Two distinct dynamical processes near the dynamical tropopause (2-PVU surface) and their relation are discussed in this study: stratosphere–troposphere exchange (STE) and the formation of distinct potential vorticity (PV) structures in the form of stratospheric and tropospheric streamers and cutoffs on isentropic surfaces. Two previously compiled climatologies based upon the 15-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-15) dataset (from 1979 to 1993) are used to establish and quantify the link between STE and these PV structures.
An event-based analysis reveals a strong relation between the two processes. For instance, on isentropes below 320 K, 30%–50% of the stratospheric streamers are associated with downward STE. In the reverse perspective, between 60% and 80% of all STE events between 290 and 350 K are found in the vicinity of at least one PV structure. On different isentropes, the averaged downward (STT) and upward (TST) mass fluxes associated with PV structures are quantified.
As a novel quantity, the activity of a particular PV structure is measured as the STT/TST flux per unit length of its boundary on the considered isentropic level. The STT activity for stratospheric streamers and the TST activity of tropospheric streamers reach similar values of 3 × 109 kg km−1 h−1. Thereby, the flux is not uniformly distributed along a streamer’s boundary. STT (TST) is found preferentially on the upstream (downstream) side of stratospheric streamers, and vice versa for tropospheric streamers. This asymmetry is lost for cutoffs, for which an essentially uniform distribution results along the boundaries.
Finally, the link between STE and PV structures shows considerable geographical variability. Particularly striking is the fact that nearly all deep STT events (reaching levels below 700 hPa) over central Europe and the North American west coast are associated with a stratospheric streamer.
Transport between the stratosphere and the troposphere (STE) is of great interest since these two regions of the atmosphere differ significantly in their characteristics (static stability, chemical composition). Many studies have shed light on the physical processes that lead to such a transport across the boundary between the two regions; that is, across the tropopause. Several dynamical processes have been identified to be associated with STE: tropopause folds near the polar jet (Danielsen 1968; Lamarque and Hess 1994), folds near the subtropical jet (Baray et al. 2000; Traub and Lelieveld 2003), cutoff lows (Ebel et al. 1991; Price and Vaughan 1993; Wirth 1995), mesoscale convective systems and thunderstorms (Poulida et al. 1996), breaking gravity waves (Lamarque et al. 1996), and filamentation and fragmentation of stratospheric streamers (Appenzeller and Davies 1992; Appenzeller et al. 1996a). These studies highlight the importance of synoptic- and mesoscale processes for STE. Strong focus was also given to these scales in the review of Stohl et al. (2003), in contrast to the earlier review by Holton et al. (1995), which emphasized mainly the global-scale aspects of STE.
Most of the previous studies focused on individual events and did not provide a climatological picture. The value of detailed case studies is the gain in insight into the physical processes that lead to the exchange of air mass across the tropopause. On the other hand, the limiting aspect is the possible lack of representativeness of the derived STE fluxes. In fact, many case studies are selected especially for the clear occurrence of the phenomenon of interest, and therefore should be used carefully for climatological purpose.
The aim of this study is to discuss the climatological aspects of the event-based link between potential vorticity streamers and cutoffs and STE in the extratropics. To achieve this aim, detailed climatologies of the two phenomena must be available.
In the last few years, great effort has been put into obtaining such climatologies. First approaches toward an STE climatology concentrated on hemispheric budget calculations (Haynes et al. 1991; Holton et al. 1995; Appenzeller et al. 1996b) and did not resolve the individual physical processes underlying STE. The synoptic- and mesoscale processes were in the focus of detailed Eulerian and Lagrangian methods. The Eulerian methods turned out to be difficult to apply to real datasets [see Wirth and Egger (1999) for a critical analysis]. Wirth and Egger showed the robustness of a Lagrangian method compared to the Eulerian ones, and Wernli and Davies (1997) and Meloen et al. (2001) applied Lagrangian approaches to single events. Later, Stohl (2001) and Wernli and Bourqui (2002) provided one-year Lagrangian climatologies of STE. Based on their confidence in the method, the climatologies were extended to the whole 15-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-15) period from 1979 to 1993 within the research project Influence of Stratosphere–Troposphere Exchange in a Changing Climate on Atmospheric Transport and Oxidation Capacity (STACCATO; Sprenger and Wernli 2003; James et al. 2003a, b; Stohl et al. 2003).
