N 2 O Temporal Variability from the Middle Troposphere to the Middle Stratosphere Based on Airborne and Balloon-Borne Observations during the Period 1987–2018

: Nitrous oxide (N 2 O) is the fourth most important greenhouse gas in the atmosphere and is considered the most important current source gas emission for global stratospheric ozone depletion (O 3 ). It has natural and anthropogenic sources, mainly as an unintended by-product of food production activities. This work examines the identiﬁcation and quantiﬁcation of trends in the N 2 O concentration from the middle troposphere to the middle stratosphere (MTMS) by in situ and remote sensing observations. The temporal variability of N 2 O is addressed using a comprehensive dataset of in situ and remote sensing N 2 O concentrations based on aircraft and balloon measurements in the MTMS from 1987 to 2018. We determine N 2 O trends in the MTMS, based on observations. This consistent dataset was also used to study the N 2 O seasonal cycle to investigate the relationship


Introduction
Nitrous oxide (N 2 O) plays a critical role in Earth's atmosphere. In the troposphere, it absorbs infrared radiation and thus contributes to global warming. Because of this absorption capacity and its long lifetime of 118 ± 7 years (average value derived from [1,2]), N 2 O is the fourth most important greenhouse gas in the atmosphere [3]. Natural N 2 O emissions mainly come from bacterial nitrification and de-nitrification reactions in soils and the oceans. The primary anthropogenic sources are the use of nitrogen fertilizers in agriculture for food production, with minor contributions from the combustion of biomass and biofuels, traffic, and some industrial activities such as chemical production [4]. The primary atmospheric sink for N 2 O is photolysis in the stratosphere, which produces N 2 and O. However, a small fraction of N 2 O is destroyed by reaction with excited oxygen atoms (O( 1 D)). The latter reaction has two pathways, one being the primary pathway to generate NO in the stratosphere. NO can then play many important roles in the stratosphere. Of particular importance is its ability to catalytically destroy stratospheric ozone (O 3 ) in the cycle involving nitrogen oxides (NO x = NO + NO 2 ) ( [5] and references therein). Ravishankara et al. [6] showed that anthropogenic N 2 O emissions are currently the largest contributor to ozone-depleting substances' emissions. N 2 O is well mixed in the troposphere due to its stability and long residence time. It is transported into the stratosphere primarily through the tropics (Brewer-Dobson circulation) and shows a general decrease in concentration with altitude in the stratosphere due to the reactions cited above. The Brewer-Dobson circulation generates a latitudinal gradient; N 2 O stratospheric concentrations peak near the equator and decrease towards the poles. A difference in tropospheric concentration is also observed between the two hemispheres, where the Northern Hemisphere, with its larger terrestrial surface and population, is the primary source of N 2 O emissions [7].
Since 1970, the tropospheric N 2 O concentration measured at the surface has increased at a roughly constant growth rate [8]. It is expected to continue rising in line with increasing human population, as emissions are tied mainly to food production. Global mean N 2 O volume mixing ratios rose by 0.8 ppb yr −1 [9], resulting in the annual surface global mean N 2 O mole fraction reaching 336 ppb [9], compared to its pre-industrial value of 271 ppb [4,9]. In 2016, N 2 O contributed 0.19 W m −2 to global radiative forcing, approximately 10% of that for CO 2 [9]. As emissions of ozone-depleting substances (ODS) diminish in accordance with the Montreal Protocol and subsequent amendments, N 2 O, together with CH 4 and CO 2 , will become the main drivers of global stratospheric O 3 change in the second half of the 21st century.
Ground-based measurements have limited spatial coverage and do not cover the globe equally. In situ measurements from aircraft and balloon campaigns cover a broader area, with a dense observation network, in particular, due to the deployment of measurements onboard commercial aircraft. These observations lead to a more global picture of trace gas distribution with less potential bias due to restricted or preferred measurement areas. Furthermore, this has the advantage of providing direct in situ measurements over the vertical column, with no model based a priori, in contrast to column measurements from space or the ground. Direct in situ measurements also offer the advantage of providing a reliable approach to monitoring the temporal trend in N 2 O concentration, as the continuous improvement in measurement techniques gives access to accurate measurements. However, the improvement in techniques (or changes in techniques over time) can also introduce bias in the detection of trends. This bias is minimized by using similar N 2 O standards for various techniques. The statistical methods described here can also reduce errors.
