As outlined in Sect. 1, we employ output from four reanalysis models in this study: ERA-Interim, JRA-55, MERRA, and MERRA-2. ERA-Interim is available from 1979 to the present on an approximately 80 km horizontal grid and at 60 vertical model levels with a model top of 0.1 hPa . JRA-55 is available from 1958 to the present on a ∼ 60 km horizontal grid . Similar to ERA-Interim, JRA-55 has 60 vertical model levels with a model top of 0.1 hPa. MERRA is available from 1979 to 2016 at 0.5∘ × 0.667∘ horizontal resolution and at 72 vertical model levels with a model top of 0.01 hPa . MERRA-2 has a similar design to MERRA, but is available at a slightly finer horizontal resolution of 0.5∘ × 0.625∘ from 1979 to the present . Although the horizontal and vertical resolution is similar in MERRA and MERRA-2, numerical improvements in MERRA-2 are expected to better represent UTLS processes. We use both MERRA and MERRA-2 to show improvements with respect to UTLS processes, specifically STE. For a more detailed discussion of reanalyses and their differences, see .

Furthermore, we employ 3-D output at 6 h intervals from each reanalysis in this study. All of the data are interpolated to a regular 1∘ × 1∘ latitude–longitude grid for analysis. Model output is also used to calculate secondary variables for analysis: tropopause pressure (using the World Meteorological Organization lapse-rate tropopause (LRT) defined by ), potential temperature (θ), and potential vorticity (PV) on the native model levels (i.e., no vertical interpolation is performed). It is important to note that, while the interpolation to a regular horizontal grid acts to slightly coarsen the original data, the interpolation has no measurable effect on the LRT altitude distribution and, given the 6 h time resolution, is expected to have little impact on trajectory model solutions e.g., seeand references therein.

The tropopause definition employed in STE studies is critical to their outcome since it represents the boundary between troposphere and stratosphere and the location where dynamical processes and associated transport are evaluated. Many previous STE studies have used a “dynamical” tropopause to represent the troposphere–stratosphere boundary, for which a PV isosurface such as 2 PVU (1 PVU = 10-6 km2 kg-1 s-1) is used . However, several studies demonstrate that STE estimates can be largely sensitive to small changes in the PV isosurface used. For example, their Fig. 6 made Lagrangian estimates of STE using multiple control surfaces, including isobaric surfaces and potential vorticity isosurfaces, and found downward mass flux ranged from 1 to 4 ×1017 kg year-1. used 30 years of ERA-Interim to produce a climatology of Rossby wave breaking events and associated STE in the subtropics and demonstrated that varying the PV boundary from 2 to 4 PVU resulted in a reversal of the net transport direction (i.e., TST or STT). Despite these known sensitivities, many studies have continued to employ a dynamic tropopause to avoid challenging STE calculations in the vicinity of the sharp LRT discontinuity near the subtropical jet known as the “tropopause break” e.g.,. Because PV is a quasi-conserved quantity in an adiabatic and frictionless flow, it is treated as a quasi-material surface and can provide a continuous boundary through the tropopause break. An additional aspect of a PV-based method that is problematic for global STE studies is the fact that PV values converge to zero at the Equator, such that an isosurface does not coincide with the altitude of the tropical tropopause south of the tropopause break. As a result, most studies that use a PV-based method in the extratropics select an alternative surface to represent the tropopause in the tropics (e.g., cold point altitude, isentropic surface).

