The Brewer–Dobson circulation BDC; in the stratosphere is characterized by upwelling of tropospheric air to the stratosphere in the tropics, followed by poleward transport in the stratosphere and extra-tropical downwelling. For tracer-transport purposes the BDC is often divided into an advective component, the residual mean meridional circulation (hereafter residual circulation) and a quasi-horizontal two-way mixing, which causes net transport of tracers but not of mass .

The BDC is driven by tropospheric waves breaking into the stratosphere , which transfer angular momentum and force the stratosphere away from its radiative equilibrium. This is balanced by a poleward displacement of air masses, which implies tropical upwelling and extra-tropical downwelling . The residual circulation can be further separated into three branches: the transition branch, the shallow branch and the deep branch . The transition branch encompasses the upper part of the transition layer between the troposphere and the stratosphere the tropical tropopause layer;; the shallow branch is a year-round, lower stratospheric, two-cell system driven by breaking of synoptic-scale waves; and the deep branch is driven by Rossby and gravity waves breaking in the middle and high parts of the stratosphere during winter . The contributions of different wave types to driving the BDC branches has been quantified using the downward control principle, which states that the poleward mass flux across an isentropic surface is controlled by the Rossby or gravity waves breaking above that level , and using eddy heat flux calculations as an estimate of the wave activity from the troposphere e.g.,.

The quasi-horizontal two-way mixing is generated by two-way transport due to the adiabatic motion of Rossby waves. In the stratosphere this motion is ultimately combined with molecular diffusion which makes the total process irreversible . The two-way mixing is stronger in a specific latitudinal region of the winter stratosphere, the “surf zone” , and in the subtropical lower stratosphere all year round e.g., Fig.1 of. The mixing process homogenizes the tracer concentration in the surf zone and creates sharp tracer and potential vorticity (PV) gradients on its edges (in the subtropics and at the polar vortex edge), indicating an inhibition of mixing. For this reason, the subtropics and the polar vortex edge are often called transport barriers .

The BDC plays a major role in controlling the spatial and temporal distributions of chemical tracers, such as ozone, water vapor, aerosols and greenhouse gases, as well as in coupling stratospheric processes with the climate system . The natural variability of the atmosphere largely influences the BDC . All three branches of the BDC are affected by changes in sea surface temperatures and the El Niño–Southern Oscillation as well as the phase of the quasi-biennial oscillation QBO, and the Arctic oscillation .

Modeling studies have predicted an acceleration of the BDC over the last few decades and the 21st century due to the increase in well-mixed greenhouse gases and ozone-depleting substances , but these results cannot be evaluated easily because the BDC cannot be observed directly . Observational studies over short periods (typically 2003–2012) show significant evidence of a changing BDC in the boreal lower stratosphere , but balloon-borne observations of SF6 and CO2 in the northern midlatitudes show a nonsignificant trend of the deep branch of the BDC over the past few decades . This difficulty in deriving observational trends in the BDC can be partly attributed to the spatial and temporal sparseness of the observations as well as its large dynamical variability and the uncertainty of trends derived from nonlinearly increasing tracers . Before investigating multi-decadal changes of the BDC, it is important to perform an accurate evaluation of its climatological state and interannual variability, which is the aim of this paper.

In this study, we use N2O as a tracer to study the BDC. N2O is continuously emitted in the troposphere (with larger abundances in the Northern Hemisphere, NH) and transported into the stratosphere where it is destroyed by photodissociation and, to a lesser extent, by reaction with O(1D). The estimated lifetime of N2O is approximately 120 years, which makes it an excellent long-lived tracer for transport studies in the middle atmosphere .

We use the transformed Eulerian mean TEM, analysis to separate the local rates of change of N2O due to transport and chemistry . The transport term can be further separated into the contribution of isentropic mixing and residual advection, as done previously for O3 and CO . The isentropic mixing and the residual advection can be additionally separated in their horizontal and vertical contributions. In the tropical lower stratosphere, the distinction between vertical and horizontal transport is important, as they impact the seasonality of N2O differently in the northern and southern tropics . We choose to focus our study on the horizontal mixing and vertical advection, because their magnitudes are larger than the vertical mixing and the meridional residual advection in most of the stratosphere.

