The FTIR interferometers record interferograms from sunlight that are Fourier-transformed into solar absorption spectra. Trace gas abundances, such as ozone abundances, are retrieved from these spectra by using line-by-line spectral fitting softwares (SFIT4, , or PROFFIT, ), including radiative transfer models. Forward model inputs include spectroscopic parameters, climatological a priori information on trace gases concentrations, and 6-hourly pressure and temperature profile information from NCEP. The pressure and temperature-dependences of the ozone line-shapes enable us to retrieve low-vertical resolution profiles, with four to five distinct degrees of freedom for signal (DOFS), spanning the troposphere and stratosphere from approximately 0–48 km .

In this study, we use FTIR ozone data sets from the Network for the Detection of Atmospheric Composition Change (NDACC) (https://ndacc.larc.nasa.gov/, last access: 8 June 2026). This network gathers the data sets of 160 ground-based instruments monitoring various components of the atmosphere from 73 active sites around the globe since 1990. This network enables detection of long-term trends, validation of other data sets and models . There are six NDACC FTIR instruments within the Arctic: Ny-Ålesund, Eureka, Kiruna, Harestua, St-Petersburg and Thule, see Table . These instruments are Bruker high-resolution (<0.005 cm⁻¹) spectrometers. The retrieval strategy used at all these sites is standardized by the InfraRed Working Group (IRWG) . It has been recently updated from the previous version described in details in to an improved strategy (IRWG2023), based on the HITRAN2020 molecular spectroscopic database , specific spectral microwindows (around 1000 cm⁻¹) fitted to avoid interference with water vapor lines, an updated regularization scheme (Tikhonov) and an updated a priori (WACCMv7 IRWG, ). More details on this new strategy used here can be found in the Appendix of , where it was shown to reduce biases with other instruments in Lauder, New Zealand from 1 %–3 % for all partial columns as well as to reduce drifts.

In addition, we consider a new ozone time series obtained by applying a new retrieval (in the 3040 cm⁻¹ region following the strategy of and ) to spectra recorded by the Sodankylä instrument that is part of the Total Carbon Column Observing Network (TCCON). The resulting vertical profiles contain lower DOFS of approximately 2.5, concentrated on the stratospheric layers, see Table .

For all time series, the uncertainty on ozone partial columns is obtained from the propagation of the retrieved profile uncertainties. Random and systematic uncertainties are themselves obtained using optimal estimation . The random error of partial columns additionally contains a smoothing error estimated from the WACCMv7 covariance matrix at each site. In Table we provide the mean of the obtained uncertainties in percent for each partial column considered in this paper and the total column of ozone (TCO). The partial columns are based on FTIR DOFS that are explicitly given here for NDACC products and for the Sodankylä product.

Ozonesondes are small, light-weight devices flown on weather balloons that measure the vertical profile of ozone based on the titration of ozone in a neutral buffered potassium iodide sensing solution, with a precision better than ± (3–5) % and an accuracy of approximately ± (5–10) % for up to 30 km altitude . However, changes in preparation and operation procedures, manufacturer type, sensing solution strength, and processing might result in biases in the time series, compromising any reliable ozone trends assessment. Therefore, a homogenization activity, correcting for those biases following recommendations in and has been undertaken, with all the homogenized ozonesonde data stored and described within the framework of the Tropospheric Ozone Assessment Report Phase II (TOAR-II) Focus Working Group HEGIFTOM (Harmonization and Evaluation of Ground-based Instruments for Free-Tropospheric Ozone Measurements, see also ). In that study, the data from the Canadian Arctic sites Resolute, Alert, and Eureka and the European Arctic sites Scoresbysund, Ny-Ålesund, Sodankylä and Lerwick have been used. More details on the specific homogenization steps needed to correct those data sets are provided in for Resolute, Alert, and Eureka and in for Scoresbysund, Ny-Ålesund, and Sodankylä.

In this study, we cap sondes profiles at 26 km so that the mid-stratospheric column contains at least 60 % of all measured profiles at all sites (in some sites such as Alert and Resolute, less than 50 % to 40 % of profiles reach up to 30 km because the sondes balloon burst before that altitude). We sum profiles over the partial columns defined in Sect. . Random measurement uncertainties on profile points are also propagated to obtain partial columns uncertainties. When a profile doesn't provide uncertainties, we use the mean uncertainties of other profiles from the same site. Extreme outliers are found in the data after summing the profiles into partial columns. They are removed by applying a very loose percentile filter: for q1 and q3 the 25th and 75th percentiles, we remove datapoints lying beyond q3+8(q3-q1) or below q1-8(q3-q1) for each partial column time series.

