N2 O rate of change as a diagnostic of the Brewer-Dobson Circulation in the stratosphere

The Brewer-Dobson Circulation (BDC) determines the distribution of long-lived tracers in the stratosphere; therefore, their changes can be used to diagnose changes in the BDC. We investigate decadal (2005-2018) trends of nitrous oxide (N2O) stratospheric columns (12-40 km) as measured by four Fourier transform infrared (FTIR) ground-based instruments and by the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS), and compare them with simulations by two models: a chemistry-transport model (CTM) driven by four diﬀerent reanalyses, and the Whole Atmosphere Chemistry-Climate Model (WACCM). The limited sensitivity of the FTIR instruments can hide negative N2O trends in the mid-stratosphere because of the large increase in the lowermost stratosphere. When applying the ACE-FTS sampling on model datasets, the reanalyses by the European Centre for Medium Range Weather Forecast (ECMWF) compare best with ACE-FTS, but the N2O trends are consistently exaggerated. Model sensitivity tests show that while decadal N2O trends reﬂect changes in transport, these trends are less signiﬁcant in the northern extratropics due to the larger variability of transport over timescales shorter than two years in that region. We further investigate the N2O Transformed Eulerian Mean (TEM) budget in three model datasets. The TEM analysis shows that enhanced advection aﬀects the stratospheric N2O trends more than changes in mixing. While no ideal observational dataset currently exists, this model study of N2O trends still provides new insights about the BDC and its changes thanks to relevant sensitivity tests and the TEM analysis.

are consistently exaggerated.Model sensitivity tests show that while decadal N2O trends reflect changes in transport, these trends are less significant in the northern extratropics due to the larger variability of transport over timescales shorter than two years in that region.We further investigate the N2O Transformed Eulerian Mean (TEM) budget in three model datasets.The TEM analysis shows that enhanced advection affects the stratospheric N2O trends more than changes in mixing.While no ideal observational dataset currently exists, this model study of N2O trends still provides new insights about the BDC and its changes thanks to relevant sensitivity tests and the TEM analysis.

Introduction
Nitrous oxide (N 2 O) is continuously emitted in the troposphere, with a nearly constant rate of change of 2% per decade, and transported into the stratosphere, where it is destroyed by photodissociation mainly in the Tropics above 35 km (Tian et al., 2020).
The atmospheric lifetime of N 2 O is approximately 120 years, which makes it an excellent tracer for stratospheric transport studies (Seinfeld & Pandis, 2016).Within the stratosphere, the lifetime of N 2 O depends also on the solar activity because of its influence on the photolysis rates, with slightly decreased lifetime during solar maxima and increased lifetime during solar minima (Prather et al., 2015).
N 2 O enters the stratosphere in the Tropics, and is transported towards higher latitudes by the Brewer-Dobson Circulation (BDC, Dobson et al., 1929;Brewer, 1949;Dob-son, 1956).The BDC is driven by the breaking of tropospheric waves that propagate into the stratosphere (e.g., Charney & Drazin, 1961) and is often separated into an advective component, the residual mean meridional circulation (hereafter residual circulation), and a mixing component (Garny et al., 2014).The residual circulation consists in upwelling in the Tropics, followed by poleward flow and downwelling over the middle and high latitudes (Plumb, 2002).The mixing is a two-way exchange of mass that, within the stratosphere, occurs mostly on isentropic surfaces, thus, it is mainly quasi-horizontal (Shepherd, 2007).The BDC has a significant impact in determining the stratospheric distribution of chemical tracers, like ozone and greenhouse gases (e.g., Butchart, 2014), and in maintaing the observed meridional and vertical temperature structure of the stratosphere (Holton, 2004).Long-term changes in the BDC can have significant impacts on the climate system.One of the most important is the eff ect on the recovery of stratospheric ozone, as a changing BDC would result in changes of its meridional distribution (e.g., Shepherd, 2008;Dhomse et al., 2018).Changes in the BDC also impact the lifetime of Ozone Depleting Substances (ODS) in the stratosphere (Butchart & Scaife, 2001;Waugh & Hall, 2002), as well as the water vapor entering the stratosphere through the Tropics (e.g., Randel & Park, 2019).The troposphere is also aff ected by BDC changes because of the impact on the mass exchange with the stratosphere (e.g., ozone, Meul et al., 2018), and on the ultra-violet radiation reaching the surface (Meul et al., 2016).
