The numerical chemistry climate model system EMAC includes submodels describing tropospheric and middle atmosphere processes and their interaction with ocean, land and human influences . It uses the second version of the Modular Earth Submodel System (MESSy2) to link different submodels for physical and chemical processes in the atmosphere . The core atmospheric model of EMAC is the 5th generation of the European Centre Hamburg general circulation model ECHAM5 . Atmospheric tracer management in MESSy is treated with the submodel TRACER , providing an interface structure (memory and data management) to couple chemical processes with the base model. In the standard setup of EMAC, tracers are transported by the flux-form semi-Lagrangian (FFSL) transport scheme of . EMAC employs a hybrid pressure grid structure and vertical (kinematic) velocities for tracer transport are calculated internally by the transport scheme as a residual from the horizontal flux divergence using the continuity equation . Furthermore, transport by vertical diffusion is parametrized .

The Lagrangian chemistry transport model CLaMS combines forward trajectories with parametrized small-scale mixing. Small-scale mixing is implemented in a physical manner, such that mixing is induced by deformations in the large-scale flow. The model uses an isentropic vertical coordinate (potential temperature) throughout the stratosphere, with the cross-isentropic vertical velocity deduced from the total diabatic heating rate, including all-sky radiative, latent and turbulent heating contributions (here taken from ERA-Interim reanalysis, see Sect. ). Further details of the model setup used here can be found in .

A particular advantage of CLaMS Lagrangian transport is that the trajectory calculation is non-diffusive per se, and that the strength of diffusion induced by parametrized small-scale mixing may be controlled. For that reason, a critical Lyapunov exponent λc has to be specified, which controls the relative distance between model grid points to be affected by mixing for details see e.g.,.

Table  gives an overview over all model simulations used for the present study. A detailed description of these listed simulations will be given within this section.

In the Earth System Chemistry integrated Modelling (“ESCiMo”) initiative , reference simulations (RC) as defined by the IGAC/SPARC Chemistry–Climate Model Initiative (CCMI) and described in detail by were performed. In our study we focus on two of these ESCiMo reference simulations (namely RC1-base-07 and RC1SD-base-07), both conducted in the T42L90MA resolution. This resolution has a spherical truncation of T42 (corresponding to a quadratic Gaussian grid of approx. 2.8 by 2.8 in latitude and longitude) and a vertical resolution of 90 hybrid pressure levels with the uppermost level centered at 0.01 hPa.

The first simulation we use is RC1-base-07 (in the following referred to EMAC-RC1), a free-running hindcast simulation, ranging from 1960 to 2011. The sea surface temperatures (SSTs) and the sea ice concentrations (SICs) are used from the HADISST database, provided by the UK Met Office Hadley Centre (available via http://www.metoffice.gov.uk/hadobs/hadisst/).

The second simulation we use is RC1SD-base-07 (in the following referred to EMAC-RC1SD), a hindcast simulation with specified dynamics (SD), ranging from 1980 to 2011. Nudging is done by a Newtonian relaxation technique towards 6-hourly ECMWF reanalysis data (ERA-Interim, ). The nudging of the prognostic variables, divergence, vorticity, temperature and the (logarithm of the) surface pressure is applied in spectral space with a corresponding relaxation time of 48, 6, 24 and 24 h, respectively. Global mean temperature is also included. Nudging is applied in the troposphere from above the boundary layer up to 5 hPa, with nudging coefficients decreasing with height above 10 hPa (for details see ). Nudging further implies that SSTs and SICs are used from ERA-Interim reanalysis data.

For the simulations of this paper the transport model CLaMS was driven with meteorological data from ERA-Interim reanalysis over the period 1990–2011. Cross-isentropic vertical velocity has been deduced from the reanalysis forecast total diabatic heating rate see. We carried out a high-resolution reference simulations (CLaMS-ERAI), with the critical Lyapunov exponent chosen as λc=1.5 day-1, resulting in good agreement with observed trace gas distributions as shown in several recent publications e.g.,. Furthermore, for the investigation of model diffusion effects we carried out two low-resolution sensitivity simulations, both driven by ERA-Interim meteorology but with varying the strength of parametrized small-scale mixing (either λ=1.5 day-1 or λ=1.0 day-1). The sensitivity simulation with λ=1.5 day-1 (CLaMS-L1.5) is close to the ERA-Interim reference simulation (only difference is horizontal resolution) and the simulation with λ=1.0 day-1 (CLaMS-L1.0) includes enhanced parametrized mixing causing stronger diffusion.