The LRT, on the other hand, has been shown to commonly coincide with the sharpest stability and chemical transitions between the troposphere and stratosphere globally e.g.,. This is due to the fact that a single PV value does not coincide with the LRT and chemical transition everywhere, with PV values at the tropopause ranging from at least 1 to 6 PVU in the extratropics. As a result, some recent studies advocate for and employ a PV gradient-based tropopause for STE studies e.g.,, but such an approach continues to suffer from an inability to represent the troposphere–stratosphere transition in the tropics. One exception to the success of the LRT as a reliable troposphere–stratosphere boundary is in the Antarctic region during austral winter, where reduced stability in the upper troposphere leads to an erroneously high LRT altitude . However, this issue is limited to latitudes poleward of 60∘ S (∼ 6 % of Earth's area) and about 3 months out of the year. For these reasons, we use the LRT to represent the global troposphere–stratosphere boundary in this study but leverage beneficial information from PV analyses to identify irreversible transport. A detailed outline of this approach is provided in the following subsection. Apart from infrequent biases in the LRT altitude, its uncertainty is comparable to the UTLS vertical resolution of the dataset used, which varies amongst the reanalysis models. An approximate altitude range of the UTLS is 8–14 km in the extratropics and 13–18 km in the tropics. Vertical resolution in MERRA and MERRA-2 is about 1 km throughout the extratropical and tropical UTLS, whereas JRA-55 and ERA-Interim vertical resolution ranges from about 750 m in the extratropical UTLS to about 1100 m in the tropical UTLS. These differences in resolution may contribute to differences in STE found between the reanalyses outlined in the remainder of the paper.

Trajectory calculations (∼6×109) in this study are performed using the TRAJ3D model developed by and updated in . Parcels are initialized daily at 00:00 UTC every 1∘ in longitude and latitude and every 20 hPa at altitudes relative to the LRT. Analogous to STE methods in previous studies, preliminary selection of STE parcels is dependent upon whether trajectories cross the LRT within the initial 24 h downstream. This selection is a straightforward process and only requires the initial and final parcel pressure and coincident tropopause pressures. For instance, if a parcel pressure is initially lower than its coincident tropopause pressure and one day downstream the parcel pressure is greater than its coincident tropopause pressure, it is flagged as possible STT (regardless of the geometric evolution of the parcel). All potential STE parcels are then advected 5 days forward and backward in time from the initial parcel locations for further analysis.

To ensure that transient (intermittent tropopause-crossing) STE parcels are not erroneously counted and represented as irreversible exchange, a filtering method is applied. Two criteria are necessary to identify irreversible transport: (i) a residence time (τ) and (ii) a parcel PV change occurring during the 10-day trajectory period. Based on a sensitivity study by , a long residence time, longer than 24 h, can decrease estimates of irreversible transport and change the direction of the annual net STE. Also, a 4-day residence time allows STE processes with longer transport timescales to be identified. Here, we chose a strict residence time criteria, τ, of 96 h. The second filtering criteria require an absolute PV change of 0.5 PVU from the initial parcel value to that 5 days downstream. The PV criteria represent a dynamic change in a parcel's characteristics from the influence of diabatic or frictional effects (i.e., mixing). Parcels that meet the required criteria are retained as irreversible exchange.

To examine irreversible STE mass flux, we compute the mass of each parcel based on the following equation: M=1ga02cos⁡ϕΔλΔϕΔp, where Earth's gravitational acceleration and radius are denoted by g and a0, respectively, and ϕ, λ, and p represent latitude, longitude, and pressure scales of each parcel. Since the parcel resolution is constant, parcel mass decreases from the Equator to the poles. Therefore, a greater number of transported parcels are required in the extratropical and polar latitudes to achieve equivalent STE to that in the tropics and subtropics. We bin STE parcels on a global grid with a longitude–latitude resolution of 2∘ for analysis. For this purpose, the 1-day downstream parcel locations are used in an attempt to better represent the locations where STE occurred. Slight differences in the locations of STE in the comparisons with Š14 in Sect.  (below) may be due to this choice, since Š14 use their initial parcel locations for binning.

In an attempt to evaluate the role of individual large-scale STE processes globally, we separate transport into three regional categories: tropics, subtropics (i.e., between the tropical UT and extratropical LS), and extratropics. STT and TST occur in each of the three regions and are counted separately. For large-scale STE processes, exchanges in the subtropics are known to correspond primarily with Rossby wave breaking, which is a quasi-horizontal (or isentropic) process. Exchanges in the extratropics and tropics, however, are associated with other processes, such as extratropical cyclones, stratospheric intrusions, downwelling in the extratropics and upwelling in the tropics.