Given the relevance of the BDC changes, understanding them is thus fundamental to fully comprehend the past and future evolution of climate.Simulations by Chemistry-Climate Models (CCMs) robustly project an acceleration of the BDC throughout the stratosphere in recent and coming decades due to the increase of greenhouse gases (e.g., Abalos et al., 2021).On the other hand, Oberländer-Hayn et al. (2016) argue that the global BDC trends in the lower stratosphere in CCMs are caused to a large extent by a lift of the tropopause level in response to global warming rather than an actual speedup of the circulation.Another significant impact of the increase of greenhouse gases is the shrinkage of the stratosphere, i.e., the combination of the tropopause rise and the downward shift of the height of the pressure levels above 55 km, that results from its cooling over the last decades (Pisoft et al., 2021).Modelling studies have shown that this stratospheric shrinking can impact the BDC and modulate its changes over the past decades ( Šácha et al., 2019;Eichinger & Šácha, 2020).Such modulation consists in a BDC acceleration similar to that resulting from the impact of the tropopause lift (Eichinger & Šácha, 2020).
In addition, CCMs simulations show that also the vertical and meridional structure of the BDC has changed in the past decades in response to climate change (Hardiman et al., 2014).Other modeling studies have shown that mixing, both on resolved and unresolved scales, also plays an important role in the simulated magnitudes of the BDC changes in addition to changes in the residual circulation among CCMs (e.g., Eichinger et al., 2019).Recent studies have also shown that ODS, through their impact on ozone, play a significant role in the modeled BDC changes (Abalos et al., 2019).In particular, the ODS decrease resulting from the Montreal Protocol, will reduce the global warminginduced acceleration of the BDC and potentially lead to hemispheric asymmetries in the BDC trends (Polvani et al., 2019).
The BDC and its changes cannot be measured directly (e.g., Minschwaner et al., 2016), but can be indirectly examined from measurements of stratospheric long-lived tracers (e.g., Engel et al., 2009;Hegglin et al., 2014) or temperature (Fu et al., 2015).Re- ing to a possible slowdown of the BDC), which is in contrast with the modeling studies that simulate a significant acceleration of the BDC over the same region (e.g., Abalos et al., 2021).These discrepancies can be partly attributed to the temporal and spatial sparseness of the measurements and to uncertainties in the mean AoA trends derived from real tracers (Garcia et al., 2011;Fritsch et al., 2020).In addition to ground-based measurements, space-borne observations have been used to compute mean AoA trends as well (e.g., Stiller et al., 2012;Haenel et al., 2015).These observational studies using remote sensing measurements have shown a hemispheric asymmetry in the mean AoA trends over 2002-2012, with positive changes in the Northern Hemisphere (NH) and negative changes in the Southern Hemisphere (SH) (e.g., Mahieu et al., 2014;Stiller et al., 2017).The mean AoA indirectly obtained from satellite measurements in these studies does not allow the separation between residual circulation and mixing, which was proven to be important in CCMs (Dietmüller et al., 2018). However, Linz et al. (2021) showed that the eff ect of mixing can be explicitly calculated using AoA vertical gradients from both models and satellite measurements.In addition, von Clarmann and Grabowski (2021) (similarly to the early study of Holton & Choi, 1988) proposed an alternative method to infer the stratospheric circulation from satellite measurements of long-lived tracers by a direct inversion of the continuity equation.