Brewer and Dobson spectrophotometers use sunlight in the UV range (approximately 305–340 nm) to extract the total column of ozone by comparing relative intensities for pairs of selected wavelengths. All Brewer and Dobson total column data sets used in this study are obtained from the World Ozone and Ultraviolet Radiation Data Centre (WOUDC), one of six World Data Centres part of the Global Atmosphere Watch programme of the World Meteorological Organization. It provides total column ozone and vertical profile data from over 500 registered stations (https://woudc.org/, last access: 8 June 2026). We use Brewer total column measurements from Resolute, Sondrestrom, Alert, Eureka, Vindeln, Oslo, Andoya and Dobson total column measurements from Lerwick, Barrow, Reykjavik, Fairbanks and Vindeln. They are given as daily measurements obtained from several measurements averaged together with a standard deviation estimate. When the standard deviation is not provided, we use a generic random error of 1 % for direct sun observation (DS) and 5 % for other types of measurement (zenith-sun ZS, focused-moon FM) see e.g., . The Brewer in Alert has calibration issues concerning ZS measurements so these are excluded from the dataset. For all Brewer measurements we restrict to airmass factors μ<3.5 for single monochromator instruments (MKII, MKIV and MKV). Finally, most stations have measurements taken by several instruments, so we average all same-day observations with a weighted mean.

While Dobson and Brewer data sets only provide a total column measurement of the ozone abundance, ozonesondes and FTIR present vertically-resolved profiles. Since this vertical resolution only contains four to five DOFS for the FTIR, we divide the troposphere and stratosphere into four layers (see Table ) to obtain four partial columns of ozone, each containing approximately one DOFS for the FTIR (see Table ). The specific choice of boundaries for these layers reflects the need for merging FTIR with sonde data sets.

Since we work with fixed altitudes defining partial columns boundaries, we do not follow the tropopause variations in time. Note that since FTIR provides low-resolution profiles, a clear-cut disentanglement of tropospheric and lower-stratospheric measurements is impossible and some mixing is necessarily present. The choice of 0–8 km reflects the averaged Arctic tropopause limit while satisfying the constraint on FTIR DOFS.

In addition to the partial columns defined in Table , we consider an alternative lower stratospheric column from 10–17 km in Sect. to ease comparison to satellite products, plus another upper stratospheric column from 32–48 km in Sect. to better compare with trend literature that often considers the upper stratospheric layer higher up.

From those ozone columns we first calculate daily mean time series, and from those we obtain monthly mean time series. We then use the monthly mean time series to calculate relative (Eq. ) and absolute (Eq. ) anomalies: 1anommonthx,yeary=O3monthx,yeary-O3monthxO3monthx;2abs.anommonthx,yeary=O3monthx,yeary-O3monthx; with 3O3monthx=1n+1∑y=start yearstart year+nO3monthx,yeary, the ozone mean for each month of the year averaging over n years of each data set, from start year to start year+n. Using anomalies when merging different data sets instead of monthly means removes the issues related to merging biased data

We use comparisons with two different satellite data sets, IASI-CDR and MEGRIDOP, to investigate the quality of all the ground-based time series described above and to evaluate the presence of drifts in satellites for the whole Arctic zonal mean (i.e., a weighted mean of all ground-based stations datasets within the 60–90° N region), both in the total column and for each partial column defined in Sect. .

The IASI-CDR dataset is a homogeneous ozone Climate Data Record (CDR) based on the Infrared Atmospheric Sounding Interferometer observations recently produced by EUMETSAT on behalf of AC SAF (AC SAF, 2025). The IASI-CDR O3 product has been validated in , who reported small total ozone biases (< 1 %–2 %), tropospheric differences of 10 %–12 %, and long-term drifts below 3 % per decade. It accurately captures seasonal and interannual variability and highlights a decrease in tropospheric ozone, notably in the tropics and Europe. Here, IASI-CDR O3 total columns are obtained from the combined AERIS Level-3 monthly IASI-CDR Metop-A (2007–2013) and Metop-B (2013–2024) products, called hereafter IASI-A + B . Partial columns are derived from merged monthly mean gridded profiles computed from the AERIS Level-2 daily IASI-CDR Metop-A and B products as in , called IASI-AB hereafter. Both data sets cover 2007–2024 and we use daytime observations only.

The MErged GRIdded Dataset of Ozone Profiles (MEGRIDOP) was generated using data from six limb and occultation satellite instruments (OSIRIS, GOMOS, MIPAS, SCIAMACHY, Aura MLS, OMPS-LP SNPP). We use the Level-3 gridded monthly time series from 2001 until 2024, which has a 10° lat. × 20° lon. horizontal resolution and a vertical coverage from 10–50 km.

Our aim here is not to validate the satellite products but rather to compare satellite and ground-based time series to diagnose potential problems related to the calculation of trends from those time series. Therefore, we do not time-collocate satellites and ground-based measurements but instead we compute drifts by comparing monthly deseasonalized relative anomalies, that will later be used for trends computations. The time series of satellites are spatially collocated within their respective spatial grid with the ground-based instruments locations listed in Table . To compare satellite and ground-based time series, we define the difference of anomalies in percent: 4diffsat-GBi=anomsati-anomGBi⋅100%, from which we obtain the relative bias and the scaled mean absolute deviation (MAD_s) between the two time series (scaling with 1.4826 gives an equivalence to the 2σ of Gaussian statistics): 5bias=mediandiffsat-GBi;6MADs=1.4826⋅mediandiffsat-GBi-bias. We then apply a robust linear regression (Theil-Sen method, ) on the difference diffsat-GBi (Eq. ) to obtain the trend of this difference, i.e., the drift and its associated error, as shown in Fig. for the Vindeln Brewer against IASI-A + B ozone total column.