As mentioned above, stratospheric mean age of air is defined as the residence time of air parcels in the stratosphere e.g.,. It is affected both by the residual circulation and by eddy mixing. In global models an AoA tracer is implemented as an inert tracer with linearly increasing boundary conditions (“clock-tracer”; ). AoA at a certain grid point in the stratosphere is then calculated as the time lag between the local tracer mixing ratio (at this certain grid point) and the current mixing ratio at a reference point. In the EMAC simulation setup AoA is obtained from linearly increasing mixing ratios of an inert synthetic tracer (age of air tracer; see Table A1 in ). The AoA tracer is emitted into the lowermost model level. The reference point is set at the tropical tropopause for age tracer mixing ratios between 10∘ S and 10∘ N as the height of thermal tropopause. Note here, that the results do not change substantially, if the zonal band is varied seasonally.

In CLaMS there is an analogous AoA tracer emitted into in the lowest model layer. Mean age in the stratosphere is calculated as the time lag between the local tracer mixing ratio and the mixing ratio at the boundary layer. To be consistent with EMAC, the AoA value at 340 K between 10∘ S and 10∘ N (corresponding approximately the height of the tropical tropopause) is subtracted from AoA. Here we use the 340 K surface as tropical tropopause (although it is lying below the real tropical tropopause), as we want to be consistent with the residual circulation transit time calculation, which includes the tropical tropopause layer (see next section).

The RCTT is the hypothetical age, air would have if it was only transported by the residual circulation, without eddy mixing. For the EMAC simulation output, RCTTs are calculated following by calculating backward trajectories that are driven by the transformed Eulerian-mean (TEM) meridional and vertical daily velocities (referred to as residual velocities) with a standard fourth-order Runge–Kutta integration. The results of RCTT differ only little whether daily or monthly values of the residual velocities are used. The backward trajectories are initialized on a grid with 64 latitudes and 42 pressure levels (from 200 to 5 hPa). The residual meridional velocity v‾∗ and the vertical velocities w‾∗ are calculated following with data from 6-hourly model output. The backward trajectories are terminated when they reach the thermal tropopause. The elapsed time is then the residual circulation transit time. A detailed description is given by .

For the CLaMS simulation the RCTTs are calculated likewise by running backward trajectories, but in isentropic coordinates using the mean diabatic residual circulation velocities (v‾∗, Q‾∗), until they cross the 340 K surface in the tropics. The tropical band is set between 30∘ N and 30∘ S, as the entry latitudes for the shallow branch are close to the polar flanks of the tropics see and thus a more narrow latitude band (10∘ N–10∘ S) would cause that trajectories coming down poleward of 10∘ N–10∘ S would be lost (this is assumed to be similar for EMAC). For the isentropic formulation in CLaMS the residual circulation velocities (v‾∗, Q‾∗) are calculated as the mass-weighted meridional and vertical wind velocities, based on the cross-isentropic vertical velocity Q=θ˙ .

The different calculation frameworks for EMAC and CLaMS data (kinematic vs. diabatic vertical velocities) causes differences in the results, with a noisier structure for the kinematic vertical velocity see. However, as the internal vertical coordinates in EMAC and CLaMS are pressure and potential temperature, respectively, calculating residual circulation and mixing diagnostics in the two different coordinate systems is more consistent with the respective model simulation. For comparison between the two models, we interpolate the CLaMS zonal mean data to pressure levels. Moreover, for comparing the data it must be considered that there are differences in the reference surface (tropopause in EMAC vs. 340 K in CLaMS), which likely causes a difference in RCTT of 40–60 days, as Q∗=0.7–1 K day-1 in that region. Another important aspect to note is the different treatment of trajectories at the model top. In CLaMS the data top is lower and trajectories are not considered if they reach the top. So there might be lower transit times (missing data) at high altitudes and the results may not be so reliable in regions poleward of about 60∘ N or 60∘ S.