In this paper, we assemble N 2 O aircraft and balloon measurements from research campaigns covering 1987-2018 for altitudes ranging up to the mid-stratosphere. Our objective is to use these observations to evaluate the N 2 O trend from the middle troposphere to the middle stratosphere (MTMS), and compare it with the trend obtained with surface and satellite observations. This paper is structured as follows. Section 2 describes the different datasets (aircraft, balloon) and the use of statistical analysis to provide quality control on the data. Section 3 presents and discusses the results for the temporal variability and the seasonal zonal mean values of N 2 O derived from aircraft/balloon measurements. We end with Section 4, which summarizes the results and puts the historical observed abundance in perspective with future projections.

Aircraft and Balloon Observations
The data we have compiled here represent the most extensive dataset among those available from research aircraft and balloon campaigns; they are listed in Appendix A. Almost 2.5 million measurements from 53 research campaigns have been collected from 1987 until 2018 at pressure levels ranging from 600 to 5 hPa. This unique dataset includes measurements from stratospheric balloon flights, the Space Shuttles, instrumented commercial aircraft, and several research aircraft campaigns. The research aircraft campaigns include measurements using the ER-2, Global Hawk and DC8 (managed by NASA Armstrong (Dryden) Flight Research Center, USA), WB57 (managed by NASA Johnson Space Center, USA), the Learjet (managed by Enviscope GFD, Germany) and HALO and Falcon (managed by DLR, Germany), the NSF/NCAR HIAPER Gulfstream GV (Broomfield, Colorado, USA, managed by EOL's Research Aviation Facility), and the Geophysica M55 (produced by Myasishchev Design Bureau, Zhukovsky, Russia). The measurements were performed using three kinds of instruments: (1) optical instruments (in situ spectrometers, remote sensing spectrometers, and radiometers), (2) online instruments, and (3) offline chromatographic techniques (using NOAA standard scale), listed in Table 1 (more information about campaigns is given in Appendix A). Figure 1 illustrates the spatial and seasonal coverage of all the gathered data. The global coverage shows that all the continents are represented; however, some have fewer observations than others. Overall, the measurements cover broad altitude and latitude ranges, with pressure levels reaching values as low as about 5 hPa (~35 km), mainly in the Northern Hemisphere. A greater coverage for all latitudes and seasons down to 40 hPa is seen in Figure 1b. We use the observations between 600 hPa (free troposphere,~4 km) and 5 hPa (midstratosphere) for this study. In winter and summer, the coverage of the latitudes between 0 • and 90 • S for pressures lower than 40 hPa is sparse compared to the other seasons. The observations mainly cover North America, a large part of Europe, New Zealand, and the southern part of South America, and are densest in the Northern Hemisphere.

Quality Control and Representativity of the Data
One of the major issues with inhomogeneous data is the inevitable presence of outliers. Outlier identification requires the ability to compare observations collected under similar conditions (same latitude and pressure). Such identification is routinely done by binning the data according to latitude and pressure (first finding a suitable compromise between bin size and the number of observations in each bin) and then detecting outliers in each bin. This approach is challenged here by the sparsity of the observations. To overcome Atmosphere 2023, 14, 585 4 of 23 this problem, we developed a different approach that avoids binning by using the high reproducibility of the concentration profiles.

Contact Person References
Optical Techniques ALIAS C. R. Webster [10] ALIAS-II AL L. Christensen [10] ARGUS N2 M. Loewenstein [11] ASUR H. Küllmann, A. Kleinböhl [12] ATLAS M. Loewenstein [13] ATLAS N2 James Podolske [13] ATMOS M. R. Gunson [14] DACOM G. S. Diskin [15] FIRS-2 K. Jucks [16] MIPAS-B F. Friedl-Vallon, G. Wetzel [17] MkIV G. C. Toon TRAC and HIRES T. Schuck, J. Williams [45] As a first check, we take advantage of the expected monotonic vertical profiles and use only the measurements made over a given location. For example, for in situ measurements, we only use observations made during the ascent or descent phase of the balloon/aircraft, and not those collected during altitude plateaus. Latitude changes during plateaus can sometimes be important, however, as they might potentially modify the N 2 O concentration at the same altitude. Some flights had to be split into several profiles.

