Depending on their vertical coordinate system and the reanalysis data used as input, one may distinguish between kinematic and diabatic transport models . Diabatic models use isentropic (θ) or hybrid σ-θ vertical coordinates and calculate the vertical transport from diabatic heating rates which may be read from the input reanalysis or recomputed using a separate radiation scheme. Kinematic transport models, on the other hand, need only the surface pressure and horizontal wind fields on input. These models are usually set on a different grid than their input reanalysis dataset. Since this prevents the direct usage of the vertical wind component in the reanalysis, they rely on mass continuity to derive the vertical mass fluxes corresponding to their own grid. The present study uses the kinematic transport model developed for the Belgian Assimilation System for Chemical ObsErvations BASCOE: see. Its advection module is the flux-form semi-Lagrangian (FFSL) scheme configured to follow closely the recommendations of .

We briefly summarize here this configuration because it has an important impact on the simulated distribution of AoA in the stratosphere. The FFSL advection scheme is run on a evenly spaced latitude–longitude grid with 2∘×2.5∘ increments. This grid spacing is typical for current simulations of stratospheric chemistry and transport over several decades . Using the FFSL algorithm, showed that this is the minimum resolution allowing a realistic representation of the tropical and high-latitude mixing barriers. The FFSL algorithm does not require satisfaction of the Courant–Friedrichs–Lewy (CFL) condition in the longitudinal direction, which is a big computational advantage for regular longitude–latitude grids. The time step is set to 30 min by default and automatically split into integer fractions in order to satisfy the CFL condition in the meridional direction. The algorithmic structure of the FFSL scheme allows multiple choices for monotonicity constraints that have implications on the subgrid tracer distribution used to calculate fluxes across cell edges. These choices are made separately in the longitudinal, meridional and vertical directions. showed that AoA calculations are very sensitive to the choice of constraint in the vertical direction: realistic results require a positive–definite piecewise parabolic method, where the constraint on the subgrid distribution is only strong enough to prevent generation of negative values but overshoots and undershoots are allowed. There is no representation of convection in the model nor any explicit mechanism for horizontal diffusion.

The age of air is defined as the spectrum of transit times from a source region to a given location, with the tropical tropopause usually defining the source region for studies of the stratosphere. In the case of an ideal tracer which increases linearly in the source region and has no photochemical productions or losses, one can obtain the mean of this spectrum (denoted here as AoA) at any time and location from the corresponding mixing ratio of the tracer: in such a case, the AoA is simply the time elapsed since the ideal tracer had the same mixing ratio in the source region . Here, we follow this classical approach, using for most simulations the 100 hPa isobar between latitudes 10∘ S and 10∘ N as the source region. In one case, we have used the surface as source region in order to enable a comparison with a long time series of balloon observations (see Sect. ). The output AoA datasets are interpolated from model levels to constant pressure levels using the instantaneous and two-dimensional input surface pressures, i.e., prior to any averaging in the longitudinal or time dimension.

We compute and compare the AoA in five recent reanalyses which are described in detail by : ERA-Interim European Centre for Medium-Range Weather Forecasts Interim Reanalysis;, JRA-55 Japanese 55-year Reanalysis;, MERRA Modern Era Retrospective Analysis for Research and Applications;, MERRA-2 and NCEP-CFSR National Centers for Environmental Prediction – Climate Forecast System Reanalysis;. These datasets were used over the period January 1980 to December 2015, except for NCEP-CFSR which originally ended in December 2010 and is extended here with the CFSv2 dataset Climate Forecast System version 2; from January 2011 to December 2014. Hereafter, we use “ERA-I” to refer to ERA-Interim and “CFSR” to refer to the combined NCEP-CFSR reanalyses.