In EMAC the top level is higher and trajectories are artificially kept at the model top and advected horizontally in the top layer until they travel to lower levels. Due to the high model top at 0.01 hPa and weak vertical velocities there, the error for RCTTs calculated up to 5 hPa is small.

Besides the transport through the residual circulation, AoA is a function of mixing . As pointed out by , mixing between the tropics and extratropics can cause additional aging by recirculation of aged air, which is mixed from the mid-latitudes to the tropical pipe. This process is called “aging by mixing”. In their study proposed that in global models aging by mixing can be interpreted as the difference between simulated AoA and RCTT, assuming that mixing processes on unresolved scales (namely parametrized and numerical diffusion) are small.

Recently, calculated aging by mixing explicitly on resolved scales (in the following termed as “resolved aging by mixing”) using the zonal mean isentropic tracer continuity equation e.g.,, which can be reformulated for AoA e.g.,. The formulation for the zonal mean continuity equation for AoA in isentropic coordinates is explained in detail by and by . For the CLaMS simulation, where the potential temperature is the vertical coordinate, this analysis is used to calculate the local mixing tendency (M). Resolved aging by mixing is then given by integrating the explicitly calculated local mixing tendency M along a residual circulation trajectory ending at a given location and time, which is the path followed by this air parcel if advected by the residual circulation .

As EMAC data are given on pressure coordinates the calculation of the local mixing tendencies must be adapted. The TEM continuity equation for zonal mean tracer concentrations in pressure coordinates is described by . Following this equation can be used to derive the tendency equation for AoA (Γ). In the following the notation of is used with overbars for zonal means and primes for the deviations from the zonal means. The AoA tendency equation (consisting of two residual circulation contributions and two eddy-mixing contributions for details see is given by ∂Γ∂t=1-v‾∗∂Γ∂y+ezH1cos⁡(φ)∂Mycos⁡(φ)∂y-w‾∗∂Γ∂z+ezH∂Mz∂z. Here, v‾∗ and w‾∗ denote the meridional and vertical component of the residual circulation, respectively, z is the height, φ denotes the latitude and H is the scale height (here we assume H to be 7 km, which is the most standard choice, although stratospheric values of H vary between 6.4 and 7 km, this is true for both models). The total local mixing tendency M is the sum of the horizontal and the vertical component of the local mixing tendency in the tendency equation for AoA (third and fifth term on the right side). The eddy-flux components My and Mz are defined as My=-e-zHv′Γ′‾-v′T′‾S∂Γ∂z and Mz=-e-zHw′Γ′‾+v′T′‾S∂Γ∂y, where v′, w′ and T′ are the deviations of vertical and horizontal velocity and temperature from their zonal mean values. S denotes a stability term defined by S=H×N2/R (with H=7 km, R=287 m2 s-1 K-1 and N2 being the Brunt–Väisälä frequency).

As mentioned above, resolved aging by mixing can be defined as the non-local, integrated mixing effect. This means integrating M=ezH1cos⁡(φ)∂Mycos⁡(φ)∂y+ezH∂Mz∂z along a residual circulation trajectory, gives the value of resolved aging by mixing at the starting location and time of the trajectory : Γ‾(t)=RCTT+∫t0tMdt′. As mentioned above, the effect of aging by mixing on mean age can be also obtained by the difference between AoA and RCTT . This estimate is easier to deduce than the exact calculation (Eq. ), but may include effects due to unresolved processes see. Understanding these unresolved processes may be important to explain inter-model spread in AoA. Another advantage of calculating resolved aging by mixing is that the local mixing tendencies are available. Investigation of the local mixing tendencies provides a further insight into the processes causing AoA changes . Subtracting “resolved aging by mixing” from “aging by mixing” provides the effect of mixing on unresolved scales, which we define as “aging by diffusion”.

