Composite analysis of the tropopause inversion layer in extratropical baroclinic waves

The evolution of the tropopause inversion layer (TIL) during cyclogenesis in the North Atlantic storm track is investigated using operational meteorological analysis data (Integrated Forecast System from the European Centre for Medium-Range Weather Forecasts). For this a total of 130 cyclones have been analysed during the months August through October between 2010 and 2014 over the North Atlantic. Their paths of migration along with associated flow features in the upper troposphere and lower stratosphere (UTLS) have been tracked based on the mean sea level pressure field. Subsets of the 130 cyclones have been used for composite analysis using minimum sea level pressure to filter the cyclones based on their strength. The composite structure of the TIL strength distribution in connection with the overall UTLS flow strongly resembles the structure of the individual cyclones. Key results are that a strong dipole in TIL strength forms in regions of cyclonic wrap-up of UTLS air masses of different origin and isentropic potential vorticity. These air masses are associated with the cyclonic rotation of the underlying cyclones. The maximum values of enhanced static stability above the tropopause occur north and northeast of the cyclone centre, vertically aligned with outflow regions of strong updraft and cloud formation up to the tropopause, which are situated in anticyclonic flow patterns in the upper troposphere. These regions are co-located with a maximum of vertical shear of the horizontal wind. The strong wind shear within the TIL results in a local minimum of Richardson numbers, representing the possibility for turbulent instability and potential mixing (or air mass exchange) within regions of enhanced static stability in the lowermost stratosphere.


Introduction
The tropopause inversion layer (TIL) is a ubiquitous feature of the upper troposphere/lower stratosphere (UTLS) region in equatorial, midlatitude, and polar regions (e.g., Birner et al., 2002;Gettelman and Wang, 2015). It is commonly defined as a vertically confined layer of enhanced static stability and is usually analysed using the squared Brunt Väisälä frequency, 20 N 2 = gΘ −1 ∂ z Θ (Birner et al., 2002). In the extratropics, the TIL is co-located to a region of strong trace gas gradients between the troposphere and the stratosphere (Hegglin et al., 2009;Kunz et al., 2009;Schmidt et al., 2010), which define the extratropical transition layer (Ex-TL, Pan et al. (2004); Hegglin et al. (2009)), or mixing layer (Hoor et al., 2002(Hoor et al., , 2004. This co-location sometimes led to the assumption that the TIL might inhibit cross-tropopause transport (Hegglin et al., 2009;Gettelman and Wang, 2015), however, evidence for this relation is still missing. Moreover, the TIL is essential for the vertical 25 propagation of waves on different scales, ranging from small scale gravity waves to large scale Rossby waves (e.g., Birner, 2006;Sjoberg and Birner, 2014;Gisinger et al., 2017). The sharp jump in static stability at the tropopause from mean tropospheric values of N 2 = 1 × 10 −4 s −2 to mean stratospheric values of N 2 = 4 × 10 −4 s −2 or to the even larger values defining the TIL results in a maximum of the so called refractive index controlling the upward propagation of waves, and leading to partial or even total wave reflection at the tropopause. 5 This study focusses on the evolution of the TIL at midlatitudes, where the flow in the UTLS is largely dominated by baroclinic planetary and synoptic scale waves. The role of such waves on the formation and maintenance of the TIL in midlatitudes has been the subject of a variety of scientific studies. Idealised modelling studies showed that the TIL can be formed due to conservative dynamics. Wirth (2003Wirth ( , 2004 performed potential vorticity (PV) inversions on axisymmetric PV anomalies of different sign in an idealised background atmosphere, pointing out an adiabatic sharpening mechanism of the lower strato-10 spheric temperature profile related to the convergence of the secondary circulation vertical wind in anticyclonic flow. They were furthermore able to show that the advection of enhanced static stability from low to high latitudes plays an important role for the lower stratospheric N 2 maximum in anticyclonic flow. Wirth and Szabo (2007) performed baroclinic life cycle simulations with a comprehensive numerical weather prediction model and were able to confirm the concept of an adiabatic sharpening mechanism of the tropopause. Following up on these results, Erler and Wirth (2011) performed adiabatic baroclinic life cycle 15 simulations with the same setup and concluded that breaking of baroclinic waves is an important process for the irreversible and permanent formation of a residual TIL as evident in the zonal or temporal mean state. Kunkel et al. (2014) performed similar baroclinic life cycle experiments with the focus on the impact of inertia-gravity waves on the thermal structure in the UTLS. They found that these waves, after being emitted from imbalances along the jet, modulate the ambient thermodynamic variables such as the static stability N 2 and persistently modify the TIL structure through the dissipation of the gravity waves. 