The CLaMS trajectory module (TRAJ) performs the full-Lagrangian, non-diffusive, three-dimensional advection of an ensemble of air parcels . The numerical integration is based on a fourth-order Runge–Kutta scheme.

Required input fields are horizontal and vertical winds, e.g. from ERA-Interim reanalysis products . The representation of the vertical winds depends on the choice of the vertical coordinate system. It is possible to use different vertical coordinates in CLaMS – e.g. potential temperature $\mathit{\theta }$ in which case vertical winds would be determined as $\dot{\mathit{\theta }}=Q$, with $Q$ the diabatic heating rate. In this study, we use the hybrid $\mathit{\sigma }$–$\mathit{\theta }$ coordinate $\mathit{\zeta }$, with $\dot{\mathit{\zeta }}$ as vertical velocity, as proposed by . The $\mathit{\zeta }$-coordinate combines the terrain-following $\mathit{\sigma }$-coordinate ($\mathit{\sigma }=\frac{p}{p_{\mathrm{s}}}$ where $p_{\mathrm{s}}$ is surface pressure) for the troposphere and the $\mathit{\theta }$-coordinate for the radiation-dominated stratosphere, and $\mathit{\zeta }$ is defined as follows: $$\mathit{\zeta }=\mathit{\theta }\cdot f\left(\mathit{\sigma }\right)$$ with $$f\left(\mathit{\sigma }\right)=\left\{\begin{array}{ll}\sin \left(\frac{\mathit{\pi }}{\mathrm{2}},\frac{\mathrm{1}-\mathit{\sigma }}{\mathrm{1}-{\mathit{\sigma }}_{\mathrm{r}}}\right)& \mathit{\sigma }>{\mathit{\sigma }}_{\mathrm{r}}\\ \mathrm{1}& \mathit{\sigma }\le {\mathit{\sigma }}_{\mathrm{r}}\end{array}\right.$$

The implementation of $\mathit{\zeta }$ as vertical coordinate in CLaMS is described in detail in . In the present study, we use ${\mathit{\sigma }}_{\mathrm{r}}=\frac{p_{\mathrm{r}}}{p_{\mathrm{s}}}$ which means that above the reference height $p_{\mathrm{r}}$ (300 hPa in this study) $\mathit{\zeta }$ is equal to the potential temperature $\mathit{\theta }$.

CLaMS comprises a mixing module (MIX), so that the air parcels are not completely isolated, but some exchange takes place in situations where strong flow deformation is present in the atmosphere. This constitutes the irreversible part of the CLaMS transport. The mixing of the air parcels in the CLaMS module MIX is controlled by the horizontal strain and vertical shear of the wind field . The mixing routine is usually called every 24 h after the trajectory transport. One mixing event contains the following steps: first, discrete vertical layers are defined according to an entropy criterion such that each of those layers contains approximately the same number of air parcels for details see. Second, the following procedure is done separately for each layer: nearest neighbours of each air parcel are identified using Delaunay triangulation on a horizontal projection of the vertical layer. If the distance between two neighbouring air parcels exceeds a critical distance $r_{+}^{\mathrm{c}}$ after time step $\mathrm{\Delta }t$, as defined in Eq. (), a new air parcel is inserted in the middle. In cases where two air parcels are closer than a critical distance $r_{-}^{\mathrm{c}}$, they are merged such that they form one new air parcel. In other cases, no mixing occurs. The critical radii $r_{\pm }^{\mathrm{c}}$ are defined as follows : $$r_{\pm }^{\mathrm{c}}=r_{\mathrm{0}}\exp (\pm {\mathit{\lambda }}_{\mathrm{c}}\mathrm{\Delta }t)$$

In Eq. (), $r_{\mathrm{0}}$ is the mean horizontal distance of air parcels in the layer. The critical Lyapunov exponent ${\mathit{\lambda }}_{\mathrm{c}}$, a measure for the deformation in the flow, determines the critical radii $r_{\pm }^{\mathrm{c}}$ and thus the mixing strength in the model. The impact of the uncertainty in the mixing strength is investigated in and through varying the parameter ${\mathit{\lambda }}_{\mathrm{c}}$. The pure Lagrangian trajectory advection by TRAJ (Sect. ) is numerically non-diffusive. The mixing adds some diffusion to the CLaMS Lagrangian transport (i.e. advection and mixing). The advantage of the CLaMS mixing procedure is that it is built in a physically based manner, i.e. mixing occurs in regions of strong flow deformation and thus where it is expected in reality.