The zonal annual mean of AoA, RCTT, resolved aging by mixing and aging by diffusion, averaged over the time period 1990–2011, for the simulations EMAC-RC1 (left column), EMAC-RC1SD (middle column) and CLaMS-ERAI (right column) are illustrated in Fig. . Note that the model data of CLaMS-ERAI are interpolated to pressure coordinates. All simulations show the typical pattern of AoA distribution with lower AoA in the tropical lower stratosphere and older air in the extratropical middle stratosphere (see Fig. a). Comparing AoA of these simulations to observations shows that in EMAC-RC1 and in EMAC-RC1SD AoA are (a bit) younger at 50 hPa compared to MIPAS observations seetheir Fig. 24. Note, however, that SF6-derived AoA from MIPAS is larger compared to in situ measurements see e.g.,, and that in CLaMS-ERAI AoA is in good agreement with observations in the lower stratosphere see.

Before discussing the differences in the three model simulations, we investigate the effects that drive the AoA patterns. As shown in previous studies e.g.,, AoA (Fig. a) largely differs from RCTT (Fig. b) in magnitude and structure for all simulations: RCTT follows the structure of the residual circulation. In most regions RCTT is lower than AoA, only at high latitudes in the lowermost stratosphere RCTT is higher. This shows that aging by mixing plays an important role for AoA. However, as said before, parametrized and/or numerical diffusion is included in the aging by mixing term (see Sect. ). Therefore, we show resolved aging by mixing in Fig. . Consistently for all simulations resolved mixing leads to additional aging in most parts of the stratosphere, with maximum resolved aging by mixing in the mid-latitude middle stratosphere, as mixing between the tropics and the extratropics leads to recirculation of air parcels. Only in the extratropical lowermost stratosphere, where mixing with tropospheric air occurs, resolved aging by mixing leads to a decrease in AoA. If looking at the pattern of the local mixing tendencies (see Fig. ), a further insight into the processes causing the resolved aging by mixing pattern is provided . Large positive local mixing tendencies are present in the tropics and subtropics (in-mixing of aged air from high latitudes) and negative local mixing tendencies can be found at high latitudes for all three simulations. In the subtropics strongest positive local mixing tendencies occur below 50 hPa. These local mixing tendencies affect AoA above that level, so that resolved aging by mixing (Fig. c) increases with height, as more mixing levels contribute to resolved aging by mixing .

The effect of aging by diffusion (Fig. d) shows that diffusion mainly leads to additional aging in all simulations. However, in general, the effect of aging by diffusion on AoA is relatively small (about 10 %). The result, that diffusion mainly makes air older is interesting, because it was suggested before that diffusion leads to too young age in models because they are too diffusive e.g.,. For the two EMAC simulations the maximal values of aging by diffusion are found in southern high latitudes (at 30–60 hPa), while aging by diffusion is negative in mid-latitudes. In EMAC, unresolved diffusion is caused by numerical diffusion of the advection scheme and parametrized vertical diffusion. We assume, that numerical diffusion dominates, as we could show with the tropical leaky pipe model (this model is described in Sect. ), that vertical diffusion leads to a decrease in tropical AoA. Thus, we expect strong local diffusion where AoA gradients are strong, and a strong local diffusion tendency, where the second derivative of AoA is large (after Fick's law diffusion is proportional to d2AoA/dy2). Aging by diffusion as shown in Fig. d is then the integrated effect over the local diffusion tendencies. The strong positive effect of aging by diffusion at 60∘ S arises from the increasing gradient in AoA associated with the polar vortex. In CLaMS-ERAI, aging by diffusion is overall smaller compared to EMAC, and its pattern structurally strongly differs from EMAC. In CLaMS, unresolved diffusion arises from local subgrid-scale mixing, that is flow dependent and thus simulated in a physical manner.

Furthermore, we analyze the differences in AoA (and in the effects that drive AoA) between the different model simulations. Although we have seen that the overall climatological structure agrees quite well for the shown simulations, there are differences in detail (see Fig. ). Thus, in order to better compare the climatological structure, Fig.  presents the absolute differences between EMAC-RC1 and EMAC-RC1SD (left column) and between EMAC-RC1SD and CLaMS-ERAI (right column) for AoA, RCTT, resolved aging by mixing, aging by diffusion and additionally for the local mixing tendencies. Note that for building the difference between EMAC and CLaMS, we calculate the values relative to the same tropical reference layer of 100 hPa (not done in Fig. ), as for CLaMS the transit time ends when the backward trajectories are crossing the 340 K surface, whereas for EMAC transit times end when trajectories cross the tropopause.

