Types of Coupling between the Stratospheric Polar Vortex and Tropospheric Polar Vortex, and Tropospheric Circulation Anomalies Associated with Each Type in Boreal Winter

Abstract

Fifty years of daily ERA5 reanalysis data are employed to investigate the linkages between the strength of the stratospheric polar vortex and the tropospheric polar vortex during the boreal winter. The strong coupling events, anomalies in both the stratospheric and tropospheric polar vortices, can be classified into four configurations, each representing the distinct characteristics of planetary wave vertical propagation and tropospheric circulation anomalies. The findings reveal the following patterns: (1) Strong stratospheric polar vortex and weak tropospheric polar vortex periods are associated with anomalous downward E-P flux from the stratosphere to the troposphere, predominantly induced by planetary waves 1 and 2. Warm anomalies occur along the North Atlantic coasts, while cold anomalies are evident over Eastern Europe and East Asia at the surface. (2) Weak stratospheric polar vortex and strong tropospheric polar vortex periods exhibit anomalous upward E-P flux in high latitudes, with dominant wave 1, and anomalous downward E-P flux in the middle latitudes, dominated by wave 2. Warm anomalies are observed over North America, Western Europe, and the northern side of the Gulf of Oman at the surface. (3) Strong stratospheric polar vortex and strong tropospheric polar vortex periods feature anomalous downward E-P flux in high latitudes, dominated by wave 1, and anomalous upward E-P flux in middle latitudes, with a wave 2 predominance. Warm anomalies prevail over Northeast Asia, Southern Europe, and North America at the surface. (4) Weak stratospheric polar vortex and weak tropospheric polar vortex periods display anomalous upward E-P flux in mid-to-high latitudes, predominantly with wave 1. In contrast to the tropospheric circulation anomalies observed in the third category, this pattern results in the presence of cold anomalies over Northeast Asia, Southern Europe, and North America.

1. Introduction

The dynamic interaction between the stratosphere and the troposphere is a prominent research area within the Stratospheric Processes and their Role in Climate (SPARC) project [1,2]. In recent years, there has been growing interest in investigating the stratosphere–troposphere interaction. As early as 1977, research indicated that circulation anomalies in the stratosphere could influence the troposphere [3]. Subsequent studies have further demonstrated that the stratosphere is not solely passively influenced by upward propagating anomalies from the troposphere as it can also exert an influence on tropospheric weather [1,4,5,6]. The downward coupling of anomalies in the polar stratosphere plays a crucial role in driving low-frequency variations in tropospheric circulation and temperature, making it a source of predictability for surface weather and climate [7,8,9]. Planetary-scale Rossby waves serve as a fundamental mechanism for the vertical coupling between the stratosphere and troposphere [10]. These waves are primarily generated in the troposphere and establish a connection with the stratosphere when the mean flow is westerly [11,12].

The polar vortex (PV) is a coherent system spanning the Arctic stratosphere and troposphere, and its strength and position changes are intricately connected to the boreal weather system [13,14,15,16]. For instance, in the boreal winter, the core of the PV frequently shifts towards North America or Eurasia, resulting in the influence of cold air on surface temperatures in these regions. This phenomenon can even lead to extreme cold events [17,18]. Research on the dynamic coupling between the stratosphere and the troposphere often centers around the vertical propagation of anomalies within the PV, specifically focusing on the investigation of the Arctic Oscillation (AO). Perturbations occurring in the upper stratospheric AO propagate downward to the troposphere and surface within approximately three weeks [19,20], significantly influencing tropospheric weather circulation. The propagation signal of this anomaly can also be evaluated through the Northern Hemisphere Annular Mode (NAM) [21]. The dynamical coupling between the stratosphere and troposphere, as described by the NAM index, is based on the gradual downward propagation of geopotential height and zonal wind anomalies [22], which, in turn, can regulate the strength of stratospheric PV through thermodynamic processes in the troposphere. This forcing mechanism is commonly described as Rossby vertical propagation and is represented by the Plumb and Eliassen-Palm wave activity fluxes [23]. Furthermore, sudden stratospheric warming (SSW), a significant event associated with disturbances in the PV, has been extensively investigated due to its notable impacts on the troposphere [24,25,26,27,28].

