The global circulation of the stratosphere, known as the Brewer–Dobson circulation , is a crucial factor controlling the lower stratospheric composition of radiatively active trace gases; therefore, it plays an important role in the Earth's radiation budget and in climate. Hence, a realistic representation of the BDC is a prerequisite for reliable climate model predictions. However, current climate models and observations disagree regarding long-term changes of the BDC e.g.. Climate models simulate a strengthening and accelerating circulation which is not evident from observations, representing a major uncertainty in current model predictions seefor a recent review. The BDC is characterised by the slow upwelling in the tropics from the troposphere across the tropical tropopause layer (TTL) into the stratosphere, followed by poleward motion in the stratosphere and downwelling at middle and high latitudes. From the perspective of tracer transport, the BDC includes a residual mean mass circulation and additional two-way eddy mixing, which causes net transport of tracers but not mass e.g.. The residual mean mass circulation may be separated into two different main branches . On the one hand, a shallow circulation branch transports air masses to middle latitude regions at lower levels above the tropopause within a few months to about 2 years. A deep circulation branch, on the other hand, causes transport deep into the stratosphere and downwelling at high latitudes on a timescale of several years . The stratospheric BDC is mechanically driven by the transfer of momentum from breaking atmospheric waves to the zonal flow . The shallow circulation branch is mainly driven by synoptic and planetary-scale waves, and the deep branch is mainly driven by planetary waves propagating deep into the stratosphere e.g.. Results from an idealised model suggest that the strength of the shallow circulation branch is largely controlled by the strength of wave sources in the troposphere . The strength of the deep circulation branch, in comparison, appears to be largely controlled by the propagation conditions for waves in the stratosphere.

As the BDC is a zonal mean circulation and related wind velocities are small residuals, directly measuring the circulation is not possible e.g.. A common measure of the BDC is the age of air, which represents the timescale for transport through the stratosphere. By definition, age of air measures the speed of the circulation. Strictly, due to atmospheric mixing processes on a multitude of scales, a stratospheric air parcel is not characterised by a single transport timescale but by a transit time distribution. This transit time distribution is termed the “age of air spectrum” . Commonly used reference surfaces for measuring the transit time are the tropical tropopause or the tropical surface e.g.. The first moment of the age spectrum distribution, termed the “mean age of air”, can be estimated from observations of specific trace gas species with linearly increasing mixing ratios in the troposphere, as is approximately the case for CO2 and SF6 . Similar to a tracer, the mean age is affected by both the residual mean mass circulation and atmospheric mixing processes e.g., which complicates an unambiguous interpretation of mean age changes in terms of processes. The full age spectrum allows for a clearer interpretation, but its deduction from observations is much more challenging and usually hinges on simplifying assumptions like the stationarity of the flow or a specific parameterization of the age spectrum shape e.g.. Ongoing modelling studies suggest promising new methods for deducing the age spectrum based on either an improved parametric approach or an inversion approach . However, applicability to measurement data remains to be shown.

The BDC is characterised by variability on very different timescales. Seasonal variability in the BDC is caused by seasonality in wave driving, which is stronger in boreal than austral winter due to larger wave excitation by orography in the Northern Hemisphere (NH). As a result, tropical upwelling and related extratropical downwelling (in the NH) maximise in boreal winter e.g.. On inter-annual timescales, the BDC is significantly modulated by the stratospheric Quasi-Biennial Oscillation (QBO) e.g., by the El Niño–Southern Oscillation (ENSO) e.g. and by stratospheric aerosol injected by volcanic eruptions e.g.. In the long term, climate models simulate a robust strengthening of the BDC with global warming, resulting in an increase of the tropical upwelling mass flux as well as in a global decrease of the stratospheric mean age of air over the last decades and into the future e.g.. In contrast, estimates of the mean age of air from balloon observations of long-lived trace gas species in the NH middle latitudes above about 24 km show no significant long-term trend . Additional recent balloon measurements corroborate this result . A recent, improved analysis of the same balloon observations confirms the insignificant (weakly positive) mean age trend above about 24 km, but shows a negative mean age trend below this level . Indications of a negative mean age trend in the lowermost stratosphere around the year 2000 have also been found from aircraft observations of mean age . Hence, in particular in the stratosphere above about 24 km, climate models results are not consistent with observations regarding trends in the BDC.

The strengthening BDC trend in models is clearly related to greenhouse gas-induced tropospheric warming. This warming strengthens the subtropical jets, thereby shifting the critical levels for wave breaking upwards and equatorwards and intensifying the mechanical forcing of the BDC e.g.. A recent study by indicates that the BDC trend is consistent with the expansion of the troposphere and an associated upward shift of the tropopause with climate change.