The drift is estimated as the median of the slopes of all lines connecting all possible pairs of points. The standard Theil-Sen confidence interval estimates assume the time series have no autocorrelation, but by computing the autocorrelation on the regression residuals (as the Pearson correlation coefficient between the residuals at t and at t+1(lag-1)), we find that 13 % of our data sets have an autocorrelation comprised between 0.2 and 0.35 in absolute value. To rigorously account for this small autocorrelation, we have therefore applied the block bootstrap method to evaluate the confidence intervals of our estimated Theil-Sen drifts . We have used 1000 bootstrap samples and a block size of n1/3, where n is the length of the dataset. The Theil-Sen method was applied on each bootstrap sample. The 2σ-error estimate given for each drift value corresponds to the 95 % confidence interval, calculated by multiplying the square root of the bootstrap estimate of variance by z=1.96, i.e. the inverse of the standard normal cumulative distribution function FN(z)=α/2, where α=0.95.

We make the assumption that problems in individual stations data sets can be identified by comparing to the two satellite data sets, while drifts in individual satellite dataset can be identified with combined ground-based data sets. In Sect. , we validate each individual ground-based dataset by detecting outliers in the drifts with respect to satellites, and then in Sect. , we evaluate satellites by computing their Arctic zonal mean drift with respect to the weighted mean of all validated ground-based time series.

MEGRIDOP is based on Limb satellites that do not measure in the troposphere, so ground-based measurements of the tropospheric column and the total column can only be compared to IASI-CDR (see Fig. for a visual representation of the vertical coverage of profile data sets versus the chosen partial column layers). Moreover, because MEGRIDOP only starts at 10 km, we consider an alternative lower stratospheric column from 10–17 km. This alternative lower stratospheric partial column can be easily computed and still retains enough DOFS for the FTIR (see Table ). The reason why we selected 8–17 km as our main lower stratosphere column is because we want to be able to compare total column trends to the sum of partial column trends.

We do not identify any outliers in the total column ground-based time series. We find all drifts lay within |1.6%perdecade| (see Fig. ). Only the drifts in Fairbanks and Kiruna are at the limit of 2σ significance, reaching respectively (-1.17±1.16) % per decade and (+1.22±1.15) % per decade. Although it might indicate potential issues in those timeseries around 2007, we do not exclude them from our trend analysis, as these drift values are small and we will in fact consider the full 2000–2024 period for trends.

In the troposphere, IASI-CDR exhibits a significant negative drift of at least -5 % per decade with seven of the ground-based instruments (see Fig. ). The Scoresbysund sonde stands out as the only significant positive drift of IASI, signaling an issue with this ground-based dataset. We checked that this large drift is not due to a different of time-sampling between the sonde data sets and the satellites: applying different filters on the minimal number of sonde measurements per month doesn't change the drifts values.

Turning to the stratospheric column drifts of both IASI (on the 2007–2024 period) and MEGRIDOP (on the 2001–2024 period) with respect to all individual ground-based instruments in Fig. , we find that the Scoresbysund sonde also stands as an outlier in the lower and mid-stratosphere for both satellites. The drift is associated with a negative offset in the Scoresbysund ozone concentrations at most altitude levels in the ozonesonde time series since 2016 with respect to the previous years. Indeed, we have verified that the Scoresbysund's sonde dataset does not show any significant drift with respect to MEGRIDOP over the prior 2001–2015 period, where we found a drift of approximately 4 % per decade in the 10–17 km layer and of approximately 2 % per decade in the 17–26 km layer, both non-significant. This drop in 2016 coincides with a change of ozonesonde pump battery and pump temperature sensor types, possibly responsible for the lower recorded pump temperatures (around −10 K), and a radiosonde type change, creating a possible offset in the atmospheric pressure measurements (switch from pressure sensor to GPS height-derived pressure measurements). Too low pump temperatures might point to freezing solutions and too low signal readings, as noted at another ozonesonde site , and the radiosonde pressure offset might shift of the entire profile with +1.5 hPa at mid-stratospheric pressure levels. A total column ozone drop-off of -5.6 % with respect to OMI satellite overpass measurements has been mentioned for Scoresbysund around 2016 (change of ozonesonde serial batch number) in , but the operational, non-homogenized, time series was used in that study. Therefore, at least a part of this drop-off is due to the fact that a -3 % to -4 % ozone bias correction has been implemented in the vertical profiles (transfer functions defined in ) of the non-homogenized time series from 2016 onwards only, although it should also have been applied to earlier parts of the time series (e.g. from mid 2001 to 2015), as it has been done in the homogenized time series used here. Unfortunately, the homogenization did not seem to resolve all issues occurring around 2016, which need further investigation and the development of adequate correction algorithms, so we remove the Scoresbysund ozonesonde dataset from our study.

The Resolute sonde also appears as an outlier in MEGRIDOP's drifts for the lower and mid-stratosphere but not in IASI-CDR's drifts. By comparing the drifts on the same time period (2007–2024), the MEGRIDOP's drifts at Resolute disappear, see Fig. . In fact, we see a progressive diminution of the drift that becomes non-significant starting from 2005. This is probably the signal of a jump in the sonde dataset possibly due to instrumentation changes. Recalibrations in the data sets to account for these various changes have already been performed in Resolute (see ) but additional jumps cannot be excluded. Despite these recalibrations, it was found in Fig. 17 of and Fig. 3 of that the Resolute sonde exhibits stronger significant negative trends in the lower stratosphere than other sondes in the Arctic (except for the Churchill sonde that lies equatorward). To avoid effects of this potential jump, we consider the Resolute sonde dataset only starting from 2005.