Each reanalysis is available on two vertical grids: the native grid of the underlying atmospheric model (product on “model levels”) and an output grid of constant pressures (product interpolated to “pressure levels”). Our simulations are run on the native model levels in order to account for the different vertical resolution of each reanalysis system and also to avoid any interference from the interpolation methods used to deliver the products on constant pressure levels. All reanalysis systems use the hybrid sigma-pressure vertical coordinate with levels extending from the surface up to ∼0.266 hPa (∼57 km height) in CFSR, 0.1 hPa (∼64 km) in ERA-I and JRA-55, or 0.01 hPa (∼78 km) in MERRA and MERRA-2. The reader is referred to for a comparison of the vertical resolutions of the reanalysis systems.

The forecast models use two different frameworks to discretize their primitive variables on the horizontal plane: MERRA and MERRA-2 solve for mass fluxes on a regular latitude–longitude grid , while ERA-I, JRA-55 and CFSR use spectral dynamical cores; i.e., they solve for vorticity and divergence expressed on a spherical harmonics basis e.g.,. Users of the reanalyses often download velocity fields which are derived from the primitive variables and evaluated on varying regular grids: these may be reduced Gaussian grids (ERA-I and JRA-55), regular Gaussian grids (CFSR) or regular latitude–longitude grids (MERRA and MERRA-2). This preprocessing is described in detail in the next subsection.

We use in all cases the analyses valid at 00:00, 06:00, 12:00 and 18:00 UTC, i.e., datasets with a 6 h time resolution. The assimilation procedure for MERRA and MERRA-2 uses an iterative predictor–corrector approach, generating two separate sets of reanalysis products designated ANA for analysis state and ASM for assimilated state . The latter products use a 6 h corrector forecast centered on the analysis time and an incremental analysis update to apply the previously calculated assimilation increment gradually rather than abruptly at the analysis time . Thanks to this procedure, the ASM products have smaller wind imbalances than the ANA products ; hence, they are preferable for tracer transport simulations. We used the ASM products in MERRA-2 but could not do so with MERRA, where the ASM products are only available on constant pressure levels. Since we aim to evaluate each reanalysis on its native vertical grid, we had to fall back on the ANA product in the case of MERRA.

The BASCOE transport model (hereafter BASCOE TM) is used as a tool to perform a fair comparison of advective transport in each reanalysis dataset, using their native vertical grids but a common, low-resolution latitude–longitude grid. It requires on input the surface pressure and horizontal velocity on a so-called Arakawa-C grid; i.e., the zonal wind u must be staggered in longitude and the meridional wind v must be staggered in latitude. As indicated by its name, the FFSL algorithm evaluates internally the corresponding mass fluxes and derives the vertical winds (w) from mass conservation. Hence, the reanalysis datasets must be carefully preprocessed from spectral or high-resolution gridded fields to the low-resolution C grid. We have paid special attention to this preprocessing of the reanalyses to make sure that the different types of wind fields are expressed in a consistent manner for our transport algorithm.

Due to its assimilation procedure, the early ERA-40 reanalysis contained large dynamical imbalances which deteriorated the Brewer–Dobson circulation through excessive upward motion in the tropics and excessive transport from the tropics to the midlatitudes . described a similar issue with MERRA and proposed to use time-averaged input wind fields in order to remove these imbalances, but this approach is available only for MERRA and MERRA-2. To filter out such dynamical imbalances, BASCOE uses a preprocessor which was originally developed only for the analyses computed by the European Centre for Medium-Range Weather Forecast (ECMWF) including ERA-I . Using the primitive variables of spectral dynamical cores, i.e., the vorticity and divergence expressed on a spherical harmonics basis, this preprocessor evaluates the zonal and meridional winds on a regular latitude–longitude grid while correcting for the small inconsistencies in the pressure tendency compared with the divergence fields. This correction ensures consistent mass fields even in the presence of spurious surface pressure increments which may be caused by data assimilation.

Our preprocessing for the five reanalysis systems is based on this algorithm, with a preliminary derivation of the spherical harmonics coefficients of vorticity, divergence and surface pressure for the reanalyses other than ERA-I. In all cases, these spectral coefficients are truncated at wavenumber 47 to avoid aliasing on the 2∘×2.5∘ target grid Sect. 7.4.

