Ozonesonde data over 1970–2021 at 141 ozonesonde stations worldwide (Fig. 1) were downloaded from the World Ozone and Ultraviolet Radiation Data Centre (WOUDC; https://woudc.org/archive/Archive-NewFormat/OzoneSonde_1.0_1/, last access: 4 December 2024) or, where available, homogenized data from Southern Hemisphere ADditional OZonesondes (SHADOZ; 10.57721/SHADOZ-V06) and HEGIFTOM (https://hegiftom.meteo.be/datasets/ozonesondes, last access: 28 September 2024). The homogenized ozonesonde stations from HEGIFTOM include ozonesonde stations from the SHADOZ network (Thompson et al., 2017; Witte et al., 2017, 2018), the Canadian network (Tarasick et al., 2016), the US network (Sterling et al., 2018), the Network for the Detection of Atmospheric Composition Change (NDACC) and several individual stations (Van Malderen et al., 2016; Witte et al., 2019; Ancellet et al., 2022), with an overall uncertainty of 3 %–5 % in both the stratosphere and troposphere. Ozonesonde data from the Beijing Nanjiao Meteorological Observatory (39.81° N, 116.47° E) in Beijing, China, are provided by the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences. The ozone profiles at Beijing are measured by the Brewer-Mast type GPSO3 ozonesonde and the IAP electrochemical concentration cell (ECC) ozonesonde, which are in fair agreement with commercial ECC ozonesondes (Wang et al., 2003; Xuan et al., 2004; Bian et al., 2007) in both laboratory and field experiments (Zhang et al., 2021; Zeng et al., 2023). In total, data from 43 more stations were used in TOST-v2 than in TOST-v1 (Liu et al., 2013b).

Figure 1a provides an overview of the distribution of the ozonesonde stations, the number of profiles and the beginning year for every station. Most of the stations with data before the 1980s are located in North America, Europe and east Asia. The majority of the stations in the Southern Hemisphere started measurement in the 1990s or later, and so the Southern Hemisphere contains a smaller number of ozone profiles than in the Northern Hemisphere. Figure 1b shows that the total number of ozonesonde profiles per year has almost doubled since the 1990s and reached a maximum in the late 2000s, with over 3000 profiles per year. Since then, the number of ozonesonde profiles available on the WOUDC site has declined slightly to 2000–3000 profiles per year. The average annual number of profiles per station has slightly increased since the 1990s and has stabilized at about 40 profiles per year.

All the ozonesonde profiles were processed into 1 km vertical resolution by integrating and averaging the ozone mixing ratio in 1 km layers from the sea level. The ozonesonde data above 26 km were excluded as the data above this height show large uncertainties at midlatitudes and high latitudes (Fioletov et al., 2006).

Forward and backward trajectories in 4 d were simulated every 6 h using the version 5.2 HYSPLIT model (Stein et al., 2015). HYSPLIT was driven by the reanalysis of hourly meteorological data from the National Centers for Environmental Prediction – National Center for Atmospheric Research (NCEP/NCAR), which has a horizontal resolution of 2.5° by 2.5° in latitude and longitude and 17 vertical levels from the surface to 10 hPa (Kalney et al., 1996). The length of the trajectories influences the spatial coverage and accuracy of the ozone mapping. Generally, uncertainties increase rapidly along the trajectories, with typical errors of about 100–200 km d⁻¹ (Stohl, 1998). Trajectories have horizontal uncertainties of 350–400 km after 3 d and 600–1000 km after 4 d in the Northern Hemisphere (Engström and Magnusson, 2009). Trajectories show typical vertical deviations of about 200, 800 and 1000 m after 2, 4 and 6 d in the stratosphere and even greater uncertainties in the troposphere (Stohl and Seibert, 1998). Therefore, to limit trajectory errors, 4 d trajectories were used herein, following previous studies (Tarasick et al., 2010; Liu et al., 2013a, b).