Isentropic potential vorticity (PV) streamers and cutoffs are dynamically significant structures in the upper troposphere/lower stratosphere (Hoskins et al. 1985). Here, stratospheric PV streamers are defined as narrow filaments of high-PV air, which extends far toward the equator. Correspondingly, tropospheric PV streamers refer to elongated filaments of low-PV air that extends far toward the pole. These PV streamers can eventually break up into distinct high- (stratospheric) or low- (tropospheric) PV cutoffs. Despite their significance, only few studies exist that focus on seasonal and geographical variability of PV streamers and cutoffs. Postel and Hitchman (1999) considered breaking Rossby waves along the subtropical tropopause, and Waugh and Polvani (2000) looked at stratospheric intrusions into the tropical upper troposphere. Both studies focus on the subtropical region and could be of interest to STE in this region. For the extratropics Wernli and Sprenger (2007) identified stratospheric and tropospheric PV streamers and cutoffs for the whole ERA-15 period. The number of climatological studies on cutoffs is even more limited. Price and Vaughan (1992) discuss the statistics of cutoff low systems, which are often associated with stratospheric PV cutoffs.
In this study, we rely on the 15-yr climatologies of STE (Sprenger and Wernli 2003) and of PV streamers and cutoffs (Wernli and Sprenger 2007). In the following, a detailed event-based approach will address the following key questions: What percentage of STE is associated with PV structures? How strong are stratosphere → troposphere transport (STT) and troposphere → stratosphere transport (TST) mass fluxes that are related to a typical PV structure? Where does STE take place relative to the PV structure’s position? Finally, are there geographical regions where the link between STE and PV structures is particularly strong or weak? The used datasets are shortly described in section 2. A comparison of the geographical distributions of the two climatologies in section 3 further motivates an event-based analysis for quantifying the link between the two (section 4). Then, section 5 discusses the position of STT/TST relative to PV structures, and section 6 the geographical variability of the link. Finally, in section 7, a measure for a PV structure’s exchange activity is defined.
All analyses in this study are based upon datasets that were independently derived from the ERA-15 reanalysis. This reanalysis comprises the years 1979 to 1993, with a 6-h time resolution. The horizontal resolution is T106, corresponding to approximately 1°, and 31 hybrid levels are used in the vertical. The analysis scheme itself is based upon optimal interpolation. Further details concerning ERA-15 are available from Gibson et al. (1997).
The first dataset is a 15-yr Lagrangian analysis of cross-tropopause mass exchange, and is presented in detail in Sprenger and Wernli (2003). For every diagnosed exchange event in the 15-yr ERA period the following quantities are archived: time, latitude, longitude, and potential temperature where the exchange trajectory crosses the tropopause. The resulting dataset distinguishes between STT and TST, and additionally between vertically shallow and deep exchange events. Exchange trajectories that reach (for STT) or originate from (for TST) levels below 700 hPa are classified as deep STE events. To exclude spurious exchange events, which move to and fro along the tropopause, a stringent residence time criterion is applied. Every TST trajectory must stay at least 96 h in the troposphere before crossing the tropopause and 96 h in the stratosphere thereafter, and vice versa for STT.
The second dataset is a 15-yr climatology of stratospheric and tropospheric PV structures, as introduced by Wernli and Sprenger (2007). Stratospheric PV structures refer to both elongated streamers and cutoffs of stratospheric air and will be referred to as SPV. Correspondingly, TPV is used for tropospheric PV structures. This dataset comprises latitude and longitude of the PV structures on isentropic surfaces. The temporal resolution is 6 h and the PV structures are identified on the isentropic surfaces from 290 up to 350 K with a vertical spacing of 5 K.
3. Climatological perspective
First, we compare the geographical distribution of the two climatologies on selected isentropes in a qualitative way. Figure 1 shows STT and TST mass fluxes superimposed on frequencies of stratospheric and tropospheric PV structures for the 310- and 340-K isentropes during winter. All STE events are considered that occur within ±5 K of the specified isentropes.