Figure compares the results of the BASCOE TM driven by ERA-I with those by a reference Eulerian model, using the standard layout of zonal means at 20 km height and at equatorial, middle and polar latitudes e.g.,. Both models transport idealized tracers which increase linearly at the tropical tropopause and are driven during 20 years by repeating reanalyses of the year 2000. The reference model is TOMCAT, driven by ERA-I analyses with 6-hourly updates. At 20 km height, we use the results published by Fig. 28, while the vertical profiles are those published by Fig. 1. Some observational context is provided with in situ observations of SF6 and CO2 .

Very good agreement is obtained between TOMCAT and BASCOE TM. At 20 km height, the results are nearly identical except in the Southern Hemisphere, where TOMCAT delivers a slightly weaker latitudinal gradient, resulting in a difference of around 0.5 years above the South Pole between both models. All three vertical profiles show that TOMCAT delivers slightly weaker vertical gradients in the lower stratosphere than the BASCOE TM. This results in younger midstratospheric AoA by TOMCAT, but here also the largest difference does not exceed 0.5 years (latitude 5∘ S, height 45 km).

The AoA distributions are first averaged over the period 2002–2007 in order to remove seasonal and quasi-biennial oscillations and also to allow comparisons with the distribution most recently derived from MIPAS observations of SF6 .

The global distribution of AoA is first compared with latitude–pressure cross-sections. The ERA-I reanalysis is taken as reference because it delivers intermediate values and has been used in AoA studies with several other transport models see, e.g.,. Figure  shows the latitude–height cross-sections of AoA for the period 2002–2007, with a noticeable hemispheric asymmetry: as expected, the latitudinal gradient is significantly stronger in the southern midlatitudes and polar regions than in the Northern Hemisphere, and old air masses reach much lower altitudes above the Antarctic than above the Arctic (e.g., the 5-year isoline starts at 50 hPa above the South Pole and ends at 20 hPa above the North Pole). This is qualitatively confirmed by AoA derived from MIPAS observations of SF6 for the same period Fig. 7d.

The four other reanalyses deliver noticeably different distributions of AoA (Fig. ). One can distinguish JRA-55 and CFSR as the “younger reanalyses”, with AoA not exceeding 5 years in the polar upper stratosphere, MERRA as the “older reanalysis”, with maximum AoA values as large as 6.5 years, and ERA-I with intermediate results (5.8 years in the same regions). MERRA-2 is a special case, with upper stratospheric values similar to those reached by ERA-I but quite different latitudinal gradients. The hemispheric asymmetry is more pronounced with ERA-I than with any other reanalysis, e.g., the 3- and 4-year isolines (JRA-55 and CFSR, respectively) or the 5-year isoline (MERRA-2 and MERRA) reach nearly the same level above the North Pole as above the South Pole. MERRA-2 stands out in the middle stratosphere with nearly vertical isolines, i.e., very small vertical gradients which are not supported by MIPAS observations .

While this qualitative comparison of the AoA distributions points to different gradients in the midlatitudes and polar regions, the relative differences with respect to ERA-I are largest in the tropical lower stratosphere (bottom row of Fig. ). Hence, we focus on this region and its differences with the midlatitudes. Figure , inspired by the AoA intercomparisons in CCMs , shows the intercomparison of AoA zonal means at 50 hPa, at tropical and northern midlatitudes, and the AoA difference between these two latitude bands.