Ozone mixing ratios from each sounding at the 26 levels were assigned to the corresponding forward and backward trajectory paths. These ozone values at positions every 6 h along the 4 d backward and forward trajectories (32 positions for each level for both forward and backward trajectories) were averaged in bins of 5° latitude and 5° longitude, for each 1 km altitude for every month. This bin size corresponds both to the typical uncertainties of 4 d trajectories discussed above and to the typical ozone correlation length (500–1500 km) in the troposphere and the stratosphere (Liu et al., 2009). To produce the mapping with pressure altitudes, we also averaged the 4 d backward and forward trajectories in bins of 5° latitude and 5° longitude for every month, using the pressure altitudes generated by HYSPLIT trajectories. The 26 pressure altitudes are 950, 850, 750, 650, 550, 450, 400, 350, 300, 250, 225, 200, 175, 150, 125, 100, 90, 80, 70, 60, 50, 40, 35, 30, 25 and 20 hPa, following the pressure coordinates in the European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5). Ozonesonde profiles in both the troposphere and stratosphere were used. In addition, the ozonesonde data at the 26 levels are separated into the troposphere and stratosphere from the measured ozonesonde temperature profile, following the World Meteorological Organization (WMO) definition of the tropopause. In this way, two datasets are constructed using ozonesonde data in the troposphere (troposphere-only) and in the stratosphere (stratosphere-only). The troposphere-only and stratosphere-only fields are helpful to calculate the tropopause in modeling studies, as the average tropopause height is usually not specified in the full-atmosphere field.

Based on this mapping, TOST-v2 was constructed at 26 altitude levels in two altitude coordinates (by geometric levels and pressure levels), from two altitude starting levels (altitude above sea level and altitude above ground level), for three temporal resolutions (in the seasonal mean for each year, the annual means for each year from 1970 to 2021 and monthly means for each decade from the 1970s to the 2010s) and with three types of data fields (trop-stra, troposphere-only and stratosphere-only) for users' convenience (Table 1). In TOST-v2, we also generated the corresponding datasets that show ozone variation at three percentile levels (25, 50 and 75th). Examples presented in this paper all use TOST at geometric coordinates with altitudes above sea level. For this coordinate system, both ozonesonde profiles and mapped data necessarily begin at the altitude of the surface, leaving the levels below the topography of the Earth's surface as null if the levels are above the sea level.

Errors in the mapped data can come from trajectory errors and from ignoring ozone chemistry (production and loss) along the transport pathway and deposition in the surface layer (Liu et al., 2013a). Differences between the results of backward and forward trajectory mapping can provide a measure of these errors, since in the absence of such errors the results of forward-only and backward-only trajectory mapping should be identical. Therefore, mappings from the forward-only and backward-only trajectories were compared as an initial quality check. Figure S1 in the Supplement shows monthly means (January and July) in 2000 at 3–4 and 19–20 km, for forward-only and backward-only mapping. In general, the differences between the two mappings are commonly less than 15 % and have no distinct pattern, indicating that trajectory errors are not dependent on the direction of the trajectories. These modest differences between forward-only and backward-only trajectory-mapped ozone fields also validate the reliability of this trajectory-mapping method; both backward and forward trajectories, therefore, were combined in TOST to achieve better averages and higher spatial coverage.

To comprehensively validate TOST, we compare TOST with actual ozonesonde, satellite, and aircraft observations. Multiple metrics were used to indicate the level of agreement between the TOST and other data. We used the correlation coefficient (R) to present the agreement of the two compared data, and linear fitting coefficient with the intercept set to 0 to show the overall tendency of overestimation or underestimation. We also used relative difference (RD) to represent the relative difference between the two compared data and used bias and root mean square difference (RMSD) to show the absolute difference between the two compared data. Details of the metrics can be found in Sect. S1 in the Supplement.

First, we show the overall comparison in monthly mean ozone concentrations between ozonesonde and trajectory-derived values without the inputs of the stations being tested (Traj-Derived), from all the existing stations at all altitude levels. Note that the actual TOST dataset would be better than “Traj-Derived ozone”, especially at the sampling locations because the input of the local station is included in the TOST dataset. Because of the large range of ozone concentrations in the troposphere and stratosphere (0–6000 ppb), we divide the altitude levels into three to present the overall accuracy of TOST in the lower troposphere (ozone concentrations below 50 ppb), the upper troposphere (ozone concentrations between 50 and 150 ppb) and the stratosphere (ozone concentrations over 150 ppb).