Chemistry climate models (CCMs) include the full representation of dynamical, radiative and chemical processes in the atmosphere as well as their interactions. In particular, they combine the feedbacks of the chemical tracers on the heat budget and dynamics, which ultimately affects tracer transport. We use version 4 of the Whole Atmosphere Community Climate Model WACCM; to simulate the N2O TEM budget in the stratosphere for the 2005–2014 period. WACCM has been widely used for studies of tracers' transport in the stratosphere and upper troposphere based on the TEM analysis e.g.,. WACCM simulations of the climatological N2O over the 2005–2014 period have also been evaluated favorably with satellite observations in the stratosphere .

In order to assess their representation of the atmospheric processes, CCMs are often compared to reanalyses e.g.,. Reanalysis products merge dynamical atmospheric observations (e.g., surface pressure, wind and temperature) with a global forecast model using an assimilation scheme to offer the best reproduction of the past climate. They provide a multivariate, consistent record of the global atmospheric state. Reanalyses are made using different assimilation methods and forecast models , and they are often compared among each other and with CCMs . The SPARC (Stratosphere-troposphere Processes And their Role in Climate) Reanalysis Intercomparison Project (S-RIP) coordinates the intercomparison of all major global atmospheric reanalyses and provides reports to document these results .

Meteorological fields from reanalyses are often used to drive chemistry transport models (CTMs) in order to study the BDC through a common diagnostic, namely the age of air AoA;, and simulate realistic distributions of chemical tracers . Thanks to their simplicity, CTMs are useful to compare different reanalyses within the same transport framework, thereby contributing to the study of the BDC in S-RIP chapter 5 of the S-RIP report; see Fig. 1 in. CTMs may use either sigma-pressure levels with a kinematic transport scheme and vertical velocities simply derived from mass conservation or isentropic levels with a diabatic transport scheme . Recent intercomparisons showed that the AoA depends to a large extent on the input reanalysis, both using the kinematic approach and the diabatic approach .

Here, we use the same CTM as for the kinematic AoA study, i.e., the Belgian Assimilation System of Chemical ObsErvation (BASCOE) CTM. Observations of another long-lived stratospheric tracer, HCFC-22, were recently interpreted with WACCM and BASCOE CTM simulations, showing the interest of this model intercomparison . In order to contribute further to the S-RIP BDC activity, four different dynamical reanalyses are used here to drive the BASCOE CTM simulations, compute the N2O TEM budget and compare its components with the results derived from WACCM, namely the European Centre for Medium-Range Weather Forecasts Interim reanalysis ERA-Interim;, the Japanese 55-year Reanalysis JRA-55;, and the Modern-Era Retrospective analysis for Research and Applications version 1 MERRA; and version 2 MERRA-2;.

While dynamical reanalyses do not assimilate observations of chemical compounds, chemical reanalyses achieve this step and can be used to evaluate CCMs or study differences between instruments using the reanalysis as a transfer tool . To our knowledge, chemical reanalyses driven by meteorological fields from modern dynamical reanalyses have not been used to study tracer transport in the stratosphere using the TEM framework. WACCM and the CTM experiments are compared with a chemical reanalysis of the Aura Microwave Limb Sounder (MLS) using the BASCOE data assimilation system (DAS) driven by the ERA-Interim reanalysis BRAM2;.

To summarize, in this study we analyze the representation of the BDC in WACCM through an analysis of the TEM budget of N2O, and we evaluate the simulation of this budget through comparisons with the BASCOE CTM (driven by four dynamical reanalyses) and the BRAM2 chemical reanalysis. In Sect. , we describe the datasets used in the study and the TEM analysis of N2O. In Sect. , we analyze the seasonal mean patterns of the TEM N2O budget in each dataset and their differences. Sections  and investigate the mean annual cycle and the variability of the N2O TEM budget terms, respectively, with a focus on the differences between the datasets. Section  concludes the study with a summary of our findings and directions for possible future research.

This work uses seven datasets that were generated by WACCM, the BASCOE CTM and the BASCOE DAS. Table  provides an overview of these datasets and their main differences, and the next three subsections provide details about the models and systems that generated them.