Concerning BDC changes over decadal periods, horizontal circulation shifts in the latitudinal direction also cause important effects. This has recently been shown for a southward circulation shift from 2002 to 2012 which likely caused a hemispheric dipole mean age change pattern (the age increased in the NH and decreased in the SH) as observed by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite instrument . Ensembles of climate model simulations may include mean age change patterns which are more complex than a global decrease and even have some resemblance to MIPAS observations . Hence, to simulate observed past BDC changes it is important to correctly represent variability on inter-annual to decadal timescales in the models. For interpreting mean age trends, the consideration of atmospheric mixing processes turns out to be particularly important e.g..

Meteorological reanalyses combine a global weather forecast model with atmospheric observations through a data assimilation system to provide an optimal estimate of the atmospheric state from the past to present. These reanalyses are based on an unchanged forecast model version and assimilation system to minimise artificial changes in the state variables due to changes in the reanalysis system. However, as the observational data sets included in the assimilation change over time, abrupt state changes may still occur to some degree, rendering reanalysis-based trend studies challenging. Considering more than one reanalysis in such studies increases the reliability of results considerably. The Stratosphere-troposphere Processes And their Role in Climate (SPARC) Reanalysis Intercomparison Project (S-RIP) aims at an inter-comparison of the current generation reanalysis products, as described by . The present paper contributes to this project by comparing the representation of the stratospheric BDC in the three most modern reanalysis products: (i) ERA-Interim from the European Centre for Medium-Range Weather Forecasts (ECMWF), (ii) JRA-55 from the Japanese Meteorological Agency and (iii) MERRA-2 from the National Aeronautics and Space Administration (NASA).

Past analyses have shown that modern reanalyses provide an improved representation of the BDC e.g. compared with older reanalysis products like the ECMWF's ERA-40 reanalysis e.g.. In particular, ERA-Interim has been shown to combine a negative mean age trend throughout most regions of the stratosphere with a weakly positive age trend in the NH above about 24 km, similar to existing balloon observations . Moreover, the hemispheric dipole age trend pattern as observed by MIPAS from 2002 to 2012 turns out to be reproduced, at least qualitatively, by ERA-Interim-driven simulations . However, the robustness of these results concerning the representation of the BDC in different reanalyses is an open question.

A very recent study by compares the BDC in various reanalyses by using a kinematic transport model (Belgian Assimilation System for Chemical ObsErvations, BASCOE) within the scope of the S-RIP project. The results presented here are based on a diabatic transport model (for further details see Sect. ) and therefore complement the study by regarding the representation of vertical transport. The main goal of our paper is to assess the robustness of the climatology and seasonality of the BDC as well as its trends in current generation reanalyses, as imprinted on stratospheric age of air. For that reason, we calculate and analyse the mean age of air as well as the full time-dependent stratospheric age spectrum, which has not been used for a model inter-comparison of the BDC to date.

The modelling method (transport model and age of air diagnostics) is described in Sect. . In Sect.  the climatology and seasonality of age of air from different reanalyses is compared before considering trends in Sect. . Section  provides a comparison to existing observational mean age estimates, and Sect.  discusses the results, in particular compared to the results from the complementary model study of .

The Chemical Lagrangian Model of the Stratosphere (CLaMS) is a Lagrangian model for calculating transport and chemistry for trace gas species based on the motion of 3-D forward trajectories and an additional parameterised representation of atmospheric small-scale mixing processes . Parameterised mixing in the model is driven by deformations in the large-scale flow, such that, in regions of large flow deformations, strong mixing occurs . Model transport is calculated in an isentropic vertical coordinate framework with potential temperature θ being the vertical coordinate throughout the stratosphere and upper troposphere, and with the cross-isentropic vertical velocity deduced from the total diabatic heating rate (of the respective reanalysis forecast), including effects of radiative and turbulent heating, as well as latent heat release. Further details about the CLaMS model set-up used in this study can be found in .

As described by , and briefly reviewed in the following, we calculate the age of air spectrum for each reanalysis from multiple tracer pulses and the mean age from the spectrum. The age spectrum G is a boundary value Greens function for the continuity equation of a conserved and passive trace gas species e.g. and relates the trace gas mixing ratio χ(r,t) at location r and time t to the mixing ratio χ0(t) at the boundary surface, where it is assumed to be uniform e.g.: 1χ(r,t)=∫0∞dτχ0(t-τ)G(r,t,τ). Here, the integration is taken along transit time τ, and the boundary surface is usually taken to be the tropical tropopause or the tropical surface, a particularly common choice in models. The age spectrum calculation applied in this study is set up analogously to the approach described by , and similarly to the calculation in the GEOS climate model . The calculation method is based on N=60 inert pulse tracers, approximating a delta distribution lower boundary condition χ0i(t)=δ(t-ti) with i=1,…,60, defining tracer pulses at source times ti. For such a set of pulse tracers, the age spectrum at transit time τi is related to the tracer mixing ratio of the ith species via 2G(r,t,τi)=χi(r,t); hence the age spectrum can be directly calculated from the pulse tracer mixing ratios in the simulation.

