Stratosphere-troposphere exchange (STE) plays an important role in the composition and dynamics of the upper troposphere and lower stratosphere (UTLS). The net mass and constituent flux during stratosphere-to-troposphere (STT, downward) and troposphere-to-stratosphere (TST, upward) transport is determined by the large-scale, wave-driven Brewer-Dobson circulation . The net mass exchange exhibits pronounced seasonality although its amplitude is small compared to the gross upward and downward transports, and in the climatological mean it is upward in the tropics and downward in the extratropics . However, there are local processes that control exactly when and where the exchange of air across the tropopause occurs . This study focuses on TST in the extratropics, which is relevant in terms of the potential transport of water vapour and pollutants into the lower stratosphere. TST can therefore lead to large positive humidity anomalies in the lower stratosphere , with important implications for the global radiative balance .

Both STT and TST exhibit pronounced seasonality and geographical variability e.g.,, which is partly shaped by the occurrence of specific weather systems often associated with STE. Specific weather systems that embed the local processes leading to STE have been investigated in case studies and climatologically. For example, these studies looked at STE in relation to monsoon circulations , deep convective systems in the tropics , overshooting convection in the mid-latitudes , Rossby wave breaking , tropopause folds , and extratropical cyclones . Note that these flow systems are not mutually exclusive, since tropopause folds, for example, often co-occur with Rossby wave breaking and extratropical cyclone intensification. STE turns out to be particularly prominent in tropopause folds , and several case studies have quantified STE in deep tropopause folds e.g.,. While these studies provide valuable information about the meteorological context of STE in specific case studies, they do not climatologically identify the relative role of the physical processes associated with STE.

The dynamical tropopause definition – identifying the tropopause as an isosurface of potential vorticity (PV) – offers an ideal conceptual framework to discuss physical processes related to STE. In the absence of diabatic and frictional processes, PV is a materially conserved quantity , meaning an air parcel cannot cross the dynamical tropopause. In other words, STT and TST require processes that do not conserve PV to occur near the tropopause, which can be explored using the equation for the material PV tendency (see Sect.  and Eq.  for more details). In the UTLS regions, the diabatic and frictional processes that can modify PV include turbulence, radiation, and cloud processes involving phase changes of water. Thus far, the role of these processes for STT and/or TST has only been studied on a case-by-case basis e.g.,. For example, showed how convective systems can lead to turbulent mixing in the lower stratosphere due to the breaking of gravity waves induced by deep convection, essentially leading to STT. emphasized the importance of the latent heating gradient at the tropopause level above the warm sector of a surface cyclone. While they found that this region is responsible for the majority of the cross-tropopause exchange associated with an extratropical cyclone, they also identified TST-conducive regions where large PV tendencies resulted from the radiative heating gradient alone. They argued that, at the tropopause level, even a weak radiative heating gradient can lead to a strong PV tendency as this also depends on vorticity, which can have local maxima near the tropopause. conducted a process-based analysis of STT and TST associated with a PV filament and in its environment. They concluded that TST near the filament and south of the ridge upstream was mainly due to radiative processes. Based on previous studies and their own work, they showed that the direction of radiation-induced STE depends greatly on the height to which convection can reach, i.e., the cloud top. looked at the effect of radiative processes on STE in upper troposphere anticyclones. They attributed TST mass exchange to the vertical gradient of radiative heating and noted that some of it is controlled by the temperature anomaly profile within the anticyclone. Their model did not include clouds or aerosols. A common theme in these studies is the noticeable case-to-case variability of the involved processes, which emphasizes the need for a climatological investigation .