The intercomparison at 50 hPa (Fig. a) shows again the important disagreement between the five model simulations. JRA-55 yields the youngest AoA at all latitudes with values ranging from 0.8 years at the Equator to 3.6 years at the South Pole, while MERRA and MERRA-2 yield the oldest AoA with 1.6 years at the Equator and around 5 years at the South Pole. CFSR and ERA-I yield intermediate results with nearly identical values in the northern extratropics but different latitude gradients between the tropics and Southern Hemisphere. The sole simulation to deliver a minimum AoA in the southern tropics is driven by CFSR, which yields the minimum AoA at 6∘ S. In the other simulations, this minimum is either exactly at the Equator (JRA-55, MERRA) or slightly north of the Equator (ERA-I, MERRA-2). In the Southern Hemisphere, CFSR results in AoA nearly as young as JRA-55, while ERA-I reaches larger values which are very close to the observations. Overall, the spread between the five simulations at 50 hPa is larger than the 1σ observational uncertainties in the tropics and nearly as large in the extratropics. Since the reanalyses are constrained by very similar satellite datasets, they could have been expected to deliver more similar AoA than an intercomparison of unconstrained climate models. Yet we note that the spread shown in Fig. a is as large as in an intercomparison of seven CCMs Fig. 2.

The vertical profiles of AoA (Fig. b and c) confirm that this large spread and general hierarchy of AoA (youngest with JRA-55, oldest with MERRA and MERRA-2) are found at all stratospheric levels. In the northern midlatitudes (35–45∘ N, Fig. c) MERRA-2 stands out with vertical gradients which are larger in the lower stratosphere but smaller in the upper stratosphere than in all other reanalyses. While the intermediate values by ERA-I and CFSR agree well with observations in the tropics (10∘ S–10∘ N, Fig. b), this is not the case in the northern midlatitudes, where only MERRA and MERRA-2 deliver AoA as old as the observations.

The AoA differences between the tropics and midlatitudes are directly related to the inverse of the tropical upwelling velocity and independent of quasi-horizontal mixing: a smaller AoA latitudinal gradient indicates faster tropical ascent . These “latitudinal gradients of AoA” were used in several CCM intercomparisons . Figure d shows this diagnostic for the five reanalyses, i.e., the differences between the AoA profiles in Fig. c and b. Except for MERRA-2, the profiles of AoA differences delivered by the four other reanalyses agree much more closely than the AoA profiles themselves, at least during the 2002–2007 period. The spread of AoA differences between the four reanalyses reaches a maximum of 0.2 years at 30 hPa, much tighter than the spread of 0.8 years in the corresponding intercomparison of six CCMs Fig. 3c. While there is good agreement with the observation-derived AoA differences below 60 and at 10 hPa, these four reanalyses significantly underestimate it at intermediate pressure levels. This indicates an overestimation of the tropical upwelling obtained with ERA-I, CFSR, JRA-55 and MERRA in the lower stratosphere. MERRA and MERRA-2 yield larger AoA at northern midlatitudes than the three other reanalyses. In the case of MERRA-2, this results in a profile of AoA differences which are significantly larger than the profiles obtained with the four other reanalyses but agrees much better with the profile derived from the observations. Hence, MERRA-2 apparently underestimates the tropical upwelling in the lowermost stratosphere (100–60 hPa), agrees better with the observations at 50 hPa than the four other reanalyses and is in accordance with them at higher levels.

The Pinatubo eruption, which started on 15 June 1991, is expected to have had a significant impact on AoA . The assimilation of satellite radiance measurements by the Advanced Microwave Sounding Unit (AMSU) started in 1998 (on 1 August in ERA-I and JRA-55, and 1 November in CFSR, MERRA and MERRA-2) and was repeatedly shown to have a important influence on their description of the stratospheric dynamics e.g.,. Hence, we repeat the latitudinal gradient diagnostic but for the period 1992–1997, i.e., after the Pinatubo eruption and before the ingestion of AMSU radiances (Fig. ). The general outcome is the same as during the later period: the tropical ascent is too fast with all reanalyses except with MERRA-2. Yet MERRA-2 provides a better match with the observations during this earlier period, and the four other reanalyses do not agree as closely.