To approximate the delta distribution characteristics, pulse tracer mixing ratios are set to one in the lowest (orography following) model layer (approximately the boundary layer) in the tropics between 15∘ S and 15∘ N for 30 days. The 60 different species are pulsed every other month (first species in the first month, second species in the third month, etc.), such that after 10 years of simulation all species have been pulsed. Hence, after every 10 years the first species is reset to zero and pulsed again. This boundary impulse (time-)evolving response (BIER) method resolves the age spectrum along 10 years of the transit time axis with a bin size of 2 months.

The mean age of air is then calculated as the first moment of the age spectrum: 3Γ(r,t)=∫0∞dττG(r,t,τ). As the mean age strongly depends on the age spectrum tail, which generally shows an exponential decay after about 4–5 years e.g., the effect of the finite age spectrum tail on the mean age may be corrected by fitting an exponentially decaying function e.g.. Hence, a corrected age spectrum may be defined by extrapolating the spectrum tail for transit times τ>τ*=10 using 4Gcorr(r,t,τ)=G(r,t,τ*)e-(τ-τ*)ξ(r,t), with G(r,t,τ*) the age spectrum value at 10 years, and the tail decay timescale ξ(r,t) (depending on location and time) being estimated from the exponential fit to the spectrum at transit times between 5 and 10 years. As the full age spectrum is the probability distribution of transit times, it is generally normalised to unity. However, due to the truncation of the simulated spectrum at 10 years, the integration of the spectrum over transit time leads to a norm less than one (see Fig. ): 5N10=∫010yeardτG(r,t,τ)<∫0∞dτG(r,t,τ)=1. Including the exponential tail correction improves the normalisation, but small differences to unity remain due to the finite resolution along the transit time axis. On the one hand, including the correction generally improves comparisons of mean age to observations. On the other hand, MERRA-2 age spectra show a much more pronounced tail without a clear exponential decay over 10 years in some cases (see Sect. ), violating the necessary assumption for the finite tail correction. Hence, for most parts of the analysis we simply consider the finite tail age spectra over 10 years without including the tail correction. This simplifies the interpretation of the comparison of different reanalyses by only considering the resolved part of the age spectrum. Effects of the unresolved tail and the finite tail correction are further discussed in Sect. .

Two other age spectrum-based transport diagnostics are the modal age, which is the transit time of the maximum age spectrum peak, and the age spectrum width 6Δ(r,t)=12∫0∞dτ[τ-Γ(r,t)]2G(r,t,τ). The spectrum width is strongly influenced by long transit times in the spectrum tail and therefore is usually considered a measure of the strength of recirculation e.g.. The modal age, in comparison, can be interpreted as a measure of the residual circulation in the tropics and in the winter stratosphere as it is closely related to the residual circulation transit time in these regions. As additional diagnostics for the interpretation of processes affecting zonal mean mean age we consider residual circulation transit times RCTTs, and the net mixing effect on mean age “ageing by mixing”, in Sect. . The RCTT is the transit time of a (hypothetical) air parcel if it was transported by the residual circulation alone and, by definition, solely includes effects of the residual circulation . For this paper, RCTTs are calculated with the CLaMS trajectory module and using the zonal mean diabatic residual circulation in isentropic coordinates (v‾*,Q‾*) . Here, Q denotes the diabatic heating rate, v denotes the meridional velocity component, overlined quantities denote mass-weighted zonal averages and primed quantities represent the respective fluctuations therefrom e.g.chap. 9.4; hence, v‾*=(σv‾)/σ‾, and Q‾*=(σQ‾)/σ‾.

In addition, the zonal mean mean age Γ‾ is affected by mixing processes in the atmosphere. The local effect of this mixing, the local eddy mixing tendency, is represented in the zonal mean (isentropic) tracer continuity equation for mean age by the divergence M of a 2-D mixing flux vector e.g.Eq. 9.4.21. The net mixing effect on the zonal mean mean age, the ageing by mixing, is then calculated by integrating the local eddy mixing tendency M along residual circulation trajectories x(t) : 7Γ‾(x,t)=τRCTT(x,t)+∫t0tM(x(t′))dt′. Here, τRCTT is the RCTT, for transport from the 340 K isentropic surface in the tropics (30∘ S–30∘ N), and t0 is the time when the trajectory intersected the 340 K surface. As proposed by and recently further evidenced by , the net eddy mixing effect can be well approximated by the difference between the mean age and the RCTT. We apply this approximation in the following without explicitly calculating the mixing effect (see Sect. ). For further details about the RCTT and the ageing by mixing calculation see .

The CLaMS simulations are driven with horizontal winds and diabatic heating rates from the three most recent reanalysis data sets: ERA-Interim, JRA-55 and MERRA-2. The simulations for ERA-Interim and JRA-55 both start on 1 January 1979, whereas the MERRA-2 simulation starts on 1 January 1980. Due to the specific pulse tracer set-up described above it takes 10 years of simulation until all pulse tracers have been set and the age spectrum can be evaluated. To enable the age of air analysis beginning in 1979 (in 1980 for MERRA-2), for comparison with balloon-borne mean age measurements in Sect. , a 10-year-long model spin-up is carried out by repeating conditions of the first simulation year. However, the simulated age of air before 1989 includes the effect of the spin-up and most parts of the analysis presented here are restricted to the time period from 1989 to 2015. For MERRA-2, the year 1989 still includes a very weak spin-up effect, but without any effect on our conclusions, as all results of the paper could be analogously derived for the 1990–2015 period (not shown).