We classify regions as tropical if they lie equatorward of the “tropopause break” and extratropical if they lie poleward of the break. Similar to previous studies, the tropopause break is defined as the LRT altitude frequency minimum between tropical (15–17 km or < 150 hPa) and extratropical (8–12 km or > 150 hPa) modes in global and hemispheric distributions e.g.,and Fig.  here. Analysis of tropopause altitudes in each reanalysis model reveals that, despite slight differences in LRT altitudes, the tropopause break can be routinely identified in each using a tropopause pressure threshold of 150 hPa. Therefore, we set trajectories with STE as tropical if the tropopause pressure at the initial parcel location is less than 150 hPa, and extratropical otherwise.

Similarly, classifying subtropical STE involves evaluating both its tropopause break-relative location and tropopause-relative altitude during advection. In particular, if a parcel is initially located below the tropical tropopause and located above the extratropical tropopause 5 days downstream, it will be flagged as subtropical TST (i.e., exchanged poleward thorough the tropopause break). Alternatively, if a parcel is initially located above the extratropical tropopause and located below the tropical tropopause 5 days downstream, it is flagged as subtropical STT (i.e., exchanged equatorward through the tropopause break). Remaining parcels are flagged as either exchange occurring only in the extratropics or tropics. There is one important exception that must be accounted for: stratospheric intrusions below the subtropical jet. In order to identify these parcels as STE in the extratropics and not in the subtropics, we require an additional condition for STT in the subtropics: both initial and final parcel pressures must be less than (above) the initial extratropical tropopause pressure. See Fig.  for a detailed schematic of the identification method.

Global spatial distributions of annually averaged STT and TST mass fluxes are shown in the right and left columns of Fig. , respectively. All of the models are similar regarding peak STT regions, with the largest differences found in contrasting the magnitudes of downward transport. Total STT mass fluxes are maximized along the Northern Hemisphere (NH) Atlantic and Pacific extratropical storm tracks in each reanalysis model. Among the four reanalyses, ERA-Interim and JRA-55 STT mass fluxes are largest (Fig. a and c) with a maximum of ∼ 300 kg s-1 km-2 in the core of NH cyclone tracks. In the Southern Hemisphere (SH) the STT mass fluxes are largest within the subtropical latitudes along the western coasts of the continents. The largest SH STT maximum in each reanalysis is located along the subtropical coast of Chile. This is a confined but dominant region of STT mass flux and is greatest in JRA-55 (∼ 350 kg s-1 km-2) and weakest in MERRA (∼ 200 kg s-1 km-2). Another common region of elevated STT in the SH occurs over a broad area in the extratropics along the west coast of Antarctica. A noteworthy difference among reanalyses regarding STT mass fluxes is found within the tropics, where the location of peak STT mass flux varies considerably. Peak regions of tropical STT are found along the Equator across the Indian Ocean in JRA-55 and ERA-Interim, but are found to be displaced south of the Equator in both MERRA reanalyses.

Annually averaged geographic distributions of TST mass fluxes show considerably larger magnitudes and broader maxima within the tropical latitudes compared to STT (right column Fig. ). Spatially, maxima in tropical TST mass fluxes coincide with minima in STT mass flux. Distinct maxima of tropical TST mass fluxes are evident in the South China Sea, the west Pacific, the Caribbean Sea, and southeast Asia. Within the subtropics, a narrow band of TST extends from China into the east Pacific and is consistent among the reanalyses. Comparison of TST among the reanalyses reveals two modes: regionally (or latitudinally) symmetric in ERA-Interim and JRA-55, and regionally asymmetric in MERRA and MERRA-2. The regional asymmetry in MERRA and MERRA-2 is due to significantly enhanced TST mass fluxes in the extratropics compared to the remaining reanalyses, with extratropical TST near ∼ 400 kg s-1 km-2 globally in MERRA and MERRA-2 and near ∼ 200 kg s-1 km-2 in ERA-Interim and JRA-55. Another inconsistency among the reanalyses is the location of peak TST in the tropical western Pacific. The peak tropical TST location in JRA-55 and ERA-Interim is highest in the NH but extends across the Equator, whereas MERRA and MERRA-2 show a peak located mostly in the NH.