Reanalysis datasets try to fill the gap between observations and free-running models, providing a global multi-decadal and continuous state of the past atmosphere by assimilating available observations.Dynamical fields from reanalyses can be used to drive Chemistry-Transport Models (CTMs) to simulate the distribution of real and synthetic tracers in the atmosphere.In the past decade, these CTM experiments have been used to investigate BDC changes in reanalyses using the AoA diagnostic (e.g., Monge-Sanz et al., 2012;Diallo et al., 2012;Ploeger et al., 2015).However, significant diff erences exist in the BDC changes obtained from diff erent reanalyses, both over multi-decadal and decadal time scales (e.g., Abalos et al., 2015;Chabrillat et al., 2018).Furthermore, the computation of mean AoA largely depends on whether the kinematic velocities or the heating rates are used to drive the CTMs, leading to significant diff erences within the same reanalysis (Ploeger et al., 2019).
This  et al., 1994).Within the TEM framework, the impact of transport can be further separated into the impact from the residual circulation and mixing, as was done for ozone and carbon monoxide in Abalos et al. (2013).It is important to note that the mixing obtained from the TEM analysis generally includes contributions from advective transport that are not represented by the residual circulation (Holton, 2004)

Data and Methods
This section describes the observational and model data as well as the methods used in this study (see Tables 1 and 2).Throughout the study, we will refer to the CCMs and the BASCOE CTM simulations as "models" to distinguish them from the observations obtained from the FTIR and ACE-FTS.For the sake of brevity, we refer to M2020 for a more detailed description of the dataset (BASCOE CTM, WACCM version 4, and S-RIP reanalyses) and methods (TEM framework) already used there.

Ground-based FTIR Observations
We  The BASCOE CTM is built on a kinematic transport module (that takes as input the surface pressure and the horizontal winds) with a flux-form semi-Lagrangian (FFSL) advection scheme (Lin & Rood, 1996).The FFSL scheme is run on a common horizontal grid of 2 • x2.5 • for all the reanalyses, while the vertical grid depends on the input re-  et al., 2020).The horizontal resolution is 31 km, with hourly output frequency, and the vertical grid ranges from the surface to 0.01 hPa with 137 levels and with 300-600 m ver-tical spacing in the troposphere and stratosphere, which increases to 1-3 km above 30 km.ERA5 suff ers from a cold bias in the lower stratosphere from 2000 to 2006.For this reason, a new analysis (ERA5.1) has been produced for that period to correct for that bias (Simmons et al., 2020).In this study, the BASCOE CTM was driven by ERA5.1 for the 2000-2006 period.For computational reasons, the vertical resolution is reduced to 86 levels from the original 137 keeping the original vertical spacing in the stratosphere, and we used 6-hourly (0000, 0600, 1200, 1800 UTC) data.As done for the other reanalyses, the ERA5 data on the fine 31-km grid were truncated at wavenumber 47 to avoid aliasing on the target 2.5 • x2 • horizontal grid (Chabrillat et al., 2018).
In order to further investigate the contribution of transport in ERA5, we performed

TEM Diagnostics
For stratospheric tracers, the TEM diagnostics (Andrews et al., 1987) allows separating the impact of transport and chemistry on the zonal mean local rate of change of a tracer with mixing ratio χ : where The transport terms in Eq. 1 can be grouped as follows: where ADV = ( − v * χ y − w * χ z ) and M IX = e z/H ∇ • M represent the contribution of the residual circulation and of the resolved mixing, respectively.We refer to M2020 for a more detailed description of the TEM framework applied to the N 2 O mixing ratios in the stratosphere and for a comprehensive discussion of the contribution of each term to the N 2 O budget.

Derivation of Trends with the Dynamical Linear Modelling Tool
In this study, we investigate decadal trends using the Dynamical Linear Modeling For a given atmospheric time-seriesy t , a generic DLM model is composed of four components: a linear background trend, a seasonal cycle with 12-and 6-months periods, forcing terms decribed by a number of regressor variables and an auto-regressive com-ponent: Furthermore, the auto-regressive process in the DLM is computed within the model run together with the other parameters, not as a post-run correction as done in the MLR, and its uncertainties are carefully taken into account within the error propagation.In addition, the standard DLM implementation has time-varying (heteroscedastic) uncertainty distribution, when time-varying uncertainties are available.DLM was recently used to investigate stratospheric ozone trends in observations and models (Ball et al., 2017(Ball et al., , 2018)).A more detailed description of the DLM models and their implementation can be found in Laine et al. (2014).For a more comprehensive review of time-series analysis using DLM, refer to Durbin and Koopman (2012).