The three different reanalyses used here have been recently described by , with further details given by for ERA-Interim, by for JRA-55 and by for MERRA-2. For driving the CLaMS model simulations, reanalysis horizontal winds and diabatic heating rates from the reanalysis forecast are used on native model levels and with a horizontal resolution of 1∘×1∘ in latitude and longitude. The age of air results from the different simulations have been interpolated to potential temperature levels (same for all reanalyses) and monthly zonal mean climatologies have been created.

Climatological mean age data (1989–2015) from the three reanalyses for boreal winter (December–February, DJF) and summer (June–August, JJA) are compared in Fig. . Throughout most parts of the stratosphere JRA-55 shows the youngest mean age and MERRA-2 shows the oldest mean age. Values for ERA-Interim lie in between. However, in the tropical lower stratosphere below about 700 K potential temperature (about 20 hPa) ERA-Interim shows the youngest mean age of the three reanalyses, which is consistent with overly strong tropical upwelling as documented in the literature e.g..

The MERRA-2 mean age is substantially older than the other reanalyses, with the largest relative differences in the tropical stratosphere (e.g. about 2.5 years for MERRA-2 at about 500 K (about 50 hPa) compared to about 1.5 years for ERA-Interim). Moreover, at high latitudes the MERRA-2 mean age is clearly older, reaching maximum values of more than 5.5 years in the southern polar vortex compared with less than 5 years for ERA-Interim and JRA-55 (note that these values are calculated from the age spectrum over 10 years and that actual mean ages are higher).

Despite these differences in climatological average mean age values, seasonal variations (as estimated from December–February to June–August differences) are very similar in the three reanalyses. The youngest air is found in the tropical stratosphere during boreal winter, when the BDC upwelling maximises. Conversely, the oldest air occurs in the high-latitude stratosphere during wintertime and is related to the strongest downwelling within the deep BDC branch in that region and season. Furthermore, a flushing of the summertime lower stratosphere with young air masses from the tropics e.g. is evident in all reanalyses. This summertime flushing shows a robust hemispheric asymmetry, and is stronger in the NH than in the SH .

More details about stratospheric transport can be observed in the age spectrum, presented in Fig.  for the tropics, middle and high latitudes on the 500 K potential temperature surface. The tropical age spectra show an almost unimodal shape with a clear peak at short transit times, and only very weak additional peaks and a decaying tail at larger transit times. In middle and high latitudes the age spectra show distinct multiple peaks caused mainly by the seasonality of transport into the stratosphere e.g.. These multiple spectrum peaks are robustly found for all reanalyses, again indicating robustness in the representation of seasonal variations in stratospheric transport in modern reanalyses. In general, ERA-Interim and JRA-55 age spectra are very similar for all regions, but MERRA-2 spectra differ more substantially. In particular, for MERRA-2 the secondary peaks at higher ages are delayed by a few months compared with ERA-Interim and JRA-55, again indicating slower transport for MERRA-2. At high latitudes, the modal age (transit time of the maximum spectrum peak) for MERRA-2 may occur with a delay of more than a year (e.g. Fig. c). In all regions the modal peak is shifted to larger transit times (higher ages) for MERRA-2. In particular, the spectrum tail is much more pronounced for MERRA-2 (e.g. Fig. f), with age spectrum values more than twice as large as ERA-Interim and JRA-55 at transit times larger than about 8 years. Hence, there is a substantially larger fraction of very old air for MERRA-2 than for ERA-Interim and JRA-55.

The global view of the age spectrum in the lowest stratosphere at 400 K is presented in Fig. . The 400 K isentrope has been chosen as a representative level for the shallow BDC branch. The robust representation of transport seasonality is again evident from the similar occurrence of the multiple spectrum peaks. In particular, the modal peak (modal age) of the tropical age spectra is shifted to younger ages in boreal winter, which is consistent with faster wintertime BDC upwelling. The strong flushing of the Northern Hemisphere , and to a lesser degree also of the Southern Hemisphere, is clearly visible in the extension of the modal peak (white diamonds) from the tropics into the summer hemisphere in all reanalyses. This extension of the tropical young air signal deep into the summer hemisphere is consistent with the general understanding of a less isolated tropics and stronger isentropic mixing causing horizontal exchange between the tropics and the extratropics during summer.