The difference in the free-running simulation (EMAC-RC1) and the nudged simulation (EMAC-RC1SD) are presented in Fig.  (left column). EMAC-RC1 has somewhat lower AoA (up to 0.75 years) than EMAC-RC1SD in all regions, with largest differences occurring in the Southern Hemisphere. The younger air in EMAC-RC1 can be explained through lower residual circulation transit times (see Fig. b) due to faster circulation. It is known that the free-running model overestimates planetary wave activity in the Southern Hemisphere, that drives a stronger residual circulation and leads to a too weak polar vortex (; ; R. Deckert and D. Cai, personal communication, 2016).

Also quite big differences are present in the respective resolved aging by mixing pattern: in the tropical lower stratosphere and in polar regions less resolved aging by mixing, and at about 60∘ N and 60∘ S more resolved aging by mixing (being more pronounced in the Southern Hemisphere) is found in EMAC-RC1. These differences can be explained due to the fact that local mixing tendencies are weaker in the tropical lower stratosphere in EMAC-RC1 compared with EMAC-RC1SD (consistent to the fact that the jet regions are less pronounced in EMAC-RC1; see ) and also in the polar regions. Thus, besides the lower RCTT, an overall reduced resolved aging by mixing is also leads to the younger air in EMAC-RC1. Differences in aging by diffusion also can be found in the two EMAC simulations (Fig. d), showing the opposite effect of resolved aging by mixing (Fig. c). As in EMAC-RC1, the polar jet (polar vortex) in the Southern Hemisphere is significantly too weak see; therefore, more mixing occurs cross the vortex edge, leading to a weaker gradient in AoA, and thus to less aging by diffusion.

Finally, we focus on the differences between EMAC-RC1SD and CLaMS-ERAI in Fig.  (right column). Mean AoA simulated in EMAC-RC1SD and CLaMS-ERAI may differ by more than a year, despite the fact that the two simulations are both driven by ERA-Interim data. However, while CLaMS is directly driven by ERA-Interim data using diabatic heating rates as vertical velocities, the EMAC-RC1SD simulation is nudged to ERA-Interim horizontal winds and temperatures. As recently pointed out by , the residual circulation calculated from reanalysis data using different estimates (from the direct TEM residual velocities, from the momentum balance, and from the thermodynamic balance, i.e., the diabatic circulation) differs strongly in mean magnitude (up to 40 %), likely due to data assimilation. The fact that direct and momentum-based estimates are different in ERA-Interim is confirmed in Fig. a, where the vertical structure of the annual-mean tropical upwelling (i.e., vertical advection by the residual circulation) over the 30∘ S–30∘ N latitude band, calculated with the direct estimate (black line) and the momentum-based estimate (blue line) is shown for ERAI-Interim (dashed lines) and also for the nudged simulation EMAC-RC1SD (solid lines). Note, that the estimates are plotted relative to the direct estimate of EMAC-RC1SD such that EMAC-RC1SD (black solid line) equals 1 throughout the vertical profile. The residual circulation in the nudged EMAC-RC1SD simulation (black solid line) lies in between the direct and momentum-based estimate of the residual circulation of ERA-Interim (Fig. a). Furthermore, it also differs from the diabatic circulation in ERA-Interim seetheir Fig. 6, which is used in CLaMS. It is interesting that the two residual circulation estimates are also different for EMAC-RC1SD. In contrast, in the free-running simulation EMAC-RC1 the two estimates are nearly identical (figure not shown), as EMAC-RC1 simulates consistent data. Thus, it is clear that CLaMS-ERAI and EMAC-RC1SD have a different circulation due to the different estimates of the residual circulation (this is also apparent in the different transit times of EMAC-RC1SD and CLaMS-ERAI in Fig. b). Furthermore, the EMAC-RC1SD simulation is nudged only up to 5 hPa; thus, the circulation above also differs from ERA-Interim (see Fig. a).