Quality Control and Representativity of the Data
One of the major issues with inhomogeneous data is the inevitable presence of outliers. Outlier identification requires the ability to compare observations collected under similar conditions (same latitude and pressure). Such identification is routinely done by binning the data according to latitude and pressure (first finding a suitable compromise between bin size and the number of observations in each bin) and then detecting outliers in each bin. This approach is challenged here by the sparsity of the observations. To overcome this problem, we developed a different approach that avoids binning by using the high reproducibility of the concentration profiles.
As a first check, we take advantage of the expected monotonic vertical profiles and use only the measurements made over a given location. For example, for in situ measurements, we only use observations made during the ascent or descent phase of the balloon/aircraft, and not those collected during altitude plateaus. Latitude changes during plateaus can sometimes be important, however, as they might potentially modify the N2O concentration at the same altitude. Some flights had to be split into several profiles.
Next, we exploit the reproducibility of the profiles. Figure 2 illustrates N2O concentration profiles versus pressure and shows that they all have a similar shape, although with greater relative dispersion in the stratosphere. This reproducibility of the concentration profiles suggests that each can be expressed by the same shape (regardless of its amplitude) with minor changes. One can then considerably simplify the analysis by describing these profiles as a combination of characteristic shapes, hereafter called modes. In Appendix B, we show that the salient features of all profiles can be adequately described by a linear combination of only two modes. That is, the observed concentration profile ( ) of the k'th observation at pressure p can be approximated by the model ̂ ( ): Next, we exploit the reproducibility of the profiles. Figure 2 illustrates N 2 O concentration profiles versus pressure and shows that they all have a similar shape, although with greater relative dispersion in the stratosphere. This reproducibility of the concentration profiles suggests that each can be expressed by the same shape (regardless of its amplitude) with minor changes. One can then considerably simplify the analysis by describing these profiles as a combination of characteristic shapes, hereafter called modes.
In Appendix B, we show that the salient features of all profiles can be adequately described by a linear combination of only two modes. That is, the observed concentration profile c k (p) of the k th observation at pressure p can be approximated by the modelĉ k (p): where m 1 (p) and m 2 (p) are the two modes, and A 1,k and A 2,k are their respective amplitudes. The two modes can be interpreted as representative profiles such that the observed concentration is a latitude-dependent linear combination of them. The presence of two modes implies the existence of only two degrees of freedom in the observed profile shapes. This number of degrees results from a trade-off between the data quality and the observed shapes' diversity. Its low value is a consequence of the similarity of all the shapes displayed in Figure 2.
The two modes are displayed in Figure 2. Their amplitudes are arbitrary because they are scaled by A i,k . We estimate both by blind source separation [46], which is closely related to the simpler and better-known empirical orthogonal functions [47].
Let us stress that the modes are statistical and therefore have no immediate physical meaning. Nevertheless, mode 1 can readily be associated with a typical profile, whereas mode 2 expresses the correction to describe regimes with enhanced N 2 O concentrations in the stratosphere. Figure 3 shows the amplitude of both modes versus latitude and reveals a clear latitudinal dependence, with increasing scatter at high latitudes. As expected, mode 1 is dominant. However, mode 2, which captures regimes with relatively higher stratospheric N 2 O concentrations, increases rapidly at high latitudes. The sum of the two amplitudes is approximately constant because all concentrations must eventually reach the same value in the lower troposphere. Finally, we compare the observed concentration profile ( ) with the model ̂ ( from Equation (1) to locate outliers for each profile. We compute their difference and us the sum of squares as a global measure of discrepancy: Finally, we compare the observed concentration profile c k (p) with the modelĉ k (p) from Equation (1) to locate outliers for each profile. We compute their difference and use the sum of squares as a global measure of discrepancy: We normalize the value of J k to the number of observations to facilitate the comparison of profiles with different vertical extents. Hence, larger the J k , more the k th profile differs from the family of observed profiles. For each pressure, the distribution of J reveals a core of relatively small values with an exponential tail of large errors. In the following, we set the cutoff at 90th percentiles to retain the smallest values only. In doing so, we discard those observations whose profiles belong to the largest 10% of values of J. A visual inspection of these profiles confirms that they indeed show suspicious variations with pressure and/or contain anomalous peaks.