The subtropics in Fig.  are characterised as transition regions between approximately monomodal tropical age spectra and middle- and high-latitude spectra with distinct multiple peaks. The contrast between tropical and extratropical age spectra is strongest in the respective winter hemisphere, which is indicative of a stronger subtropical jet and related transport barrier compared to the summer hemisphere. For MERRA-2, the transition between tropical and extratropical age spectra is more dilute, indicating stronger exchange between tropics and middle latitudes in the lowest stratosphere. This stronger exchange likely results in a stronger recirculation of extratropical aged air masses into the tropics, causing older air throughout the stratosphere.

Very similar results emerge from the comparison of the age spectra at higher levels in the stratosphere (here 600 K in Fig. ), where the deep BDC branch dominates transport. The seasonality in tropical upwelling (faster in boreal winter) as well as in subtropical transport barriers (stronger in boreal winter) is robustly represented in the different reanalysis data sets. In particular the older modal age for MERRA-2 in the tropics, evident at 400 K (Fig. ), becomes even more clear at 600 K.

This shift of the tropical modal age to longer transit times is related to a slower tropical upwelling for MERRA-2, which is consistent with the comparison of reanalysis climatological total diabatic heating rates shown in Fig. . In particular throughout the tropical tropopause layer e.g. and up to about 500 K the MERRA-2 heating rates are lower than for the other reanalyses (Fig. ). Below the tropopause around the level of zero radiative heating (around 360 K) there is even a cooling layer evident in the MERRA-2 heating rates causing a “bottleneck” structure in annual mean upwelling. The differences in heating rates could be related to ozone differences between the reanalyses e.g.. ERA-Interim uses prescribed climatological ozone fields for the radiative calculations, including a potential high bias in ozone concentrations in the tropical lower stratosphere e.g.. JRA-55, in comparison, uses prescribed time-varying ozone fields from a model simulations , and MERRA-2 uses interactive ozone for radiation and heating rate calculations e.g..

Regarding the age spectrum, MERRA-2 further shows a weaker gradient between tropical and extratropical age spectra compared with the other reanalyses at 600 K (Fig. ). This weaker tropical–extratropical contrast indicates stronger exchange between tropics and extratropics and a weaker subtropical transport barrier. Furthermore, the MERRA-2 age spectra at 600 K show a more pronounced spectrum tail, as previously noted. Differences in the age spectrum tail at transit times larger than about 5 years cannot be caused by the differences in the diabatic circulation (in Fig. ) alone, because related transit times along the residual circulation are generally below about 5 years e.g.Fig. 2. Therefore, the more pronounced spectrum tail for MERRA-2 compared with ERA-Interim and JRA-55 is likely a result of the stronger recirculation of air into the tropics at lower levels. Recirculation into the tropics, particularly at low levels, causes air masses to circulate through the stratosphere within the BDC several times before sinking back into the troposphere and significantly increases the age e.g.. Therefore, an increased recirculation enhances the fraction of aged air masses and hence the tail of the age spectrum e.g..

Figure  further compares the characteristics of the spectrum tail between the three reanalyses by showing the spectrum normalisation (coloured shading) and the tail decrease timescale (blue contours). The spectrum norm was calculated as the integral of the age spectrum over 10 years (Eq. ), and the tail decrease timescale was calculated as the exponential decrease rate of the spectrum tail at transit times larger than 5 years (Eq. ). As the model age spectra are truncated after 10 years (see Sect. ) a stronger spectrum tail will result in a less stringent normalisation condition and in a larger difference of the age spectrum norm from unity. Indeed, Fig.  shows that the MERRA-2 age spectra are less well normalised, with a norm below 0.8 throughout large regions of the stratosphere, whereas for ERA-Interim and JRA-55 the norm is always above 0.9 (in the lower part of the stratosphere even above about 0.95). This lack of normalisation of the MERRA-2 age spectra is clearly related to a much larger tail decrease timescale (global average 5.13 years) compared with ERA-Interim (2.84 years) and JRA-55 (2.91 years). Compared to the climate model simulated age spectra of , with a global average tail decay timescale of 2.77 years, ERA-Interim and JRA-55 show comparable values, whereas MERRA-2 differs substantially.

In the following, we analyse trends in age of air for the same periods as considered by to simplify the comparison to their results in Sect. . We refer to 1989–2015 as “long-term” trends and to 1989–2001 (“pre-2000” in the following) and 2002–2015 (“post-2000”) as “decadal” trends. It should be noted that even the long-term period spans only 27 years, which is relatively short compared with climate model simulation periods but is the longest period we can obtain from the reanalyses without including spin-up effects in the results (see Sect. ). Throughout the paper, trends are calculated from the linear regression of monthly mean time series after deseasonalising (by subtracting the mean annual cycle), and the significance is measured in multiples of the standard deviation of the linear trend.

To assess the reliability of the representation of the stratospheric BDC in different reanalyses, the mean age of air is compared to the mean age estimated from observations of the long-lived trace gas species SF6 and CO2. Figure a compares latitude sections of mean age from reanalysis, airborne in situ observations (same data as shown in , based on various measurements; ) and MIPAS satellite observations of SF6 at 500 K potential temperature (20 km for the observations).