On 310 K, the patterns for STT and SPV match fairly well. The absolute maxima are found for both climatologies over the Mediterranean/Eastern European sector, although with STT slightly shifted to the southwest relative to SPV. Such a shift might be expected since exchange often takes place at the southwestern tip of SPV (see section 5). Secondary maxima over the eastern Pacific and western United States also match well. Figure 1 also suggests a substantial regional variability in the link between SPV and STT. For instance, a stronger relationship seems to exist over the Mediterranean than east of Lake Baikal or over the western North Pacific. On 340 K, the maxima of STT and SPV again match fairly well, but STT is significantly reduced relative to 310 K while the SPV maxima reach comparable values. This suggests that STT associated with SPV is stronger on 310 than on 340 K.
A relationship exists also between TST and SPV (consider the gray shading in the lower panels and the contour lines in the upper panels of Fig. 1). The TST maxima are north of the SPV maxima, in contrast to the maxima of STT which are slightly farther south. This indicates that TST is located more on the northern flanks and STT more near the southern tip of SPV. This will be further investigated in section 5. Overall, the link between TST and SPV appears to be weaker than the one between STT and SPV.
The relationship between TPV and TST is shown in the lower panels of Fig. 1. A good match is discernible on 310 K. An essentially zonally symmetric ring around 50°N marks the positions where TST and TPV occur. On 340 K this link is less evident. In particular, the local TPV maximum over the eastern Pacific does not go along with a corresponding TST maximum.
Finally, STT is shifted toward the south relative to TPV on both isentropes (consider the gray shading in the upper panels and the contour lines in the lower panels of Fig. 1). This indicates that STT can be expected only at the southernmost parts of a TPV and that the link between TPV and STT is weaker than the one between SPV and STT.
Concluding, this qualitative comparison of the climatologies of PV structures and STE hints toward a link between the two dynamical features. It appears to be stronger between corresponding phenomena (SPV/STT and TPV/TST) and also depends on the considered isentropic level. Furthermore, the relative shift between PV structures and STE maxima indicates that STE is asymmetrically distributed around PV structures. These preliminary conclusions set the background for the event-based analysis in the next section. There, we circumvent the caveats and dangers for misinterpretation, which are possible if relying only on simple superposition of two climatological distributions.
4. Event-based perspective
In this section the link between PV structures and STE is quantitatively established for individual events. This analysis is performed in two ways. The first approach addresses questions like: Given a PV structure, what is the probability that STE takes place in its vicinity? The second approach asks the reversed question: Given a STE event, how likely does it occur near a PV structure? We will refer to the former as the PV structure perspective and to the latter as the STE perspective.
a. PV structure perspective
Here, the following strategy is applied: For each PV structure on a specific isentropic surface it is checked whether STT or TST is found within a horizontal distance of 300 km, a vertical distance of ±5 K, and a time interval of ±1 h. If this is the case, the PV structure is regarded as linked with STE.
Figure 2 gives the percentage of PV structures that are linked to STT or TST. During winter months [December–February (DJF)], about 50% of stratospheric streamers on 300 K are linked with STT (Fig. 2a). This percentage decreases when considering higher isentropes (about 30% on 320 K). The link between tropospheric streamers and STT shows a qualitatively similar pattern, but the values are lower (about 30% on 300 K, Fig. 2a). Stratospheric cutoffs are expected to be primarily related to STT events. This link reaches values of about 20% to 30% in winter; that is, smaller values than obtained for streamers. This indicates that some stratospheric cutoffs do not erode and thus contribute to STT, but are, in fact, reabsorbed at later times by the stratospheric PV reservoir. Another possibility is that erosion is slow and that cutoffs are not associated with STE every 6 h during their life cycle. Our method considers every time instant independently and therefore a link value of 25% does not mean that 75% of the cutoffs never experience STT during their life cycle. Finally, tropospheric cutoffs are only rarely associated with STT (Fig. 2a). During summer (Fig. 2e) the maximum percentage for the link between STT and the PV structures is shifted toward higher isentropes (320 K) and the values are in general larger. This shift is to a large extent associated with the seasonal cycle of the isentropic surfaces.