20 The role of diabatic processes in the TIL formation during baroclinic life cycle simulations was then studied by Kunkel et al. (2016), who attributed the relative to the adiabatic case stronger TIL evolution to diabatic processes related to moist dynamics and radiative effects of clouds reaching up to the tropopause. The stratospheric residual circulation also contributes significantly to the sharpening of the tropopause (Birner, 2010) especially at midlatitudes and during winter, where the downwelling in the extratropics induces a warming which lowers the tropopause and results in a strong localised positive forcing on the 25 static stability. Randel et al. (2007) performed radiative transfer model calculations to compare the radiative effect of realistic measurementbased mean ozone-and water vapour profiles to profiles with varying gradients of both constituents at tropopause height. They linked the strong gradients of ozone and water vapour at the tropopause to a dipole of the radiative forcing with cooling below and heating above the local tropopause. In turn this leads to an enhancement of static stability in the lower stratosphere. GPS-RO temperature profiles, and were able to attribute a major part of the instantaneous TIL signal in midlatitudes to the transient and reversible modulations caused by planetary-and synoptic-scale waves. In conclusion, these previous works show that planetary and synoptic scale waves in the UTLS region play a major role on one hand concerning the instantaneous and potentially reversible sharpening of the lower stratospheric temperature gradients, as well as on the other hand the formation of an irreversible and permanent residual background TIL.

5
The goal of this study is to complement the previous studies by analysing common structures of the TIL evolution in baroclinic waves over the North Atlantic. For this we use ECMWF operational analysis data over a five year period, and first focus on the evolution of the TIL in individual life cycles, and second derive composites of life cycles to analyse common patterns in the evolution of the lower stratospheric static stability over a set of 130 individual baroclinic life cycles over the North Atlantic.
The evaluation of average atmospheric properties with composites especially in the vicinity of cyclones was used in a vari-10 ety of previous studies, and based on a variety of underlying data. Wang and Rogers (2001)  year Weather Research and Forecasting (WRF) regional model data simulation, with one focus among others on the UTLS PV forcing on the overall life cycle evolution and its synergy with the tropospheric development of the cyclones. To our knowledge the presented study is the first to focus on the TIL and correlated features in the context of cyclone composites.
The paper is structured as follows. In Sect. 2 we present the data set, the surface cyclone tracking algorithm and our approach 20 to derive composites of different dynamical and thermodynamical variables in the UTLS. In Sect. 3 we illustrate the evolution of the UTLS features for two different life cycles which remarkably resemble the well known life cycles LC1 and LC2 from Thorncroft et al. (1993). In Sect. 4 we present composites of a variety of variables from different subsets of the cyclones emphasising the evolution of the TIL in baroclinic life cycles as well as associated flow features. We close our discussion in Sect. 5 by summarising our findings and putting them into perspective of previous studies. 25 2 Data and methods

ECMWF operational analysis data
For the detection of cyclone tracks we use operational analysis fields from the integrated forecast system (IFS) from the European Centre for Medium-Range Weather Forecasts (ECMWF), for August to October from 2010 until 2014. The spatial extent of the area covers the North Atlantic from 60 • W to 20 • E and from 20 • N to 75 • N, and therefore encompasses the 30 autumn maximum of Atlantic storm tracks (Wernli and Schwierz, 2006). We use six hourly available analysis fields during We decided to use the operational analysis data over e.g. the a more consistent reanalysis data set like ERA-Interim, due to the finer vertical resolution in the tropopause region. While ERA-Interim with 60 model levels has a vertical grid spacing of about 1 km in the UTLS, the operational analysis has a vertical grid spacing of about 300-400 m, depending on the tropopause 5 location and on the vertical grid spacing of L91 and of L137. In particular, this leads to a much better representation of the static stability in the lower stratosphere. The formation of the TIL in numerical models is known to be sensitive to the horizontal and vertical resolution as well as their ratio (e.g., Birner, 2006;Wirth and Szabo, 2007;Son and Polvani, 2007;Erler and Wirth, 2011).