Figure 2a–f show the overall ozone comparisons between ozonesonde (Sonde-Observed) and Traj-Derived ozone in the entire study period (Fig. 2a–c) and each decade (Fig. 2d–f). Each dot in Fig. 2a–c represents the paired ozone concentrations from Traj-Derived and Sonde-Observed values in each month at each latitude–longitude–altitude grid cell, and the color indicates the density of the dots. Overall, in the lower troposphere (Fig. 2a), the Sonde-Observed and Traj-Derived ozone concentrations agree well, with an R of 0.69 and an RMSD of 7.5 ppb, a low bias (0.7 ppb) and a low RD (1.8 %). The linear fit for the entire study period shows a slope of 0.99. In the upper troposphere (Fig. 2b), the agreement between the Sonde-Observed and Traj-Derived ozone concentration is moderately lower, with a linear fitting coefficient of 1.01 and RMSD of 21.1 ppb, and higher bias (2.9 ppb) and RD (4.0 %) than those in the lower troposphere. This lower agreement in the upper troposphere is owed to the greater influence of stratosphere–troposphere exchange (STE) in the upper troposphere, where trajectories by the Lagrangian dispersion model (such as HYSPLIT) show substantially increased deviations due to the strong turbulence and convection (Stohl et al., 2002). The positive bias may imply that STE is slightly overestimated in HYSPLIT. In the stratosphere (Fig. 2c), the overall agreement between the Sonde-Observed and Traj-Derived ozone concentrations has a linear fitting coefficient of 0.97 and an RMSD of 416.9 ppb. The RD is only 0.5 %, indicating higher reliability of Traj-Derived in the stratosphere.

This validation method compares ozonesonde station data with Traj-Derived ozone, i.e., the ozone found by averaging trajectories that come from other stations. Before the 1990s, RDs were smaller than 0 and R values were smaller than 0.60 (Fig. 2d and e) in the lower troposphere, indicating a tendency to underestimate the Traj-Derived ozone in the lower troposphere. After the 1990s, owing to the additional ozonesonde measurements provided by SHADOZ in the tropics, the underestimation of Traj-Derived ozone in the lower troposphere is greatly reduced, and the R value increases to >0.71 (Fig. 2d and e). Similarly, with the additional ozonesonde measurements after the 1990s, the R values in the upper troposphere increased from <0.50 to >0.58 (Fig. 2d). In all decades, the agreement between Sonde-Observed and Traj-Derived ozone in the stratosphere is the best, with an R value of ∼0.97. The RD in each decade is small (-0.3 %–1.4 %), indicating no systematic underestimation or overestimation in the stratospheric Traj-Derived data. However, in the upper troposphere, ozone concentrations are slightly overestimated by Traj-Derived ozone data concentrations, with RD of 0.6 %–4.5 %.

Figure 3 examines how the RD between the ozonesondes and Traj-Derived ozone values varies with altitude, presenting the frequency distributions of RD across all stations, at every other altitude level and in each decade. The RD distributions are based on the monthly ozone concentration difference between the actual ozonesonde and Traj-Derived data from all the existing stations at the corresponding altitude level and decade. The distributions of RD show little skewness in these altitudes and decades, indicating no systematic bias during the study period. The overall interquartile ranges (25–75th), denoted by thick red lines with the widths given in red values, indicate that RD is between -30 % to 30 % and the widths of interquartile ranges are between 9 % and 61 %, with the lowest interquartile ranges (-10 % to 10 %) and widths (9 % to 30 %) of RD in the stratosphere and lower–middle troposphere. Higher interquartile ranges of RD appear in the 13–19 km altitude range, where the upper troposphere–lower stratosphere (UTLS) region is located, and are due to the large vertical gradients of ozone concentrations in the UTLS and the variability of the tropopause (Millán et al., 2023). The surface (boundary layer) ozone, however, shows a positive bias of the median of up to 12 %, in all decades, suggesting that TOST, which neglects ozone chemistry and deposition processes, tends to overestimate ozone concentrations there.