Figure  shows the averaged time evolution of simulated AoA according to the five reanalyses, from 1989 to 2015 at 50 hPa in the midlatitudes. The results are smoothed with a 1-year running mean in order to highlight the long-term trends. The overall hierarchy of ages shown on previous figures for years 2002–2007 holds for the whole 1989–2015 period: MERRA and MERRA-2 deliver the oldest AoA, JRA-55 and CFSR the youngest. While MERRA and MERRA-2 agree well in the Southern Hemisphere, this is not the case in the Northern Hemisphere, where MERRA-2 starts with much older values. A rapid decrease of MERRA-2 values during the 1990s allows these two datasets to reach better agreement after 1998, i.e., the beginning of AMSU assimilation. The possible causes for this apparently anomalous behavior of MERRA-2 will be discussed in Sect. . The MERRA output in the Northern Hemisphere delivers seasonal cycles with much larger amplitudes than those obtained from all other reanalyses. This will be investigated in the next section.

The Pinatubo eruption does not appear to have any impact on the simulated AoA at 50 hPa except with MERRA-2 which shows an increase in the southern midlatitudes. The same time series for the tropical latitude band (30∘ S–30∘ N) does not show any impact of the Pinatubo eruption either (not shown). This absence of volcanic impact in the other reanalyses is even more evident in a deseasonalized time series of the extrapolar lower stratosphere (Fig. ). This diagnostic is inspired by , who showed a significant impact of the Pinatubo eruption on AoA using ERA-I and JRA-55 but with another offline transport model. Since our results contradict this finding, this issue will also be further discussed in Sect. .

Figure  displays time series of AoA in the middle stratosphere (mean values between 30 and 5 hPa). The left plot compares the model results in the Northern Hemisphere with balloon observations that have been collected since the 1970s , where the derivation of AoA uses the surface as reference and the outer error bars denote the overall uncertainty of the mean-age value including an assessment of the representativeness of a single profile . To allow a consistent comparison, the solid lines in Fig.  show modeled AoA using the surface as reference, i.e., AoA evaluated from a tracer which uses as boundary condition a global constant increasing linearly with time at the surface. This boundary condition is propagated to the free troposphere through vertical diffusion with a coefficient Kzz decreasing from an arbitrary value of 10 m2 s-1 at the surface to zero at the pressure level halfway between the surface and the tropopause. Figure b compares the resulting time series in the tropics with the usual calculation of AoA using the tropical tropopause as reference (dashed lines). The differences between the two calculations represent the transit times from the surface to the tropical tropopause, are nearly independent of the simulated year and range between 3 months (with ERA-I or JRA-55) and 6 months (with MERRA). These values are close to the longest transit times reported in a recent intercomparison of global models indicating slow transport from the surface to the tropical tropopause which we attribute to the omission of deep convective transport in our model. While the surface-based model AoA (solid lines in Fig. ) may be slightly overestimated, these biases have no significant interannual variations and do not hinder the intercomparison between reanalyses.

The spread between the five simulations is as large as the observational uncertainties, highlighting again the importance of the disagreement between the five reanalyses. In the northern midlatitudes (Fig. a), no reanalysis delivers any change larger than half a year over the whole period (1989–2015) except for MERRA-2 which indicates a large decrease of 0.8 years, but this decrease starts from values much larger than the observations and happens mostly before 2000. ERA-I delivers a weakly positive trend over the period 1989–2015, and we will assess in Sect.  that this trend in the model results is significant. While the overall trend simulated with ERA-I is in agreement with the balloon observations, this comparison should be considered with great caution because the sign of the AoA trend is not significant in the observations and modeled trends over periods as long as 30 years are often not significant when the ideal tracer is sampled like the available observations of stratospheric tracers .