We use analysis data on model levels which provides the best vertical resolution in the UTLS of roughly 300 m. Many of the 10 desired variables such as the temperature T , the three-dimensional wind (u, v, ω), the cloud ice water content ciwc and relative vorticity ζ rel are directly provided by the ECMWF, while other quantities have to be derived from the primary fields, such as static stability N 2 , potential vorticity P V , vertical wind shear S 2 , and the Richardson number Ri.
We define the strength of the TIL as the maximum in static stability within 3 km above the lapse rate tropopause. The lapse rate tropopause is defined as the lowest level where the temperature lapse rate falls below 2.0 K km −1 and its average between 15 this level and all higher levels within 2 km above this level remains below this value (WMO, 1957). We do this, since the high resolution data shows large variability in the UTLS region, with often several maxima evident above the tropopause.
Therefore, we find this definition of the TIL strength to be preferable over e.g. the first maximum in static stability above a threshold (4 × 10 −4 s −2 , e.g., Gettelman and Wang, 2015).

20
A major goal of this study is to analyse the evolution of dynamical features in the UTLS in life cycles of baroclinic waves, and link these with the evolution of the static stability N 2 above the tropopause. Baroclinic life cycles up to the point of breaking are often associated with surface cyclones (e.g., Thorncroft et al., 1993), and the flow in the UTLS above these cyclones is an important region in regard to the enhancement in static stability above the tropopause. Several methods are available to trace cyclones, using e.g. the associated maximum in relative vorticity on lower oder middle tropospheric pressure levels, or the 25 minimum in mean sea level (MSL) pressure. The IMILAST experiment (Neu et al., 2013) showed that many of these methods achieve comparable results. We tested several methods with short time periods and with comparable results. Ultimately, we decided to use the sea level pressure field due to the smoothness of this field compared to e.g. the relative vorticity, which makes it easier to identify cyclone centres. Our algorithm therefore identifies surface cyclones in the MSL pressure field and traces them in time and space. 30 The tracking algorithm is based on Hanley and Caballero (2012), and searches local minima in the MSL pressure field. Since our data has a fine horizontal grid spacing and is limited to the North Atlantic, we had to partly adapt the tracking algorithm to our data set. The major steps are 1.) smoothing of the MSL pressure field, 2.) identification of all local minima at all time steps, and 3.) the connection of the local minima from consecutive time steps to cyclone tracks. The following paragraph will give more details.
A local minimum in a gridded MSL pressure field is defined as a grid point having a lower value than its surrounding 8 grid points. To reduce the amount of local MSL pressure minima found at each time step, a Cressman filter (Cressman, 1959) is applied, averaging each grid point in the field with its neighbouring grid points within a radius r < r 0 (r 0 being 500 km), using weights of (r 2 0 − r 2 )/(r 2 0 + r 2 ). The smoothed field exhibits less local minima, reducing the amount of criteria needed to define 5 a cyclone center, without altering the tracks of the cyclones fundamentally. After applying the Cressman filter and following once more Hanley and Caballero (2012), the MSL pressure field at each time step is projected onto an area-preserving Lambert projection centred at the North Pole, to counteract the bias in zonal resolution caused by the convergence of the meridians on the native latitude-longitude-grid. The projected MSL pressure field is then interpolated onto a regular equidistant grid with 28 km grid spacing, which corresponds to the 0.25 • horizontal resolution at the equator. The algorithm now searches and saves 10 every local minimum in the MSL pressure field, with two extra criteria being applied: 1.) an upper threshold of p t = 1007.25 hPa, and 2.) the neglection of all minima located over orography higher than 1500 m. The first criterium replaces the pressure gradient criterium applied in Hanley and Caballero (2012), since the limitation to a regional domain makes it difficult to calculate consistent pressure gradients. The value for p t was determined by testing several values below 1013.25 hPa, with 1007.25 hPa being the largest value of minimum MSL pressure where our algorithm was able to connect the local minima to 15 coherent cyclone tracks. Our algorithm therefore neglects very weak minima in the pressure field, but since weak cyclones or cyclones in very early/very late stages of their life cycles are often not strongly connected to the upper tropospheric flow, it is sufficient for this study to track them not from their very first nor until their very last appearance. Also we are focussing on the time periods around the mature stage of the baroclinic waves, i.e. when the MSL pressure reaches its lowest values. The second criterion is another result of the IMILAST experiment (Neu et al., 2013) and is applied due to the error associated with 20 reducing the surface level pressure to sea level from such altitudes.