Figures and show the DJF and JJA means of three contributions to the N2O TEM budget, respectively, namely the horizontal mixing My, the vertical advection Az and the residual terms ϵ, for WACCM-CCMI, JRA-55, MERRA-2 and BRAM2. For those datasets, the remaining terms of the TEM budget (Ay, Mz and P-L) for DJF and JJA are shown in Supplement Figs. S1 and S2, respectively. The full N2O TEM budgets obtained with MERRA and ERAI for DJF and JJA are shown in Figs. S3 and S4, respectively. In the case of WACCM-CCMI, the seasonal means were computed separately for each realization, and we verified that the ensemble means show the same features as the individual realizations. Large differences arise in the dynamical terms of the TEM budget between summer and winter for both hemispheres in the extra-tropics. The strong seasonality of the deep branch of the BDC and of the transport barriers are the causes of these differences, as for the seasonal variations of the age of air spectrum .

We also reproduced the results of Fig. 8 for the WACCM-CCMI multi-model mean and the reanalysis mean in DJF (Figs. S5 and S5, respectively). The WACCM-CCMI and the reanalysis means agree with the Community Climate Model version 2 of the early 1990s with regard to the general pattern of the TEM terms, although both deliver stronger contributions, especially the reanalyses mean.

We first compare the contribution of Az across the datasets in Figs.  and . The tropical upwelling increases the abundance of N2O mostly in the mid–high stratosphere (between 1 and 15 hPa) with the maximum contribution in the summer tropics, whereas the downwelling decreases it mostly in the wintertime extra-tropics in the middle and low stratosphere (between 5 and 100 hPa). This reflects the path followed by the deep branch of the BDC . During boreal winter, these features are very similar across all datasets (Fig. ), but noticeable differences appear during the austral winter (Fig. ): the tropical upwelling has a larger secondary maximum in the southern tropics with JRA-55 and MERRA-2 than with the other datasets, and the extra-tropical downwelling extends to the South Pole in WACCM-CCMI and JRA-55 whereas it is mostly confined to the midlatitudinal surf zone in the other reanalyses. In the lower stratosphere, Az shows the contribution of the residual advection by the shallow branch of the BDC to the N2O abundances in the winter and summer hemispheres. The two-cell structure, consisting of upwelling of N2O in the subtropics and downwelling in the extra-tropics, consistently agrees across all datasets. The meridional residual advection term Ay contributes to the poleward transport of air masses in the middle stratosphere, mostly during the winter, and its contribution to the N2O TEM budget is weaker than Az. Ay agrees well among the datasets in boreal winter (Figs. S1, S3), while during austral winter WACCM-CCMI overestimates it by around 30∘ S compared with the reanalyses (Figs. S2, S4).

We move now to the mixing contributions to the N2O budget. The horizontal mixing is the predominant contribution to the poleward tracer transport in the middle and lower stratosphere , as it flattens the tracer gradients generated by the residual advection. In the N2O TEM budget during boreal winter, My mostly balances the extra-tropical downwelling and part of the tropical upwelling (Figs. S3, S4). The surf zone is characterized by strong horizontal mixing, depicted here as large positive My contributions, and delimited by transport barriers which appear as intense gradients of My in the winter hemispheres (panels b, e, h and k in Figs.  and ). In the wintertime NH, the patterns of My are similar in all datasets (Fig. ), but the effect of horizontal eddy mixing on N2O is stronger in the reanalyses than in WACCM-CCMI. In Sect. , we quantitatively analyze the differences in the mid-stratospheric My between datasets. The residual terms in the reanalyses (Fig. c, f, i, l) are largest in the middle stratosphere at the latitudes of the transport barriers, and their signs are opposite to My.