This pre-processing allows us to create a matrix of "typical" profiles binned according to pressure (between 600 and 5 hPa) for 1820 profiles. Next, for each large latitude band defining the high latitudes or polar (±  • N), midlatitudes (±  • N), and tropics (±30 • N), we create a profile and extract a standard deviation. Therefore, we create five profiles that allow us to sort the data set in terms of outliers and exclude particular dynamic cases such as tropical intrusions.
Following this, we process all measurements and classify them according to the five latitude bands. All data that are not within ±3 σ of the average profiles are excluded; they represent 2.6% of the total. These data are not only outliers but potentially also special dynamic cases such as tropical or tropospheric intrusions, stratospheric descents, etc., which would lead to biases in calculating the means. In total, 2,435,700 N 2 O measurements are extracted that way (97.4% of the original total) for all latitudes and pressures between 600 and 5 hPa.

Data Handling
From the curated dataset, we create a 3D grid of latitudes, pressures, and time with latitudes for South and North Polar areas (±  • N), northern and southern midlatitudes (±  • N) and tropics (±30 • ), and with 24 pressure levels (from 600 hPa to 5 hPa) and seasons of each year (1987-2018), i.e., 5 latitudes boxes × 23 pressure boxes × 4 seasons × 32 years as 14,720 "boxes." To take into account that some measurements are more precise than others in the same box, the instrumental error-weighted average is calculated following this equation: where n is the number of measurements in one box, w i ∝ 1/err 2 i is the normalized weight with ∑ n i=1 w i = 1, and x i is the N 2 O concentration for the measurement i associated with the instrumental error err i .
For each box, the standard deviation of the weighted average is calculated: These calculations allow us to extract the slope of the concentration versus time (Section 3.1) and the trend in ppb/yr for each latitude band and pressure level.
Additional insight can be gained by taking the N 2 O zonal mean over all the years. Boxes of latitude and pressure are created with latitude bins every 10 • , and with 60 pressure levels (from 600 hPa to 5 hPa) and four seasons (i.e., 18 latitude boxes × 59 pressure boxes × 4 seasons as 4248 "boxes"). Equations (3) and (4) are applied for each box with x i recalculated to the concentration of 2018 by applying a factor corresponding to the trend extracted in Section 3.1 as follows: where t is the time (in years) of the measurement. From these boxes, we estimate and discuss zonal means in Section 3.2.