In the upper stratosphere (26–48 km, Fig. ), IASI-CDR possesses small negative drifts everywhere except at Kiruna, where it shows a singular significant positive drift above 3 % per decade. The drift of MEGRIDOP in Kiruna doesn't particularly stand out on the 2001–2024 period, but if we restrict both satellites to the same 2007–2022 time period (Kiruna time series stops in 2022, see Table ), we observe a similar pattern where all drifts are non-significant and within 3 % per decade except in Kiruna where they reach 3.65±2.97 % per decade for IASI-CDR and 4.92±2.58 % per decade for MEGRIDOP, see Fig. . There are no records of possible issues with the Kiruna FTIR time series and visual scrutiny of its monthly mean and anomalies time series doesn't reveal obvious jumps. As the drift value with MEGRIDOP using the full time series (Fig. ) is comparable to other FTIR stations (although significant at Kiruna), we retain Kiruna for our trend analysis on the full time period.

Finally, in the total stratospheric column (10–50 km, Fig. ), IASI-CDR does not exhibit any significant drift except with the FTIR at Sodankylä. That time series is retrieved from a different spectral range than other NDACC FTIR products but there is no trace in previous studies of a potential drift due to this method of retrieval . It is also the only time series that starts in 2012 so the starting date for IASI-CDR comparison is different from all other data sets.

Having set aside ground-based time series with identified problems, we average all remaining data sets by a weighted mean (weights are given by the inverse squared uncertainties), and compare this average with the mean of satellites time series at the site locations. The resulting zonal mean drifts of IASI-CDR and MEGRIDOP are presented in Fig. .

The zonal mean drift of IASI-CDR total column is of -0.62±0.94 % per decade. This is a very small uncertainty and it shows that the IASI-CDR Level 3 AERIS total column product doesn't show a drift over its full time series.

In the troposphere we find a negative significant drift of IASI-CDR of -3.47±2.54 % per decade. Since the sensitivity of IASI in the troposphere is low, with an average number of DOFs <0.45, the a priori has a strong influence on the retrieved measurements in the troposphere. Degrading the ground-based data sets to the IASI sensitivity by smoothing their profiles with the IASI averaging kernels was found to shift the IASI drift by -2.3 % per decade on average in the Arctic troposphere in . However, the smoothing formula must be performed on each individual profiles: the averaging kernel are non-linear objects and smoothing averaged monthly data is not equivalent to averaging individually smoothed profiles, and can introduce additional errors. We therefore do not smooth the ground-based data sets here. This means that we probably underestimate the tropospheric IASI drift by 2 %. Note that the much smaller drift obtained by in the Arctic troposphere of −1.5±1.8 % per decade is biased due to the use of the Scoresbysund sonde dataset in the validation, see the Table S1 of with individual stations drifts. By excluding this dataset and including FTIR, we find a larger and significant drift of the IASI Arctic troposphere. A more detailed validation using time-collocated pairs of smoothed Level-2 measurements is necessary to evaluate the exact amplitude of this drift and whether it represents a real stability issue.

IASI-CDR doesn't show any significant drift in the lower, middle and total stratosphere. In the lower stratosphere the individual drifts are all within |5%perdecade|, with a zonal mean drift of 2.25±3.17 % per decade. In the middle and total stratosphere individual drifts lay within |3%perdecade|, with a zonal mean drift of -1.19±2.26 % per decade and -0.79±1.12 % per decade, respectively.

The MEGRIDOP data shows a positive drift with respect to the zonal mean of all ground-based instruments in the lower and upper stratosphere with drifts of 2.76±1.77 % per decade and 1.97±1.18 % per decade, respectively. The smallness of the uncertainties reinforces our assumption that the zonal mean drift captures the true satellite drifts, while averaging out individual ground-based instruments errors and drifts.

In the mid-stratosphere, the zonal mean drift of MEGRIDOP is only 0.27±0.96 % per decade while all individual drifts lay within |2.3%perdecade|.

Finally, in the total stratospheric column, MEGRIDOP's zonal mean drift is slightly positive significant: 0.88±0.73 % per decade. All individual drifts are within |2.1%perdecade|. The smallness of the uncertainty is here also remarkable, but is expected to be smaller in MEGRIDOP than for IASI-CDR since the time period of comparison is more extended.

The Scoresbysund sonde is strongly negatively drifted. The drift is probably associated with the many instrumental changes around 2016 that cannot be fully corrected for. This is important as this sonde was used in the past for validation of satellites whose drift could have been overestimated or underestimated accordingly, as in . We don't use this time series in our trend analysis.