In the next step the algorithm connects minima from consecutive time steps by searching in a given radius for the nearest minimum. For minima associated with a new formed cyclone the search radius in the second time step is 720 km from the position where the cyclone first appears. For minima already existing for two or more time steps the algorithm follows Wernli and Schwierz (2006) with a 'first guess' approach, where the first guess location of the cyclone is a linear continuation of the 25 track in latitude-longitude-coordinates: Wernli and Schwierz (2006) introduce the factor of 0.75 because cyclone movement tends to get slower during a cyclone's life cycle. The corresponding MSL pressure minimum is then defined as the nearest minimum from x * (t n+1 ) within a radius of 840 km. For more information concerning the values of the search radii and the first guess approach see Hanley and Caballero (2012) and Wernli and Schwierz (2006).
Following yet another result from the IMILAST experiment (Neu et al., 2013) only cyclones with a lifetime of at least 24 hours 30 are further considered which translates to at least five 6-hourly time steps in the IFS analysis data. The algorithm furthermore neglects cyclones with less than two time steps before and/or after the global minimum in MSL pressure along their path to make sure that the actual intensification period is covered by the data. We want to emphasize that due to these two criteria only extratropical cyclones are selected. Tropical cyclones in extratropical transition emerging from the western edge of our data region which might have a strong signal in the MSL field but no real intensification period are neglected by the algorithm.   Figure 1 shows the cyclone paths tracked by the algorithm after applying all criteria. The distribution of tracks matches well with the climatological cyclone frequencies described in Wernli and Schwierz (2006). Aside from the large accumulation over the North Atlantic there are also several tracks located over North Africa and the Mediterranean Sea. The relatively small number of tracks over the Mediterranean Sea can be explained by the p t = 1007.25 hPa upper limit criterium, and the fact that these Mediterranean cyclones hardly exhibit strong minima in the MSL pressure field. This study focusses on Atlantic storm 5 tracks, therefore the cyclones over North Africa an the Mediterranean Sea are sorted out by a geographical criterium.

Composites of extratropical cyclones
Ultimately, we want to analyse the variability of the tropopause inversion layer within extratropical baroclinic waves. For this, we compute composites of the cyclones at the time of maximum intensity which we define as the occurrence of the global minimum surface pressure along the track. We select a subset of the gridded data for each cyclone by rotating the pole of a  In the special case of composites of horizontal or quasi-horizontal variables like the potential vorticity on an isentropic surface or the TIL strength, we first calculate the fields for each cyclone and then afterwards the mean. This method preserves more information because the three-dimensional tropopause based averaging still smoothes vertical information due to the variability 10 of e.g. the height of the maximum in N 2 above the tropopause. In contrast to other studies analysing cyclone composites (e.g., Bengtsson et al., 2007;Catto et al., 2010), we keep the orientation of each individual cyclone instead of rotating them dependent on their path of migration. In our case this approach leads to a better representation of the dynamical and thermodynamical features in the UTLS.
3 The lower stratospheric static stability evolution during two baroclinic wave breaking events 15 Before we present the result of the cyclone composite, we first discuss two cases of individual cyclones and associated TIL evolution over the North Atlantic. We choose these cases since both cyclones are associated with upper tropospheric baroclinic wave breaking events very similar to the ones described in idealised baroclinic life cycle simulations. The first case study shows an evolution comparable to an LC2 (life cycle 2), while the second one exhibits distinct features of an LC1 (life cycle 1) wave breaking event (Thorncroft et al., 1993). Although the waves occur consecutively in time and space, they are not interacting directly and the cyclones at surface level evolve relatively isolated from each other, in contrast to multi-cyclone-centres as described for example by Hanley and Caballero (2012).
3.1 Baroclinic wave with LC2 characteristics    Figure 5 shows the subsequent baroclinic wave breaking event 3 days later over the North Atlantic. The mean sea level pressure on 16 October still shows two distinct minima, the decaying northern one associated with the previous wave breaking event, as well as a newly formed minimum. The background state of the UTLS is still significantly distorted due to wave breaking 10 event of the LC2 described in Sect. 3.1. Similar to the previous case a relatively small scale baroclinic wave is evident in the IPV field above the underlaying surface cyclone centre. In contrast to the previous case, as the surface cyclone grows stronger and the upper air wave enters the wrap-up phase ( Figure 5 middle row), the initially cyclonically tilted trough with enhanced values of IPV turns anticyclonically and later on a substantial part of the trough penetrates the jet in its excursion southwards.

