitude, $\varphi$ represents the latitude and ranges from 30° to 75°, ${\varphi _{\text{N}}} = \varphi + 15^\circ$, ${\varphi _{\text{S}}} = \varphi - 15^\circ$, and ${\varphi _{{\text{S}}2}} = \varphi - 30^\circ$. When the criteria ${\text{GHGS}}\left( {\lambda ,\varphi } \right) > 0$, ${\text{GHGN}}\left( {\lambda ,\varphi } \right) < - 10{\text{m}}/^\circ {\text{lat}}$, and ${\text{GHG}}{{\text{S}}_2}\left( {\lambda ,\varphi } \right) < - 5{\text{m}}/^\circ {\text{lat}}$ are satisfied simultaneously, instantaneous atmospheric blocking is identified, and this day is regarded as a blocked day. The winter (December–February) atmospheric blocking frequency is measured by the percentage of blocked days per winter. Although we do not apply to this instantaneous blocking any duration criterion as commonly used (e.g. Davini et al 2012a), it is convenient to investigate the interannual impact of the blocking on the storm track. Additionally, this approach was already used by previous studies (e.g. Prodhomme et al 2016, Davini and D'Andrea 2020).

2.2.2. Storm track representation

Bandpass statistics have been confirmed to be a useful tool to measure storm track activity (Chang 2009). The vertically integrated (from 925 to 250 hPa) eddy kinetic energy is used to represent the WNAST. The synoptic-scale (2.5–6 day) component is separated by the Lanczos bandpass filter (Duchon 1979). The storm track strength index (STSI; Yang et al 2018, 2020a) is defined by setting a threshold that is the median of the WNAST amplitudes of all of the grid points within a domain of (30°–75° N, 100° W–30° E). The threshold is set each winter and applied to all the grid points. The use of median strength threshold can better represent storm track activities by dynamically capturing the main body of WNAST in each calculation. The mean of the values greater than the threshold in all the grids is defined as the STSI which can be expressed as:

$$\begin{align*}{\text{STSI}} = \sum\limits_1^N {\text{W}} {\text{NAS}}{{\text{T}}_{{\text{amp}}}}/N,\end{align*}$$

where denotes the number of grid points with the WNAST amplitude larger than the threshold and ${\text{WNAS}}{{\text{T}}_{{\text{amp}}}}$ represents the amplitude of the WNAST at the grid point.

2.2.3. Liang-Kleeman information flow theory

A recent rigorous causality formalism based on the Liang-Kleeman information flow theory (Liang and Kleeman 2005, Liang 2008, 2014), which has been widely used for causality analysis in the field of earth sciences (e.g. Liang 2014, Stips et al 2016, Jiang et al 2019, Yang et al 2021a), is applied to reveal the causal relationship between the occurrence frequency of atmospheric blocking and the intensity of the WNAST. Information flow is considered a measure of causality, where the exchange of information between two events indicates not only the quantity but also the direction of causality (Liang 2016). Specifically, for two time series ${X_1}$ and ${X_2}$, the information flow (Liang 2014) from the latter to the former can be expressed as follows:

$$\begin{align*}{T_{2 \to 1}} = \frac{{{C_{11}}{C_{12}}{C_{2,d1}} - C_{12}^2{C_{1,d1}}}}{{C_{11}^2{C_{22}} - {C_{11}}C_{12}^2}},\end{align*}$$

where ${C_{ij}}$ denotes the sample covariance between ${X_i}$ and ${X_j}$, ${C_{i,dj}}$ denotes the covariance between ${X_i}$ and the Euler forward finite difference of ${X_j}$. The flow in the opposite direction, ${T_{1 \to 2}}$, can be directly written out by switching subscripts 1 and 2. The units are in nats per unit time. Note that nat is the natural unit of information, which is expressed as a natural logarithm (Weik 2001). If the calculated result is zero, then ${X_2}$ does not affect the change in ${X_1}$; that is, ${X_2}$ is not the cause of ${X_1}$, and there is no causal relationship between them. However, if it is nonzero, then ${X_2}$ is the cause of ${X_1}$. The code of Liang-Kleeman information flow can be found at www.ncoads.cn/article/show/63.aspx.