We fed the DLM model with monthly data, running 3000 samples where the first 1000 were considered as a warmup and discarded.We also tried 10000 realizations and 3000 as warmup with very similar results (not shown).We performed several sensitivity tests to determine the appropriate values of the initial model parameters, i.e., the degree of time-dependence of the linear trend and seasonal cycles, in order to allow a reasonable time-dependence without being unrealistic.The diff erent combinations of these values did not provide significant diff erences, so we kept the recommended values.
The linear trends are computed from the distribution of the fit samples µ t as the diff erence between the end and start dates of the considered period (delta=µ ), weighted by the number of the years.From the resulting delta distribution, the uncertainties associated with the trend are computed as the percentage of its positive (negative) values.This percentage can be interpreted as the posterior probability that the trend is positive (negative) between the considered dates.In this way, we do not make any assumption on the shape of the distribution of the trends.
3 Stratospheric N 2 O Columns and their Trends In the Tropics and above the lower stratospheric mid-latitudes, the N 2 O abundances are inversely proportional to the mean AoA (Andrews et al., 2001;Strahan et al., 2011;Galytska et al., 2019).The stratospheric N 2 O columns at mid-latitudes considered here      For WACCM, the strength of the N 2 O meridional dipole is globally reduced compared to ACE-FTS, with weaker and not significant negative N 2 O trends over the NH.However, WACCM-REFD1 performs better than WACCM-REFC1 over the SH, with stronger and significant positive N 2 O trends that reach 30 hPa, similarly to those obtained with ACE-FTS in the same region.This improvement is possibly related to the changes in the parametrization of the gravity waves (i.e., small-scale tropospheric waves that drive the BDC) in WACCM version 6 compared to version 4 that followed the increase of its cently, Strahan et al. (2020) used ground-based observations of nitric acid and hydrogen chloride to investigate hemispheric-dependent BDC changes in the stratosphere.Similarly, space-borne observations of stratospheric tracers are often used to investigate decadal changes in the BDC using, e.g., hydrogen fluoride (Harrison et al., 2016), ozone (Nedoluha et al., 2015) or N 2 O (Han et al., 2019).Measurements of stratospheric tracers are often used to calculate the mean Age of Air (AoA, Hall & Plumb, 1994).The mean AoA is a widely used diagnostic for stratospheric transport and is defined as the transit time of an air parcel from the tropical tropopause (or the surface, depending on the defini-tion) to a certain point of the stratosphere (Waugh & Hall, 2002).Engel et al. (2017) used balloon-borne observations of carbon dioxide and methane to derive mean AoA trends above the northern mid-latitudes in the mid-lower stratosphere.Engel et al. (2017) found positive but not statistically significant mean AoA trends over about 40 years (correspond- use ground-based measurements of stratospheric N 2 O columns obtained at four stations that are part of NDACC: Lauder (New Zealand, 45 • S), Wollongong (Australia, 34 • S), Izaña (Spain, 28 • N) and Jungfraujoch (Switzerland, 46 • N)(Zhou et al., 2019).The solar absorption spectra under clear-sky conditions with the ground-based FTIR measurements taken under the auspices of the NDACC allow the acquisition of long-term consistent data sets.The stations have been chosen at the mid-latitudes and subtropics where the observed BDC changes are the largest (e.g.,Strahan et al., 2020).At Jungfraujoch, measurements have been obtained from two spectrometers: an instrument developed at the University ofLiège (1984Liège ( -2008)), and a Bruker IFS 120HR(early 1990(early  's-present) (Zander et al., 2008;; Prignon et al., 2019).In this study, we use the spectra taken by the Bruker spectrometer to investigate the most recent period.Groundbased measurements of N 2 O profiles at Lauder started in 2001 with a Bruker 120HR