N 2 O Trend in the UTLS
As explained in Section 2.3, N 2 O concentrations versus time are calculated for each pressure level and each of the five latitude bins (30 • or 60 • range) shown in the figure. The slopes of the concentration versus time plots (a linear trend is applied for the entire period) are extracted, taking into account the standard deviation of each bin, the statistical coefficient F (Fisher's test), and the critical t-value at 95% confidence. The slope in ppb/yr is retained only if the coefficient F is higher than the critical t-value. The more the F value exceeds the critical t-value, the more the trend can be considered linear. The F coefficient and the critical t-value are also shown in Figure 5. Taking into account data from 1987 to 2018 permits validation of the F-test. An example is represented in Figure 5 for a specified pressure range in the upper troposphere (from +20 to +50 hPa compared to the tropopause pressure; see next paragraph for an explanation of the pressure range) for each latitude band described above. exceeds the critical t-value, the more the trend can be considered linear. The F coeffic and the critical t-value are also shown in Figure 5. Taking into account data from 198 2018 permits validation of the F-test. An example is represented in Figure 5 for a speci pressure range in the upper troposphere (from +20 to +50 hPa compared to the tropopa pressure; see next paragraph for an explanation of the pressure range) for each latit band described above. Figure 5. N2O trend in the upper troposphere (from +20 to +50 hPa compared to the tropop pressure) versus time for the South Polar region (deep blue), southern midlatitudes (turquo tropics (red), northern midlatitudes (orange) and North Polar region (yellow). The error bars re sent the standard deviation for each box (0.25-year range and pressure level). For each latitude b the slope in ppb/yr is calculated by using linear regression, taking into account the standard de tion of each box; the standard deviation of the slope is also calculated (σ) along with the associ F value (Fisher's test) and the critical t-value at 95% confidence. The more the F value exceed critical t-value, the more the trend can be considered linear. Figure 6 shows the trend of N2O in ppb per year for all data selected between 1 and 2018 according to the latitude bands: North and South Polar regions (±[90-60]° northern and southern midlatitudes (± ° N) and tropics (±30°). The vertical axis resents the altitude in pressure relative to the pressure at the tropopause. The tropopa pressure according to latitude has been determined from studies of ERA-interim d from ECMWF [48]. The error bars represent the standard deviation of the slope for plot concentration versus time (see, e.g., Figure 5). The trends range between 0.8 ppb/yr in the upper troposphere (up to 350 hPa greater than the tropopause pressure) Figure 5. N 2 O trend in the upper troposphere (from +20 to +50 hPa compared to the tropopause pressure) versus time for the South Polar region (deep blue), southern midlatitudes (turquoise), tropics (red), northern midlatitudes (orange) and North Polar region (yellow). The error bars represent the standard deviation for each box (0.25-year range and pressure level). For each latitude band, the slope in ppb/yr is calculated by using linear regression, taking into account the standard deviation of each box; the standard deviation of the slope is also calculated (σ) along with the associated F value (Fisher's test) and the critical t-value at 95% confidence. The more the F value exceeds the critical t-value, the more the trend can be considered linear. Figure 6 shows the trend of N 2 O in ppb per year for all data selected between 1987 and 2018 according to the latitude bands: North and South Polar regions (±  • N), northern and southern midlatitudes (±  • N) and tropics (±30 • ). The vertical axis represents the altitude in pressure relative to the pressure at the tropopause. The tropopause pressure according to latitude has been determined from studies of ERAinterim data from ECMWF [48]. The error bars represent the standard deviation of the slope for the plot concentration versus time (see, e.g., Figure 5). The trends range between 0.8-1.1 ppb/yr in the upper troposphere (up to 350 hPa greater than the tropopause pressure) and 0.64-1.20 ppb/yr in the lower stratosphere (up to 150 hPa less than the tropopause pressure). The data in the stratosphere show more uncertainty, as illustrated by the larger error bar in this part of the atmosphere. Indeed, fewer measurements are available in the stratosphere compared to the troposphere. The average trend is 0.89 ± 0.07 ppb/yr (1σ) in the upper troposphere and 0.96 ± 0.15 ppb/yr (1σ) in the lower stratosphere. Taking into account the uncertainties (one sigma), the difference in the two trends is insignificant. The trend in the southern midlatitude (60-30 • S) band seems larger than the others, most visible for pressures relative to the tropopause up to 150 hPa. However, it is important to note that the southern midlatitudes are the least sampled, so lower statistics may also contribute to this difference in the trend. osphere compared to the troposphere. The average trend is 0.89 ± 0.07 ppb/yr (1σ) in the upper troposphere and 0.96 ± 0.15 ppb/yr (1σ) in the lower stratosphere. Taking into account the uncertainties (one sigma), the difference in the two trends is insignificant. The trend in the southern midlatitude (60-30° S) band seems larger than the others, most visible for pressures relative to the tropopause up to 150 hPa. However, it is important to note that the southern midlatitudes are the least sampled, so lower statistics may also contribute to this difference in the trend.  The trend according to WMO [9] mean surface data (0.80 ppb/yr) is represented by a black circle and for convenient visualization at +750 hPa pressure relative to the tropopause (WMO ground measurements: AGAGE in situ NOAA, flask and in situ, CSIRO, flask, WMO/GAW) [9]. ACE v4 mean (0.799 ± 0.024 ppb/yr) for latitude ranges ±60 • and altitudes between 5.5 and 10.5 km is represented by a purple circle at +170 hPa relative to the tropopause [49].