Figure 1(a) shows the climatological winter atmospheric blocking occurrence frequency and storm track amplitude over the North Atlantic and Europe. Two peaks of atmospheric blocking occurrence frequency are located over Europe and Greenland, which are known as the EB and GB, respectively. Note that when a one-dimensional definition (Tibaldi and Molteni 1990) is used to detect atmospheric blocking, the EB and GB cannot be distinguished conveniently, and they are often referred to as the Atlantic-Europe blocking. The maximum frequency of EB over the North Sea achieving more than 13% of blocked days per winter is larger than that of GB. It can be clearly observed that the WNAST is geographically closely bound to atmospheric blocking, emerging west of EB and south of GB. To quantitatively examine the relationships between the WNAST and the two types of atmospheric blocking, the EB index (EBI) and GB index (GBI) are defined by the normalized domain-averaged blocking frequency over 40°–65° N, 20° W–40° E and 60°–75° N, 60°–20° W, respectively.

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Figure 1(b) presents the time series of winter-mean STSI, EBI and GBI. The equivalent degrees of freedom range from 65 to 70 after taking serial lag-one autocorrelation into account (Bretherton et al 1999). All three indices exhibit prominent interannual variations. There is a significant out-of-phase relationship between the STSI and the GBI, and their correlation coefficient is −0.38 with a 99% confidence level based on a two-sided Student's t test, indicating that frequent GB corresponds to weakened WNAST. In contrast, the correlation coefficient between the STSI and the EBI is 0.44, which suggests that the frequent EB is significantly associated with a strengthened WNAST. It is interesting that the two types of atmospheric blocking, EB and GB, neighboring the WNAST have opposite interannual relationships with WNAST intensity.

By applying the Liang-Kleeman information flow theory, an information flow from the EB occurrence frequency to the WNAST intensity: ${ }{T_{{\text{EB}} \to {\text{ST}}}} = - 21.7$ (unit: nats s⁻¹), and an information flow from the GB occurrence frequency to the WNAST intensity: ${ }{T_{{\text{EB}} \to {\text{ST}}}} = - 19.4$ nats s⁻¹ suggest that the occurrence frequencies of EB and GB are the cause of the WNAST intensity. In fact, an information flow from the intensity WNAST to the occurrence frequency of atmospheric blocking is also nonzero, which implies a mutually causal relationship between them and the interaction between the high-frequency eddies and the intermediate-frequency eddies (Jiang et al 2013). However, the present study primarily focuses on the impacts of the EG and GB on the WNAST.

To obtain the anomalous WNAST distribution related to the two types of atmospheric blocking, composite analysis is performed by taking one standard deviation of the EBI and GBI as the criterion. Based on this method, 10 (8) winters, including 1948/49, 1952/53, 1963/64, 1975/76, 1990/91, 1991/92, 1992/93, 2004/05, 2005/06, and 2016/17 (1950/51, 1959/60, 1965/66, 1969/70, 1985/86, 1994/95, 2013/14, and 2015/16), with a high (low) occurrence frequency of EB, and 9 (9) winters, including 1962/63, 1976/77, 1978/79, 1986/87, 1995/96, 2000/01, 2006/07, 2009/10, and 2012/13 (1951/52, 1973/74, 1980/81, 1982/83, 1983/84, 1988/89, 2011/12, 2014/15, and 2017/18), with a high (low) occurrence frequency of GB, were selected. Note that a few winters, such as 1962/63 and 2012/2013, that should have been chosen by both EB and GB for the composite, are reserved by only one of them. Figure 2 shows the composite WNAST anomalies associated with the two types of atmospheric blocking. There is a meridional dipole distribution of the EB-related WNAST anomalies, with significantly positive anomalies occurring on the northeastern flank of the climatological WNAST and prominently negative anomalies appearing over the Iberian Peninsula and the Mediterranean (figure 2(a)). Although the magnitudes of the two anomalous peak amplitudes within the meridional dipole distribution are generally comparable, the area of positive anomalies is obviously larger than that of negative anomalies, which may directly result in the in-phase relationship between the EB occurrence frequency and the WNAST intensity. In addition, such a meridional dipole distribution is conducive to the northward displacement of the eastern WNAST.