The link between PV structures and TST is shown in Figs. 2b,f for winter and summer, respectively. Here the highest percentages are reached for tropospheric streamers with approximately equal values (about 40%) in summer (at 320 K) and in winter (at 305 K). The percentage of stratospheric streamers that are linked with TST is quite large, but nearly always smaller than for tropospheric streamers. Similarly, tropospheric cutoffs are significantly more often linked with TST than stratospheric cutoffs. This illustrates the primordial relationship between SPV and STT and between TPV and TST, respectively.
Finally, the percentage of PV structures linked with deep STT (Figs. 2c,g) and deep TST (Figs. 2d,h) is considered. Remarkably high values (up to about 20% on 300 K) are found for stratospheric streamers and deep STT in winter. This percentage even increases to 24% (28%) if only the largest 50% (10%) of all stratospheric streamers are considered. A significant link is also discernible between stratospheric and tropospheric streamers and deep TST (about 10%). Interestingly, both types of streamers reach similar values, in contrast to deep STT where stratospheric streamers are predominant.
To account for all STE events in the vicinity of PV structures, Table 1 gives the averaged STT and TST mass fluxes associated with individual PV structures at three isentropic levels during winter. At all three levels stratospheric streamers are predominantly associated with STT, but TST reaches approximately 50% of the STT flux. For tropospheric streamers a reversed pattern is found; however the overall TST flux associated with tropospheric streamers is smaller than the STT flux associated with stratospheric streamers. Finally, the fluxes associated with cutoffs are significantly smaller than the fluxes linked to streamers. There is a clear sensitivity of the fluxes to the area of the PV structures. For instance, on 320 K the STT flux per stratospheric streamer is 0.68 × 1012 kg h−1 if all streamers are considered. This value changes to 0.31 × 1012 kg h−1 (1.04 × 1012 kg h−1) for streamers with below (above) median area. A similar dependence on the area is found for all types of PV structures.
b. STE perspective
Here we pose the question: Is a particular STT or TST event associated with a PV structure. The methodology is similar to the one used in the previous section: It is checked whether there are PV structures near the particular STE event. In the horizontal, a radius of 300 km is used to search for PV structures. In the vertical, the nearest two isentropic levels of the PV structure climatology are considered. Note that the STE event can take place at any isentropic level, whereas the PV structures are identified only on a stack of isentropes with 5-K vertical spacing. For similar reasons, consideration is given only to STE events within a time window of ±1 h around the ERA-15 analysis times; that is, the times at which the PV structures are identified.
In Fig. 3 the link between STT and TST with any type of PV structure is given as a function of potential temperature for winter and summer. The percentages are very high. STT is in approximately 80% of the cases found in the vicinity of PV structures. The corresponding values for TST are of the same order of magnitude. However, deviations are found for summer at low isentropic levels (below 315 K) and for winter at high isentropic levels (above 340 K). From 300 to 330 K for winter (320 to 350 K for summer) the percentages of STT and TST are rather constant. These isentropes intersect the tropopause in the midlatitudes between approximately 30° and 70°N (see Fig. 1 in Liniger and Davies 2004). Hence, the link of STE and PV structures is particularly strong in the midlatitudes. In contrast, in the subtropics Sprenger and Wernli (2003) showed that approximately 50%–70% of STE events take place in the vicinity of tropopause folds. This implies that STE occurs mainly near quasi-stationary tropopause folds in the subtropics and near the more transient PV streamers and cutoffs in the midlatitudes.
5. Preferred locations for STE
In this section, consideration is given to the typical location of STE along the PV structure boundaries. Four illustrating cases are shown in Fig. 4. The identified PV structures on 320 K are marked with a bold black line and stars (open circles) mark the positions of STT (TST) events between 315 and 325 K and within a time window of 1 h around the time of the PV structures.1
The cases illustrate that STT (TST) occurs predominantly upstream (downstream) of a stratospheric streamer and vice versa for tropospheric streamers. The cooccurrence of STT and TST is significantly reduced for cutoffs. Furthermore, the streamer’s upstream/downstream STE asymmetry is replaced by a more symmetrical pattern for cutoffs. To get representative results, composites of many PV structures and their associated STE fluxes are depicted in Fig. 5. For instance, Fig. 5a considers all stratospheric streamers on 320 K during winter with an area larger than the median area 5 × 105 km2. For each streamer in the composite, the surrounding STT flux is determined and centered at the streamer’s center of mass. The superposition of all these patterns shows that the composite’s STT maximum is found on the western flank of the stratospheric streamers. Typically the STT flux reaches 100 kg km−2 s−1 and the area-integrated STT flux associated with the streamer is 1.03 × 1012 kg h−1 (cf. with Table 1). As an additional interesting feature, the averaged stratospheric streamers show a slight southwest–northeast (SW–NE) orientation. This corresponds to the LC1 upper-level PV pattern, as introduced by Thorncroft et al. (1993).