Figure 4 exemplifies comparisons in vertical profiles between Sonde-Observed and Traj-Derived ozone profiles at individual stations in different seasons. Four stations with sufficient data coverage (>15 years) were selected from the Antarctic coastal region (Syowa), Europe (Hohenpeissenberg), North America (Boulder) and east Asia (Beijing). The decadal-mean (1990s and 2000s) profiles in January and July are used to compare the performance of Traj-Derived ozone profiles in boreal winter and summer. In general, the Traj-Derived profiles can capture the vertical ozone variation in different seasons, with good correlation (R>0.99) and high accuracy (bias <100 ppb, RD <10 %) in comparison to the actual ozonesonde profiles. The comparison at Syowa shows a larger bias, but much of this is due to the fact that in the 1990s this station launched the Japanese KC-79 carbon-iodine sonde, while other stations in the Southern Hemisphere launched ECC sondes; the Traj-Derived profiles would therefore be expected to be 10 %–20 % higher in the troposphere and about 5 % higher in the lower stratosphere (Smit and Kley, 1998). The excellent agreement in tropospheric ozone at Hohenpeissenberg is likely due to frequent and dense European ozonesonde observations; similar cases also are seen at Uccle, Payerne and Praha. Larger discrepancies are shown near the planetary boundary layer (PBL) and UTLS, as the simulated trajectories over these regions have more uncertainties (Stohl and Seibert, 1998; Sicard et al., 2019), and ozone chemistry and deposition are potentially important in the PBL at timescales similar to those of the longer trajectories (4 d) (Prather et al., 2023; Prather and Zhu, 2024).

To compare with satellite data, we first validated the Traj-Derived ozone profiles against ozonesonde measurements. The corresponding validation was conducted for the satellite data of SAGE and MLS for the same period, location and altitude. The sets of ozonesonde, Traj-Derived and satellite data were selected only when all three datasets were available for the same month, decade and grid cell, to ensure that both the Traj-Derived and satellite data could be independently evaluated by the ozonesondes. As MLS data at altitudes below 261 hPa are not recommended (Livesey et al., 2022), we only compare both satellite datasets above this altitude, i.e., ∼16–26 km. Figure 5 shows the time series of the vertical variation of monthly RD from 16–26 km between Traj-Derived and SAGE ozone profiles from 1985–2005 (Fig. 5c and f) and between Traj-Derived and MLS ozone from 2005–2019 (Fig. 5i and l). SAGE ozone data are reliable above 20 km (Kremser et al., 2020), having a mean RD of about -10 %–10 % above this altitude, similar to that of Traj-Derived ozone. Between 16 and 20 km, SAGE ozone concentrations are lower than the Traj-Derived ozone by 5 % to 10 % (Fig. 5f), as Traj-Derived ozone overestimates the ozonesondes by 9 % to 15 % (Fig. 5e). Over the MLS period from 2005 to 2019, TOST ozone at all altitudes between 16 and 26 km agrees with actual ozonesondes better than during the SAGE period (Fig. 5h and k vs. Fig. 5b and e). Accordingly, the Traj-Derived ozone concentrations show good agreement with MLS ozone above 22 km but are lower than MLS ozone below 20 km (Fig. 5i and l), as MLS generally overestimates ozone concentrations below 20 km (Fig. 5g and j).

Figure S3 compares the RMSD of Traj-Derived and satellite ozone in different latitude zones from 16–26 km. Compared to SAGE in the 1990s, the Traj-Derived ozone has comparable RMSDs in the Northern Hemisphere, yet higher RMSDs in the Southern Hemisphere, due to the fewer ozonesonde stations there. MLS ozone also shows lower RMSDs in the Southern Hemisphere, but higher RMSDs in the Northern Hemisphere.

Table S3 summarizes the evaluation of both Traj-Derived and satellite ozone against the ozonesondes over 16–26 km. The Traj-Derived and SAGE ozone values show a high correlation (R=0.95 or greater in all cases) with actual ozonesondes. The Traj-Derived ozone data show RDs of -1% to +2% in the 1980s and 1990s and just -0.3% to +0.4% in the 2000s and 2010s, while the SAGE ozone data show RDs of -4% to +0.5%, and the MLS data show RDs of -2% to +11%.