spectrometer, replaced in 2018 (with 6 months overlap) by a Bruker 125HR(Strong et al.,     2008; Zhou et al., 2019).The Lauder station is particularly relevant as is the only FTIR site of NDACC located in the SH mid-latitudes.The Wollongong station has provided data for the SH subtropics since 1996.Solar spectra were measured with a Bomem instrument until 2007, which was then replaced by a Bruker 125HR(Griffi th et al., 2012).N 2 O profiles are also measured at the Izaña Observatory since 1999.This high-altitude station is characterized by excellent conditions for FTIR spectroscopy, with clear sky conditions for most of the year.Observations started using a Bruker 120M spectrometer and continued, since 2005, with a Bruker 125HR(García et al., 2021).The retrieval code for the N 2 O profiles is the for the Jungfraujoch, Lauder and Wollongong stations, and PROFITT9 for the Izaña station(Zhou et al., 2019).We consider stratospheric N 2 O columns between 12 and 40 km of altitute because the instruments at all stations are the most sensitive to the measured N 2 O profiles over this stratospheric region (not shown).The degrees of freedom for signal (DOFS), which quantify the vertical resolution of the measurement(Rodgers, 2000), vary largely between the stations.For N 2 O, the stratospheric DOFS between 12 and 40 km of the instruments in the SH are approximately 2, allowing the separation of two layers within the stratosphere.On the other hand, the stratospheric DOFS of the instruments in the NH are around 1.5 for Izaña, and 1 for Jungfraujoch, limiting the analysis to one stratospheric layer between 12 and 40 km.Thus, in order to perform a fair comparison, we compute one stratospheric N 2 O column between 12 and 40 km for all stations.In order to take into account the limited sensitivity of the FTIR measurements, we smooth the ACE-FTS data and the model output on the FTIR vertical grid using the FTIR averaging kernels as described inLangerock et al. (2015).
analysis.The chemical scheme explicitly solves for stratospheric chemistry, and includes 65 chemical species and 243 reactions (Prignon et al., 2019).ERAI and JRA55 have 60 levels up to 0.1 hPa, MERRA2 has 72 levels up to 0.01 hPa.The model setup, as well as the boundary conditions (including those for N 2 O ), are the ones used in Prignon et al. (2019), M2020 and Prignon et al. (2021).Readers are directed towards Chabrillat et al. (2018) for a detailed description of the BASCOE CTM and its driving by the ERAI, JRA55 and MERRA2 reanalyses.The ERA5 reanalysis is the fifth generation of reanalysis produced by the ECMWF and covers the 1979-present period, with a programmed extension back to 1950 (Hersbach two sensitivity tests with the BASCOE CTM driven by that reanalysis.To isolate the contribution of transport, the first sensitivity test consists of a fixed N 2 O run, i.e., a BAS-COE CTM simulation where N 2 O does not increase over time.We accomplished that by performing a BASCOE CTM run exactly as the ERA5 simulation but keeping the N 2 O volume mixing ratios at the surface fixed to their values at the beginning of the simulation (cst-N 2 O).Any N 2 O trend for the cst-N 2 O simulation is therefore due only to the eff ect of transport.The second sensitivity test is a perpetual year simulation that is complementary to cst-N 2 O, and consists of an experiment where the transport does not change over time(cst-dyn).In order to include a complete Quasi Biennial Oscillation cycle(QBO, Baldwin et al., 2001), we used the years 2006 and 2007 from ERA5.1 and ERA5, respectively.Those years are unusual (but convenient) because the QBO lasted exactly 24 months (see the zonal wind data at Singapore https://www.geo.fu-berlin.de/met/ag/strat/produkte/qbo/singapore.dat).We used the dynamics of the year 2006 to simulate even years and from the year 2007 for odd years.All the N 2 O changes simulated by cst-dyn are due to its constant increase at the surface.2.4 WACCMIn this study, we use two versions of WACCM: version 4 (Marsh et al., 2013; Garcia et al., 2017) and version 6 (Gettelman et al., 2019).WACCM version 4 (WACCM4) is the atmospheric