To better understand the differences and similarities of STT and TST geographic distributions, we can decompose both transport directions into separate regions of exchange to determine their contributions to the differences observed in total STE. The extratropical spatial distributions of STT and TST are shown in Fig. . One significant characteristic shown is the dominance of STT over TST in the extratropics indicated by ERA-Interim, JRA-55, and MERRA-2, especially over the NH and SH storm tracks. MERRA, however, shows the opposite behavior. As in the global STT distributions, the largest STT mass fluxes in the extratropics coincide with the NH cyclone tracks. In the SH, the STT mass fluxes are largest poleward of 60∘ S. Also, STT maxima across the subtropical SH, particularly the Chilean coast, are detected but magnitudes are weaker than those in total STT. More generally, STT mass fluxes in the extratropics are largest in JRA-55 and weakest in MERRA. TST in the extratropics, similar to STT, is found to be spatially consistent amongst the reanalyses, with the only apparent differences being the localized maxima near 60∘ N in MERRA and MERRA-2 that are not observed in ERA-Interim or JRA-55. In addition, TST in the extratropics in MERRA is generally larger than the remaining reanalyses.

STT and TST mass fluxes and their geographic distributions within the tropics are shown in Fig. . While both TST and STT mass fluxes are similar in magnitude between the reanalyses, there are slight offsets in the location and width of the identified maxima. For example, no two models agree on the precise location, zonal extent, or meridional extent of the TST maxima in the western Pacific. The offsets in STT and TST maxima outlined in the discussion of Fig.  above are also evident in the maps of STT in the tropics.

Lastly, Fig.  shows geographic distributions of STT and TST in the subtropics (i.e., which occur between the tropics and extratropics across the tropopause break). These maps reveal that transport in the subtropics is (1) generally weaker than transport in the tropics and extratropics in each model, (2) dominated by poleward transport through the tropopause break in each hemisphere (i.e., TST), and (3) preferentially distributed over the ocean basins and extends poleward downstream of the ocean basins in agreement with known evolution of Rossby wave breaking events; e.g., see Fig. 9 from. In reference to the total STE geographic distributions, it is evident that the influence of poleward and equatorward transport in the subtropics directly corresponds to the maxima in total STT and TST, which is expected due to its association with the tropopause break.

In an effort to quantitatively summarize some of the apparent differences identified in the analysis of geographic distributions, globally integrated and annually averaged STE mass fluxes from each reanalysis are provided in Table . Total STT mass flux is similar among JRA-55, ERA-Interim, and MERRA-2, while the STT mass flux in MERRA is at least 25 % lower. In the other direction, TST mass flux totals are significantly higher in MERRA (∼ 51 %) and MERRA-2 (∼ 29 %) compared to those from ERA-Interim and JRA-55.

Net STE is expected to be near zero, or balanced, over a long time period as a result of mass continuity. However, all reanalyses result in a net exchange that is either positive or negative (i.e., net TST or STT, respectively). Net mass fluxes in JRA-55 and ERA-Interim are both negative (STT dominant), but the net flux amounts to only ∼ 4 % of the total flux (TST plus STT). However, net mass fluxes in MERRA and MERRA-2 are both positive and amount to about 33 and 12 % of their total fluxes, respectively.

Table  also includes the integrated mass fluxes of the three transport subregions. Net tropical STE fluxes are positive and of similar magnitude in all four reanalyses, while extratropical STE fluxes are negative (STT dominant) in JRA-55 and ERA-Interim, marginally negative in MERRA-2, and positive (TST dominant) in MERRA. Similar to tropical STE, net subtropical fluxes are all positive (TST dominant), with magnitudes in MERRA-2 and MERRA 2–3 times as large as those in ERA-Interim and JRA-55.