Baroclinic wave with LC1 characteristics
The jet splits into two jet streaks (middle row Figure 5d.) and the trough gets thinned, eventually producing a cut-off ( Figure   15 6). These wave breaking characteristics meet the definition of an LC1 as described by Thorncroft et al. (1993). During the evolution of the cyclone the relations between tropospheric IPV, anticyclonic relative vorticity at tropopause height, and an enhancement in static stability above the tropopause are all evident. The regions of maximum static stability with values up to N 2 = 10 × 10 −4 s −2 are again located inside the ridge of low IPV air wrapping up around the underlaying cyclone centre  about the time of maximum cyclone intensity. The thinning and southward moving trough itself exhibits low values of static stability N 2 above the tropopause, in agreement with its positive relative vorticity, but the flow around the trough shows no distinct strong signal in the quasi-horizontal static stability distribution, especially when compared to the cyclonic wrap-up 24 hours earlier. Figure 6 shows a comparable evolution about two days later for the secondary cyclone associated with the cut-off which 5 formed from the thinning streamer. This cyclone was also tracked by the algorithm and while it is weaker and exhibits less horizontal extend than the two previous cases, the region of maximum static stability with values of up to N 2 = 10 × 10 −4 s −2 still evolves inside the wrapped up low-IPV air. The wrapped up cut-off exhibits maximum static stability values of about N 2 = 4 × 10 −4 s −2 . The regions of high static stability above the tropopause are horizontally coherent with the occlusion as well as the region of outflow of ascending air masses into the jet.

10
In conclusion, we analysed two subsequent baroclinic life cycles, the first resembling an LC2, and the second an LC1 when compared with idealised baroclinic life cycle simulations. In both cases the regions of strongest enhancement in static stability above the tropopause are located inside the ridge of low-IPV air moving northward from low latitudes and wrapping up around the underlaying primary cyclone about the time of maximum cyclone intensity. The flow around the southward excursion of the trough in the LC1 wave exhibits no distinct signal, until a secondary cyclone associated with the cut-off from the trough 15 evolves. This cyclone-linked behaviour can also be seen in the idealised baroclinic life cycle simulations from Erler and Wirth (2011). Their Figure 4 shows a comparable evolution of the TIL strength with consideration that there are two northern surface cyclone intensification periods and one cut-off related cyclone forming at low latitudes.
Based on the analysis of these two case studies, we further motivate the analysis of the evolution of the TIL during baroclinic life cycles based on the flow above surface cyclones. We recognise that surface cyclones exist which are not linked to baroclinic  In the following section we present composites of upper tropospheric / lower stratospheric flow features to define a mean characteristic evolution of the flow features in the UTLS above surface cyclones during baroclinic wave breaking events. We compute composites of subsets of the tracked cyclones based on the surface cyclone strength, because we expect the strength to be a good indicator for the amount of coupling between the surface cyclone and the flow in the UTLS. We abstain from presenting composites from cyclone subsets based on other criteria because the amount of cyclones tracked in our data set 10 quickly reduces to a statistically non-significant amount when specific criteria are applied. Figure 7 shows the quasi-horizontal composites of selected features from the 76 strong cyclones with p msl, min ≤ 990 hPa.