Studying anomalies in the positioning and intensity of the stratospheric polar vortex often leads to disruptions in tropospheric circulation patterns, a focal point in investigations of stratosphere–troposphere interactions. These interactions manifest across various temporal scales. At the weather scale, phenomena such as the upward propagation of tropospheric planetary waves result in stratospheric sudden warming events [29,30]. On an extended timescale, anomalies in stratospheric circulation patterns descending to the troposphere induce extensive surface cold outbreaks [7]. Over seasonal or semi-annual scales, a linkage exists between the semi-annual oscillation (SAO) signal of temperatures in the mid-latitude upper-troposphere–lower-stratosphere region and the SAO signal of sea surface temperatures in extratropical regions [31]. Furthermore, events involving Rossby wave breaking near the tropopause contribute to the exchange of materials between the stratosphere and troposphere [32,33], representing a distinct facet of their interaction.

In existing research, specific weather instances are often scrutinized, or long-term numerical simulations are employed to ascertain the climatic repercussions of stratospheric vortex anomalies. This study, however, adopts a more direct approach, statistically analyzing the concurrent correspondence between daily winter stratospheric polar vortices and tropospheric polar vortices, irrespective of temporal scales. This methodology avoids singling out particular cases and instead directly extracts coupled relationships and their associated probabilities from extensive datasets. Further investigation is warranted into tropospheric circulation anomalies corresponding to these newly defined coupled events.

2. Data and Methods

2.1. Data

The daily ERA5 reanalysis, including geopotential, zonal wind, meridional wind, temperature, and 2 m temperature, is provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) for the period of November to March from 1971 to 2020 (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels?tab=form, accessed on 27 March 2023). The data are presented with a horizontal resolution of 2° × 2°. Daily variable anomalies refer to the quantitative differences between the values of a specific variable on a given day and its corresponding interannual average for the same day.

2.2. Methods

2.2.1. Empirical Orthogonal Function

The empirical orthogonal function (EOF) is an analytical method extensively employed in meteorological research to extract essential temporal and spatial characteristics from data [34].

2.2.2. Harmonic Analysis

By conducting zonal harmonic analysis on meteorological field data, it is possible to derive the corresponding zonal mean field as well as perturbations at various wavenumbers. This enables the examination of the Rossby wave structure at different scales [35], which can be expressed as:

$$\begin{array}{c}\hfill y_x=\overline{y}+{\displaystyle \sum _{k=1}^{n/2}}\left[C_k\mathit{cos}\left(\frac{2\pi k}{n}x-{\varphi }_k\right)\right]\hfill \\ \hfill =\overline{y}+{\displaystyle \sum _{k=1}^{n/2}}\left[A_k\mathit{cos}\left(\frac{2\pi k}{n}x\right)+B_k\mathit{sin}\left(\frac{2\pi k}{n}x\right)\right]\hfill \end{array}$$

(1)

where $A_k$, $B_{k,}$ and the phase ${\varphi }_k$ are given by:

$$A_k=\frac{2}{n}{{\displaystyle \sum }}_{x=1}^n{y}_t\mathit{cos}\left(\frac{2\pi k}{n}x\right)$$

(2)

$$B_k=\frac{2}{n}{{\displaystyle \sum }}_{x=1}^n{y}_t\mathit{sin}\left(\frac{2\pi k}{n}x\right)$$

(3)

$${\varphi }_k=\left\{\begin{array}{c}arctan\left(\frac{B_k}{A_k}\right), A_k>0\\ arctan\left(\frac{B_k}{A_k}\right)\pm \pi , A_k<0 \\ \frac{\pi }{2}, A_k=0\end{array}\right.$$

(4)

K = 1, 2, 3 … represents the zonal wave number, and $C_k=\sqrt{A_k^2+B_k^2}$ denotes the amplitude of each wave number.

2.2.3. E-P Flux

The Eliassen-Palm flux, defined in the two-dimensional meridional plane [36], represents the direction of propagation of planetary wave energy. Its divergence can modulate the mean westerly momentum. In the spherical coordinate system, considering Earth’s rotation, the Eliassen-Palm flux in P coordinates [37] can be expressed as:

$$\left\{\begin{array}{c}{F}_{\left(\phi \right)}=-r_0\mathit{cos}\phi \overline{u^{\prime }{v}^{\prime }}\\ F_{\left(p\right)}=f{r}_0\mathit{cos}\phi \frac{\overline{v^{\prime }{\theta }^{\prime }}}{\overline{{\theta }_p}}\end{array}\right.$$

(5)

$F_{\left(\phi \right)}$ and $F_{\left(p\right)}$ denote the vortex momentum flux and heat flux, respectively, per unit mass of air due to fluctuating effects.