Annually and zonally integrated latitudinal distributions of STE (TST, STT, and net) are shown in Fig. . Meridional distributions, similar to geographic distributions, demonstrate the latitudinal dependence of STE and offer a more quantitative comparison of the regional differences. Once again, we show both total STE and that separated by the regions of transport in the meridional distributions (with tropical and extratropical STE combined in this case).

Total STE meridional distributions (Fig. a) show similar latitudinal variations in TST and STT in each model, but differences in the magnitude of each transport direction lead to large differences in net STE, especially in the extratropics. The meridional distributions of STE in the extratropics and tropics combined (Fig. b) and in the subtropics (Fig. c) demonstrate that the majority of these differences can be attributed to extratropical and tropical STE, though TST plays an important role in the subtropics and is clearly much larger in the MERRA and MERRA-2 reanalyses (especially in the NH).

In addition to understanding regional differences in STE, examining differences in the seasonality of transport can be important for determining the significance of STE on UTLS composition throughout the year. Annual cycles of normalized STT and TST in the extratropics are presented in Fig.  and separated by hemisphere, while normalized annual cycles for the tropics are shown in Fig. . Mass fluxes of STT and TST are normalized using the maximum and minimum monthly means over the 15-year period: Ni=month‾i-MINmonth‾MAXmonth‾-MINmonth‾, where month‾i is the monthly mean for each month (i=1–12) and Ni is now the ith normalized monthly mean mass flux. Normalized STT mass fluxes are similar among the models in the NH and SH extratropics, but the hemispheres differ in the timing of annual minimum and maximum STT. Annual STT is at maximum and minimum in late winter (DJF) and late summer (JJA) in the NH, while the maximum and minimum STT occur during early autumn (MAM) and spring (SON) in the SH. One unique difference in STT is apparent in the SH during austral summer, where MERRA-2 normalized mass fluxes are considerably smaller during those months compared to the other reanalyses. Although the reanalyses show similar seasonality for STT, there are some differences in monthly variability. While there are no uniform differences in variability within the hemispheres or among the reanalyses, the monthly variabilities are considerably larger in the SH. Annual cycles of extratropical TST (bottom row of Fig. ) have similar modes and hemispheric differences in monthly variability to that of STT, especially in the NH. However, there is an apparent 1- to 2-month offset in the minima and maxima of TST and STT in each hemisphere.

There are more apparent differences in the normalized annual cycles of TST and STT in the tropics (Fig. ). In particular, normalized TST in the tropics reveals two preferred seasonal cycles. In JRA-55 and ERA-Interim, TST is weakly bimodal, with local maxima occurring during the NH winter (DJF) and summer (JJA). MERRA and MERRA-2, on the other hand, are broadly unimodal and reach a maximum during the NH summer and minimum in NH fall (SON). STT seasonality in the tropics is more consistent amongst the reanalyses, with general agreement of STT peaking in the late NH summer and early fall.

While the normalized annual cycles of TST and STT demonstrate the seasonality of STE, they do not represent amplitudes (i.e., MAX(month‾)-MIN(month‾)) of seasonality among the reanalyses. Table  provides annual cycle amplitudes for each transport direction, transport region, and hemisphere. Annual cycle amplitudes are similar among the reanalyses for extratropical STT, subtropical TST, and tropical TST, while largely different for extratropical TST (especially in the NH), subtropical STT, and tropical STT.

Annual cycles of net STE are shown in the top row of Fig.  and left non-normalized to show the combined effects of differences in seasonality and in dominance of STE pathway. MERRA and MERRA-2 show a positive net cross-tropopause mass flux (TST) throughout their annual cycles in the NH. Alternatively, JRA-55 and ERA-Interim exhibit a NH seasonal cycle that is STT dominant in the winter and early spring and TST dominant in the summer. In the SH, JRA-55 and ERA-Interim again show consistent seasonality and are STT dominant through most of the year and only briefly positive during the summertime (DJF). While similar in shape, MERRA-2 exhibits positive net exchange that spans all seasons but winter (JJA). MERRA, as in the NH, exhibits only positive net STE and a weaker annual cycle compared to the other reanalyses. The largest monthly net STE mass flux variability is found in the annual cycles of MERRA.