In this study, we focus specifically on the importance of radiation for TST. A challenging aspect of radiative PV modification is that it can occur even without the presence of a specific weather system (e.g., extratropical cyclones or tropopause folds). estimated that under (relatively) clear-sky conditions in a blocking anticyclone, radiation is responsible for a 1 pvu increase in five days. As mentioned, in the absence of clouds, the necessary radiative temperature and PV tendencies can arise from the vertical humidity and temperature profiles in the UTLS alone. In such a favourable environment, air parcel trajectories can accumulate PV over longer periods and over greater distances. In the presence of clouds, in particular cold-top cirrus clouds in the extratropical UTLS, the vertical temperature tendency signal is also largely modified by cloud-top cooling and cloud-base heating . According to PV theory, this results in an increase in PV above cooling, a decrease in PV between cooling and heating, and an increase in PV below the heating . In turn, the cloud-radiative response is modified by the temperature, ice water content (IWC), and ice crystal number concentration of the cirrus cloud . Similar magnitude PV tendencies are also present in larger mid-latitude cloud systems with cirrus tops within extratropical cyclones. For instance, demonstrated that the combination of radiation and latent heating processes related to a warm conveyor belt (WCB) cloud created a PV dipole that intensified the PV gradient at the tropopause. showed in a case study of an extratropical cyclone and the upper-level ridge downstream that radiative PV tendencies are largest close to sharp moisture gradients and exhibit local maxima above clouds. investigated the effect of microphysics on the WCB and the PV modifications due to different processes. Following the trajectories along and above the WCB, they concluded that those within a WCB experience a larger negative PV modification due to cloud processes. However, trajectories above the WCB (and thus above the cloud) are affected by cloud-top cooling and experience a PV gain due to the vertical temperature gradient. A similar situation was described by , who studied the formation and the impact on PV of a cirrus cloud and found a strong PV increase due to cloud-top cooling, which modified the UTLS structure. studied the effect of radiation on the evolution of the extratropical cyclone in an idealized setup and concluded that radiation can modify the large-scale flow through changes in microphysical heating. All these examples of pure cirrus and mixed-phase clouds result in significant variability and uncertainty in the final radiation-induced PV modification. The combination of the “week or so” timescale given by and the relatively weak estimated values of instantaneous PV tendencies due to radiation, compared to turbulence and cloud processes, makes the systematic study of radiation-induced STE challenging. Due to these smaller values, the relevance of radiation may have been overlooked in some case studies. The extended timescale compared to other physical processes requires a different diagnostic approach which would also shed light on the duration of the accumulation period of radiative PV tendencies.

The overall goal of this study is to climatologically quantify the relevance of radiation in TST in the Northern Hemisphere extratropics using a Lagrangian approach. For reasons of computational feasibility, we decided to focus on a recent 10-year period in one hemisphere, assuming that the physics of TST is the same in the Southern Hemisphere and in slightly earlier periods. We opted for a Lagrangian approach because (as we motivated and hypothesized above) for radiative processes to be relevant in TST, modest instantaneous PV rates must accumulate along the flow to reach the substantial PV increase required for TST. Three important methodological decisions are required to address the overall goal:

How to identify TST events? Here we will use a modified version of the approach established in previous studies .

The specific research questions addressed in this study are as follows:

Q1: What is the radiative contribution to TST and what fraction of TST events are dominated by radiation?

Our study is entirely based on ERA5 reanalysis (Sect. 2.1). The methods include the identification of TST trajectories (Sect. 2.2), the quantification of diabatic PV modifications along these trajectories (Sect. 2.3), and the approach to quantify the specific role of radiation (Sect. 2.4).

The final TST dataset for the 10-year period includes 35.4 million trajectories following the initialization criteria and the filtering (Sect. ). Firstly, we conduct a statistical analysis of the radiative contribution to TST (frad), followed by a discussion of the geographical distribution of TST and, in particular, of radiatively dominated TST. We use the distribution of APV_rad (Fig. a) to define four categories of TST trajectories based on the radiative PV contribution, as explained in the following paragraph.

Figure a shows the statistical distribution of APV_rad values for all TST trajectories. Note that because APVtot∼1 pvu, a value of APVrad=0.5 pvu corresponds roughly to a value of frad=50 %. A certain fraction of TST trajectories (16 %) has a negative PV contribution from radiation, but the majority (59 %) of TST trajectories show a small positive contribution from radiation with APV_rad values between 0 and 0.25 pvu. The distribution is strongly skewed

The distribution of radiative PV changes along trajectories is skewed because of the selection bias related to our choice of focusing on TST trajectories. If a similar analysis was performed along randomly selected trajectories in the upper troposphere, the radiative PV changes are expected to be symmetrically centred at zero.