In the austral winter, over the Antarctic polar cap and below 30 hPa, My agrees remarkably well in all datasets (Fig. ). Closer to the vortex edge and above 30 hPa, the wintertime decrease in N2O is mainly due to downwelling in WACCM-CCMI, whereas the reanalyses, especially BRAM2, show that the horizontal mixing plays a major role (Fig. ). The impact of horizontal mixing on N2O inside the wintertime polar vortex is not negligible e.g.,, as Rossby wave breaking occurs there as well as in the surf zone. In contrast to the reanalyses, in WACCM-CCMI the My contribution is close to zero in the Antarctic vortex and maximum along the vortex edge (Fig. ). This disagreement can be related to differences in the zonal wind: it is overestimated in WACCM above 30 km at subpolar latitudes compared with MERRA , and the polar jet is not tilted equatorward as in the reanalyses see black thin lines in Figs.  and 3 of. However, the differences in My and Az above the Antarctic in winter should be put into perspective with the relatively large residual terms that point to incomplete TEM budgets in the reanalyses (Figs.  and S4 right columns). Near the Antarctic polar vortex, the assumptions of the TEM analysis (such as small amplitude waves) are less valid, leading to larger errors in the evaluation of the mean transport and eddy fluxes .

As the relative importance of the residual is considerable above the Antarctic in the reanalyses (Fig. ), it is necessary to better understand its physical meaning. applied the TEM continuity equation to the age of air in CCM simulations. Computing the “resolved aging by mixing” (i.e., the AoA counterpart of My+Mz) as the time integral of the local mixing tendency along the residual circulation trajectories and the “total aging by mixing” as the difference between the mean AoA (mAoA) and the residual circulation transit time, they defined the “aging by mixing on unresolved scales” (i.e., by diffusion) as the difference between the latter and the former. This “aging by diffusion”, which can be related by construction to our residual term, arises around 60∘ S from the gradients due to the polar vortex edge. Even though we use a real tracer (N2O), we find a qualitative agreement with this analysis based on AoA: our residual term is larger in regions characterized by strong gradients such as the Antarctic vortex edge and larger with dynamics constrained to a reanalysis than with a free-running CCM see EMAC results in Fig. 1d by. Thus, we interpret the residual as the sum of mixing at unresolved scales and numerical errors .

In the summertime lower stratosphere, we note a stronger contribution of My to the N2O abundances above the subtropical jets in both hemispheres and for all datasets compared with higher levels in summer (panels b, e, h and k in Figs.  and ). This behavior is consistent with calculations of the effective diffusivity and age spectra . It is due to transient Rossby waves that cannot travel further up into the stratosphere owing to the presence of critical lines, i.e., where the phase velocity of the wave matches the background wind velocity, generally leading to wave breaking . In particular, above the northern tropics during the boreal summer (Figs. , S2, S4), horizontal mixing is primarily associated with the Asian monsoon anticyclone, and it causes a decrease in N2O . In the lower stratosphere, the contributions from My combine with that from Az in the total impact of the shallow branch of the BDC on N2O all year round .

The vertical mixing contribution Mz is very small during boreal winter, except in the middle and lower stratosphere poleward of 60∘ N, where it tends to balance the My contribution (Figs. S1, S3). In austral winter, there is a strong disagreement between WACCM-CCMI and the reanalyses around 60∘ S between 5 and 15 hPa (Fig. S2). WACCM-CCMI simulates a strong Mz contribution at the polar jet core that decreases the N2O abundances and tends to balance My, whereas Mz is weaker and increases N2O in the higher stratosphere in the reanalyses.

In the next section, we focus on a single level in the middle stratosphere to quantitatively study the disagreement between WACCM-CCMI and the reanalyses.

After investigating the seasonal means of Az and My, it is interesting to examine their climatological mean annual cycles in order to study the month-to-month variations over the year and their dependance on the latitude in the middle stratosphere. The cycles are shown for three latitude bands in each hemisphere corresponding to the tropics (0–20∘), the surf zones (40–60∘) and the polar regions (60–80∘). For WACCM-CCMI, we examine the envelope (the yellow shaded areas in Figs. 5–12) of the three model realizations in order to evaluate the role of the internal variability and its relative importance for each month and latitude band. In the following, we will consider BRAM2 as the reference when comparing N2O mixing ratios between datasets, because its dynamics and chemistry are both constrained by observational datasets.