Overall, the reanalysis mean age lies within the uncertainty range of the observations. In the tropics, the in situ observed mean age is significantly lower than the reanalysis age, with only ERA-Interim reaching similar values. However, MIPAS shows a much older mean age (above 2 years), which is similar to MERRA-2 values. Compared to the in situ observations, age gradients in the subtropics are too weak for all reanalyses due to the higher tropical age values. In the middle and high latitudes, ERA-Interim and JRA-55 agree closely with CO2-based mean age observations, whereas MERRA-2 agrees better with the SF6-based mean age.

As the reanalysis age spectrum is truncated at 10 years, the respective mean age is biased low by definition. This low bias can be corrected by applying a correction for the finite age spectrum tail (see Sect. ), and the corrected mean ages are also compared to the observations in Fig. a (dashed lines). For all reanalyses the tail correction increases the mean age. This effect is moderate for ERA-Interim and JRA-55, such that the corrected reanalysis mean age remains within the observational uncertainty range. For MERRA-2, in contrast, the effect of the tail correction is large, increasing the mean age by more than 2 years at high latitudes. As a consequence, the tail-corrected MERRA-2 mean age is clearly out of the observational uncertainty range (the tail correction effects will be discussed further below).

A long-term observational mean age time series only exists for NH middle latitudes from balloon-borne measurements of SF6 and CO2 . Long-term time series of reanalysis mean age in the NH middle latitudes (averaged between 40 and 50∘ N and 600 and 1200 K, which is approximately equivalent to the vertical layer for the observations of 30–5 hPa) are compared against this balloon observation time series in Fig. b (note, that data points before 1989 include spin-up effects, see Sect. ). Clearly, the uncertainty arising from using different reanalyses is of a similar magnitude as the uncertainty in the observations, such that no conclusion is possible regarding which reanalysis scenario is most realistic. However, The mean age trends substantially differ between the reanalyses with negative trends for JRA-55 (-0.17±0.01 yr decade-1) and MERRA-2 (-0.18±0.01 yr decade-1) and a positive trend for ERA-Interim (0.07±0.01 yr decade-1), Hence, ERA-Interim appears to agree best with the observed (non-significant) trend of 0.15±0.18 yr decade-1 by . A “best fit” to the observational time series results from applying the finite tail correction to the ERA-Interim mean age, which is in remarkably good agreement with the observations, regarding absolute values, variability and trend (red dashed line).

Figure a shows a much stronger sensitivity to the tail correction for the MERRA-2 mean age compared with the other reanalyses. This stronger sensitivity for MERRA-2 results from differences in the spectrum tail compared with the other two reanalyses (see Fig. ), with a substantially slower tail decrease for MERRA-2. Figure  illustrates a case of extreme differences between the reanalyses (June 1992 at 700 K potential temperature and 46∘ N). For ERA-Interim, the age spectrum values decrease substantially over the 10 years of transit time (more than an order of magnitude), indicating a strongly decaying spectrum tail. For MERRA-2, in contrast, the tail decrease is much slower, leading to a substantially larger tail decay timescale and to a less strict normalisation, as previously discussed above (Fig. ). This longer tail decay timescale causes the finite tail correction applied to the age spectra resolved over 10 years to have a much larger effect for MERRA-2 than for ERA-Interim and JRA-55. Figure  further shows that for MERRA-2 even the assumption of an exponentially decaying age spectrum tail after about 5 years, which has generally been found to be valid for observations and models , is violated in some cases. Hence, the exponential finite tail correction is not applicable for the MERRA-2 age spectra over 10 years of transit time. For that reason, the inter-comparison presented in this paper is based on the uncorrected age spectrum.

Potential long-term changes in the stratospheric Brewer–Dobson circulation and their relation to anthropogenically forced climate change have been the subject of intense debate over recent years. Climate models show a significant strengthening and acceleration of the BDC , resulting in a global negative mean age trend e.g.. Trace gas observations, in comparison, show no indication of a significant long-term mean age trend . Studies based on reanalysis meteorology have also provided a diverse picture of mean age trends e.g. which is partly related to the different trend periods considered.

In view of such diversity in past published mean age trends, the qualitative agreement between the “long-term” trends for 1989–2015 in the lower stratosphere (below about 30 hPa) presented here for the newest three reanalyses is remarkable (Fig. ). In general, the mean age trend is negative throughout the lower stratosphere with the largest values in the tropical and SH lower stratosphere, indicating an accelerating shallow BDC branch. These negative long-term mean age trends in current reanalyses appear to be largely consistent with mean age trends from climate models over even longer periods (century), representing the forced response of the BDC to increasing greenhouse gas levels. Consistent with these negative mean age trends and the related shift of the age spectrum peak (modal age) towards shorter transit times (e.g. Fig. ), most current reanalyses show an increasing tropical mass flux and decreasing residual circulation transit times (Thomas Birner, personal communication, 2018). However, further pointed out that residual circulation trends may strongly depend on the method used for calculating upwelling velocities.