WMO-reported N 2 O average mixing ratio from ground-based AGAGE in situ (Global), NOAA flask and in situ (Global), and CSIRO flask (Global) data [9] is also represented in Figure 6 with a value of 0.80 ppb/yr. Similarly, the mean value of 0.799± 0.024 ppb/yr from the ACE-FTS instrument data on SCISAT [49] is plotted for a band of latitude between 60 • S and 60 • N and altitudes between 5.5 and 10.5 km, corresponding to a medium pressure   Figure 6 of 0.89 ppb/yr is used to calculate the N 2 O concentration for each measurement and adjusted to 2018 as explained in Section 2.3, Equation (5). Then, considering the adjusted datasets, instrumental error-weighted averages are calculated in latitude boxes of 10 • width (for all longitudes) and 60 pressure levels (from 600 hPa to 5 hPa). The dataset shows good coverage of latitudes, except for high southern latitudes (above 60 • S) in DJF, MAM, and JJA. N 2 O concentrations vary between 320 and 340 ppb throughout the troposphere. This observation is consistent with the location of N 2 O sources, mainly at the surface (biological sources from soil and water, and anthropogenic sources mainly agricultural soil and animals breeding) and sinks present in the stratosphere (photodissociation and reaction with excited oxygen atoms, O( 1 D)), see [50] and reference therein. As observed in the study of Kuttippurath et al. [12], which shows N 2 O zonal means for ASUR data, the influence of the stratospheric transport on the N 2 O zonal mean is also visible. Indeed, the N 2 O VMR (volume mixing ratio) in DJF in the northern latitude (>60 • N) stratosphere is lower (180 ppbv around 60 hPa and 10 ppbv around 10 hPa) compared to the other seasons (around 230 ppbv at 60 hPa for JJA), indicating diabatic descent of air in the polar vortex in the winter season (e.g., [51,52]). High concentrations in the lower tropical stratosphere from 100 to 20 hPa predominantly during the northern winter season (DJF) compared to the summer season (JJA) suggest an increase of the tropical upwelling during this season due to Brewer-Dobson circulation. A maximum in tropical upwelling in the DJF season was previously suggested based on trace gas observations and radiative-dynamical calculations ( [53] and references therein). The same references predict a minimum in upwelling in the JJA season, as also observed in Figure 7.

Discussion Relative to Atmospheric Circulation and Trends
Studies have shown that changes in the Brewer-Dobson circulation (BDC) im both long-lived and short-term trends in the variability of stratospheric chemical tr such as HCl and N2O. Recently, one of these studies identified an increase in the con

Discussion Relative to Atmospheric Circulation and Trends
Studies have shown that changes in the Brewer-Dobson circulation (BDC) impact both long-lived and short-term trends in the variability of stratospheric chemical tracers such as HCl and N 2 O. Recently, one of these studies identified an increase in the concentration of the long-lived trace gas HCl in the Northern Hemisphere (NH) midlatitude stratosphere from 2005 to 2011, despite well-documented decreases in surface emissions of organic chlorine-containing gases over this period [54]. A chemical transport model (CTM) driven by ERA-interim reanalysis meteorological fields suggested that this short-term HCl trend occurred over several consecutive years, transporting older stratospheric air characterized by the larger relative conversion of organic chlorine-containing source gases to HCl from the upper stratosphere to the lower stratosphere. With regard to N 2 O, the suggested enhanced downwelling branch of the residual circulation in the Northern Hemisphere (NH) transports more N 2 O-poor air from the upper stratosphere to the lower stratosphere [55] as discussed in Section 3.2. In addition to suggesting the modification of the NH circulation, this study also suggested a weakened downwelling and enhanced poleward flow in the Southern Hemisphere (SH), which brought more low-latitude air to the SH middle latitudes. Unfortunately, due to the lack of N 2 O measurements in the SH at some seasons, this part cannot be supported conclusively by our analysis.