In comparison, TST events (Fig. 5c) are predominantly found along the northeastern part of a stratospheric streamer. Note that the maximum of the TST flux is less localized than the STT maximum and the peak TST fluxes (60 kg km−2 s−1) reach only about half the STT peak fluxes (120 kg km−2 s−1). Nevertheless, it is remarkable that STT and TST fluxes of stratospheric streamers are comparable in magnitude. The area-integrated TST flux yields 0.44 × 1012 kg h−1, compared to 1.03 × 1012 kg h−1 for the STT flux.
Composites for tropospheric streamers are shown in Figs. 5b,d. STT occurs near the southeastern part of the streamer, whereas maximal TST flux is found on the western flank. The STE fluxes are less localized than for stratospheric streamers, particularly for TST. The area-integrated STT and TST fluxes amount to 0.44 × 1012 kg h−1 and 0.7 × 1012 kg h−1, respectively. In accordance with Table 1 the overall STE fluxes of tropospheric streamers are somewhat smaller than for stratospheric streamers. Finally note that in the mean the tropospheric streamers show no slanted orientation.
At other isentropic surfaces (not shown), essentially the same pattern emerges for stratospheric streamers, with only minor differences. At 300 K the SW–NE tilt of the stratospheric streamer composite disappears. This indicates a more symmetric occurrence of LC1 and LC2 type streamers. In contrast, at the higher 340-K isentrope the tilt of the streamer composite is more pronounced.
Cutoffs are expected to exhibit different patterns of STT and TST than streamers. This is illustrated in Fig. 6, which shows composites of cutoffs and their associated STE fluxes. Since cutoffs detach from the tropospheric or stratospheric PV reservoir on an isentropic surface, they lose the memory to the predetached asymmetric state and its dynamics. A completely detached quasi-circular cutoff is associated with an axisymmetric circulation. Therefore, STT and TST are essentially symmetrically distributed around stratospheric and tropospheric cutoffs, respectively (Figs. 6a,d).
Finally, the position of STT (TST) relative to tropospheric (stratospheric) cutoffs exhibits an asymmetry. For instance, TST is found predominantly to the north of the stratospheric cutoff (Fig. 6c) and originates primarily from the time and location of the detachment. An analog argument shows that STT should be predominantly found on the southern side of the tropospheric cutoffs, as discernible in Fig. 6b.
6. Sensitivity of link to geographical region
In the previous sections, the link between STE and PV structures was considered as a function of potential temperature. Here, focus is given to the geographical variability of the link.
Figure 7 shows the winter-mean STT flux integrated between 290 and 350 K, which is or is not linked with a stratospheric PV structure (the link being defined as in section 4b). The plots can be compared to Fig. 2a in Sprenger and Wernli (2003) where the total STT flux is depicted. The STT flux linked with stratospheric PV structures is predominantly found in bands extending from the central Pacific to the west coast of the United States and from Nova Scotia to Eastern Europe. The not-linked STT flux, on the other hand, is found preferentially in the western Pacific and in a localized maximum between the southern tip of Greenland and Iceland. It is associated either with TPV or broad troughs (potentially with pronounced tropopause folds) that are not classified here as PV streamers. Overall, most of the STT flux is linked to a stratospheric PV structure. This reverses for tropospheric PV structures (not shown). The STT flux that is not linked to a tropospheric PV structure is significantly larger than the one that is linked.