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From figure 2(b), we can see that the influence of the GB on the WNAST is basically opposite to that of the EB. The significantly negative WNAST anomalies associated with the frequent GB arise on the northeastern flank of the WNAST climatology, while noticeably positive anomalies emerge west of the Strait of Gibraltar. The out-of-phase relationship between the GBI and STSI may be attributed to the amplitude of the negative WNAST anomalies being larger than that of positive anomalies. The distribution of the GB-related WNAST anomalies favors the southward migration of the eastern WNAST, which is contrary to the impact of the EB. Thus, the downstream structure of the composite WNAST during high occurrence frequencies of EB (figure 2(a)) and GB (figure 2(b)) winters shows a poleward deflection and zonal horizontal, respectively, relative to the climatology (figure 1(a)).

In addition, another two commonly used Eulerian storm track diagnostics are used to further identify the contrasting influences of the EB and GB on the WNAST. For the lower-tropospheric meridional eddy heat flux, the EB-related anomalous distribution is dominated by significantly positive anomalies (figure 2(c)); however, there are prominently negative anomalies associated with the frequent GB occurring on the north side of its climatology (figure 2(d)). For the standard deviation of the filtered geopotential height at 500 hPa, the anomalous distributions related to the frequent EB (figure 2(e)) and GB (figure 2(f)) are essentially consistent with those of eddy kinetic energy. Therefore, the contrasting impacts of the EB and GB on the WNAST are strong enough to consider this as a robust and important result.

In boreal wintertime, the North Atlantic Oscillation (NAO) is the dominant mode of variability in the North Atlantic-European area and is strongly related to variations of the WNAST (e.g. Hurrell et al 2003, Cattiaux et al 2010, Luo et al 2011). The NAO is also closely linked with the GB (e.g. Woollings et al 2008, Davini et al 2012b, Yao and Luo 2014). It is natural that one may wonder whether interannual impacts of the EB and GB on the WNAST is just the signature of the NAO. To address this issue, we investigate relationships between the NAO and EB, GB, and WNAST. The monthly NAO index (NAOI) spanning from 1950 to 2018 is obtained from the National Oceanic and Atmospheric Administration/Climate Prediction Center. The correlation coefficients between the winter NAOI and the EBI, GBI, and STSI are 0.10, −0.85 and 0.44, respectively, which indicates that the NAOI and the EBI are largely uncorrelated and the interannual influence of the EB on the WNAST is independent of the NAO. The NAOI is strongly negatively related to the GBI and has a significantly positive correlation relationship with the STSI.

To further examine the role of the NAO in the impact of the GB on the WNAST, we also perform composite analysis by taking one standard deviation of the NAOI as the criterion; 10 (10) winters, including 1962/63, 1963/64, 1968/69, 1976/77, 1977/78, 1978/79, 1984/85, 1995/96, 2009/10, and 2010/11 (1951/52, 1956/57, 1982/83, 1983/84, 1988/89, 1993/94, 1994/95, 1999/2000, 2011/12, and 2014/15), with a weak (strong) NAOI, are selected. Note that the operation of composite difference between strong and weak winters are opposite in the GBI and NAOI due to their significant out-of-phase relationship. Figure 3(a) shows the composite difference in the WNAST between weak and strong NAOI winters. We can see that that the spatial pattern of anomalous WNAST related to the NAO also exhibits a meridional dipole with significantly positive WNAST anomalies occurring in the southern part, which is consistent with the anomalous WNAST associated with the GB (figure 2(b)). It suggests that the GB-related WNAST anomalies are largely associated with the NAO.

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To demonstrate that the interannual impact of the GB alone on the WNAST is also significant, composite difference between strong and weak GBI winters is performed by excluding weak and strong NAOI winters, respectively. In this way, there are 4 (3) winters, including 1986/87, 2000/01, 2006/07, and 2012/13 (1973/74, 1980/81, and 2017/18), with a strong (weak) GBI, are selected. Figure 3(b) shows the composite difference in the WNAST between strong (1986/87, 2000/01, 2006/07, and 2012/13) and weak (1973/74, 1980/81, and 2017/18) GBI winters. We can see that the anomalous WNAST related to the GB alone is basically consistent with the result shown in figure 2(b), which indicates that the influence of the GB alone on the WNAST is significant.