The divergence of the E-P flux F in spherical P coordinates is given by:

$$\nabla ·F=\frac{1}{r_0\mathit{cos}\phi }\frac{\partial }{\partial \phi }\left(F_{\left(\phi \right)}\mathit{cos}\phi \right)+\frac{\partial }{\partial p}\left(F_{\left(p\right)}\right)$$

(6)

It represents the change in angular momentum per unit mass of air, where $r_0$, $f$, $\theta$, and $\phi$ are the radius of the Earth, the Coriolis parameter, the potential temperature, and the latitude, respectively; u and v are the latitudinal and longitudinal winds. The superscripts ‘-’ and ‘′’ denote the latitudinal mean and the latitudinal deviation, respectively. ${\theta }_p$ denotes the vertical gradient of $\theta$ in P coordinates.

3. Types of Coupling between the Stratospheric PV and Tropospheric PV

3.1. The Definition of Strong PV and Weak PV

For the period from 1971 to 2020 (November to March), geopotential height anomalies were calculated relative to the daily multi-year mean state using the ERA5 data. The analysis focused on the boreal, ranging from 20°N to 90°N. Prior to analysis, trends were removed, and the empirical orthogonal function (EOF) decomposition was applied. The tropospheric PV was represented at 500 hPa, and the stratospheric PV was represented at 30 hPa. The spatial distribution of the first mode revealed an inverse phase distribution between the polar and extrapolar regions for both the 500 hPa and 30 hPa geopotential height anomalies (refer to Figure 1a,b). However, there were differences at mid and low latitudes: the 30 hPa geopotential height anomalies displayed a zonal symmetric distribution, while the 500 hPa geopotential height anomalies exhibited three positive centers, primarily located over Western Europe, Northeast Asia, and North America (the weakest center). To quantify the intensity of the PV in the troposphere and stratosphere, the standardized time coefficients corresponding to this spatial mode were defined as PV intensity indices. A large positive index indicated a strong PV, while a large negative index indicated a weak PV.

PV events occurring from November 1971 to March 2020 (total 7550 days, approximate 151 days per year) were classified based on the PV strength index. A threshold of 0.842-times the standard deviation was used for classification. Events with a PV index exceeding 0.842-times the standard deviation (top 20%) were labeled as strong PV events, while those with a PV index lower than −0.842-times the standard deviation (bottom 20%) were categorized as weak PV events. These two categories are collectively referred to as anomalous PV events. Events falling between these two thresholds were classified as normal PV events.

3.2. Types of Coupling between the Stratospheric PV and the Tropospheric PV

Based on the classification criteria in Section 3.1, the total events were divided into four categories, and the results are summarized in

Table 1. Statistics of different coupling types between the stratospheric PV and tropospheric PV in boreal winter, 1971–2020.

Coupling Types of PV	Occurrence Days	Proportion
Anomalies in both the stratosphere and the troposphere	1200	15.90%
Stratospheric anomaly and tropospheric normal	1540	20.40%
Stratospheric normal and tropospheric anomaly	1783	23.60%
Normal in both the stratosphere and the troposphere	3027	40.10%

. The anomalous PV events occurring simultaneously in the stratosphere and troposphere layers, known as strong coupling events, occurred 1200 times, representing the lowest frequency at 15.90% of the total. Anomalous PV events only in the stratosphere occurred 1540 times, accounting for 20.40% of the total. Similarly, there were 1783 anomalous PV events only in the troposphere, making up 23.60% of the total. The highest frequency, with 3027 normal PV events or 40.10% of the total, was observed in both the stratosphere and the troposphere.

For the subset of strong coupling events (total 1200 days), anomalies in both the stratosphere and the troposphere, further classification and statistical analysis were conducted, as summarized in

Table 2. Classification of PV anomalies in both the stratosphere and the troposphere in boreal winter, 1971–2020.