The original CLaMS version contains a detailed stratospheric chemistry scheme CHEM, involving around 150 species. The numerical solver is based on the ASAD code . For coupling to a climate model a simplified version of CHEM was used which is more suitable for long-term simulations. The simplified scheme is called every 24 h and uses daily-mean photolysis rates. It allows the stratospheric loss of long-lived tracers (${\mathrm{CCl}}_{\mathrm{3}}\mathrm{F}$ (CFC-11), ${\mathrm{CCl}}_{\mathrm{2}}{\mathrm{F}}_{\mathrm{2}}$ (CFC-12), ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$, and ${\mathrm{CH}}_{\mathrm{4}}$) to be reproduced. It further describes the water vapour production by methane-oxidation in the stratosphere. The simplified chemistry scheme is described in more detail in .

This section provides a short description of the architecture of the MESSy interface. A more detailed description is given in . The code of MESSy is structured, such that each FORTRAN95 module is assigned to one of the following four layers:

the base model layer (BML): this part contains the source code of the base model. This can be for instance a climate model (ECHAM5 in our study), a simple boxmodel, or a regional weather forecast model.

The CLaMS main modules TRAJ, MIX, and CHEM were modified and integrated as new submodels in the MESSy interface structure. Other submodels, e.g. for the dehydration by cirrus cloud formation (CIRRUS) or for CLaMS boundary conditions (BMIX) were also included. Since the CLaMS modules have been redesigned as independent MESSy submodels, within MESSy they are called CLAMS-TRAJ, CLAMSMIX, CLAMSCHEM, etc. For the sake of readability, we name them here throughout the text without the prefix CLAMS.

There are two ways to use these CLaMS submodels in the MESSy interface (Fig. ). The first option is to run the coupled version with the ECHAM5 basemodel (left box in Fig. ). In this case, horizontal winds driving the isentropic CLaMS trajectories are calculated by ECHAM5. Likewise, the vertical, cross-isentropic velocities are deduced from diabatic heating rates from the climate model. The heating rates result from several process parameterizations, like radiation, convection and clouds, gravity wave drag, and vertical diffusion. The dominant terms in the heating rate budget are radiation and (where applicable) latent heat release from cloud formation. The MESSy interface also provides the possibility for two-way coupling between processes. Thus, trace gas distributions derived by CLaMS could serve as input for the EMAC radiation calculation.

The second possible basemodel is the newly developed CLaMS basemodel (right box in Fig. ). Here, the meteorological input fields are read from external data files, e.g. from ERA-Interim reanalysis data. Running the CLaMS basemodel delivers the same result as the original CLaMS model that is not included in the MESSy interface. The single modules of the original version were represented as individual Fortran90 programs, which were started by a shell script. Technically, the new CLaMS basemodel replaces the shell script that was used to run the original version of CLaMS. In the original version, data exchange between the modules was achieved through NetCDF files. In contrast, in the MESSy version, the communication between the different submodels is carried out via the interface structure in the BMIL, therefore no external data files are required.

Figure  shows horizontal age of air distributions of EMAC-FFSL and EMAC/CLaMS at 450 K for August and October in the Southern Hemisphere. In August (top panels), there are older air masses inside the vortex in EMAC/CLaMS than in EMAC-FFSL. Inside the vortex the air is up to 0.5 years younger in EMAC-FFSL. In contrast, EMAC/CLaMS shows younger air outside the vortex. In October (bottom panels), the age of air differences inside the vortex have increased to values of 0.8 years. The differences are larger than in October because the processes that dominate the vortex evolution are different. During August, diabatic downwelling is the most important process in the vortex. It is found that in August the diabatic vertical velocities in EMAC/CLaMS are larger in the downwelling region of the polar vortex than the respective kinematic vertical velocities in EMAC-FFSL. This leads to the small differences in age of air in August that are displayed in the top right panel of Fig. . However, in October downwelling weakens so that the relative impact of horizontal transport through the vortex edge and mixing on the age of air distribution increases . During the period when the transport barrier controls horizontal mixing, the differences in age of air are larger than during the earlier period when downwelling is the most important process.

Similar to age of air, the simulated patterns of long-lived tracers are mainly controlled by transport but allow a comparison against measurements. For the Antarctic polar vortex region, we also compared vertical profiles of simulated CFC-11 and ${\mathrm{CH}}_{\mathrm{4}}$ with profiles from measurement climatologies of the Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS). The ACE-FTS climatology contains monthly zonal mean values for 14 species. It does not include error budget estimates, but comparisons with measurements from other instruments show differences in the order of 10 % for CFC-11 and ${\mathrm{CH}}_{\mathrm{4}}$ . The climatology includes ACE-FTS measurements from February 2004 to February 2009.