Therefore, decadal-scale dynamical variability can have distinct and different impacts on hemispheric long-lived chemical tracers' variability and trends. Observed hemispheric asymmetry in stratospheric trends is also discussed in [56]. This work used 25 years of column observations from the Network for the Detection of Atmospheric Composition Change (NDACC), along with the above-mentioned Aura MLS observations and the CTM results driven by Modern-Era Retrospective analysis for Research and Applications Version (MERRA2). The results from this work showed extratropical variability with a 5-to 7-year period driven by interactions of the atmospheric circulation and the quasi-biennial oscillation in tropical winds. This previous "unrecognized variability" is large relative to hemispheric transport trends and may bias regression trends of stratospheric species.

Summary and Outlook
This paper presents the first compilation of the majority of existing N 2 O balloon and aircraft measurements performed between 1987 and 2018, ranging from the middle troposphere to the middle stratosphere. First, we pre-processed the data by blind source separation to exclude particular dynamic cases and outliers. This approach avoids the need for binning the data by latitude and longitude to identify anomalous profiles. With this dataset, we calculated instrumental error-weighted averages in boxes over a wide range of latitudes (North and South Pole, midlatitudes, tropics) and over 10 • latitude boxes for pressure levels ranging from 600 hPa to 5 hPa. We extracted trends between 1987 and 2018 (a linear trend is applied for the entire period) and revealed an increase in N 2 O concentration of 0.89 ± 0.07 ppb/yr in the upper troposphereand 0.96 ± 0.15 ppb/yr in the lower stratosphere. The growth of this potent greenhouse gas, as observed at the ground and remotely by satellites, is confirmed in situ in the UTLS, the most important region of the atmosphere for the Earth's radiative balance. We extracted the zonal mean from the whole dataset and illustrated its evolution with seasons DJF, MAM, JJA, and SON. The N 2 O zonal mean highlights, as explained in other studies, the atmospheric circulation, with an increase in tropical upwelling during DJF and stratospheric polar descent during northern (or boreal) winter.
With the decrease in halocarbon concentrations, N 2 O emissions will become the primary ozone-depleting substance in the future [6]. However, the impact of N 2 O depends on the levels of CO 2 and, to a lesser extent, CH 4 [57,58]. The reactivity of N 2 O depends largely on the temperature of the stratosphere, and increasing CO 2 (and CH 4 ) cools the stratosphere [59]. Therefore, it is difficult to quantify the impact of increasing N 2 O on ozone depletion without accounting for CO 2 and CH 4 . Figure 8 shows the concentration of N 2 O in the troposphere between 1987 and 2018 from aircraft and balloon measurements from our study and from Representative Concentration Pathways (RCP) scenarios [60]. The N 2 O concentration with an increase of 0.89 ppb/yr (as observed in the troposphere in our study) is also shown. If N 2 O emission levels remain constant, the concentrations follow the RCP 6.0 or 8.5 scenarios. According to the study by Revell et al. [58] (in Figure 1), the CO 2 and CH 4 levels with the RCP 6,0 scenario result in ozone depletion potentials (ODP) of 0.019 for N 2 O and, therefore, comparable potential as the actual ODP (0.017) as suggested by [6]. Only the anthropogenic emissions part is controllable, and most of this comes from fertilizers used in agriculture, which are difficult to substitute. Models can address the question of the anthropogenic component of the observed N 2 O increase. In addition, climate change may also affect the natural part of the emissions, which is difficult to predict. The role of the "changing" Brewer-Dobson circulation (BDC) in affecting the transport, mixing, and chemistry of long-lived trace gases must be assessed for quantifying the future ozone recovery and, therefore, the estimated return date to a condition before the 1987 Montreal Protocol on Substances that Deplete the Ozone Layer was established [61]. Recently, Minganti et al. [62] examined the impact of the BDC on the N2O budget in a chemistry-climate model (CCM) and CTM driven with dynamical reanalysis. This analysis used the transformed Eulerian mean (TEM) framework, specifically using the tracer continuity equation derived from the TEM formula to examine the N2O climatological (2005-2014) seasonal means and climatological annual cycles of the vertical residual advection and the horizontal mixing in these models. A follow-up study evaluated the N2O rate of change to