The corresponding plots for the link between TST flux and tropospheric PV structures are shown in the lower panels of Fig. 7 (to compare with Fig. 2b in Sprenger and Wernli 2003). Three maxima are discernible for the link with stratospheric PV structures: over the western Pacific, over Labrador Sea, and over Eastern Europe. A significant TST flux that is not associated with tropospheric PV structures is found over the pole and the Labrador Sea.
The link between deep STE and PV structures is shown in Fig. 8. Deep STT over the U.S. West Coast and over central Europe is often linked with a stratospheric PV structures. The deep STT flux that is not linked to stratospheric PV structures is considerably smaller than the one that is linked and it is restricted to a narrow region at the entrance of the North Pacific storm track and to a band from the southern tip of Greenland to Iceland. Note particularly that nearly all deep STT events over Europe are linked with a stratospheric streamer. A similarly striking pattern emerges for deep TST and tropospheric PV structures. Over the western North Atlantic approximately equal parts of the flux are and are not associated with tropospheric PV structures. Over the western and central North Pacific, on the other hand, the linked flux is significantly stronger than the one that is not linked.
7. STE activity of PV structures
The larger a PV structure, the more likely it is linked with STE. This is shown in Fig. 9 in which the percentage of PV structures on 320 K that are linked with at least one STE event is plotted against their boundary length. The percentage of stratospheric streamers linked to at least one STT event is approximately 30% at 320 K (as already seen in Fig. 3a). Figure 9a illustrates that this percentage decreases to near 10% for a streamer contour length of 2000 km and increases to near 60% for a length of 10 000 km.
The dependence on the boundary length is more or less linear and discernible for all types of PV structures, for TST as well as for STT (Fig. 9b), and on several isentropes (not shown). Note that the slope for the link between SPV and STT is larger than the slope for the link between stratospheric PV structures and TST. This again confirms that the boundary of a SPV structure is more susceptible to STT than to TST. An analog, but reversed situation is found for the link between TPV and STE: The slopes for the link of tropospheric PV structures with TST are larger than the ones with STT. The discrepancy in the slopes is particularly evident for small to medium size PV structures (contour length <6000 km) and vanishes essentially for very large PV structures.
STE takes place across the boundary of a PV structure. Therefore, the STE flux per unit length of the PV structure’s boundary is introduced as a useful measure of its STE activity. Figure 10, shows for winter and summer the mean length (in km) and the STT and TST activity (both in 109 kg km−1 h−1) as a function of potential temperature. A clear increase is discernible for all types of PV structures toward lower isentropes. Note also that the mean PV structure’s length remains fairly constant over the considered range of potential temperatures. At the lowest isentropic levels, the STE activity flattens or even decreases again. The flattening is particularly evident for summer TST, which becomes essentially constant below 325 K.
In this study, we presented a detailed analysis of the link between PV structures (streamers and cutoffs) and STE on a stack of isentropic surfaces from 290 to 360 K with a 5-K interval. The analysis is based upon the 15 years of the ERA-15 dataset (from 1979 until 1993), which was previously used to derive separate climatologies of PV structures (Wernli and Sprenger 2007) and STE (Sprenger and Wernli 2003).
The geographical overlap of the two climatologies indicates a link between PV structures and STE (Fig. 1), but remains qualitative in nature. An event-based approach was applied to quantify the link. This refinement basically addressed the following two questions: (i) Is an individual PV structure linked with either STT or TST and (ii) is an individual STT or TST event linked with a PV structure? The answers significantly depend on the isentropic level and the season. Therefore, a concise analysis must necessarily rely on several isentropic levels and on seasonal comparisons. The main results from this quantitative analysis are:
Potential vorticity structures are often linked with STE (referring to the above question i). For instance, during summer more than 50% of the stratospheric streamers on 320 K are associated with STT (Fig. 2e). This value is lower for tropospheric streamers and stratospheric cutoffs (30%) and minimum for tropospheric cutoffs (10%). Similar values exist during winter with maxima shifted to lower (about 300 K) isentropic surfaces (Fig. 2a).
Particularly in winter, PV structures are linked with so-called deep STE events, that is, with STT and TST events that reach to or originate from the planetary boundary layer, respectively (Figs. 2c,d,g,h). Approximately 15% (10%) of stratospheric streamers at 300 K are associated with at least a deep STT (TST) event. For tropospheric streamers the corresponding values are 7% for STT and 10% for TST. With increasing area of the PV streamers, the percentages significantly increase and reach typically up to 30% for the largest 10% of all streamers.