It is expected that TOST would outperform satellite instruments in measurements below the tropopause, as satellite measurements are hampered by the large stratospheric ozone burden that satellite instruments must look through. Yet, our comparisons suggest that even above 15 km, where SAGE and MLS are considered most reliable (Wang et al., 2002; Kremser et al., 2020; Livesey et al., 2022), TOST can provide comparable or better accuracy.

We compare TOST ozone with the IAGOS dataset in the lower troposphere from 1994–2021 (Fig. 6). Note that this comparison is between the full TOST (not Traj-derived) and IAGOS datasets here. TOST ozone values are generally higher than IAGOS with a mean bias of 2.2 ppb and R of 0.49, but RDs (5.8 %) and RMSD (8.8 ppb) are low. The linear fit has a slope of 1.03. The two ozone datasets employ different measurement techniques and atmospheric sampling (Petetin et al., 2018). Previous studies have reported that IAGOS ozone values are systematically lower than ozonesonde values, typically by 5 %–10 % in the troposphere (Tilmes et al., 2012; Zbinden et al., 2013; Staufer et al., 2013, 2014; Tanimoto et al., 2015; D. W. Tarasick et al., 2019). The comparisons in Fig. 6 are consistent with these earlier estimates, as the RD indicates that IAGOS measurements average 6 % lower than TOST.

As noted in Sect. 2.3, the ozone concentrations in a grid in a month are determined by the ozone concentrations along all the trajectories passing through that grid cell in that month. Therefore, an estimate of the random uncertainty of TOST may be obtained from the standard error of the mean in each grid cell. Note that this may not be a true estimate of the standard error, as some cells may contain more than one value from an individual trajectory, so these values are not independent and the standard error calculation is biased low.

For convenience, given the large range of ozone concentrations between the stratosphere and troposphere, we use the ratio of the standard error to the mean in each of the grid cells, SE/mean (expressed in %), to estimate spatial patterns of the uncertainty. The standard error is proportional to the variability of the ozone values in a grid cell (i.e., the standard deviation) and inversely proportional to the square root of the number of data values. Thus in general, the more trajectories passing a grid cell, the more data samples for that cell and the lower the standard error for that cell. For each cell, we also calculated the number of independent samples; i.e., the trajectory originated from a single ozonesonde altitude was counted only once in a grid cell when the trajectory passes that cell regardless of how long the trajectory stays in that cell. Figure 7 shows the SE/mean and the number of independent samples in January and July of the 2000s at 3–4 and 19–20 km. Generally, the Southern Hemisphere shows higher SE/mean values (>10%) than the Northern Hemisphere (<6%), which reflects the large number (>100) of ozone soundings in the Northern Hemisphere, especially over North America and Europe. However, near the Equator, despite the higher sampling rate, the SE/mean is still as high as 15 %. Compared to the stratospheric level (19–20 km), the tropospheric level (3–4 km) shows an overall higher SE/mean. SE/mean varies less with season in the stratosphere than in the troposphere. For example, at 3–4 km, the SE/mean in January is generally <7% but becomes >10% in July in the Northern Hemisphere, and vice versa in the Southern Hemisphere. This is likely due to more vertical motion in the PBL (Stohl and Seibert, 1998; Sicard et al., 2019) so that ozone in some bins comes from multiple altitude levels, as well as increased photochemistry and biomass burning. Stratospheric intrusions to the lower troposphere are more frequent in boreal spring and summer than in winter (Terao et al., 2008; Greenslade et al., 2017) and can be responsible for much of the variability at 3–4 km (D. Tarasick et al., 2019).