We calculate trends based on merged data sets obtained from weighted means of ozone anomalies (Eq. ) time series, see Fig. from an example with the total column anomalies of Canada. All the resulting merged data sets are available on the BIRA-IASB repository . Starting from N different anomalies data sets, anomα, their weighted merging is calculated as: 7anomω-m=∑α=1Nωαanomα∑α=1Nωα. The weight used for merging is the inverse square of the anomalies errors, ωα=1/(Δanomα)2. Since systematic errors are affecting all values of the timeseries in the same way, we ignore them when considering anomalies and we only propagate random measurement uncertainties (considered as statistically independent) into the daily and monthly means of ozone columns and the monthly ozone anomalies. Starting from the individual measurements random uncertainties of the ozone timeseries ΔO3individual, we calculate the uncertainties on the daily means ΔO3day, where Nday is the number of measurements in that specific day, and then we further propagate the random error to the monthly mean to obtain ΔO3month, with Nmonth the number of days of measurement within that month: 8ΔO3μ={day or month}=1Nμ∑λ=1NμΔO3λ2,withλ={individual or day}respectively. Finally, the error on the monthly relative anomalies (Eq. ) is given by: 9Δanommonthx,yeary=1O3monthx×ΔO3monthx,yeary2+O3monthx,yeary×ΔO3monthx/O3monthx2. The random error on relative anomalies is given for each instrument and column in Table in percent.

In this section, we present the regression model and the proxies used for calculating ozone trends in the Arctic. We then analyze for each partial column the contribution of each proxies to the coefficients of determination, R2. Finally, we perform a sensitivity analysis to one of the proxies, the volume of polar stratospheric clouds.

Long term trends in Arctic stratospheric ozone due to changes in ozone depleting substances are expected to be small (within a few % per decade) while the natural ozone variability is especially high in the Arctic . This means a simple linear regression is not sufficient to detect long-term trends. In this work, trends are calculated with a multiple-linear regression (MLR) using nine different proxies summarized in Table . These proxies try to account for the natural variability of ozone, thus reducing trends uncertainties. The proxies are similar to those used by , except that for the processes included in the LOTUS MLR model , namely Solar cycle, QBO, and ENSO, we used the LOTUS prescribed data sets made publicly available within the OREGANO project (https://www.iup.uni-bremen.de/OREGANO/proxydata/, last access: 8 June 2026). For Arctic Oscillation (AO) and Brewer-Dobson Circulation (BDC) proxies, we also use data sets provided within OREGANO, for which the accumulation during winter months has been taken into account . The Volume of Polar Stratospheric Clouds (VPSC) have been calculated as the volume of air between the 370 and 550 K potential temperature levels, where the temperature is below the formation temperature of ICE or NAT clouds, using ERA5 temperature . We assumed a formation temperature of 185 K for ICE clouds and 194 K for NAT clouds . We also take into account the accumulation during winter, following . The local proxies (tropopause pressure (TP), equivalent latitude (EL) and stratospheric temperature (T)) have been taken from ERA5 reanalysis at the location of each station. Then for each region, we use as final TP, EL, and T proxies the mean of these local proxies at the sites included in a single region (Table ). The EL and T proxies are calculated for the three stratospheric columns, leading to six proxy time series (called LS, MS, and US for the lower, middle and upper stratospheric columns, see Table ). For each partial column, the mean of the EL (T) values in the corresponding ERA5 vertical layers is used. From all these proxies, only the local stratospheric temperature proxy is new compared to .

Since we use monthly anomalies (Eq. ) for the determination of the trend, all the proxies are also deseasonalized. Note that proxies are not detrended as we want our trends to only reflect the influence of ODS changes. The effect of proxies detrending will be discussed in Sect. . For now, we model the monthly anomalies time series a(t) as: 10a(t)=A1+A2⋅t+∑n=3mAn⋅Xn(t)+ε(t), where Xn(t) are the explanatory variables (i.e., proxies) with An their regression coefficient and A2 is the estimated trend. The trend error is given at the 2σ level and multiplied by a specific factor to account for autocorrelation (see , which presents an alternative to the Cochrane-Orcutt method). Finally, ε(t) is the residual (difference between the regressed model and the real data). Note that the regression coefficients can be either negative or positive.

For each trend calculated, a stepwise procedure determines the relevant proxies used in the regression , which can differ by region and partial column. Each of those relevant proxies adds an individual contribution Cfrac to the coefficient of determination R2=∑Cfrac. This individual contribution is calculated as the product of the standardized regression coefficient of the proxy with the correlation coefficient between the proxy and the observed dataset. The coefficient of determination then represents a statistical measure of the goodness of fit, i.e., how well the regressed model matches the data sets variability.

Figure presents the total coefficients of determination R2 together with the individual contributions from each proxies for the annual trends in all partial columns. Similar charts for seasonal trends are shown in Fig. in Appendix B.

Note that the temperature and equivalent latitude proxies are often correlated (up to |r|=0.8 for the TLS and TMS in the total column) but thanks to the stepwise regression method, both can be included without overfitting. In cases where the stepwise procedure still selects two proxies with high correlation, we explicitly verify that their combined use positively improves the fitting of the model to the data sets (i.e., leads to a higher coefficient R2 without increasing the uncertainty on the trends). The median value of the absolute correlations between proxies is of approximately |r|=0.15.