The percentage of STE events that occur in the vicinity of a PV structure (referring to the above question ii) amounts to between 60% and 80% irrespective of season. Hence, STE preferentially takes place where the tropopause is distorted and forms distinct PV structures. The statistical significance of this result is briefly discussed in the appendix.
Stratospheric streamers have a larger STT than TST mass flux (Table 1). At 300 K and during winter, a stratospheric streamer is associated on average with a STT flux of 1.74 × 1012 kg h−1 and a TST flux of 0.92 × 1012 kg h−1. The corresponding averaged fluxes for a tropospheric streamer are 0.65 × 1012 kg h−1 for STT and 0.95 × 1012 kg h−1 for TST. At higher isentropic levels, these fluxes are reduced in amplitude, but the ratio of major and minor fluxes remains approximately the same. Cutoffs have smaller fluxes than streamers, mainly due to their smaller size (see Figs. 5, 6). At 300 K and in winter, the STT and TST fluxes for stratospheric cutoffs are 0.69 × 1012 kg h−1 and 0.16 × 1012 kg h−1, respectively. The corresponding fluxes for tropospheric cutoffs are 0.16 × 1012 kg h−1 and 0.34 × 1012 kg h−1. Generally, the contrast between the two flux directions is larger for cutoffs than for streamers.
A PV structure’s STE flux necessarily takes place across its boundaries. The longer this boundary is, the larger the probability that the PV structure is linked with STE. This increase is essentially linear with respect to the PV structure’s length (Fig. 9).
A measure for a PV structure’s exchange activity is the STE flux per unit length of its boundary. The so-defined STT activity reaches maximum values of 3 × 109 kg km−1 h−1 for the boundaries of SPV on 300 K during winter and equally on 325 K during summer (Fig. 10). The corresponding TST activity maximum is around 2.5 × 109 kg km−1 h−1 for TPV. The peak values are remarkably similar for streamers and cutoffs. Toward higher isentropic levels, the activity considerably decreases. For instance, the STT activity of a stratospheric streamer is smaller by a factor of about 3 at 330 K compared to 300 K.
STT and TST is not randomly distributed around a streamer, but essentially related to its dynamics (Figs. 4 and 5). Medium- and large-sized stratospheric streamers (larger than 5 × 105 km2) have STT especially on their upstream side (to the west) and TST on their downstream side (to the northeast). Also, the STT flux is stronger confined and more intense. Tropospheric streamers experience STT along their southeastern boundary and TST along their western flank. For cutoffs, STT and TST are approximately randomly distributed along their boundary (Figs. 4 and 6). Hence, the cutoffs forget the dynamics that lead to their formation as they move away from the source region: they attain a circularly symmetric structure and allow STE to take place uniformly along their boundary of the cutoff.
Climatological distributions of STE and PV structures show significant deviations from zonal symmetry (Fig. 1). A similar geographical variability was found for the link between STE and PV structures. Most of the STT flux is linked to either SPV (Fig. 7). Exceptions are found in the polar region, where only few SPV are found, and in a band between the southern tip of Greenland and Iceland. TST that is linked to a TPV is found in three localized regions: the western Pacific, Labrador Sea, and Eastern Europe (Fig. 7). TST not linked with a TPV occurs mainly over the pole and south of Greenland.
Deep STT that is linked to a SPV is found over the western coast of North America and over central Europe (Fig. 8). No link to these structures is found in the westernmost Pacific (near Japan) and near the southern tip of Greenland. For deep TST, most events in the western and central Pacific are linked to a TPV. Over the western Atlantic, an approximately equal part is linked and not linked to a tropospheric PV structure.
The present study focused on the climatological (i.e., statistical) link between STE and PV structures of the extratropical tropopause in the Northern Hemisphere. While performing the analysis, we were impressed by the rich variety of individual cases. Therefore, it should be kept in mind that eventually the interplay of detailed individual case studies and climatological analyses will lead to a complete understanding of the relationship between STE and PV structures. Also this study focused exclusively on the tropopause structures and did not consider the actual physical process (radiation, condensational heating, turbulence) and their relative importance that lead to the PV changes associated with STE. The numbers given to quantify the link depend upon the parameters used to identify links. This sensitivity appears to be larger for the PV structure perspective compared to the STE perspective (see appendix).