Before exploring the possible underlying physical mechanisms behind the contrasting impacts of the EB and GB on the WNAST, it is important to investigate the anomalous atmospheric circulation associated with the frequent EB and GB. Figure 4 shows the composite geopotential height and wind field anomalies. In the middle troposphere, there are prominently EB-related positive geopotential height anomalies over western Europe (figure 4(a)), corresponding to a remarkably anomalous anticyclone. However, negative geopotential height anomalies in the lower latitudes have obviously weaker amplitudes. In the lower troposphere, anomalous westerly and easterly winds emerge in the northern and southern flanks of EB-related anticyclonic circulation (arrows in figure 4(a)), respectively. In the upper troposphere, the spatial distributions of anomalous westerly and easterly winds (figure 4(c)) are consistent with those in the lower troposphere, but the amplitudes are evidently larger, which suggests the intensified vertical shear of zonal wind.

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The atmospheric baroclinicity quantified by the maximum Eady growth rate (EGR; Lindzen and Farrell 1980) can be calculated by:

$$\begin{align*}{\text{EGR}} = 0.31f{\,}{N^{ - 1}}\partial u/\partial z,\end{align*}$$

where $f$ denotes the Coriolis parameter, denotes the Brunt-Väisälä frequency, and $\partial u/\partial z$ is the vertical shear of zonal wind. According to the linear theory of baroclinic instability (Charney 1947, Eady 1949, Lindzen and Farrell 1980), strengthened lower-tropospheric atmospheric baroclinicity provides a favorable condition for the potential intensification of synoptic-scale eddies (Hoskins and Valdes 1990). Figure 5(a) shows the EB-related composite anomalies of vertically integrated (from 925 to 700 hPa) lower-tropospheric EGR. We can see that the spatial distribution of anomalous EGR also displays a meridional dipole (figure 5(a)), which is broadly consistent with that of anomalous WNAST (figure 2(a)). Note that the structure of the anomalous EGR dipole strongly resembles the mean winter EGR (Simmonds and Li 2021). However, the area and amplitude of negative EGR anomalies are larger than those of positive EGR anomalies, suggesting that the EB-related WNAST anomalies cannot all be attributed to the anomalous EGR.

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In fact, apart from atmospheric baroclinicity, storm track activities are also largely dependent on the baroclinic energy conversion from the eddy available potential energy to the eddy kinetic energy (Cai et al 2007, Jiang et al 2013, Yang et al 2020b, 2021b). The baroclinic energy conversion (BCEC) can be expressed as:

$$\begin{align*}{\text{BCEC}} = - {\left( {{p_0}/p} \right)^{{C_{\text{v}}}/{C_{\text{p}}}}}\left( {R/g} \right)\left( {\overline {\omega {^{^{\prime}}}T{^{^{\prime}}}} } \right),\end{align*}$$

where ${p_0}$ denotes 1000 hPa, $R$ is the gas constant for dry air, $\omega$ is the vertical pressure velocity and ${C_{\text{v}}}$ (${C_{\text{p}}}$) is the specific heat of dry air at a constant volume (pressure). The prime and the overbar indicate the transient (2.5–6 day bandpass filtered) and climatological mean components, respectively. Figure 5(c) shows the EB-related composite anomalies of vertically integrated (from 925 to 250 hPa) baroclinic energy conversion. It is obvious that the area and amplitude of the EB-related positive baroclinic energy conversion anomalies are larger than those of the negative anomalies (figure 5(c)), which may explain the EB-related WNAST anomalies well.

With regard to the GB-related atmospheric circulation anomalies (figure 4(b)), there is a noticeably meridional dipole pattern of anomalous geopotential height over the North Atlantic, with positive geopotential height anomalies appearing north of 55° N. The lower-tropospheric easterly wind anomalies lying on the southern flank of the anomalous anticyclone coincide with the northern flank of the anomalous cyclone, while the westerly wind anomalies primarily arise on the southern side of the anomalous cyclone (arrows in figure 4(b)). The spatial pattern of the zonal wind anomalies in the upper troposphere (figure 4(d)) is essentially consistent with that in the lower troposphere. The GB-related vertical shear of zonal wind anomalies is responsible for the resultant EGR anomalies (figure 5(b)). We find that the amplitudes of the negative EGR anomalies are larger than those of the positive anomalies, which may result in the GB-related weakened WNAST. In addition, the GB-related baroclinic energy conversion anomalies also manifest as a noticeable meridional dipole (figure 5(d)). The area and amplitude of the GB-related negative baroclinic energy conversion anomalies on the northern side larger than those of the positive anomalies results in the weakened WNAST associated with the frequent GB.