The intercomparison in the Southern Hemisphere (Fig. c) also shows large disagreement between the long-term trends among the five reanalyses. MERRA and MERRA-2 values decrease quickly until 1995 and increase after 2007, while ERA-I values follow an opposite pattern. The long-term evolution of AoA in this region is completely different from JRA-55 (gradual decrease until 2002 followed by a stabilization) and differs yet again from CFSR (no apparent trend before 1997 and rapid increase during 1997–2003). The thin lines allow a qualitative comparison of faster variations. The seasonal signal dominates in all cases, with similar phases: AoA is oldest in fall and youngest in spring. The seasonal amplitudes are very dependent on the input reanalysis and on the considered year, so their detailed analysis is deferred to the next section. Yet we note already that some reanalyses exhibit a strong modulation of the seasonal cycle by the quasi-biennial oscillation QBO; for a general review, see, while others do not. This can be seen very clearly during the period 2005–2009 when the seasonal amplitudes of AoA by ERA-I and MERRA are approximately twice as small during the easterly phase of the QBO (i.e., in 2006 and 2008) than during the westerly phase (i.e., in 2005, 2007, 2009). This modulation of the seasonal variations is weaker in the MERRA-2 and JRA-55 datasets and absent from the CFSR dataset.

used a multiple linear regression model to study the trends of ozone total columns and vertical distribution at several ground-based stations. Here, we apply the same tool to A(t), the monthly zonal means of AoA as a function of time, latitude and pressure (after interpolation to a constant log-pressure grid with 2 km increments). The multiple linear regression model is expressed as A(t)=A0+A1⋅t+S(t)+Q(t)+ϵ(t), where t is time, A0 is the baseline value, A1 is the annual trend of AoA, and ϵ(t) represents the residuals. The term S(t) describes the seasonal variations in A(t): S(t)=S1⋅cos⁡(2πt/12)+S2⋅sin⁡(2πt/12)+S3⋅cos⁡(4πt/12)+S4⋅sin⁡(4πt/12), where the coefficients S1 to S4 describe the seasonal cycle. The term Q(t) describes the variations due to the QBO and its seasonal modulations: Q(t)=Q10(t)⋅[Q1+Q2⋅cos⁡(2πt/12)+Q3⋅sin⁡(2πt/12)+Q4⋅cos⁡(4πt/12)+Q5⋅sin⁡(4πt/12)]+Q30(t)⋅[Q6+Q7⋅cos⁡(2πt/12)+Q8⋅sin⁡(2πt/12)+Q9⋅cos⁡(4πt/12)+Q10⋅sin⁡(4πt/12)], where the explanatory variables Q10(t) and Q30(t) are the zonal winds observed above Singapore at 10 and 30 hPa (data from the FU Berlin: http://www.geo.fu-berlin.de/en/met/ag/strat/produkte/qbo/index.html, last access: 10 October 2018), and Q1 to Q10 are the coefficients associated with these two proxies, including their seasonal dependence.

The uncertainties arising from the fit are calculated for the 95 % confidence interval and corrected for autocorrelation in the residuals Eqs. 3, 4 and 6 in. Preliminary tests also included additional terms to account for the El Niño–Southern Oscillation (ENSO), the 11-year solar cycle and volcanic forcings but it was found that these terms do not impact significantly the linear trends nor the amplitudes of seasonal and quasi-biennial oscillations. Hence, they were removed from the regression model in order to avoid any overfitting of the data and to ease the interpretation of the results.

An important goal of this analysis is the determination of linear trends. As seen in Figs.  and , such trends depend closely on the considered time period. Hence, the regression model was applied not only to the whole simulation period (1989–2015) but also to an “early period” (1989–2001) and a “recent period” (2002–2015) which start after the assimilation of AMSU and on the same year as the MIPAS mission .

The amplitude of the seasonal variations is approximated by the difference between the maximum and minimum values reached by the term S(t) in the linear regression model. Figure  shows the dependence of this approximated amplitude with respect to pressure in five latitude bands for the period 2002–2015 (the results are similar for the period 1989–2001). The results with ERA-I are in agreement with an earlier modeling study Fig. 9. The vertical structure agrees broadly across all five reanalyses in the extratropics with maximum amplitudes in the lower stratosphere (around 100 hPa), except above the South Pole, where the amplitudes are maximum in the middle stratosphere (10–30 hPa). MERRA and MERRA-2 stand out with larger amplitudes in the lower stratosphere, resulting above the South Pole in a secondary maximum which is not found by the three other reanalyses. One may argue that the larger seasonal amplitudes of MERRA and MERRA-2 are a direct consequence of their larger annual means (see Fig. ) but this is not supported by the agreement of JRA-55 and CFSR with ERA-I despite their significantly younger annual means. In the tropics, ERA-I stands out with larger amplitudes in the upper stratosphere (around 5 hPa) and MERRA-2 with larger amplitudes in the lower stratosphere (around 50 hPa), while the three other reanalyses are in good agreement.