component of the Community Earth System Model version 1.2.2 (CESM, Hurrell et al., 2013), which has been developed by the U.S. National Center of Atmospheric Research.It is the extended (whole atmosphere) version of the Community Atmosphere Model version 4 (CAM4, Neale et al., 2013).WACCM4 has a longitude-latitude grid of 2.5 • x1.9 • and 66 vertical levels from the surface to about 140 km altitude, with 1.1-1.75km vertical spacing in the stratosphere.The physics of WACCM4 is the same as CAM4 and the dynamical core is a finite volume with a horizontal discretization based on a conservative flux-form semi Lagrangian (FFSL) scheme (Lin, 2004).WACCM4 is not able to internally generate the QBO; thus, it is nudged towards observations of stratospheric winds (Matthes et al., 2010).In this study, we use the WACCM4 version included within the SPARC (Stratosphere-troposphere Processes And their Role in Climate) Chemistry-Climate Model Intercomparison phase 1 (CCMI-1, Morgenstern et al., 2017).In particular, we use the REFC1 experiments (WACCM-REFC1), which consist of simulations of the recent past (1960-2018) using state-of-the-art historical forcings and observed seasurface temperatures (Morgenstern et al., 2017).For N 2 O , the boundary conditions are prescribed using the forcing recommended by the CCMI (Eyring et al., 2013).Compared to the default WACCM4 version, WACCM-REFC1 includes important modifications of the treatment of heterogeneous chemistry and of the gravity waves parameterization, which ultimately improve the simulation of ozone in the Southern Hemisphere (Garcia et al., 2017).In this study, we use three realizations of the WACCM-REFC1 configuration for the 1985-2018 period.Version 6 of WACCM (WACCM6) is the extension to the whole atmosphere of version 6 of CAM that is part of version 2 of CESM (Danabasoglu et al., 2020).The default horizontal resolution of WACCM6 is 0.9 • x1.25 • latitude-longitude, with 70 levels in the vertical from the ground to around 140 km, with vertical resolution similar to WACCM4.The transition from WACCM4 to WACCM6 involved several changes in the physics and chemistry that are described in Gettelman et al. (2019).WACCM6 is part of the Coupled Model Intercomparison Project Phase 6 (CMIP6, Eyring et al., 2016), and is used in the CCMI-2022 activity (i.e., the successor of CCMI-1, Plummer et al., 2021).Within CCMI-2022, we use the REFD1 WACCM6 experiments (WACCM-REFD1), i.e., a suite of hindcast experiments for the recent past (1960-2018) used to compare with observations.The REFD1 experiments use the databases for historical forcings and observed sea surface temperatures developed for the CMIP6.The N 2 O emissions are specified following the CMPI6 recommendation for historical simulations, i.e., following Meinshausen et al. (2020).Although WACCM6 can internally produce the QBO, the REFD1 experiments require a nudged QBO towards observed winds to ensure synchronization with historical variability.In this study, we use one realization of the WACCM-REFD1 experiments for the 1985-2018 period.
is the eddy flux vector, and (v * , w * ) are the meridional and vertical components of the residual circulation, respectively.Overbars denote zonal means and prime quantities indicate deviations from it, while subscripts indicate partial derivatives.H = 7 km is the scale height, and z ≡ − Hlog e (p/p s ) is the log-pressure altitude, with the surface pressurep s = 10 5Pa.The S term is the net rate of change due to chemistry, defined as the diff erence between the production ( P ) and loss ( L ) rates S = P − L .The contribution represents the residual of the budget, i.e., the diff erence between the actual rate of change ofχ and the sum of the transport and chemistry terms on the right-side hand of Eq. 1.
regression tool(DLM, Alsing, 2019).DLM is based on Bayesian inference and provides a number of possible models to analyze time series.Each model is characterized by some unknown parameters, and the DLM computes the posterior probability distribution of those parameters using a combination of Kalman filtering and Markov chain Monte Carlo method.