The top panels in Fig.  show profiles for September in the 80 to 70${}^{\circ }$ S latitude bin. At this time, the vortex is still stable and clearly separated from mid-latitude air. The profile of CFC-11 from EMAC/CLaMS is in good agreement with the ACE-FTS climatology, although slightly higher at 17–19 km altitude. However, the EMAC-FFSL simulation produces higher CFC-11 mixing ratios for all altitudes. This shows that the transport barrier at the edge of the polar vortex is weaker in the EMAC-FFSL simulation which results in an overestimated mixing across the vortex edge.

The top right panel of Fig.  displays the respective profiles of ${\mathrm{CH}}_{\mathrm{4}}$. Here, the same pattern as in the CFC-11 profiles is visible. The EMAC-FFSL profiles show higher concentrations than the satellite climatology. EMAC/CLaMS also exhibits higher ${\mathrm{CH}}_{\mathrm{4}}$, but is closer to the ACE-FTS measurements up to 20 $\mathrm{km}$. At higher altitudes above 30 $\mathrm{km}$ both models show higher ${\mathrm{CH}}_{\mathrm{4}}$ mixing ratios than observed. Overall, EMAC/CLaMS transport leads to an improvement of the ${\mathrm{CH}}_{\mathrm{4}}$ simulation in the vortex region, although it results in still higher mixing ratios than in the satellite climatology.

The bottom panels in Fig.  present similar plots for November for the latitude bin from 70 to 60${}^{\circ }$ S. In this month, the Antarctic vortex begins to break up. This process starts at high altitudes. The weakening of the vortex boundary is clearly visible in the ${\mathrm{CH}}_{\mathrm{4}}$ profiles in the bottom right panel. The ACE-FTS profile exhibits a pronounced kink at 20 to 25 $\mathrm{km}$ altitude. This kink appears in the profile because the vortex air masses above 25 $\mathrm{km}$ are mixed with ${\mathrm{CH}}_{\mathrm{4}}$-rich air from mid-latitudes. The kink is also visible in the EMAC/CLaMS profiles, although it is not as distinct as in the ACE-FTS climatology. The EMAC/CLaMS profiles in the latitude range from 90 to 70${}^{\circ }$ S also feature this kink, but at these most southern latitudes there are no ACE-FTS measurements available for comparison. In the EMAC-FFSL profiles, this kink is not visible. These results indicate that the vortex breakup is much better represented in the CLaMS Lagrangian transport. The kink is not visible in the respective CFC-11 profiles (bottom left panel), because the concentrations are too low to show indications of mixing between polar and mid-latitude air in the altitude range where the beginning of the vortex breakup occurs. The CFC-11 profiles of November are another example for the overall pattern of differences between the two transport schemes: with the CLaMS full-Lagrangian transport, it is possible to produce trace gas distributions that indicate a stronger polar vortex than in EMAC-FFSL, but still weaker than in the satellite climatology, which seems to be linked to the weaker horizontal winds in EMAC (see Fig. ).

In Fig.  we show ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ probability density functions (PDFs) at 550 K from 50–80${}^{\circ }$ S for the months August to November. Here, EMAC/CLaMS and EMAC-FFSL results are compared to satellite data from measurements of the Microwave Limb Sounder (MLS) onboard the NASA Aura satellite from 2005 to 2012. The satellite data used here are MLS version 3.3 data . The PDFs show a two-peak structure, indicating the separated air masses inside and outside the polar vortex. The peak at lower ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ mixing ratios at about 30 ppb characterizes the air inside the vortex. In EMAC-FFSL the lowest observed values are not reached, which indicates either that the downwelling in this model representation is too weak or that the in-mixing from mid-latitudes too strong, or both. It is also visible that the vortex breaks up too early in EMAC-FFSL, since in October the vortex peak has nearly vanished completely. In EMAC/CLaMS, the peak position is captured well in most months except for October. The peak in EMAC/CLaMS is less pronounced than in the MLS data, but the vortex boundary is less penetrable than in EMAC-FFSL. The second peak around 200 ppb indicates mid-latitude air. The mid-latitude peak is well captured in EMAC-FFSL. In EMAC/CLaMS, the peak value is about 20 ppb higher than in the measurements. The separation (i.e. the range of low probability values) between the two peaks of the PDF is an indicator for the strength of the transport barrier at the edge of the polar vortex. Here, using EMAC/CLaMS leads to a clear improvement compared to EMAC-FFSL. The separation between the two peaks is well captured in the Lagrangian transport representation. The comparison of ${\mathrm{CH}}_{\mathrm{4}}$ PDFs of EMAC/CLaMS and EMAC-FFSL with HALOE measurements shows similar results (not shown).