We now investigate the differences in the QBO among all reanalyses. have compared the monthly mean zonal wind in the equatorial stratosphere among reanalyses and found that their degree of disagreement depends on latitude, longitude, height and the phase of the QBO. They also noted a tendency for the agreement to be best near the longitude of Singapore, suggesting that the Singapore observations act as a strong constraint on all the reanalyses.

Here, we perform an intercomparison of the amplitude of the QBO signal (in years) in each reanalysis. We approximate it again as the difference between the maximum and minimum values reached by the term Q(t) in the linear regression model. Our results for ERA-I show that the QBO amplitude is largest in the subtropics around 30 hPa (not shown), which confirms again the results of . Figure  compares the results at this pressure level. Except for CFSR, the latitudinal dependence is similar in all reanalyses: the approximated QBO amplitude reaches maximum values around 15∘ latitude in both hemispheres and presents a marked minimum around the Equator. Outside of the equatorial region, the QBO amplitudes by JRA-55 are significantly smaller than by ERA-I, MERRA and MERRA-2. The amplitudes computed from CFSR show no clear structure in the Southern Hemisphere and reach large values at the North Pole.

It is difficult to infer changes in the BDC on the basis of AoA trends over periods shorter than several decades. Even in models where an ideal, linearly increasing artificial tracer is used, one has to rely on zonal-mean results over long periods to obtain trends that are clearly statistically significant . The statement that is often made that climate models simulate a decreasing age throughout the stratosphere only applies over long time periods and is not necessarily the case for the past 25 years, when most tracer measurements were taken . For example, the analysis of a 1700-year simulation showed that it takes around 30 years for a modeled BDC trend to emerge from the noise of natural climate variability assuming a 2 % dec-1 trend in the BDC; .

While linear trends of AoA over shorter periods may represent transient changes due to climate variability, such changes over timescales which are intermediate between the QBO and the multidecadal scales are still relevant to the study of stratospheric dynamics. Current research on AoA trends has largely focused on a dipole-like latitudinal structure for the period 2002–2012, which was first derived from satellite observation of SF6 by the MIPAS instrument . This structure of trends shows AoA decreasing in the Southern Hemisphere but increasing in the Northern Hemisphere, which was used to explain a recent increase of stratospheric HCl in the Northern Hemisphere and interpreted as the consequence of a southward shift of the subtropical transport barriers .

The ERA-I reanalysis supports a dipole-like latitudinal structure of AoA trends, at least since 2002. hereafter H2015 derived AoA trends from the distribution of SF6 over the period 2002–2012, using MIPAS observations and a CCM nudged towards ERA-I below 1 hPa and found a good agreement for the signs, range and latitudinal structure of AoA trends (see Figs. 6 and 10 in H2015). Here, we aim to verify our methodology through a comparison of our results with H2015, to check the consistency of AoA trends derived from the four other reanalyses and to explore the latitudinal structure of AoA trends for periods starting earlier than 2002.