We have seen in Fig. a (right column) that CLaMS-ERAI has lower AoA in most of the stratosphere (up to 1.25 years), with maximal values in the Southern Hemisphere. Only in the northern latitudes lower stratosphere younger air (up to -0.75 years) is apparent. These AoA differences are associated with differences in resolved aging by mixing, RCTT and aging by diffusion, all playing a similarly important role. EMAC-RC1SD shows mainly higher transit times (meaning slower circulation) in the Southern Hemisphere and in the northern lower stratosphere, consistent with lower AoA there. Note that differences in calculating RCTT exist, as mentioned in Sect. , with data being not comparable at high latitudes. Moreover, resolved aging by mixing differs largely between EMAC-RC1SD and CLaMS-ERAI (see Fig. c, right column), with resolved aging by mixing being mainly higher in EMAC-RC1SD (with maximum values in the mid-latitude middle stratosphere), consistent with larger RCTTs, as a slower circulation also leads to a slower recirculation, and thus to higher resolved aging by mixing. Only at the edges of the polar vortex, mainly in the Southern Hemisphere, resolved aging by mixing is higher than in CLaMS-ERAI. The pattern of the negative local mixing tendency differences in the lower mid-latitude stratosphere at 30–60∘S (Fig. e) roughly shows the reason for this negative difference there. However, keep in mind, that it is difficult to interpret resolved aging by mixing with local mixing tendencies, as it is also affected by the residual circulation (as integrated effect).

In addition, aging by diffusion has a strong effect on the AoA difference pattern (Fig. d, right column) with significantly smaller aging by diffusion in CLaMS-ERAI throughout the stratosphere, in particular in the high latitude middle stratosphere of both hemispheres maximum values (up to 1 year) can be found. Here the representation of the advection certainly affects the strength of aging by diffusion, and explains the strong difference pattern. As mentioned before in CLaMS-ERAI, small-scale mixing is parametrized by anisotropic diffusion, simulated in a physical manner, being flow dependent. In contrast EMAC-RC1SD uses the flux-form semi-Lagrangian transport scheme, where (numerical) diffusion is more pronounced in regions of strong barriers (e.g., at the arctic and antarctic polar vortex), so unresolved diffusion is higher than in CLaMS there. This is consistent with , who found in free-running simulations with the coupled model system EMAC-CLaMS, that transport barriers (polar vortex and tropical pipe) are stronger, if using the CLaMS tracer transport scheme compared to FFSL transport scheme. The stronger transport barrier in CLaMS can be also seen in Fig. a, as the AoA gradient is stronger in CLaMS-ERAI. Therefore, local mixing across the transport barriers is less efficient (see also Fig. e), and thus less air is mixed to the tropical pipe and to polar regions. Correspondingly lower resolved aging by mixing and aging by diffusion is found in CLaMS.

Sensitivity studies were performed with CLaMS to test the sensitivity to parametrized subgrid-scale mixing. In a sensitivity simulation (CLaMS-L1.0) the subgrid-scale mixing strength was enhanced (critical Lyapunov exponent λc=1 day-1) as compared to the reference simulation CLaMS-L1.5 (λc=1.5 day-1). Choosing the smaller critical Lyapunov exponent of λc=1 day-1 allows for mixing to be triggered at weaker flow deformations. Note that both choices of the small-scale mixing strength in CLaMS yield simulation results within the range of existing stratospheric observations . Figure a–c show the zonal annual mean of AoA, resolved aging by mixing and aging by diffusion for the CLaMS simulations CLaMS-1.5 (left column) and CLaMS-1.0 (middle column). Additionally the right column of Fig.  displays the differences between CLaMS-1.0 and CLaMS-1.5. Enhancing small-scale model mixing increases simulated mean age of air by a few months in most parts of the stratosphere (see Fig. ). While the residual circulation in both simulations is exactly the same (equal RCTTs), this increase is, as expected, related to an increase in both resolved aging by mixing (Fig. b) and aging by diffusion (Fig. c). Aging by diffusion increases due to enhanced small-scale mixing mainly at the edge of the tropical pipe, where steep age gradients exist, and along the subtropical jets, where strong flow deformations frequently occur.