To analyze the interannual variability of the annual cycle, we compute for each month the 1σ standard deviations of the N2O mixing ratio, My and Az across the 10 simulated years. Figure  shows the annual cycles of these standard deviations for each dataset in the polar regions (60–80∘ S and N) at 15 hPa for both hemispheres. First, we consider the variabilities of the N2O mixing ratio. In the Antarctic, during austral winter and early spring the year-to-year change in the N2O abundances is very small (Fig. a) because the duration, extension and strength of the polar vortex are very stable in a climatological sense, isolating air masses in the vortex from the highly variable midlatitudes . The variability of the N2O mixing ratio increases in October, i.e., during the breaking vortex period that is highly variable in time . Furthermore, the midlatitude air masses, which have more variable composition, become free to reach the higher latitudes during this period. In the Arctic region, the interannual variability of the N2O mixing ratio is also largest during springtime but this is spread over a longer period, i.e., from February to June (Fig. b), reflecting the large interannual variability in the duration, extension and zonal asymmetry of the Arctic polar vortex . In both polar regions, WACCM-CCMI agrees well with BRAM2, whereas the CTM experiments simulate a smaller variability.

We now look at the interannual variability of Az and My in the polar regions. Above the Antarctic, the interannual variabilities of Az and My are maximum during spring (Fig. c, e), due to the large interannual variability in vortex breakup dates . While the maximum variability of My is consistently reached in October in all of the reanalyses, WACCM-CCMI simulates an earlier maximum (September) that does not correspond to the maximum in its mean values. The lower wintertime variability of both Az and My would increase if a longer period was considered that included the exceptional Antarctic vortices of 2002 and 2019 . Above the Arctic, My and Az are most variable during winter, reflecting the frequent disruptions of the northern polar vortex by sudden stratospheric warmings SSWs;. A case study of the effect of a SSW on the N2O TEM budget showed that Az and My contribute more to this budget during the SSW event than in the seasonal mean . Thus, the large wintertime variabilities of Az and My are explained by the occurrence of seven major SSWs detected in the reanalyses for the 2005–2014 period .

In Fig. , we show the interannual variabilities of the N2O mixing ratio, My and Az for each dataset in the surf zones (40–60∘ S and N) at 15 hPa for both hemispheres. Regarding the N2O mixing ratio, the interannual variability in the southern middle latitudes reaches the lowest values during austral winter. The datasets deliver very diverse values, with WACCM showing the largest variability and JRA-55 showing the least variability across the climatological year (Fig. a). In the northern midlatitudes, the interannual variability of the N2O mixing ratio increases in late winter across all of the datasets as a response to the increased wintertime variability of the surf zone (Fig. b). The variability of WACCM-CCMI largely depends on the realization considered, except in October and November. Strong differences between ensemble members with respect to interannual variability indicate that the period considered is not long enough to explore the interannual variability in the northern midlatitudes and that the mean variability from this ensemble (with only three members) would not be representative of the internal variability of WACCM. The interannual variabilities of Az and My in the southern midlatitudes are shown in Fig. c and e, respectively. As their mean value, Az and My are most variable during austral spring and late summer in the reanalyses, whereas WACCM simulates an earlier peak during winter in the interannual variabilities of Az and My compared with the reanalyses. In the northern midlatitudes, the interannual variabilities of Az and My peak in winter, as do their mean values, and WACCM simulates smaller variabilities compared with the reanalyses (Fig. d, f).

Figure  shows the annual cycles of the standard deviations of the N2O mixing ratio, My and Az for each dataset in the tropical regions (0–20∘ S and N) at 15 hPa for both hemispheres. The interannual variability of the N2O mixing ratio in both the southern and northern tropics depends considerably on the dataset (Fig.a, b). WACCM-CCMI and the BASCOE reanalysis of the Aura MLS show very similar variabilities, especially in the southern tropics. As the QBO is the major source of variability in the tropical stratosphere , this confirms an earlier comparison that showed a good agreement between the WACCM model and MLS observations in the middle stratosphere in terms of the interannual variability of N2O due to the QBO . Among the CTM simulations, ERAI succeeds at delivering σ(X‾) values that are as large as BRAM2 and WACCM-CCMI in the southern tropics, although this is not the case in the northern tropics.