Type	Coupling Types of Both PV Anomalies	Occurrence Days	Proportion
Type1	Strong stratospheric PV and weak tropospheric PV	127	10.58%
Type2	Weak stratospheric PV and strong tropospheric PV	111	9.25%
Type3	Strong stratospheric PV and strong tropospheric PV	525	43.75%
Type4	Weak stratospheric and weak tropospheric PV	437	36.42%

. Type 1 encompasses 127 occurrences, accounting for 10.58% of the strong coupling events. These instances are characterized by strong stratospheric PV and weak tropospheric PV. Type 2 comprises 111 occurrences, representing 9.25%, with weak stratospheric PV and strong tropospheric PV. Type 3 includes 525 occurrences, making up 43.75%, and features strong stratospheric PV and strong tropospheric PV. Type 4 covers 437 occurrences, accounting for 36.42%, and exhibits weak stratospheric PV and weak tropospheric PV. It is noteworthy that the first two types of events exhibit an inverse PV intensity between the stratosphere and the troposphere, named reverse strong coupling events, with a relatively lower frequency totaling 19.83%, while the last two types of events demonstrate consistent PV intensity between the stratosphere and the troposphere, named consistent strong coupling events, with a higher frequency totaling 80.17%.

4. Vertical Propagation Characteristics of Planetary Waves in Four Types of PV Anomalies in Both the Stratosphere and the Troposphere

From the four categories of PV anomalies in both the stratosphere and the troposphere (strong coupling events), examples that occurred after 1980 and had a duration of no less than three days were selected for composite analysis. The selected reverse strong coupling events are shown in

Table 3. Persistent reversed coupling events in the stratospheric PV and the tropospheric PV.

Type		Event 1	Event 2	Event 3	Event 4	Event 5	Event 6
Type1	Start date	6 Feb. 1984	31 Jan. 1988	19 Feb. 1988	24 Feb. 2000	13 Feb. 2011
	End date	8 Feb. 1984	6 Feb. 1988	23 Feb. 1988	28 Feb. 2000	17 Feb. 2011
Type2	Start date	2 Feb. 1991	25 Dec. 1997	8 Feb. 2004	26 Feb. 2009	18 Feb. 2017	29 Dec. 2018
	End date	8 Feb. 1991	29 Dec. 1997	10 Feb. 2004	4 Mar. 2009	20 Feb. 2017	4 Jan. 2019

. Five reverse strong coupling events of type 1, strong stratospheric PV, and weak tropospheric PV were selected. The cumulative duration of these five events is 25 days. Six reverse strong coupling events of type 2, featuring weak stratospheric PV and strong tropospheric PV, amounted to 32 days. As for the two consistent strong coupling events, due to the significant number of days involved, with 388 and 318 days, respectively, they are not individually listed in the table.

The anomalous activity of planetary waves during winter is frequently linked to anomalies in the stratospheric PV [38,39], so it is valuable to investigate the characteristics and distinctions of planetary waves within the four categories of strong coupling events. In the case of strong stratospheric PV and weak tropospheric PV, the strengthening of westerly winds is observed in the stratosphere, and the overall E-P flux exhibits notable downward anomalies in the stratosphere north of 50°N (Figure 2a). The anomalous downward transfer of the E-P flux above 200 hPa is primarily attributed to the contributions of planetary waves 1 and 2. Furthermore, the E-P fluxes of waves 1 and 2 exhibit anomalous divergence, respectively, north and south of 60°N in the stratosphere, promoting the strengthening of westerly winds around the poles (Figure 2b,c). The E-P fluxes associated with planetary wave 3 primarily manifest as anomalous upwelling in the middle and high latitudes of the mid-tropospheric and lower stratosphere (i.e., 500–50 hPa, north of 50°N), which partially counterbalance the anomalous downward wave fluxes from waves 1 and 2 in this region (Figure 2d). Additionally, significant downward anomalies associated with wave 1 are observed in the high-latitude troposphere. Thus, in the case of strong stratospheric PV and weak tropospheric PV (the first type of strong coupling event), the significant downward anomalies of the wave flux in the stratosphere are primarily driven by waves 1 and 2.