The diagnosed small-scale mixing intensity diagnosed from CLaMS (estimated as the percentage of CLaMS air parcels in each latitude-level grid box influenced by parametrized small-scale mixing) consistently increases in these regions in the enhanced small-scale mixing simulation (see Fig. ). Remarkably, enhanced small-scale mixing increases not only small-scale diffusion but also aging by mixing (Fig. b), even though the flow is exactly the same. This can be understood by the fact that enhanced AoA (by unresolved diffusion) automatically leads to enhanced resolved aging by mixing (the same mixing event leads to a larger exchange in AoA, or in other words the local mixing tendency, that is given by v′AoA′‾ (see Eq. 2) increases, because AoA enhances). Therefore, subgrid diffusion has a larger impact on AoA as diagnosed by aging by diffusion due to this feedback on mixing on resolved scales.

Using the formulation of the conceptual tropical leaky pipe (TLP) model , the mixing efficiency can be defined as measure of the relative strength of mixing for details see. The mixing efficiency is defined as the ratio of the mixing mass flux to the net mass flux across the tropical barrier. The mixing efficiency is proportional to the relative enhancement of AoA by mixing, and proved to be a useful measure of the relative mixing effects. Table  gives the mixing efficiency for the simulations discussed here. In the two EMAC simulations, the mixing efficiency is similar (0.43 and 0.44) despite the different underlying dynamics. The mixing efficiency is lower by about 10 % in the CLaMS-ERAI simulation (0.39). In all simulations the mixing efficiency decreases when subtracting the effects of aging by diffusion, the difference is on the order of 11 % in EMAC and 7 % in CLaMS-ERAI. As expected, in the CLaMS simulation with enhanced subgrid mixing (CLaMS-L1.0), the mixing efficiency is higher compared to the reference simulation CLaMS-ERAI. Overall, we find that unresolved diffusion enhances the mixing efficiency. This enhancement of the mixing efficiency can be explained by more diffusion across the tropical barrier, enhancing the two-way mixing mass flux, but not the net mass flux, so that the relative mixing strength increases. The effects of unresolved mixing on the mixing efficiency are on the order of 10 %. Consistent with stronger aging by diffusion in EMAC compared to CLaMS, the mixing efficiency is higher in EMAC. The mixing efficiency appears to be a useful measure of relative mixing strength, that can be considered a model property that is affected by the numerics in the model advection (and other relevant parametrizations), rather than by the underlying dynamics (see the almost identical mixing efficiency in the two EMAC simulations in Table , although in the nudged simulation, the wave forcing is inconsistent with the residual circulation).

Figure a presents the zonal annual-mean trend of AoA from 1990 to 2011, calculated as linear trend. Stippling shows regions where trends are not significantly different from zero at the 95 % level. To understand the processes that contribute to AoA changes, also the zonal annual-mean trends of RCTT, resolved aging by mixing and aging by diffusion are shown in Fig. b–d. Again the trends for the simulations EMAC-RC1 (left column), EMAC-RC1SD (middle column) and CLaMS-ERAI (right column) are given in this panel plot. The AoA trend (Fig. a) shows a significant decrease throughout the stratosphere in all simulations. Only in CLaMS-ERAI a small positive trend is apparent in the middle stratosphere at 30–60∘ N. The negative AoA trend is in good agreement with other CCM simulations see e.g.,. Compared to the balloon-borne in situ AoA measurements of , which cover the period 1975–2005, only the CLaMS-ERAI simulation confirms their observed, insignificant slightly positive trend in the Northern Hemisphere subtropics and mid-latitudes above about 30 hPa. Furthermore, it has been shown by that the AoA trend (2002–2012) in CLaMS-ERAI also agrees well with the observed AoA trend of the MIPAS satellite instrument. In contrast, the two EMAC simulations, including the one nudged to ERA-Interim, do not reproduce the observed trend patterns. However, as discussed in Sect. 4.1 the residual circulation in reanalysis data suffer from large inaccuracies; therefore, it is not surprising that CLaMS-ERAI and EMAC-RC1SD have different trends in AoA and RCTT. Again a closer look at the vertical structure of the tropical upwelling trend (see Fig. b, trends are plotted relative to the climatological direct tropical upwelling) shows that in EMAC-RC1SD the trend of tropical upwelling (black solid line) is not identical to the momentum-based estimate of tropical upwelling (blue solid line), below 5 hPa, where nudging is applied. The comparison to ERA-Interim (dashed lines) shows that the trend in direct tropical upwelling is completely different in EMAC-RC1SD and ERA-Interim. Furthermore, the EMAC-RC1SD simulation is nudged only up to 5 hPa; thus, the circulation above also is not constrained by ERA-Interim.