The interannual variability of Az in both hemispheres can be related to the impact of the QBO on the tropical upwelling . Among MERRA, ERAI and JRA-55, the fraction of variance in deseasonalized tropical upwelling w‾∗ that is associated with the QBO is the largest with ERAI . Our findings support this conclusion, as the largest σ(Az‾) among the reanalyses is again found with ERAI (Fig. c, d). However, a detailed analysis of the impact of the QBO on the BDC as illustrated here goes beyond the scope of this study. The variability of My in the tropical regions is small compared with the extra-tropical regions (Fig. e, f), which is in agreement with calculations of effective diffusivity that show small variabilities within the tropical pipe . The reanalyses deliver a larger interannual variability in the northern tropics during boreal winter, whereas the variability of My presents a much weaker annual cycle in the southern tropics. WACCM-CCMI does not reproduce this hemispheric asymmetry, with a rather flat profile in both hemispheres and a clear underestimation in the northern tropics, as is also shown for its mean values. In the tropical regions, both the variabilities of My and Az fail to explain the good agreement in the variability of N2O between WACCM and BRAM2, as well as their disagreement with the dynamical reanalyses, because My and Az directly contribute to the N2O tendency rather than its mixing ratio.

We have evaluated the climatological (2005–2014) N2O transport processes in the stratosphere using the tracer continuity equation in the TEM formalism. In particular, we emphasized the horizontal mixing and the vertical advection terms (My and Az, respectively). The upwelling term Az reduces the N2O concentrations in the tropics and increases them in the extra-tropics, whereas My tends to reduce the meridional gradients of N2O and presents large hemispheric differences. As My or Az contribute to the local rates of change of N2O, this analysis is complementary to time-integrated diagnostics such as mAoA. The comparison investigates a variety of datasets, from a free-running chemistry climate model to a reanalysis where dynamics and chemistry are both constrained. The former comprises three realizations of the CCMI REF-C1 experiment by WACCM, and the latter is the chemical reanalysis of Aura MLS driven by ERA-Interim: BRAM2. The intercomparison also includes the BASCOE CTM driven by four dynamical reanalyses – ERAI, JRA-55, MERRA and MERRA-2 – in order to contribute to the S-RIP.

Considering the N2O mixing ratio in the middle stratosphere, all of the datasets agree with respect to the annual cycle, with the large spread in the N2O abundances of the CTM experiments (∼20%) reflecting the diversity of mAoA obtained with the same model . The upwelling term Az also agrees among the datasets, especially in the NH where WACCM closely follows the reanalyses. The horizontal mixing term My in the NH is weaker in WACCM compared with the reanalyses. In the extra-tropics, this could be attributed to the weaker forcing from the planetary waves in WACCM compared with the reanalyses. The differences in My become striking in the wintertime Antarctic, where the polar vortex plays a major role. According to the reanalyses, horizontal mixing plays an important role in that region, but that is not found by WACCM. However, this large wintertime My in the reanalyses is challenged by an almost as large residual term. It should be noted that the residual term also includes effects from mixing by diffusion. An additional WACCM run with different gravity waves in the SH is used as a sensitivity test. Over the Antarctic, this test has small impact on My, but it significantly modifies Az in the austral fall and winter due to the enhanced downwelling, and the N2O mixing ratio during spring as a consequence of a more realistic timing of the vortex breakup.

The interannual variability of the mid-stratospheric horizontal mixing term My is largest in the polar regions. It is related to the variability in the vortex breakup dates during spring in the Antarctic, whereas it is related to the highly variable polar vortex in winter in the Arctic. The interannual variability of Az is characterized by a large spread in the mid-stratospheric tropical regions where WACCM-CCMI and JRA-55 deliver a smaller contribution than the other reanalyses. This variability reflects the impact of the QBO on the tropical upwelling .

The application of the TEM framework to tracer transport with reanalyses suffers from a poor closure of the budget in the polar regions. We chose to analyze these regions nonetheless, because the differences in My between WACCM and the reanalyses are larger than the residual term, but it remains important to better understand the causes of these large uncertainties. To this end, detailed studies of transport in the polar stratosphere are needed, e.g., comparing the residual circulations with indirect estimates derived from momentum and thermodynamic balances as well as evaluating the effective diffusivity in each dataset .

The next step of this research consists of the analysis of the interannual variations of the BDC, including the impact of the QBO and the El Niño–Southern Oscillation. Further extensions of this work would include the addition of new reanalysis products such as ERA5 and an intercomparison of several CCMs as already done for the residual circulation itself .