Figure  gives the overview of the spatial climatology of the identified TST. The top row shows that total TST is most frequent in the storm track regions and over Scandinavia, with an additional local maximum over central Asia in JJA. The North Atlantic storm track signal extends from central North America to the Ural Mountains, and the North Pacific storm track signal from the Japan Sea to the Gulf of Alaska. These distributions are in agreement with previous Lagrangian studies of TST that have also found TST maxima in the storm track regions .

Throughout the seasons, the most prominent local maximum is located at the southern tip of Greenland. This peak is also present in most of the aforementioned studies, but its amplitude depends on the chosen residence time threshold, which was 24 h or more in the previous studies. With the much shorter residence time threshold here, the local maximum becomes stronger, indicating that the residence time of most TST events over the south tip of Greenland is short. The same holds for the central Asian summer peak, which was not present in previous TST climatologies. We speculate that this peak over the Pamir and Tien Shan Mountains is a result of a combination of the northward shift of the subtropical jet in summer and the fact that the Tien Shan Mountains experience a monsoon-like climate . The crossing of the tropopause in that specific region is likely possible because the subtropical jet can provide the necessary turbulent environment, or the monsoon clouds and associated humidity gradients can contribute to strong diabatic temperature tendencies. The fact that no such signal is discernible further south over the Himalayas in summer (when it could be expected due to the monsoon) or in winter (when the subtropical jet is south of the Tibetan Plateau) is most likely because trajectories were initialized only poleward of 20° N. calculated 7 d backward trajectories from the subtropical jet in the Northern Hemisphere and their results suggest that in winter a significant amount of the trajectories ending in the subtropical jet over Asia start south of 20° N.

The second row in Fig.  shows TST in category IV, and the third row its fraction of total TST. Since overall 8 % of the TST trajectories belong to this category, in regions where the relative fraction is higher than 8 % (note the black contour in the third row), the radiatively dominated category IV is more frequent than on average. In comparison to total TST, the trajectory densities of category IV in winter show even more distinct maxima over the North Atlantic and North Pacific basins with the North Atlantic signal shifted over Greenland. In relative terms, the higher than average category IV densities are located slightly northward of the maxima in the full TST climatology; largest values (of 15 % and above) are found poleward of 60° N. In spring, the category IV distribution is more uniform with lower densities than in winter (consistent with Fig. b) and relative contributions of 5 %–10 % everywhere. The summer map reveals that many central Asia trajectories seen in the total climatology belong to category IV since the relative contribution there exceeds 25 %. As to why the mountain ranges enable more radiative TST in that region would need a more in-depth investigation, which is beyond the scope of this study. Everywhere else, the category IV fraction is lower than the climatological average in summer. The autumn distribution appears to be a combination of the summer and winter regimes, with also a clear signal in central Asia and large relative contributions to TST at high latitudes.

The main insights from the spatial analysis are that (i) this TST climatology agrees fairly well with earlier longer-period climatologies (based on older reanalyses), (ii) TST in category IV tends to occur preferentially at higher latitudes in all seasons except summer, and (iii) except for local maxima over Greenland and in central Asia discussed above, radiatively dominated TST occurs rather uniformly in the entire extratropical Northern Hemisphere.

We continue to analyse the accumulation of PVR_rad in the TST duration time window (τTST) during which the 1 pvu increase happens. First, we take a look into how the average PVR_rad (hourly radiative PV rates averaged along each trajectory) and PVR_rad,MAX (maximum hourly radiative PV rate along each trajectory) during τTST differ among the categories. In addition, we show the statistical distributions of τTST for the four categories. Figure a shows that for categories II-IV with a positive radiative contribution, most of the average and maximum values of PVR_rad are below 0.03 pvu h⁻¹. The most frequent average value (solid lines) is near 0.005 pvu h⁻¹ for the smallest contribution category II (yellow line) and increases up to 0.009 pvu h⁻¹ for the radiatively dominated category IV (red line). We see the same behaviour for PVR_rad,MAX at slightly higher values. The distribution also gets flatter towards category IV. All in all, and not surprisingly, the more radiation is contributing to TST, the higher the average values of PVR_rad and PVR_rad,MAX. However, the values within each category vary strongly between almost 0 to 0.2 pvu h⁻¹ (not shown here, see distributions in Fig. a). Considering the average PVR_rad, this indicates that the PV is produced over very different time durations. Also, we conclude that PVR_rad,MAX is unlikely to be the determining factor of the radiative contribution, given its comparatively low values.