Annual cycles of the transport categorized by region also reveal important differences in the seasonality of STE and the contribution of individual processes to the total annual cycles. Net STE annual cycles in the extratropics and tropics (combined) and in the subtropics are given in Fig.  for both hemispheres. Generally, the seasonality of net mass flux in the extratropics and tropics is similar in shape to the net annual cycle of total STE in each hemisphere, with a few important differences. Specifically, the combined extratropics and tropics net STE annual cycle of MERRA-2 is shown to be STT dominant during the NH wintertime, whereas the total net STE indicates positive net exchange through all seasons. The SH combined extratropics and tropics net STE annual cycles are not significantly different from those represented by total net STE, aside from a negative shift (i.e., a greater influence of STT). Figure  shows tropical exchanges removed from the extratropics and reveals that annual cycles of STE in the tropics are similar among the reanalyses. This demonstrates that the separation in STE annual cycles in the combined hemispheric analysis (middle row of Fig. ) is due to STE in the extratropics.

For annual cycles of transport in the subtropics, all four reanalyses show similar seasonal behavior, with a minimum in late spring and early summer and a maximum during the late fall and early winter, and are TST dominant in both hemispheres. Annual cycles of subtropical transport in MERRA and MERRA-2 have a slightly larger amplitude than those in ERA-Interim and JRA-55 and are displaced at higher net positive fluxes, which is consistent with the analyses presented in Sect.  and above.

Time series of STE are examined over the 15-year period to further evaluate similarities and differences between the reanalysis models. In Fig. , global time series of STT anomalies and TST anomalies are shown with respect to their mean mass fluxes (i.e., 15-year means are removed). STT throughout the period shows two modes of long-term changes in the reanalyses: increasing mass fluxes over time in JRA-55 and ERA-Interim and decreasing mass fluxes over time in MERRA and MERRA-2. Similar long-term increases in TST can be seen in the ERA-Interim and JRA-55 time series. In the MERRA reanalyses, however, long-term changes in TST are shown to be largely increasing in MERRA and near zero in MERRA-2.

STE time series separated by region (combined extratropical and tropical, and subtropical) are shown in the middle and bottom rows of Fig. . Combined extratropical and tropical STT shows similar patterns and variability to that from total STT for each reanalysis. Mainly, there are decreasing combined extratropical and tropical STT mass fluxes in MERRA and MERRA-2 and increasing fluxes in JRA-55 and ERA-Interim. In a similar manner, combined extratropical and tropical TST is increasing over the period in ERA-Interim, JRA-55, slightly decreasing in MERRA-2, and strongly increasing in MERRA. Subtropical STE time series for all reanalyses show little to no long-term variability. There is one exception, however, with subtropical TST in MERRA showing a potential long-term increase in mass flux.

The long-term increases and decreases in STE identified in Fig.  are associated primarily with extratropical and tropical STE and are considerably large relative to the mean, especially given the relatively short time period analyzed. In order to better understand the source of these changes we also analyzed time series of extratropical and tropical STE separately (Fig. ). Based on the analyses presented thus far and conventional STE knowledge, transport in the tropics is primarily upward (TST), while it is primarily downward (STT) in the extratropics (with the exception of MERRA). These geographically separated upward STE modes are largely the result of the BDC. Thus, we expect long-term changes in TST in the tropics and STT in the extratropics to be consistent. Figure  demonstrates this well, with negligible long-term changes in STT in the tropics and apparent STT changes in the extratropics, and the opposite behavior for TST (except for MERRA). Specifically, JRA-55 and ERA-Interim show increasing STT in the extratropics and TST in tropics, whereas MERRA-2 shows decreasing mass fluxes over the 15-year period.