The three contour plots show a mean state of the UTLS flow which is in its basic features comparable to the ones discussed in the two case studies of baroclinic wave breaking events. The first contour plot shows a streamer of stratospheric IPV on 330 K reaching from north-west into the cyclone centre, with a cyclonic rotational component. Naturally, the lowest values 15 of IPV are located in the south and gradually approach the IPV values of the stratospheric streamer when rotating counterclockwise around the cyclone centre along the wrap-up. This region of strong with respect to the cyclone centre tangential gradients of IPV exhibit to large parts a negative mean relative vorticity at tropopause height and also large values of static sta-   We furthermore tested different methods of calculating an average Richardson number to check the robustness of our result. Calculating the unmodified Richardson numbers for each individual cyclone and averaging afterwards produces a very 15 fragmented mean field, but it still exhibits a region with local minima of the order of 10 1 inside the region of the TIL. Calculating the mean Richardson number from the averaged potential temperature and wind field yields a result more comparable to the modified Richardson mean, but with overall larger values for Ri, stronger separated minima, and sharper gradients of Ri. Birner et al. (2002) observed a distinct discrepancy in the vertical shear of the horizontal wind S 2 above the tropopause between the radiosonde data and ECMWF reanalysis data. This shows that the vertical wind gradients in the UTLS are not well resolved and significantly underestimated by the reanalysis data, a tendency which might still be the case in the analysis data. The fact that we see a strong maximum in S 2 above the tropopause in NWP data, while Birner et al. (2002) saw none in the mean profiles from reanalysis data, can be explained by 1.) the finer vertical and horizontal resolution in the operational 5 IFS model, and 2.) the fact that we present a composite of a specific synoptic situation which may result in a similar structure of the individual vertical profiles. Richardson numbers of the order of 5-10 still represent a stable flow, but we want to stress that these are mean values from 76 cyclones, and based on vertical gradients of N 2 and S 2 derived from a vertical grid spacing of about ∆z ≈ 300 m. Therefore, there is the possibility that turbulence is present even in regions of enhanced static stability in the lower stratosphere which might affect cross tropopause transport in these regions.
10 Figure 11 provides a strong indication that a colocation between the regions of enhanced static stability above the tropopause and the maximum in vertical shear of the horizontal wind exists. Figure 11 a.) shows the quasi-horizontal composite of the maximum in wind shear within 3 km above the tropopause for the subset of strong cyclones (p msl, min ≤ 990 hPa). It reveals together with Figure 7 that there is a colocation between the regions of maximum squared wind shear S 2 max above the tropopause and the regions of maximum enhancement in static stability N 2 max in the lower stratosphere. Figure 11  The relatively weak secondary cyclone associated with the cut-off which resulted from the LC1 wave breaking event shows a similar evolution on a smaller horizontal scale. The TIL above the individual cyclones exhibits a large temporal, horizontal, 20 and vertical variability on different scales associated to the variety of known forcing mechanisms being resolved in the high resolution NWP data.
Furthermore, we presented composites of the atmospheric state in the vicinity of different subsets of tracked cyclone centres at the point in time of maximum cyclone intensity. We find that stronger surface cyclones are associated with a sharper and more pronounced wrap-up in the UTLS flow. The composites furthermore resemble to a large degree the key features of the TIL 25 evolution and the mean flow as identified from the case studies. The regions of largest TIL enhancement are located north and northeast of the cyclone centre above the occlusion and above regions influenced by strong tropospheric updrafts and clouds reaching up to the tropopause. This indicates the importance of moist dynamical and radiative processes during the formation of the TIL (e.g., Randel et al., 2007;Kunkel et al., 2016). The composites further reveal a maximum in vertical shear of the horizontal wind S 2 within the region of strongest enhancement of static stability above the tropopause. The regions of max- 30 imum static stability and those of maximum wind shear show a remarkable overlap, horizontally as well as vertically, which is in agreement with previous studies (Birner et al., 2002;Grise et al., 2010). Richardson numbers calculated for these flow conditions favourable for turbulence reveal a region of local minima in Ri right above the tropopause at around 5 • north from the cyclone centre. This result points toward a co-location between an enhancement in static stability above the tropopause and potential turbulent mixing of tropospheric and stratospheric air masses (Kunkel et al., 2016).
We want to note that baroclinic life cycles vary in their appearance from case to case and thus the TIL evolution in individual cyclones can differ from the one described by the composite analysis. The analysis of baroclinic life cycles in other regions and seasons would of course be desirable, but is left open at this stage for later studies. The approach used in this study is now 5 applicable to a large data set, e.g. using the new ERA-5 reanalysis which has the same vertical resolution in the UTLS as the analysis data in this study.
Overall this study confirms the importance of baroclinic waves and their embedded cyclones to explain the meso-scale variability of enhanced static stability above the lapse rate tropopause in the extratropics. The high spatial and temporal resolution of the analysis data gives a better understanding on where and when static stability increases during baroclinic life cycles. The  (Erler and Wirth, 2011;Kunkel et al., 2016). They furthermore indicate that turbulent mixing might occur in regions of enhanced static stability right above the tropopause.
Author contributions. DK, PH and TK designed the research project. TK developed the model code and performed the calculations, and analysed the data with the help of DK and PH. TK prepared the manuscript with contributions from all authors.