In all columns, the tropopause pressure (TP) doesn't contribute significantly to any of the merged regions but is relevant for the single-site regions, namely Ny-Ålesund, Reykjavik and Sondrestrom. The TP is largely influenced by the seasonal cycle and therefore strongly correlates with monthly ozone means , but a correlation still persists for deseasonalized anomalies . The TP has sometimes been used as a proxy in single-site ozone trends . Because it reflects mainly local variability, in general it is not used when calculating satellite trends over zonal bands . The averaging of the TP time series over a region likely removes most of the correlations between ozone and TP at individual sites. However, a positive correlation between the ozone anomalies and the TP was found also for the North-Atlantic region in , so this feature may vary depending on location and region's size.

In the troposphere, the coefficients of determination for annual trends are relatively small (R2≤0.25). The main contributing proxies in the troposphere are the Arctic Oscillation (AO) and the lower stratosphere temperature (TLS), and to a smaller extent the tropopause pressure (TP) and the solar cycle (Solar). The three former can impact the troposphere via stratosphere-troposphere exchange. In this study we haven't included specific proxies to account for the tropospheric ozone variability as our main focus was on the stratosphere-troposphere exchange. Overall, tropospheric ozone variability is delicate and poorly understood. It can depend on local chemical emissions and processes (NO_x, CO), forest fires, vegetation changes, as well as large-scale weather patterns. Accounting for these processes requires the use of global long-term simulations as in and lies beyond the scope of our study.

In the lower and mid-stratospheric columns, we find that the main proxies contributing to the coefficient of determination are the equivalent latitude (EL) and the temperature (T) of the corresponding stratospheric layer. We see that the potential volume of polar stratospheric clouds is also very important except in the North-West Europe region, most probably because this region latitude is too low (about 60° N). Other proxies as the QBO, Solar cycle, ENSO, AO and BDC are present but with small contributions. The coefficients of determination R2 are of about 0.4 for merged regions and 0.6 for the single-site region of Ny-Ålesund.

In the upper stratospheric column, we find again a predominance of the equivalent latitude and temperature proxies of that layer. The R2 values are lower (0.2–0.35), with a marked diminution when considering the zonal mean (All Arctic). Note that for trends in the upper stratosphere, the VPSC proxy is not used, since polar stratospheric clouds form predominantly between 15 and 25 km of altitude.

For the total column, we find that the variability is mostly explained by the lower and mid-stratospheric temperature (TLS and TMS) and by the VPSC. As with partial columns, the AO, BDC, QBO, Solar cycle and equivalent latitudes account for smaller parts of the variability. The overall R2 values lay between 0.5–0.6, except in Reykjavik where it reaches beyond 0.8.

When analyzing contributing proxies to seasonal trends, shown in Fig. , we observe an overall homogeneity of proxies throughout regions, further strengthening the confidence in the results. The variability is in general best explained in spring, with R2 values about 0.7 for the total column, reasonably well explained in winter and summer, and much less well explained in autumn, especially for merged groups of several stations. This is an interesting result, as the Arctic ozone loss due to ODS is expected to be the most important during spring. The included proxies (such as VSPC which only occurs in winter and spring but also temperature and equivalent latitude) lead to better R2 values in spring, winter and summer.

The VPSC proxy has strong correlation with other proxies, in particular with the BDC (we find a correlation of -0.363 between the VPSC and the BDC proxies). A weak BDC is linked to lower temperatures and stronger vortex, and those conditions lead to more formation of PSCs . We therefore perform a sensitivity analysis to the VPSC proxy by running the trend analysis without including this proxy. We find that part of the variability explained by the VPSC is taken up by other proxies in its absence, in majority the BDC. Both VPSC and BDC proxy are linked to the same dynamical phenomena and correlate strongly with polar chemical ozone loss. The QBOs, AO, TP, EL and T contributions also increase to a lesser degree. In general, about half of the variability previously explained by the VPSC is not covered up by other proxies, resulting in a coefficient of determination R2 smaller by up to 0.3 in the lower and mid-stratosphere where the effect of VPSC is the strongest. We find that adding the VPSC proxy improves our model's fit in the total column. This emphasizes the added value of using the stepwise regression, as it enables us to simultaneously use proxies with large correlations, contrary to where VPSC had to be removed by hand to avoid overfitting.

Before turning to the analysis of the trends results, it is important to stress that some of the proxies used in the MLR can themselves exhibit a trend. Whether or not these proxies trends should be part of the ozone trends depends on what we are trying to analyze. The VPSC for instance possesses a positive trend over the last two decades , which can be related to an increase of ozone depletion in the lower and mid-stratosphere. By including this proxy, together with its trend, in our MLR, we are effectively computing the ozone trend that is not due to this VPSC-related depletion. In the context of this study, this choice is justified by our aim in assessing the impact of the Montreal Protocol and its amendments, i.e., detecting the stratospheric ozone recovery associated with the diminution of ODS in the stratosphere. Therefore, our final trend results are calculated without detrending. We have nevertheless performed a sensitivity analysis by detrending each dynamical proxy (AO, BDC, VPSC, TP, EL, T) individually to assess their impact on the effective ozone levels and our conclusions. We compare trends obtained using the original proxy versus the detrended proxy, and we calculate the difference between the two. We find this difference is always non significant within the errors of the trends.