The observed consistency in the sense of the long-term changes of TST in the tropics and STT in the extratropics in ERA-Interim, JRA-55, and MERRA-2 suggests that changes in the BDC may be responsible for this behavior. Specifically, the increasing fluxes for tropical TST and extratropical STT over time in JRA-55 and ERA-Interim indicate an acceleration of the BDC, while the decreases in MERRA-2 indicate a deceleration of the BDC. Changes in the speed of the BDC have been examined in previous studies. For example, evaluated the dynamics of the BDC using ERA-Interim, JRA-55, and MERRA and show that there is general agreement in a strengthening BDC over the period 1979–2012 by 2–5 % per decade. Observational studies show decreases in tropical stratospheric water vapor, ozone, and temperature observed by satellite, which also corresponds to an increase in tropical upwelling associated with an accelerated BDC . Chemistry–climate models have also indicated an acceleration of the BDC over time e.g.,. These previous reanalysis, observational, and modeling studies are consistent with the results from ERA-Interim and JRA-55 here, while MERRA-2 is in disagreement and MERRA does not indicate changes in the BDC over time in our analysis.

This paper is largely a comparison of STE estimates using multiple state-of-the-art reanalysis models, but we also briefly evaluate some model differences through various diagnostics here. The goal is to provide general context and logical reasoning to explain some of the aforementioned STE differences among the reanalyses.

In contrast to the vast majority of previous work, this study used the lapse-rate tropopause or LRT as the troposphere–stratosphere boundary rather than an isosurface of potential vorticity (PV) or dynamic tropopause. In order to demonstrate the impact of this choice for STE studies, we presented a comparison of STE estimates using the LRT method and results from a recent study that used a dynamic tropopause . We found that

magnitudes of STE are uniformly smaller using the LRT,

The main focus of this paper was not a method comparison, but a comparison of STE among four state-of-the-art atmospheric reanalyses. Doing so, we separated transport into several regions in order to investigate the STE climatologies both quantitatively and qualitatively. It was found that the models can be grouped into two populations: STT dominant and TST dominant (Table ). JRA-55 and ERA-Interim are STT dominant, while MERRA and MERRA-2 are TST dominant. The net transport in the STT-dominant reanalyses, however, is small relative to the total transport, while the opposite is true for the TST-dominant reanalyses.

Geographic distributions and zonal mean latitudinal distributions revealed important characteristics about the two reanalysis populations. Notably, the largest differences in STE were found in the extratropics. Geographic distributions of STT maxima were similar amongst all reanalyses, while the opposite was true for TST. MERRA was typically an outlier relative to the remaining reanalyses, but similar differences (though largely diminished) were found between MERRA-2 and the STT-dominant reanalyses (ERA-Interim and JRA-55). STE in the subtropics was found to be consistent geographically with prior studies of Rossby wave breaking events along the tropopause break e.g.,. Although geographic placement and net transport for STE in the subtropics were consistent among the models, the MERRA reanalyses showed roughly twice the magnitude of net poleward transport from the tropical troposphere into the extratropical lowermost stratosphere (i.e., TST).

Seasonality of STE amongst the reanalyses was also found to be similar for some transport regions and directions and significantly different for others. Similar to geographic consistencies observed, we found that STT and TST annual cycles in the extratropics are consistent among the reanalyses and in both hemispheres. However, seasonality of TST in the tropics was found to be weakly bimodal in STT-dominant reanalyses and unimodal in the TST-dominant reanalyses, while STT seasonality in the tropics showed smaller differences. Larger differences were found for annual cycles of net STE from the reanalyses, with MERRA showing little seasonality in each hemisphere. Differences in net STE were shown to be associated primarily with extratropical STE in each reanalysis.

Long-term changes were also investigated using time series analysis over the 15-year study period. These analyses indicated gradual increases and decreases in STT and TST mass flux for the STT-dominant models and MERRA-2, respectively. Further analyses suggested that long-term changes in total STE are associated with either an acceleration or deceleration of the BDC. Specifically, the BDC is apparently decelerating in MERRA-2 and accelerating in JRA-55 and ERA-Interim from 1996 to 2010.