In the periods of weak stratospheric PV and strong tropospheric PV, the overall E-P flux exhibits upward anomalies primarily (Figure 3a). These anomalies are mainly attributed to wave 1 (Figure 3b), with the E-P flux of wave 1 displaying anomalous convergence in the polar stratosphere, which is favorable for the weakening of the polar westerly winds (Figure 3b). In contrast, wave 2 displays a downward anomaly in the stratosphere but with a smaller amplitude compared to wave 1, which is characterized by anomalous divergence. In the troposphere, the E-P flux associated with wave 2 exhibits similar behavior to wave 1, primarily showing upward propagation (Figure 3c). Waves 2 and 3 exhibit positive E-P flux divergence in the high-latitude stratosphere, which weakens the decelerating effect of wave 1 on the zonal winds (Figure 3c,d). Additionally, a significant upward anomaly associated with wave 1 is observed in the mid-latitude troposphere. Therefore, in the case of weak stratospheric PV and strong tropospheric PV (the second type of strong coupling event), the significant upward anomaly of wave flux is primarily influenced by wave 1.

During the strong stratospheric PV and strong tropospheric PV events, anomalous downward propagation of the overall E-P flux north of 60°N in the stratosphere and anomalous upward propagation south of 60°N was displayed (Figure 4a). The anomalous downward propagation in high latitudes is primarily attributed to wave 1, while the anomalous upward propagation in mid latitudes is primarily influenced by wave 2 (Figure 4b,c). Wave 3 exhibits a relatively small magnitude of anomalous downward propagation in the stratosphere compared to waves 1 and 2. However, it displays a significant characteristic of anomalous upward propagation in the mid-latitude troposphere (Figure 4d). Therefore, in the case of strong stratospheric PV and strong tropospheric PV (the third type of strong coupling event), the prominent features include the anomalous downward propagation of wave 1 in the high-latitude stratosphere and the anomalous upward propagation of wave 2 in the mid-latitude troposphere.

In the context of weak stratospheric PV and weak tropospheric PV, the total E-P flux features an anomalous upward propagation in the high-latitude stratosphere, accompanied by anomalous convergence (Figure 5a), which is primarily attributed to the E-P flux of wave 1 in the middle to upper stratosphere (Figure 5b). In the lower stratosphere and upper troposphere, the anomalous upward propagation of wave 2 also contributes significantly (Figure 5c), while the anomaly of wave 3 is weaker compared to waves 1 and 2, primarily manifesting as anomalous downward propagation in the mid-to-high-latitude troposphere. Therefore, in the case of weak stratospheric PV and weak tropospheric PV (the fourth type of strong coupling event), the anomalous upward propagation of wave 1 is most significant in the stratosphere.

5. Tropospheric Circulation Anomalies Associated with Four Types of PV Anomalies in Both the Stratosphere and the Troposphere

Originating in the troposphere, Rossby waves interact with the mean flow as they propagate vertically upward. During this process, smaller-scale waves are filtered out, and waves 1 and 2 become dominant in the middle to upper stratosphere. In the troposphere, smaller-scale Rossby waves often affect the weather process and play a crucial role in the coupling between different atmospheric layers. Therefore, studying the significant circulation differences in the troposphere under different coupling types of stratospheric and tropospheric vortex anomalies is valuable. In this section, we analyze the average anomalies of 500 hPa geopotential height and surface 2 m temperature during periods of four different types of strong coupling events.