Figure 1
Figure1shows the linear fits of the monthly stratospheric N 2 O columns (12-40 km) at the four FTIR stations, together with the initial N 2 O columns from the observations

Figure 1 .
Figure 1.Time-series of stratospheric N2O columns (12-40 km) from observations and models at four stations.Continuous lines show the linear fit obtained by the DLM regression, dashed lines depict the N2O column data.The color code is shown in the legend.The vertical error bars in panels a,b,e,f represent the standard error of the monthly mean.Panels a,b show Lauder, panels b,d show Wollongong, panels e,g show Izaña and panels f,h show Jungfraujoch.Panels a,b,e,f: DLM fits and data for FTIR and ACE-FTS measurements and the BASCOE simulation driven by ERA5.Panels c,d,g,h: DLM fits for all the datasets considered.The model and satellite data are interpolated to the longitude and latitude of the station, and vertically regridded to match the retrieval layering schemes.After the regridding, the data were smoothed using the FTIR averaging kernels.The colored shadings represent the uncertainties from the 2.5 and 97.5 percentiles of the distributions from the DLM.

Figure 2
Figure 2 shows distributions of the trend of the stratospheric N 2 O columns obtained from the respective linear fits over the common period 2005-2018.The N 2 O trends at the surface have already been compared for a number of FTIR stations (including Lauder, Wollongong and Izaña) against observations from flask samples, showing an excellent agreement (Zhou et al., 2019).
Figure3shows latitude-vertical cross sections of the linear trends of the N 2 O mixing ratios for the various datasets, over the 2005-2018 period.In order to reduce the sampling bias, the model datasets are sampled in space and time as the ACE-FTS measurements before the computation of the trends.We use the ACE-FTS measurements as a reference, because they encompass this period with global coverage and good stability(Bernath et al., 2020(Bernath et al.,  , 2021)).In the upper stratosphere above 10 hPa, the N 2 O trends from ACE-FTS are positive, with larger trends in the NH that are found significant at lower levels than in the SH.The ERAI-driven simulation qualitatively reproduces these patterns in the upper stratosphere, while the other model datasets diff er from ACE-FTS, especially ERA5.A common feature among all datasets is an increase in N2 O above the Equator in the upper stratosphere, around 5 hPa.At those altitudes of the tropical pipe, the upward transport of N 2 O by the residual circulation reaches its maximum (see M2020).In the mid-lower stratosphere below 20 hPa, ACE-FTS shows a clear hemispherical asymmetry (meridional dipole) in the N 2 O trends, with significantly negative values in the NH and significantly positive in the SH.Above the location of Jungfraujoch (the most northern vertical green line), the negative N 2 O trend detected by ACE-FTS in the mid-lower stratosphere is responsible for the disagreement with the FTIR observations discussed in the previous section, as the layer of the stratospheric N 2 O column encompasses regions of both positive (lowermost and upper stratosphere) and negative (mid-lower stratosphere) N 2 O trends.The meridional dipole is significant also over a shorter period (2005-2012, not shown) and corroborates a number of previous findings over that period using satellite measurements of HCl (Mahieu et al., 2014) and mean AoA derived from space-borne measurements of SF 6 (Haenel et al., 2015).In regions where the N 2 O abundances are larger than 100 ppbv, i.e., approximately below 10 hPa, the N 2 O linear trends are opposite to those obtained with its product NO 2 , because the two tracers are correlated by an inverse linear relationship (Plumb & Ko, 1992).Below 20 hPa, the N 2 O meridional dipole from ACE-FTS is consistent with the pattern of the decadal trends of NO 2 obtained from independent satellite measurements (Galytska et al., 2019; Dubé et al., 2020).The meridional dipole in the N 2 O trends derived from ACE-FTS is generally reproduced by the CTM simulations, with ERAI and ERA5 delivering trends that are most similar to the satellite measurements.Prignon et al. (2021) used the same simulations as the present study to investigate global stratospheric trends of total inorganic fluorine F y .The dipoles obtained here in the N 2 O trends from the ECMWF reanalyses are consistent with the opposite trends of F y for almost the same period (Prignon et al., 2021).
in the stratospheric N 2 O columns obtained from WACCM and the CTM simulations and from satellite measurements.In Section 4, using ACE-FTS as a reference, we study the global N 2 O trends in the stratosphere and focus on the diff erences in the trend patterns among datasets.In Section 5, we investigate the N 2 O TEM budget from WACCM version 6 and a BASCOE simulation in order to separate the impact of the residual circulation and mixing on the N 2 O trends.Finally, Section 6 concludes the study with a summary of the principal findings.