Above about 30 hPa mean age trends and related circulation changes depend more strongly on the respective reanalysis considered. At these upper levels ERA-Interim shows ageing in the NH, which is not included in the other two reanalyses. Hence, long-term changes in the deep BDC branch appear to be less robustly represented in the reanalyses. The NH ageing in ERA-Interim turns out to be related to a strengthening age spectrum tail indicating changes in recirculation. The evidence for recirculation changes agrees with the results of , which showed that atmospheric mixing processes substantially affect mean age trend patterns, with the strongest effects on shorter timescales such as decades.

Over shorter periods of around a decade the reanalysis age of air trends show substantial differences. For the pre-2000 period, trends in the NH above about 600 K (approximately 24 km) are not consistent (Fig. ) due to insignificant ERA-Interim trends (Fig. d). The strong negative mean age trends in the SH and tropics, in contrast, consistently emerge from all reanalyses and likely represent the combined effects of ozone depleting substances to decrease mean age and of volcanic aerosol from the Pinatubo eruption to increase mean age at the beginning of the 1989–2001 period . In particular, regarding the effect of Pinatubo aerosol, differences in the response of the BDC and related differences in age of air between the reanalyses are evident from the middle latitude mean age time series in Fig. b. The increase in age after the Pinatubo eruption is very strong in JRA-55, is weaker in ERA-Interim and is absent in MERRA-2. These differences point to different representations of stratospheric volcanic aerosol in the reanalyses causing the differences in decadal BDC trends. In ERA-Interim and JRA-55 the effects of stratospheric volcanic aerosol are only included by the assimilation of observed temperature and wind data, as discussed in more detail by , whereas MERRA-2 additionally assimilates aerosol optical depth . Furthermore, the effect of ozone depleting substances (ODSs) is very likely differently represented in the reanalyses due to the usage of different ozone products. ERA-Interim uses an ozone climatology, JRA-55 uses time-varying ozone fields from another model simulation and MERRA-2 uses interactive ozone (see Sect. ). Hence, differences in the related effects on the BDC are to be expected.

For the post-2000 period, the age of air trends are even less consistent and no clear common circulation change emerges from the comparison of the different reanalyses (Fig. ). Remarkably, the largest differences between the reanalysis trends occur for the most recent period. This is against the general expectation that a larger consistency between reanalyses emerges for more recent periods, when observational data and the assimilation procedures are more consistent. The inconsistency in the post-2000 trends is mainly related to the fact that JRA-55 and MERRA-2 show opposite mean age trends during the 2002–2015 period throughout the stratosphere (Fig. h, i), and that only ERA-Interim shows a hemispheric dipole pattern (Fig. g). The hemispheric dipole pattern in the mean age changes in ERA-Interim is related to changes in the age spectrum tail (increasing tail in the NH and decreasing tail in the SH), pointing to changes in recirculation that are in agreement with . As the hemispheric dipole age trend pattern has been recently related to a southward circulation shift by about 5∘ , post-2000 age trend differences between the reanalyses could be caused by differences in the representation of this circulation shift.

Comparison to the recently published reanalysis mean age trends by may reveal interesting differences regarding the representation of the BDC between kinematic transport models as used in their study (BASCOE model) and diabatic transport models as used here (CLaMS). Regarding the climatology, the mean age from MERRA-2 shows substantially higher values than the other reanalyses for both diabatic and kinematic transport see Fig. , andFig. 3. The differences in diabatic heating rates, with weaker tropical upwelling for MERRA-2 (Fig. ), are qualitatively consistent with the differences in mean age in the diabatic model calculation. The fact that similar mean age differences were found by suggests that differences in the reanalysis vertical winds, which drive their kinematic model calculations, could be similar to the differences in heating rates.

However, as previously earlier, the differences in heating rates alone cannot fully explain the simulated mean age differences as shown in the following. Figure  shows the ERA-Interim climatological mean age and residual circulation transit times (RCTTs), and differences to the other reanalyses. Here, RCTTs are calculated from the diabatic residual circulation in isentropic coordinates, as described in Sect. . The mean age from MERRA-2 is older than ERA-Interim by more than 2 years throughout most parts of the stratosphere (Fig. c), whereas differences in RCTTs are below 0.5 years (Fig. f). Hence, differences in the representation of mixing processes must play a role.

The net mixing effect on mean age (ageing by mixing), calculated as the difference between the mean age and the RCTT following and further described in Sect. , is shown in Fig. g–i. This ageing by mixing is about 2 years larger for MERRA-2 than for ERA-Interim in most parts of the lower stratosphere, and clearly explains the large difference in the mean age between the reanalyses. However, ageing by mixing depends on both local mixing characteristics in the lower stratosphere and the transit time of tropical upwelling, which controls the timescale for mixing to affect the ascending air see. Hence, the differences in the ageing by mixing between ERA-Interim and MERRA-2 may be caused by either differences in local mixing (eddy diffusivity) or by differences in the RCTTs. From a tropical leaky pipe model perspective ageing by mixing is even linearly related to RCTT, with a longer RCTT causing a larger ageing by mixing . In percent, the differences in RCTTs between MERRA-2 and ERA-Interim in the tropical lower stratosphere are large (about 50 %, see blue contours in Fig. f), and likely cause a related difference in ageing by mixing. Overall, the larger ageing by mixing for MERRA-2 compared with ERA-Interim clearly causes the differences in mean age. Deeper insight into potential differences in local mixing characteristics could be gained by a reanalysis inter-comparison of effective diffusivity e.g..