To confirm this, Fig. b shows the distribution of TST duration (τTST) among the categories. We see that categories I and II tend to have shorter τTST with pronounced peaks below τTST=10 h, whereas categories III and IV show a flatter distribution with almost equal frequencies from 10 to 100 h. (The peaks in the distributions that appear every 12 h correspond to the ERA5 assimilation windows, as mentioned in Sect. .) In another perspective, for τTST=70 h and above, the fraction of category III–IV trajectories is larger than for categories I–II, meaning that if the PV increase for a TST trajectory takes longer, it is more likely to experience the increase due to radiative processes.

We now focus on category IV trajectories and analyse the possible TST pathways in terms of τTST, average PVR_rad, and PVR_rad,MAX. Figure a shows a 2D histogram of τTST and average PVR_rad coloured by PVR_rad,MAX. The hyperbolic shape indicates that τTST and PVR_rad are to a certain degree anti-correlated. But still, a small average PVR_rad can exhibit any TST duration from 20 to 120 h, and a short TST duration can accompany a wide range of average PVR_rad values. The marginal distributions in Fig.  reveal that most events have small average PVR_rad values, in agreement with Fig. a. The histogram covers average PVR_rad values of up to 0.2 pvu (compared to only 0.03 pvu in Fig. a) to show that these high values exist but they are very rare. PVR_rad,MAX tends to be larger along the inner edge of the hyperbolic distribution, but it seems to be a poor discriminating factor for determining τTST. We can conclude from the distribution that radiatively dominated TST can accumulate PV in a large variety of ways.

To illustrate some of the different pathways, Fig. b–e show example TST trajectories. The first example (Fig. b) has a long TST duration, small average PVR_rad and small PVR_rad,MAX (exact values are given within the panels). The second example (Fig. c) has also a long TST duration but slightly larger average PVR_rad and PVR_rad,MAX. Figure d, e show short τTST trajectories with medium and large average PVR_rad and PVR_rad,MAX, respectively. Maps with the pathways of these trajectories and vertical profiles along them are given in Fig. . It is interesting to take a closer look at the exact PV evolution for each trajectory and to see what kind of vertical profiles produced the PVRs relevant for TST.

Figure b shows a steady increase of PV during τTST and we see that the PVR_lw signal is small but always positive. PVR_sw reveals the diurnal cycle and tends to contribute to PV destruction whenever present. The steadiness of the PVR_lw signal indicates a rather stationary environment over almost four days. The corresponding Fig. a, b show the trajectory starting from the south-west of the Iberian Peninsula, moving first south and then over Europe and the Mediterranean Sea. The vertical profile reveals no clouds at the height of the trajectory or just below it, but the trajectory follows a constant vertical humidity gradient at the height of 300 to 200 hPa. The trajectory in Figs. c and c, d exhibits a similar steady increase of PV over 81 h but radiation contributes only during about half of τTST. The rates are 10 times larger than for the previous trajectory and indicate that it passed two regions of high PVR_rad. The trajectory stayed over North America for the 5 d period and moved above two distinct clouds with strong moisture gradients that also produced the stronger PVRs. Figures d and e, f show a fast TST (τTST=24 h) with two episodes of strong PV increase: the first one during the first 12 h of τTST and the second one immediately before crossing the tropopause. Radiation contributed strongly to the first PV increase but had little influence on the second one. It has to be kept in mind that although we are focusing on the radiatively dominated category IV, other PV non-conservative processes still affect the PV evolution. The PVR_rad,MAX occurred on top of a vertically extended cloud, which shows a strong cloud-top cooling (Fig. f). This trajectory also stands out as a two-way exchange case. The trajectory started in the stratosphere over Europe, lost some of its PV (above mountains, not due to radiation) and then quickly gained it again over a cloud system over the North Pacific. Had we applied a residence time criterion of, e.g., 24 h, this case would not have been included in this analysis. However, for the purpose of this study, it is an important example that radiation can “push” the once stratospheric air, which has transiently crossed the tropopause, back to the stratosphere. The final trajectory (Figs. e and g, h) exhibits an even shorter τTST and the PV evolution reveals again episodes with large PV increases. PVR_lw contributes to the initial PV increase with a rate of 0.6 pvu h⁻¹. This exceptional rate is related to a very strong gradient of the vertical temperature tendency due to a cloud-top cooling over another vertically extended cloud over North America related to a warm conveyor belt (Fig. h).