The mean absolute difference, calculated by subtracting the trend with the proxy detrended to the trend with no detrending, is of 0.80 % per decade for VPSC detrending, 0.59 % per decade for T detrending, 0.53 % per decade for EL detrending, 0.35 % per decade for AO detrending, 0.26 % per decade for BDC detrending and 0.10 % per decade for TP detrending. Although the differences are non-significant, the conclusions for very small trends such as in the lower stratosphere can be affected by those changes. First, VPSC detrending always lowers trends, leading to non-significant negative trends in the lower and mid-stratosphere. Ozone recovery above Canada in the mid-stratosphere becomes non significant when the VPSC is detrended. Note that the VPSC correlation with ozone is always negative, confirming that the correlation relies on the interannual variability and not on the trend, as expected. Temperature detrending has a smaller effect but drives the lower stratosphere trends towards negative values and the mid-stratosphere ones towards positive values. This is expected since in the polar lower stratosphere, the stratospheric cooling enhances the formation of VPSC where most of ozone-depleting reactions occurs, while on the other hand, the stratospheric cooling in mid-stratospheric altitude is associated with a slowing down of reaction rates of homogeneous chemistry, inducing a negative correlation between ozone and temperature . EL detrending drives the trends in lower stratosphere, upper stratosphere and total column to slightly more positive trend values. AO detrending also drives lower stratospheric trends to more negative values. Finally, TP detrending drives all individual stations trends to lower and more negative values. Since we defined layers using a fixed altitude boundary, the tropopause trend also affects tropospheric and lower stratospheric ozone trends. Detailed plots illustrating these trends comparisons are shown in Fig. in Appendix C, together with the trends obtained when including only the LOTUS proxies, i.e., Solar cycle, QBO and ENSO. The LOTUS trends are always smaller or more negative, because they do not include the VPSC, Temperatures and AO proxies. The uncertainties of the LOTUS trends are also always larger, making all LOTUS trends non-significant. Adding more proxies will always improve the R2 value, but it is non trivial that the uncertainty on the estimated trend is also improved, and this fact emphasizes the added value of our approach and of using more explanatory variables when calculating trends of a highly varying quantity such as ozone in the Arctic, and ensures that we are not overfitting our data.

We start by analyzing the total column trends results depicted in Fig. . For this and all other columns, exact numbers with the associated 2σ uncertainties, given both in % per decade and in DU per decade, are provided in Tables , and in Appendix D. We have calculated annual trends which account for the full ozone anomalies time series, as well as seasonal trends divided in winter (December–January–February), spring (March–April–May), summer (June–July–August) and autumn (September–October–November). It is important to keep in mind that due to the polar night, winter (and sometimes autumn) trends only consist of sondes profile in partial columns and of less precise measurements for Dobson and Brewer in the total column, especially at the highest latitudes where the polar night extends from October to February. We only calculate trends for time series with more than a certain number of data points (80 for annual trends and 25 for seasonal trends), so some winter or autumn trends in the total column and upper stratosphere, where only FTIR are present, are not calculated. Fewer data points during winter also implies that the variability is always larger for that season.

In the total column, trends are found to be overall positive. Except during spring, there are some small negative trends but always non-significant. The trends in Canada, Reykjavik and Sondrestrom are always positive. The Lapland trend is negative only during winter, the Alaska one only during autumn and the Ny-Ålesund one only during summer. Many positive trends are significant, especially during spring, signalling the ozone recovery.

Previous studies of the total column of ozone in Arctic have found positive significant trends in individual stations. In , combined SAOZ, GUV and Brewer measurements led to annual positive significant trends at Andøya (0.9±0.7 % per decade) and Ny-Ålesund (1.5±1.0 % per decade), and a null trend at Oslo (0.1±0.5 % per decade) for the 2000–2020 period. Those values agree with our results within the 2σ uncertainties. In , Arctic total column trends based on merged SAOZ, GUV, Brewer and Dobson measurements on one hand and on merged TOMS and OMI total column ozone (MSAT) data on the other hand, were found positive and significant for the 2000–2024 period in spring (respectively 0.75±0.61 and 1.04±0.85 DU yr⁻¹), autumn (respectively 0.88±0.23 and 0.34±0.26 DU yr⁻¹) and annually (resp. 0.65±0.39 and 0.85±0.60 DU yr⁻¹). In order to compare with literature, we calculated Arctic zonal mean trends by merging all the Arctic ground-based stations used in this work for each partial and the total column. The results are provided in Table and compare well with , although based on different instruments and methodology. Finally, we point out the significant negative ozone loss trends found in for 2000–2021 when regressing ozone loss with VPSC for the total column of ozone using chemical transport model TOMCAT/SLIMCAT, SAOZ ground-based instruments and Multi-Sensor Reanalysis (MSR2). Without the regression with VPSC, the ozone loss trend in is not significant at the 2σ level. The VPSC detrending also lowers our total column zonal mean annual trend but it remains positive and significant (1.03±0.89 % per decade). However, our study is based on three additional years, which can accounts for the difference in significance.