For the long-term mean age trends (1989–2015) both diabatic and kinematic transport representations result in very similar results for all three reanalyses, as evident from the comparison of Fig.  with Fig. 12 of . This good agreement regarding long-term trends again points to a robust representation of the effect of greenhouse gas-induced warming in forcing trends in the BDC. However, regarding decadal changes over shorter periods, the results from diabatic and kinematic transport models show more substantial differences. The strongest differences emerge for the pre-2000 period for ERA-Interim and for the post-2000 period for MERRA-2. For the former case, diabatic transport in CLaMS results in negative mean age trends throughout the SH and tropical stratosphere (Fig. d), whereas kinematic transport in BASCOE results in positive trends in these regions Fig. 12. As pre-2000 decadal trends are likely controlled by the effects of ozone depleting substances and Pinatubo volcanic aerosol on the BDC, the differences in age trends for this period point to differences in the representation of these processes between diabatic and kinematic transport. In particular differences in the effect of volcanic aerosol (e.g. due to the Pinatubo eruption in June 1991), with increasing mean age for diabatic transport and no significant age changes for kinematic transport seem to be critical, and have also been noted by . For the latter case (post-2000 period for MERRA-2), diabatic transport in CLaMS results in negative trends throughout the stratosphere (Fig. i), whereas kinematic transport in BASCOE results in positive age trends Fig. 12. Furthermore, less striking differences between diabatic and kinematic mean age trends emerge for MERRA-2 during the pre-2000 period, where kinematic age trends are more negative compared with diabatic trends Fig. f andFig. 12. Weak differences also occur for ERA-Interim from 2002 to 2015, where the NH ageing appears stronger in the diabatic age trends Fig. g andFig. 12. The causes for the differences regarding decadal trends in the BDC on shorter periods between diabatic and kinematic transport representations, as well as between the different reanalyses, are unclear to date, but appear to be a promising subject for future analysis aiming to improve consistency between the reanalyses.

We compared stratospheric mean age and the full age spectrum from simulations with the diabatic CLaMS model driven by different reanalyses (ERA-Interim, JRA-55 and MERRA-2) to investigate the robustness in the representation of the climatology, seasonality and trends of the Brewer–Dobson circulation in current generation reanalysis data sets. Considering the full (time-dependent) age spectrum in a data inter-comparison is novel and provides clearer insights into circulation differences than considering mean age alone. Climatological mean age differs significantly between the different reanalyses, with JRA-55 showing the youngest age and MERRA-2 showing the oldest age throughout almost the entire stratosphere. The substantially older mean age for MERRA-2 appears to be related to a more pronounced age spectrum tail, indicating a stronger effect of the recirculation of air into the tropics. A comparison of residual circulation and mixing effects on mean age confirms that the net mixing effect (including recirculation) is necessary to explain the mean age differences between MERRA-2 and ERA-Interim. The seasonality in the BDC is robustly represented, with very similar mean age seasonality and similar seasonal age spectrum peaks emerging for all reanalyses. Comparison to balloon-borne mean age observations reveals a similarly large spread in simulated and observed mean ages and allows no clear conclusions to be drawn regarding the reliability of the different reanalyses.

In particular, long-term trends in the lower stratosphere (below about 30 hPa) during the 1989–2015 period are robustly represented in the reanalyses mainly showing decreasing mean age, which is strongest in the SH and tropical lower stratosphere. Related to this mean age decrease is a robust shift of the age spectrum towards shorter transit times and an increase in the fraction of young air masses. These long-term age of air changes from reanalyses resemble results from climate model simulations over even longer periods, which simulate an acceleration of the shallow branch of the stratospheric BDC as the forced response to increasing greenhouse gas levels. At upper levels (above 30 hPa), mean age changes in the reanalyses appear less robust, pointing to a less robust representation of changes in the deep BDC branch.

For shorter periods of about a decade (here 1989–2001 and 2002–2015), the age of air changes are more diverse and depend on the specific reanalysis considered. These decadal age changes may even disagree in sign globally for certain periods. Moreover, the hemispheric asymmetric dipole in mean age trends for 2002–2015, as viewed by satellite observations, only emerges for ERA-Interim. Hence, decadal variability in the Brewer–Dobson circulation and the various factors involved (e.g. QBO, ENSO, ODS and volcanic aerosol) turn out not to be robustly represented in current generation reanalyses.