In summary, these examples show that radiation can contribute to TST in very different ways. This is also the reason why even within a single category with a similar radiative contribution to the PV increase, determining a common environment proves to be difficult. Both the large-scale and the small-scale environments that produce the instantaneous radiative PV rates vary greatly, albeit leading to the same result, i.e. TST. This and the simple fact that frad rarely exceeds 80 % indicate that other processes modify PV at the same time, and some of them contribute to TST also for radiatively dominated trajectories. We therefore investigate the interplay between radiation and other PV-producing processes that provide the PV change required for TST.

The TST duration, τTST, differs even for very similar APV_rad values, and thus it is most likely strongly influenced by other processes, which evidently, in most cases, dominate over the radiative processes. We therefore quantify the PV production by non-radiative temperature tendencies, APV_diab-rad, and by momentum tendencies, APVmom+R, compared to the contribution from radiation, APV_rad.

Figure  shows how these three types of processes contribute to TST in general, and in category IV in particular. In Fig. a, we compare two subsets of category IV with short and long τTST. First, we notice that the contributions from radiation (in yellow) are similar for both subsets, which confirms the results from the previous analysis that the radiative contribution itself does not strongly determine τTST. The momentum tendency contributions (green) are mainly positive and their distribution is shifted to lower values for longer τTST. In contrast, the distribution of the non-radiative temperature tendency contributions (black) shifts from largely negative values (peak at -0.1 pvu) for short τTST to an almost symmetric distribution around 0 pvu for long τTST. Both these shifts indicate that the longer the τTST, the smaller are the absolute contributions from other processes. Or in other words, τTST can be long if the relatively fast processes such as turbulence and latent heating in clouds contribute less in absolute terms. Another interpretation of Fig. a is that τTST increases when PV modification due to non-radiative temperature tendencies deviates strongly from zero, because this contribution is typically negative, i.e., opposing TST for category IV events.

Considering the three processes in a joint distribution histogram for TST events in all categories (Fig. b) helps to explain all the combinations that enable long TST durations. Firstly, we notice two gradients of τTST (colours) in the plot. One gradient appears across the APV_rad isolines (dash-dotted lines), meaning the larger the radiative contribution, the longer τTST. A second gradient, about perpendicular to the first one, is visible within the radiation dominated category IV (below the lowermost dash-dotted line), showing the importance of the contribution from other processes. To explain this, we take a closer look at the region in the scatter plot around the origin, (0,0), and the quadrants around it. In every quadrant near the origin, τTST is long because the other processes contribute very little to the TST. In the 1st and 2nd quadrants (but further away from the origin) the τTST values are shorter compared to the other two quadrants, indicating that whenever momentum tendencies contribute (positive APVmom+R), the shorter τTST gets and even shorter if also APV_diab-rad is positive (1st quadrant). The 3rd quadrant (negative APVmom+R and APV_diab-rad) shows particularly large τTST, which indicates that radiation needs more time to build up the 1 pvu while also compensating for the other processes working against TST. In the 4th quadrant (negative APVmom+R and positive APV_diab-rad) the duration is uniformly large as the other processes balance each other out and radiation alone has to build up the 1 pvu. Only when APV_diab-rad becomes larger than 1 pvu, does the TST duration become shorter again.