The linear trend is represented by A1 in the multiple regression linear model (Eq. ). It is expressed in years per decade (yr dec-1) and is deemed significant at a given grid point if its absolute value is larger than its uncertainty (as defined in Sect. ). Figure  presents the ERA-I trends during the period 2002–2012 in order to compare with H2015. In the polar regions, H2015 showed large and positive trends, while they are insignificant according to our model (Fig. ). This disagreement can be attributed to different approaches: here, we study the true age of air using a theoretical tracer with no losses, while H2015 evaluated the apparent mean age of air taking into account the mesospheric sink of SF6 which has the largest impact in the polar regions . Outside of the polar regions, Fig.  shows good agreement with both observational and modeling results in H2015, including with respect to the significance of the trends: in the 30–60 hPa (approximately 25–20 km) layer the trends are significant at all extratropical latitudes, negative in the Southern Hemisphere and positive in the Northern Hemisphere. They reach -0.6 yr dec-1 in the southern tropics and close to 0.5 yr dec-1 in the northern tropics. Our results also agree well with those obtained by a diabatic model driven by ERA-I over the same period .

Figure  compares the latitude–pressure distributions of AoA trends across all five reanalyses and for the early (1989–2001), recent (2002–2015) and overall periods (1989–2015). It is important to note that the trends over the early and overall periods should be considered with caution since there were little data to constrain the stratospheric winds until 1998 (see the discussion in the next section). The AoA trends derived from ERA-I wind fields during the early period (Fig. , upper left) grow in both hemispheres except for the northern lowermost stratosphere. During the recent period, the dipole structure derived from ERA-I (Fig. , upper middle) is similar than over the slightly shorter period 2002–2012 (Fig. ). The increases in the Northern Hemisphere become weaker but remain significant at all latitudes, although at fewer grid points. The maximum trend is located at 24∘ N and 25 hPa, where it slightly exceeds 0.3±0.2 yr dec-1. The extension of this trend analysis for the overall period (Fig. , upper right) shows a dipole structure with negative but mostly insignificant trends in the Southern Hemisphere, positive trends in the northern middle stratosphere which mostly corresponds to the region with positive trends during the 1989–2001 period, and significantly negative trends in the lowermost stratosphere at all extrapolar latitudes. The same plot also shows that the positive trend which had been inferred visually for the northern midlatitudes of the middle stratosphere (Fig. a) is significant. Our ERA-I results for the overall period partly contradict those obtained by diabatic models which use not only the wind fields from ERA-I but also its heating rates . Looking at slightly shorter periods of two decades (1989–2010 for the former and 1990–2013 for the latter), these papers reported negative AoA trends for both hemispheres below 28 km altitude. also looked at the middle stratosphere, where positive trends were found at all latitudes, suggesting that the shallow and deep Brewer–Dobson circulations may evolve in opposite directions.

Comparing the results obtained with ERA-I with those from other reanalyses, one notes immediately general agreement between ERA-I and CFSR on one hand (Fig. , first and second row) and opposite trends in JRA-55, MERRA and MERRA-2 (third to fifth row). The agreement between multidecadal trends in ERA-I and CFSR may be related to their closeness in AoA distribution and spatial gradients (Sect. ). For all reanalyses except ERA-I, the trends for the overall period (1989–2015; Fig. , right column) appear dominated by the results from the early period which are subject to caution.

To summarize, the signs of the trends depend strongly on the input reanalysis and on the considered period with values above 10 hPa varying between approximately -0.4 and 0.4 yr dec-1. JRA-55, MERRA and MERRA-2 indicate an AoA increasing globally over 2002–2015, except in the lowermost stratosphere, while ERA-I and CFSR indicate the opposite (Fig. , middle column). These trends are significant only in specific regions of the stratosphere, and the regions of significance vary depending on the considered reanalysis. ERA-I stands out as the only reanalysis yielding a dipole structure of AoA trends for the period 2002–2015, although one may note that, in the lower stratosphere, the AoA growth derived for this period from MERRA and MERRA-2 (Fig. , middle column, fourth and fifth row) is faster in the Northern Hemisphere than in the Southern Hemisphere. One notes also a reversal of the trends between the early (1989–2001) and recent (2002–2015) periods. This reversal is found for all five reanalyses and in all regions of the stratosphere but it is difficult to interpret because it goes in opposite directions in ERA-I and CFSR versus JRA-55, MERRA and MERRA-2.