We now review all partial column trends, starting with stratospheric columns. In the lower stratospheric column (8–17 km ∼ 300–100 hPa), we find stronger seasonal and regional variations of the trends, see Fig. . Most trends are non-significant, and they are all very small annually. They are usually strongly negative during winter (even significantly for Lapland), and more positive during spring. Trends for Lapland are, however, positive and significant during autumn. Considering the seasonal pattern, North-West Europe distinguishes itself from other regions with positive trends in winter and negative trends in autumn, although always non-significant. As shown in Fig. , lower stratospheric trends become smaller or more negative when considering the detrended VPSC proxy. This indicates that the positive trend in VPSC in the Arctic is delaying the expected ozone recovery in the Arctic lower stratosphere. Trends in this layer in the Arctic are reported in for individual ozonesondes as well as in for two satellite data sets (ACE-FTS and MLS). The former uses Dynamical Linear Modelling (DLM) to obtain time-varying trends on 20-years periods, from 1994–2014 to 2003–2023. It considers 6 Arctic stations'sondes data sets which are also used in the present work. We do not consider their Resolute and Scoresbysund results as we found spurious jumps for those data sets in Sect. . At all remaining stations (Eureka, Alert, Ny-Ålesund and Sodankylä), they obtain negative annual trends within 1%perdecade for their L2 (300–150 hPa ∼ 8–13 km) and L3 (150–40 hPa ∼ 13–22 km) layers for all periods after 1997–2017, with varying significance levels. These results agree within the 2σ errors margin. Besides our extended time-period and the addition of FTIR measurements, our analysis also differs in the proxies used for the regression. only considers the tropopause pressure, solar flux, Eddy heat flux (for the BDC) and the VPSC multiplied with Effective Equivalent Stratospheric Chlorine (EESC), which measures the impact of ozone-depleting stratospheric chlorine and bromine levels in the Arctic stratosphere. We have not included the EESC here because we want our trend term to reflect the impact of the declining ODS levels. Moreover, we found the temperature and equivalent latitude proxies (not included in their study) play a very important role in explaining the variability at these altitudes. The second study reports overall positive annual trends around 2 % per decade for the MLS satellite in the 250–100 hPa layer above 60° N. These trends are not significant using a simple linear regression but become larger, positive and significant when using MLR or DLM instead. The seasonal pattern matches with ours in winter with large negative trends and in spring with more positive trends. In summer we obtain negative trends contrasting their positive trends and in autumn, we observe a strong zonal difference not captured by the latitudinal band cut of the satellite. ACE-FTS trends are highly variable (sparser sampling) but also show positive trends using MLR and DLM between 200–100 hPa in the 60–70° N latitudinal band.

In the mid stratophere, see Fig. , we find positive trend values especially during spring. In Canada, trends are also positive and significant in winter and annually. There as well VPSC detrending lowers trends (see Fig. ), highlighting that ozone recovery is delayed by this effect. In , the annual trends at 20 km of altitude over the 2003–2018 period are very small on the whole region considered here, between -0.5 % per decade and +1 % per decade, but not significant anywhere. Besides, our mid-stratospheric trends exhibit a consistent seasonal cycle, with highest (positive) ozone trends during spring and lowest trends during summer (significant negative in North-West Europe). The marked zonal asymmetry between Canada and Scandinavia is discussed in the next paragraph together with the upper stratosphere.

In the upper stratosphere (Fig. ), the annual trends above North Pole are positive and significant, consistent with the results of in the 25–30 km layer and supporting the detection of ozone recovery seen in the total column trends. Seasonal trends are always non-significant, therefore we have also considered additionally the 32–48 km layer. More positive trends are generally observed at higher altitudes as in at 40 and 45 km. Indeed we find larger positive significant trends at North Pole during spring (6.06±4.19 % per decade) and annually (3.83±2.35 % per decade) for the 32–48 km layer.

In middle and upper stratosphere, we observe a zonal asymmetry as detected by satellites and models e.g. in, and attributed in to decadal changes in the dynamics of the polar vortex above the Arctic, stemming from climate change forcing. The zonal asymmetry is also visible when looking at which proxies are relevant: in the upper stratosphere, the North Pole trend is more influenced by the EL and the BDC, while the Scandinavian region is driven by the EL but to a lesser extent and slightly by temperature. Since the EL depends on the polar vortex, the zonal asymmetry is reduced by the use of that proxy, as it becomes larger in spring when detrending the EL. Similarly in the mid-stratosphere, the Canada region is the only one where the BDC plays a significant role, especially important in spring. This hints toward an explanation of the zonal asymmetry related to the atmospheric dynamics in the Arctic, in agreement with conclusions of .

Next we consider the tropospheric ozone column in Fig. . We find that all tropospheric ozone trends are always negative in North Pole, significant both annually and in spring, while Scandinavian trends are always non-significant, positive in autumn and winter and negative in spring and summer. In , the HEGIFTOM measurements using homogenized sondes, FTIR, Lidar, Umkehr and IAGOS measurements lead to merged trend results on the 2000–2022 period for the tropospheric ozone column (surf. -300 hPa) of (-1.80±0.37) ppb per decade in their European Arctic region and of (-1.09±0.57) ppb per decade in their Canadian Arctic region.

Note that our regions differ from those of because we do not consider the Scoresbysund sonde where we found a spurious drift, and we have decided to include Ny-Ålesund together with Canadian sites instead of Scandinavian ones. The correlation of Ny-Ålesund with other sites is high everywhere (0.75 annually), but when we consider seasonal correlations, we find that it correlates better with Canada in winter and spring, and better with Scandinavia in summer and autumn. This is most probably an effect of the polar vortex displacement. We have chosen to include it with Canada based on the annual correlation values.