To provide an overview of the uncertainties of TOST in different altitudinal and latitudinal zones, as well as in different seasons and decades, we calculated the RD of the monthly ozone mixing ratio between ozonesonde and Traj-Derived ozone over 1970–2021 (Fig. 8). Among altitudes, the highest RD values appear at 9–10 km over the tropopause region, and the second highest RD at the surface, while the lowest RD values are in the lower–middle troposphere (3–6 km) and stratosphere (19–26 km), consistent with Fig. 3. By season (Fig. 8b), the RD varies slightly with a lower value in JJA and SON than in other seasons. There is considerable variation in RDs with latitude (Fig. 8c); the RDs in the southern high latitudes (9–60° S) and the northern tropics (0–30° N) are higher than in other latitudinal zones. This could reflect higher horizontal gradients of ozone (e.g., stations in or outside the ozone hole) in the southern high latitudes or biases between ECC sondes and other types (the Indian and Japanese sondes) in the northern tropics. After the 1990s, the RDs are reduced markedly compared to the 1980s and 1970s (Fig. 8d), likely related to the improved data coverage in the later periods. This overview provides caveats regarding where (surface and UTLS, the northern high latitudes and tropics) and when (before the 1990s) more caution is advised when using TOST.

The improvements in TOST-v2 are attributed to the increased amount and improved quality of ozonesonde data, as well as the improved trajectory simulation and ozone mapping. Because more ozonesonde stations and more ozonesonde data have become available since the 1990s or 2000s (Table S1), more ozone profiles were used in constructing TOST-v2, leading to improved data density. Table S4 summarizes the data coverage, the number of ozonesonde stations and the number of ozonesonde profiles used for TOST-v2 and TOST-v1. The data coverage is defined as the ratio of the number of grid cells with valid annual means to the total number of grid cells in the corresponding latitudinal zone. The number of ozonesonde stations, compared to Liu et al. (2013b), increases in all latitudes by ∼50%, and the total number of ozonesonde profiles used is doubled. Data coverage increases as well, in all latitude bands, by 5 %–15 % (Table S4) and in all altitudes by a maximum of 10 % (Fig. S4).

In addition to the data density, the data quality was also improved in TOST-v2. Figure 9a–b show the distributions of ozone concentrations in TOST-v2 and TOST-v1 at the lowest level (0–1 km) for the 2000s. Over the Antarctic, gaps are observed only in TOST-v2. This is more reasonable for the sea-level data because the altitude over the Antarctic is over 1 km (Fig. S5a), where trajectories should not appear at 0–1 km. Therefore, the spatial distributions of ozone are clearly improved with this topography correction in TOST-v2, which could be attributed to the updated terrain file since HYSPLIT v5.0 (https://www.arl.noaa.gov/hysplit/hysplit-model-updates/, last access: 4 December 2024). Over the eastern Pacific, marked with an ellipse in Fig. 9a and b, TOST-v1 shows higher ozone concentrations than TOST-v2 by 30 % (Fig. 9c). Compared to the ozonesonde measurement at 0–1 km in the 2000s in these two regions (Davis station for the Antarctic and Easter Island station for the eastern Pacific), TOST-v2 agrees better with ozonesondes than TOST-v1, indicating better representation of ozone distributions (Fig. S5b).

With reference to spatial distributions at 19–20 km in the 2000s, Fig. 9d–e show that in the Antarctic and the tropical eastern Pacific, TOST-v1 values show higher concentrations than TOST-v2 (Fig. 9f). Figure S5c compares ozone concentrations from ozonesonde, TOST-v2 and TOST-v1 at 19–20 km in the 2000s at an Antarctic station (Syowa) and a tropical station (Bogotá). Compared to TOST-v1, TOST-v2 ozone values show a better agreement with the ozonesonde measurement. The difference between TOST-v2 ozone and ozonesonde measurements is 10 % and 29 % in Syowa and Bogotá stations, while in TOST-v1, ozone concentrations at these stations show 24 % and 39 % differences (Fig. S5c).

In summary, TOST has been improved in TOST-v2 with higher spatial coverage, improved description of ozone spatial distributions and a better agreement with ozonesonde measurements in both the troposphere and stratosphere. Furthermore, TOST-v2 provides additional information that shows ozone variations in three percentile levels (25, 50 and 75th). TOST-v2 is also generated in a pressure altitude coordinate for users' convenience.