understand the stratospheric Brewer-Dobson circulation in a CCM [63]. This study used both FTIR ground-based and ACE-FTS observations. Our work provides for the robust inclusion of MTMS airborne and balloon-borne observations to understand further the dynamical processes that control BDC and how these processes will affect N2O distributions in a future climate  The role of the "changing" Brewer-Dobson circulation (BDC) in affecting the transport, mixing, and chemistry of long-lived trace gases must be assessed for quantifying the future ozone recovery and, therefore, the estimated return date to a condition before the 1987 Montreal Protocol on Substances that Deplete the Ozone Layer was established [61]. Recently, Minganti et al. [62] examined the impact of the BDC on the N 2 O budget in a chemistry-climate model (CCM) and CTM driven with dynamical reanalysis. This analysis used the transformed Eulerian mean (TEM) framework, specifically using the tracer continuity equation derived from the TEM formula to examine the N 2 O climatological (2005-2014) seasonal means and climatological annual cycles of the vertical residual advection and the horizontal mixing in these models. A follow-up study evaluated the N 2 O rate of change to understand the stratospheric Brewer-Dobson circulation in a CCM [63]. This study used both FTIR ground-based and ACE-FTS observations. Our work provides for the robust inclusion of MTMS airborne and balloon-borne observations to understand further the dynamical processes that control BDC and how these processes will affect N 2 O distributions in a future climate

Appendix B
To extract the modes of the concentration profiles, we rely on blind source separation [46], which offers a powerful framework for describing multipoint observations that exhibit coherent variations. The name "blind source separation" refers to the fact that the concentration profiles are decomposed into a linear superposition of pressure-dependent modes (or sources) and their amplitudes, both of which are unknown a priori. These modes are inferred from the data (as in principal component analysis) and are not imposed a priori as with Fourier modes. Blind source separation is used in many disciplines, such as acoustics, where it helps identify different sources of sound from their mixture.
The set of modes we obtain by blind source separation is not unique and so the solution depends on the constraints we impose on these modes. Here, since we are dealing with concentrations, which cannot be negative, we force the modes m i (p) ≥ 0 and their amplitudes A i,k ≥ 0 to be positive. To enforce positivity, we use a Bayesian technique named Bayesian positive source separation [121].
An important step in blind source separation is the determination of the number of modes. This can be done in different ways. One consists in determining how many of them are required to reconstruct the salient features all the observed profiles. Here, with one mode only we can describe 69.0% of the variance of the observations. The second one describes an additional 26.5%. The other modes describe the remaining 4.5% of the variance and, therefore, can be neglected. Additionally, since our Bayesian method is probabilistic, we find that modes 3 and following have considerably larger confidence intervals than modes 1 and 2, and therefore should not be considered. That is, they become increasingly unstable and sensitive to minor details in the data.
To perform blind source separation, we store our data in a rectangular matrix, in which rows correspond to pressure levels and columns to individual records. This matrix has many data gaps because each record has a different pressure range. Unfortunately, our mode decomposition cannot handle sparse data. To overcome this problem, we start by interpolating them, using missing imputation [122]. Missing imputation is routinely used in statistics to identify missing values in a self-consistent way. Here we use a variant of the method that is closely related to blind source separation because it relies on the consistency of the concentration profiles to fill in missing data [123]. The method is iterative: it determines the modes, uses them to fit the profiles and replace missing data, and starts over again to estimate the missing modes from the augmented dataset (observations + interpolated data). Validation tests confirm that the method performs well thanks to the few (two) degrees of freedom that are present in the concentration profiles.
To summarize, we start by using missing imputation to fill in all data gaps. Following this, we use the full dataset (observations + interpolated data) to estimate the modes. The interpolated data are thereafter ignored.