The polar vortex edge is characterized by strong horizontal gradients of trace gases. For this study, ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ gradients from the simulation climatologies are compared to gradients in monthly climatologies from MLS measurements from 2005 to 2012. The MLS data have been interpolated on vertical pressure levels for each profile, binned horizontally (lat $\times$ long) and averaged for each month. MLS scans about 3500 profiles a day, thereby providing a high-frequency sampling of the global atmosphere and good statistics for creating global monthly zonal mean climatologies. For the comparison, the simulation results have been vertically smoothed in a similar way as the averaging kernel of the MLS retrievals smoothes the atmospheric profiles. show that this procedure is necessary to obtain comparable results, especially in the lower stratospheric polar regions. Figure  shows the absolute value of the horizontal ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ gradients on the isentropic surface at 450 $\mathrm{K}$ for September. The left panel displays the EMAC-FFSL results, the panel in the middle the gradient in EMAC/CLaMS, and the right panel the MLS climatological values. It is clearly visible that the ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ gradient is too weak in the EMAC-FFSL transport, with maximum values around $4.5\times {10}^{-\mathrm{5}}$ $\mathrm{ppb}{\mathrm{m}}^{-\mathrm{1}}$. The MLS data exhibit maximum values of $7.0\times {10}^{-\mathrm{5}}$ $\mathrm{ppb}{\mathrm{m}}^{-\mathrm{1}}$. The EMAC/CLaMS ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ gradient, calculated with the full Lagrangian transport scheme, shows maximum values of $6.0\times {10}^{-\mathrm{5}}$ $\mathrm{ppb}{\mathrm{m}}^{-\mathrm{1}}$. These values are still smaller than those found in the satellite data set, but they show a clear improvement in comparison to the flux-form semi-Lagrangian transport scheme.

This section presents age of air distributions in the Arctic polar vortex region at the end of winter. As the Arctic polar vortex shows substantial interannual variability, more than the Antarctic polar vortex, we do not analyse results from the 10-year climatology here. Instead, monthly mean values from the second year of the time-slice simulation are shown as an example.

Figure  shows age of air distributions in the Northern Hemisphere at the 450 $\mathrm{K}$ potential temperature level. In February, the EMAC/CLaMS simulation shows a more pronounced pattern in the age of air distribution, which is the result of a stronger polar vortex barrier and downwelling. The air inside the vortex is older and the gradient at the vortex edge is stronger when using the full-Lagrangian transport scheme. The absolute differences for age of air in February are displayed in the top right panel. This plot shows that the maximum difference in mean age of air is located inside the vortex and reaches values up to one year.

In March the vortex has split into two parts (see bottom panels in Fig. ). This structure is visible in both transport schemes, but it is more pronounced in EMAC/CLaMS. In the EMAC-FFSL representation, stronger mixing of air masses from inside and outside the vortex has taken place. Again, the differences in age of air are largest (up to 1 year) in the regions of the polar vortex.

In Fig.  we compare ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ PDFs from 60–90${}^{\circ }$ N for February and March with MLS measurements, similar to the analysis for the Southern Hemisphere. The peaks of the Northern Hemisphere PDFs are wider than in the PDFs for the Antarctic, which illustrates the larger variability of the Arctic polar vortex. The PDFs show the problems of EMAC-FFSL in representing the Arctic polar vortex. In February, the peak ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ mixing ratio in EMAC-FFSL of 170 ppb is much higher than in the measurements, for which the peak value is located around 100 ppb. The separation between the polar vortex air and the mid-latitude air is very weak in EMAC-FFSL. In March, the two-peak structure vanishes in the EMAC-FFSL PDF. EMAC/CLaMS shows improved vortex isolation compared to EMAC-FFSL. In February, the structure of the ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ PDF from measurements is well represented by EMAC/CLaMS. In March, low ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ mixing ratios below 100 ppb inside the vortex appear in EMAC/CLaMS, but they occur less often than in the measurements. Nonetheless, this constitutes a clear improvement compared to the EMAC-FFSL simulation, where no vortex structure is visible in the ${\mathrm{N}}_{\mathrm{2}}\mathrm{O}$ PDF in March.

The differences in age of air between EMAC-FFSL and EMAC/CLaMS are larger in the Northern Hemispheric vortex than in the Southern Hemispheric vortex. This can be explained by the fact that planetary wave activity is stronger in the Arctic than in the Antarctic. Thus, isentropic Rossby waves disturb the zonal symmetry of the Arctic polar vortex much more strongly than of the almost circumpolar vortex in the Antarctic stratosphere. In such a case, a Lagrangian transport scheme has an advantage over the FFSL approach by minimizing the numerical mixing in the vicinity of a disturbed transport barrier like the vortex edge. The differences between EMAC-FFSL and EMAC/CLaMS due to mixing seem to be larger than the differences due to vertical velocities. This is consistent with the analysis for the Southern Hemisphere, where the differences in age of air are most pronounced in October, when the impact of downwelling decreases and the impact of in-mixing into the vortex increases.