It is important to understand the processes that drive the AoA trends. In all three simulations, trends in resolved aging by mixing (Fig. c) contribute more to the overall AoA trend than trends in RCTT (Fig. b). However, trends in resolved aging by mixing result not only from trends in local mixing tendencies but also from changes in the residual circulation, as changes in RCTT change the time exposed to mixing see. Those effects can be separated by calculating resolved aging by mixing with fixed local mixing tendencies see. Figure  summarizes the zonal annual-mean-resolved aging by mixing trend due to circulation change for the simulations EMAC-RC1 (left column), EMAC-RC1SD (middle column) and CLaMS-ERAI (right column). All simulations agree that the resolved aging by mixing trend due to residual circulation change alone can explain the resolved aging by mixing trends above about 30 hPa (Fig. ). This is consistent with , who found the strongest effect is above about 550 K (corresponding to a pressure level of 40 hPa) at all latitudes. Below, local mixing is relevant for the resolved aging by mixing trend. In contrast, the effect of aging by diffusion on the AoA trend is very small with large regions being not significant in the EMAC simulations (see Fig. d). However, in CLaMS the trend of aging by diffusion significantly impacts AoA. Note, however, that the aging by diffusion trend pattern in CLaMS is influenced by the CLaMS RCTT calculation, which is not reliable in regions poleward about 60∘ N or 60∘ S, as many residual circulation trajectories get lost in these regions (see Sect. 3.2).

Figure  also reveals the differences in the trend patterns between the model simulations. We begin with comparing the trend pattern of EMAC-RC1 and EMAC-RC1SD (Fig. , left and middle column). Both simulations have a negative trend throughout the stratosphere, with strongest trend in the Northern Hemisphere middle stratosphere above 40 hPa. However, the AoA trend in EMAC-RC1 is notably weaker with largest differences in the Southern Hemisphere polar region. To explain these differences we have a closer look at the differences in the trends of the RCTT, aging by mixing and aging by diffusion. The most important differences are given by the aging by mixing trends, with a weaker trend in EMAC-RC1. The increase in the residual circulation is stronger in the RC1SD simulation, as seen by the stronger trends in RCTT. However, also the trends in RCTT impact the differences in the AoA trend; there is a much stronger trend in the Northern Hemisphere at about 60∘ N in EMAC-RC1SD, which might be related to a weaker vortex. Differences in the trends of aging by diffusion are difficult to interpret as they are mainly not significant.

Finally, we have a closer look at the notable differences between the AoA trend in EMAC-RC1SD and CLaMS-ERAI (Fig. , middle and right column). Although AoA decreases in most of the stratosphere in both simulations, CLaMS-ERAI shows the highest negative trend in the southern stratosphere, and EMAC-RC1SD, in contrast, in the Northern Hemisphere. The slightly positive, but insignificant trend in the Northern Hemisphere at 30hPa cannot be found in EMAC-RC1SD. In contrast, EMAC-RC1SD shows maxima in the negative AoA trends in that region. A closer inspection of the components that drive these AoA trends reveals that both the trend in RCTT and the trend in resolved aging by mixing play a role (as mentioned before). Another important difference is found in the trend in aging by diffusion, which has a significant effect on the AoA trend in CLaMS-ERAI (although does not explain the increase in AoA in the Northern Hemisphere). Particularly in the southern polar vortex a large negative trend can be found; however, as mentioned before, the CLaMS aging by diffusion pattern in regions poleward about 60∘ N or 60∘ S is not so reliable. This is not the case in the EMAC-RC1SD simulation. This fact is consistent with the parametrized subgrid-scale mixing in CLaMS, which is flow dependent. Therefore, subgrid-scale mixing is underlying a trend and as the Southern Hemisphere polar vortex is getting stronger in a cooling stratosphere e.g.,, aging by diffusion decreases there.