Finally, several diagnostics were applied to the reanalyses in order to shed light on the sources of the STE differences. We found that differences in transport are likely the result of differences in the frequency of irreversible STE rather than the magnitude of individual events. We also found the altitude of the tropopause between the STT-dominant and TST-dominant models to differ considerably in the extratropics. An analysis of vertical winds at the tropopause showed some differences between the TST-dominant and STT-dominant reanalyses, but these were not necessarily consistent with the nature of the STE differences found. Taken together, these physical and dynamical differences may be significant sources of variability for climatological analyses and it is likely that they contribute to some of the STE differences observed in this study.

The analyses in this study demonstrate that while there are some areas of agreement in the magnitude, geographic distribution, and frequency of large-scale STE among modern reanalyses, there are important differences that can lead to varying conclusions of the impact of STE on UTLS composition, the radiation budget, and climate. While this study is the first model comparison of global STE estimates, there are some limitations that could be improved upon in future work. First, the analysis time period could be increased. Each reanalysis model used in this study has output available from 1979 to 2015, roughly 2.5 times longer than that used here. Expanding the analysis period may provide improved confidence in the statistical behavior of STE regarding the long-term changes associated with the BDC (Sect. ). An extended analysis period may also reduce variability in the seasonality and regional distributions analyzed here and thus increase confidence in those results. The primary challenges with this suggested expansion in the analysis time period are the computational time required and the cost of data storage (15 years of 6 h model output and trajectory model calculations from the four reanalyses used here requires ∼ 10 TB of disk storage).

Second, while the present generation of the reanalysis models are significant advancements for studies of UTLS dynamics and associated processes over previous generations, model improvements can still be made in the UTLS. Given the limited spatiotemporal observations of STE available, it is understandable that model simulations of transport could differ considerably. However, some of these differences are likely related to basic model choices such as grid resolution. For example, the vertical grids are nearly equivalent in ERA-Interim and JRA-55, which differ considerably from that used in MERRA and MERRA-2. Notably, vertical resolution is finer at levels below the tropical tropopause in ERA-Interim and JRA-55 but finer above the tropical tropopause in the MERRA Reanalyses. Since the vertical grid resolution and placement of vertical grid levels in the UTLS may have important impacts on tropopause-relative analyses such as STE (especially since current vertical resolution of reanalyses in the UTLS is ∼ 1 km), it is important to understand the sensitivity of such analyses to this model design choice.

Third, as referred to in the Introduction, large quantitative uncertainties in STE exist from previous Eulerian and Lagrangian STE studies. In particular, estimates for STE have often been limited to specific regions or time periods or based on inadequate and/or incomplete methods (compared to those possible with current methods and computational abilities). Here, we found that mean net STE magnitudes also range considerably when an equivalent method is applied to multiple modern reanalyses (e.g., see Table ). However, few previous studies enable direct comparison with our estimates. In particular, the alternative PV-based approach by is arguably the most direct, where ERA-Interim net STE integrated globally over the 15-year period in our study is approximately 1.48×1017 kg year-1 downward (STT), while it is about 3.5 times smaller (4.2×1016 kg year-1) in the study. These differences do not necessarily suggest that one method is superior to the other, but that two largely similar Lagrangian approaches can yield substantially different results due to the employed troposphere–stratosphere boundary (e.g., see Figs.  and ).

Lastly, while this study compared STE among reanalyses and attempted to diagnose potential sources of those differences, much more work can be done to examine them. The clearest source of STE differences found was related to STT and TST event frequencies (Fig. ), but differences in the vertical winds and extratropical LRT distributions shown in Figs.  and may imply that the dynamical regimes evaluated for exchange in each reanalysis are slightly different. One approach to further evaluate the role of these differences in dynamics and boundary conditions may be to combine tropopause altitudes from one reanalysis with the winds of another reanalysis for STE trajectory calculations. Such analyses may lead to future improvements in the model grids and numerics, especially in the UTLS.