This analysis confirms that PV production due to radiation is a relatively slow process. When the radiatively dominated TST category IV shows faster PV build-up, it is caused by other physical processes contributing to the PV increase. The difference between the parts of category IV in the 2nd and the 4th quadrants indicates that the faster PV gain is mostly due to turbulent processes rather than from other non-radiative temperature tendencies.

This also supports the conclusion from Sect. , that, for most trajectories, a combination of different processes is needed to produce the PV necessary for air parcels entering the stratosphere. Therefore, a systematic analysis of the environment that TST air parcels are moving through becomes challenging. The properties of this environment can change drastically depending on what processes are involved, and a single trajectory can be influenced by the many different PV-producing and destroying processes along its way. However, as the focus of this work lies on the importance of radiation for PV production, in the following section we will analyse which atmospheric conditions determine the magnitude of the radiative PV rates and in which environments this process can become the dominant one for PV production leading to TST.

The category IV case studies analysed in Sect.  revealed a large variability in the time evolution of PVR_rad along TST trajectories, which raises the question of what determines the instantaneous PVR_rad at a certain location. Since radiation is treated in the model in vertical columns, we perform a column-based analysis of the vertical profiles of temperature, humidity, and clouds, associated with different values of PVR_rad,MAX for TST category IV (2.9 million trajectories). The distribution of PVR_rad,MAX in this category is given by the red dashed line in Fig. a.

This study quantifies systematically and climatologically the role of radiation in PV production leading to TST. We designed a method that combines a Lagrangian identification of TST with another Lagrangian framework to quantify the contribution of different physical processes to the PV modification. Specifically, the focus is on the period along the TST trajectory during which PV increases from less than 1 pvu to the crossing of the dynamical tropopause defined as the 2 pvu surface – we refer to this period as the TST duration, τTST. The PV modifications due to radiation and other processes are traced during this period and the contribution of the accumulated radiative PV tendencies (APV_rad) is quantified for each individual TST trajectory. The established TST identification method resulted in a 10-year (2012–2021) TST climatology based on ERA5 that presents similar features as previous TST climatologies based on earlier reanalysis datasets. The main conclusions of our study are summarized as follows, sorted according to the research questions posed at the end of the introduction:

Q1: 84 % of the identified TST trajectories experience a positive contribution from radiative PV tendencies (APV_rad). For 25 % of the trajectories, radiation contributes at least a quarter (0.25 pvu) to the PV increase, and in 8 % of the trajectories radiation dominates TST with APVrad>0.5 pvu. We refer to this TST category as “radiatively dominated TST,” and several detailed investigations in the paper focus on this category.

There are also a few caveats to keep in mind. The TST identification method does not apply a stratospheric residence time and hence the TST here refers to air that reaches the tropopause and can be subject to stratospheric mixing, but it does not guarantee that the air would stay in the stratosphere. Regarding the process-specific PV rates, we do not quantify the role of momentum tendencies from the model but just expect them to make up the rest of the 1 pvu increase. This means that we do not know the amplitude of the residual or the momentum tendencies separately. The study is also limited to the resolution and the process-modelling capabilities of ERA5. The PV tendencies are only as accurate as the ERA5 temperature tendencies. This, in turn, depends on how well ERA5 captures the cloud cover in the tropopause region. Given that the radiation schemes in models (including the data in this study) are run at a lower resolution, in both time and space compared to the main core, it could be an important step forward in the future to have more accurate radiative fluxes.

The cancellation or enhancement of PVRs between the different processes, as seen from the Q3 analysis, leads to the question of whether the single trajectory analysis performed here could also benefit from a focus on larger airstreams (i.e., bundles of trajectories). Another possible outlook on this would be a climatological analysis of the PVR in the UTLS region to place the PVR values seen in this study, i.e., along TST trajectories, in a greater context.

The results of this study highlight the role and importance of radiative processes in mid-latitude TST. The systematic analysis of radiative PV tendencies has been (to the best of our knowledge) applied for the first time to a large set of TST trajectories diagnosed during an extended time period. We show that radiation can be the leading process for TST and that it also contributes to the required PV production for the majority of TST trajectories, albeit the radiative PV rates typically being small in amplitude. This confirms that radiation is an essential process for understanding the dynamics of the tropopause region, especially when considering STE.