As a final caveat, we note the results presented pertain to diagnostics applied to the ERA-15 dataset. Its quality is limited by lack of observations, models errors, and approximations in the data assimilation technique. Nevertheless, this study provided, so far, the most comprehensive picture of STE and extratropical PV structures and, owing to the very large number of events included in the climatology, provides a representative picture of the important link between the two phenomena.
We thank MeteoSwiss and ECMWF for access to the ERA-15 dataset.
Likelihood and Sensitivity of a PV–STE Link
Level of significance
Figure 2 indicates a strong link between PV structures and STE, but does not specify the level of significance of the resulting values. A thorough inspection is necessary since single PV structures and STE events could accidentally be close, and thus be classified as linked by the algorithm used in this study.
Here, we assess the degree of such an accidental geographical link on one specific isentropic surface (315 K) by the following method. First, a hypothetical circular PV structure of radius 500 km is placed within a region where many STT events can be expected due to the climatological STT distribution on 315 K (here, over the Pyrenees). In this region approximately 20 STT events can be found in the range of 315 ± 4 K and within a time window of ±1 h (i.e., the specifications that define a link between STE and PV structures; see section 4a). These 20 STT events are then randomly distributed on the 315-K isentrope according to the climatological distribution, and the link analysis performed. From this Monte Carlo experiment it was found that the random probability of a link is 9.75%. This value has to be compared with the 50% found in Fig. 2a. Similar tests for other isentropic levels and other PV structures confirm the overall statistical significance of the link between STE and PV structures.
Similarly, the link between STE and PV structures (section 3b) might be accidental. A simple, though nonstringent, test is based upon a composite plot that shows the position of PV structures relative to STE events. For instance, stratospheric streamers are predominantly located to the northeast of a STT event and to the southwest of a TST event (not shown), in agreement with the corresponding plots for the PV structure perspective (Fig. 5). If the links were just accidental and, therefore, without physical meaning, the PV structures would be randomly distributed around the STE event.
A more stringent statistical test uses the following strategy: The link analysis as described in section 4b is repeated eight times but with randomly interchanged dates of the STE events. This shuffling of the dates necessarily destroys any causal link between PV structures and STE while retaining the same dataset and climatological means. The Monte Carlo experiments give typically a percentage of 16% to 23% for the link between STT and SPV, whereas the real link is approximately a factor of 2 larger.
Sensitivity on parameters
Here, the sensitivity of the results on the parameters used to define a link between a PV structure and STE is discussed. The standard parameters are horizontal (vertical) distance smaller than 300 km (5 K), and simultaneous occurrence (within a time window of ±1 h). The number of PV structures linked with STE on 320 K increases if either the horizontal search radius or the time window is increased (see Table A1 for January 1980). The bold values correspond to the standard setting for the study.
The left-hand side of the table reveals a significant sensitivity with respect to the parameter settings. Therefore, the numbers should not be taken as absolute values. Nevertheless, the standard parameters of 300 km and 1 h are physically well suited for quantifying a link between PV structures and STE, given the horizontal and temporal resolution of the reanalysis dataset and its underlying dynamics. We expect the true values to have approximately the order of magnitude for the standard setting and the other parameter settings to yield upper and lower limits.
A smaller sensitivity is found for the STE perspective (rhs). In Fig. 3, the 15-yr climatological percentages are around 80%, whereas for January 1980 a somewhat larger value of 92% results. Even for a small radius of 150 km 79% of the STT events are linked. Finally, the sensitivity with respect to the time window is weak.
Corresponding author address: Michael Sprenger, Institute for Atmospheric and Climate Science, ETH Zentrum, CH-8093 Zurich, Switzerland. Email: email@example.com
To highlight the relative position where STT and TST takes place relative to the PV structure the STT and TST residence time was reduced to 24 h (in comparison to 96 h for the rest of the paper; see section 2). This reduction leads to a better statistics, while the qualitative patterns remain the same.