In the reverse strong coupling event characterized by strong stratospheric PV and weak tropospheric PV, positive anomalies in the 500 hPa geopotential height are prominent over the Arctic region, accompanied by warm anomalies at the surface. Additionally, positive anomalies in the 500 hPa geopotential height and warm anomalies at the surface are observed along the eastern and western coasts of the North Atlantic. Conversely, negative anomalies in the 500 hPa geopotential height and cold anomalies at the surface are present in Eastern Europe and East Asia (Figure 6a). In the periods of weak stratospheric PV and strong tropospheric PV, negative anomalies in the 500 hPa geopotential height are prevalent over the polar region and the North Pacific, with cold anomalies at the surface. In contrast, positive anomalies in the 500 hPa geopotential height and warm anomalies at the surface are noted over North America, the eastern coast of the North Atlantic, and the northern side of the Gulf of Oman (Figure 6b). In the events featuring strong stratospheric PV and strong tropospheric PV, negative anomalies in the 500 hPa geopotential height prevail over the Arctic, accompanied by cold anomalies at the surface. On the contrary, positive anomalies at the 500 hPa geopotential height and warm anomalies at the surface are observed over Northeast Asia, Southern Europe, and North America (Figure 6c). During the weak stratospheric PV and weak tropospheric PV events, positive anomalies at the 500 hPa geopotential height dominate the high-latitude regions of the Arctic, extending towards North America and the North Pacific, which are accompanied by warm anomalies at the surface. Alternatively, negative anomalies at the 500 hPa geopotential height and cold anomalies at the surface are present over the mid-latitude regions of North America and the high-latitude regions of Eurasia (Figure 6d). In general, the tropospheric anomalies in the two consistent strong coupling events exhibit an annular mode structure; however, they differ in the mid latitudes, with opposite temperature anomalies observed. On the other hand, the two reverse strong coupling events display a stronger latitudinal asymmetry in the tropospheric anomalies, and these anomalies tend to extend to lower latitudes. In the events characterized by strong stratospheric PV and weak tropospheric PV, the tropospheric circulation and temperature anomalies are more complex, with multiple regional centers of cold and warm temperature anomalies observed at the surface. In contrast, the event characterized by weak stratospheric PV and strong tropospheric PV primarily leads to regional warm temperature anomalies outside the polar regions.

6. Conclusions and Discussion

Using daily ERA5 reanalysis data for the last 50 years, the intensity indices of the stratospheric and tropospheric PV in boreal winter were derived from the EOF analysis of geopotential height anomalies. The vertical propagation characteristics of the planetary waves and their corresponding tropospheric circulation anomalies were further investigated under four types of strong coupling events. The results show the following:

First, 40.10% of the total winter days are in a configuration where both the stratospheric PV and tropospheric PV are in normal states (moderate strength), 44.00% are in a configuration where one is normal and the other is anomalous, and 15.90% are in a configuration where both are anomalous.

Four distinct types of strong coupling events are categorized when both the stratospheric PV and tropospheric PV exhibit simultaneous anomalous behavior. The first type, characterized by strong stratospheric PV and weak tropospheric PV, represents 10.85% of the strong coupling days among the four types. It is influenced by mid- and high-latitude planetary waves, predominantly waves 1 and 2, leading to anomalous downward E-P flux from the stratosphere to the troposphere. The second type, featuring weak stratospheric PV and strong tropospheric PV, constitutes 9.25% of the strong coupling days. It involves anomalous upward E-P flux in high latitudes, predominantly induced by wave 1, and anomalous downward E-P flux in middle latitudes, mainly dominated by wave 2. The third type, characterized by strong stratospheric PV and strong tropospheric PV, accounts for 43.75% of the strong coupling days. It is associated with anomalous downward E-P flux in high latitudes, dominated by wave 1, and anomalous upward E-P flux in middle latitudes, with a wave 2 predominance. The fourth type, representing 36.43% of the strong coupling days, displays anomalous upward E-P flux in high latitudes, with dominant wave 1.

During various types of strong coupling events, notable disparities in tropospheric circulation anomalies are observed in mid-latitude regions. In the context of strong stratospheric PV and weak tropospheric PV, warm anomalies manifest on both sides of the North Atlantic, while Eastern Europe and East Asia encounter cold anomalies. In the periods of weak stratospheric PV and strong tropospheric PV, North America, Western Europe, and the northern side of the Gulf of Oman witness warm anomalies. Events featuring strong stratospheric PV and strong tropospheric PV bring about warm anomalies in Northeast Asia, Southern Europe, and North America. Lastly, events characterized by weak stratospheric PV and weak tropospheric PV lead to cold anomalies in the aforementioned regions, presenting an opposite pattern to the third type.

In existing research, considerable effort has been devoted to studying the interaction between the stratospheric potential vorticity and tropospheric anomalies. This has involved examining various time scales to understand their relationship, often by analyzing specific weather events or using climate simulations [9,40,41]. Some studies have also explored the role of the stratospheric vortex on the troposphere, considering aspects like its displacement and splitting [42,43,44]. However, the day-by-day collaborative connection of the variabilities in strength between the predominant zonal mean characteristics in the stratosphere and the troposphere during winter have been underexplored. Furthermore, such investigations encompass a comprehensive dataset covering all winter days, which minimizes the influence of case-specific selection.