Table 1 .
Overview of the models and satellite measurements used in this study.

Table 2 .
Overview of FTIR stations considered in this study.
2.2 Spaceborne Measurements -ACE-FTSACE-FTS, onboard the SCISAT Canadian satellite, was launched in August 2003 on a high inclination (74 • ) low earth orbit (650 km) and is still in operation in 2022(Bernath     et al., 2005; Bernath, 2017).The ACE-FTS instrument measures the infrared absorptions from solar occultations between 2.2 and 13.3 µm with a spectral resolution of 0.02 cm −1 .This allows the retrieval of vertically resolved mixing ratio profiles for 44 molecules and 24 isotopologues from each measurement(Bernath et al., 2020).In our study, N 2 O profiles are filtered for outliers using the method described in Sheese et al. (2017) and are then vertically regridded to a constant pressure vertical grid using a mass-conservative scheme(Bader et al., 2017).For trend analysis, profiles are monthly averaged on latitude bins with 5 • spacing from pole to pole.
In order to compare the trend analysis of model simulations with those obtained by ACE-FTS, the model datasets are first re-sampled from their native temporal and spatial grids (model space) to match those of ACE-FTS (observational space).This is important in particular due to the low sampling of ACE-FTS -only 30 daily profiles due to the solar occultation method.The re-sampling is done by finding model output adjacent in time to each ACE-FTS profile (BASCOE and WACCM datasets used in this study have, respectively, 6 hourly and daily output) and then by linearly interpolating the model values in time and space at the profile geolocation.The re-sampled model datasets are then averaged over a month as done with ACE-FTS.2.3 BASCOE CTM and Driving ReanalysesIn this study, we use the BASCOE CTM driven by four dynamical reanalyses: the European Centre for Medium-Range Weather Forecast Interim reanalysis (ERAI, Dee et al., 2011), and its newer version ERA5 (Hersbach et al., 2020), the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA2, Gelaro et al., 2017), and the Japanese 55-year Reanalysis (JRA55, Kobayashi et al., 2015).In the following, we provide a brief overview of the BASCOE CTM and the ERAI, MERRA2 and JRA55 reanalyses, as more detailed information can be found in such companion studies: Chabrillat et al. (2018); Prignon et al. (2019, 2021) and M2020.Since ERA5 is not detailed in these publications, we provide a more detailed description.
In Eq. 3, the terms β i,t z i,t represent the contribution to y t from the regressors, where in DLM can vary with time (i.e., they are non-parametric).Their degrees of time-dependence are the unknown model parameters and are initially set by the user and inferred from the data during the model run.
).Above Lauder, the N 2 O trends obtained with ERA5 and JRA55 are in good agreement with the FTIR measurements, but are underestimated in WACCM-REFD1 (around 25%) with no particular improvement with respect to WACCM-REFC1.The ERAI simulation delivers the largest N 2 O trends, with more than 30% diff erence with respect to the FTIR measurements.At Wollongong, the N 2 O trend obtained with the FTIR measurements is the smallest because the N 2 O increase above that station is smoother compared to the other datasets.Interestingly, the N 2 O trend simulated by WACCM-REFD1is the closest to the trend obtained from the FTIR observations, while the trend obtained with ERA5 is almost twice as large.As for Lauder, the N 2 O trends obtained from ERAI are the largest at this station.Above Izaña, WACCM-REFD1 agrees remarkably well with the FTIR (diff erence around 3%), while the trend from ERA5 lies between the trends measured from FTIR and ACE-FTS, with around 20% diff erence compared to FTIR.