As a 3-dimensional ozone dataset, TOST can depict both horizontal and vertical ozone distributions, as well as long-term ozone variation. Figure 10 shows distributions of decadal-mean TOST ozone at 3–4 and 19–20 km in four seasons of the 2000s. At 3–4 km in the troposphere, ozone concentrations are higher over the continent in the Northern Hemisphere, especially in MAM and DJF (>50 ppb), reflecting the ozone production from the photochemical reactions of anthropogenic and natural emissions. In addition, the continental outflow from the southern USA (in MAM) and the biomass-burning-produced ozone in southern Africa (in JJA and SON) are well captured and in agreement with satellite observations (Fishman et al., 1990; Ebojie et al., 2016). At 19–20 km in the stratosphere (Fig. 10e–h), ozone concentrations are higher near the poles than in the tropics, due to the impact of the Brewer–Dobson circulation. The North Pole has higher ozone concentrations than the South Pole in DJF and MAM, and vice versa in JJA and SON, reflecting the seasonality of the Brewer–Dobson circulation. Also at 19–20 km, the ozone concentrations are lower over Asia in JJA (Fig. 10f) than in other seasons, reflecting the transport of ozone by the Asian summer monsoon from the tropics (Gettelman et al., 2004; Bian et al., 2020).

Although trajectory mapping fills in much of the global spatial domain, large gaps can still be found, particularly in the tropics, where ozone soundings are less dense. Since some applications require a default ozone value at all grid cells, a gap-filled and smoothed ozone dataset is also provided for the decadal-mean ozone in each month and the annual mean ozone, by fitting the maps at each level with a linear combination of spherical functions (Liu et al., 2013b). As shown in Fig. 10i–p, small-scale variations and extreme values are reduced in the smoothed ozone fields, while broad patterns of the ozone distribution are retained, making these smoothed maps valuable for qualitative visualization of the spatial, seasonal and decadal variations in ozone at different altitudes. They should, however, be used for any kind of quantitative analysis with great caution, as these data, where gaps exist in the unsmoothed TOST dataset, may be interpolated from the original measurement that is far in distance, and thus the degree to which they represent the true ozone value should be carefully examined. For example, erroneous conclusions have been inferred from the smoothed TOST-v1 over the tropics, with very limited observations before 1998, where the smoothed data were mostly interpolated from higher latitudes (Chipperfield et al., 2022). In addition, smoothing, as noted, filters small-scale variations and extreme values and retains ozone variations on large scales, which should be borne in mind when using the smoothed data. The smoothed dataset has not been quantitatively evaluated in any way.

Figure 11a–d show the latitude–altitude distribution of TOST ozone in each season averaged over 1970–2021. The steep changes in ozone concentration from <100 to >500 ppb in the vicinity of the tropopause (the black lines in Fig. 11a–d, calculated from the NCEP/NCAR reanalysis) are well captured. Due to the Brewer–Dobson circulation, ozone concentrations above the tropopause increase with latitude from the tropics to the poles, which is also well reflected in the latitude–altitude distribution. TOST ozone concentrations around 12–13 km are higher in spring (600–800 ppb) than in the other seasons (<500 ppb) over northern midlatitudes (45–60° N), which reflects the stronger Brewer–Dobson circulation in spring (Holton et al., 1995). Figure 11e shows the monthly mean TOST ozone time series from 1970 to 2021, averaged over 30–70° N at each level. Clear seasonal cycles are well captured every year.

One of the advantages of TOST is its long-term coverage, which enables investigation of variations in ozone back to the 1970s. While analysis of long-term ozone trends in the troposphere with TOST is underway in separate projects, here we show an application of TOST data for studying lower-stratospheric ozone changes. Following the implementation of the Montreal Protocol and its amendments, recent studies have found an increase in upper stratospheric ozone since the late 1990s (Chipperfield et al., 2017; Szeląg et al., 2020; Dunn et al., 2023). However, the lower stratospheric ozone trend remains highly uncertain (Ball et al., 2020). Quantifying lower stratospheric ozone trends depends largely on the quality of the observational datasets (Li et al., 2023). While the trend is commonly analyzed with individual ozonesonde time series, it is challenging to assess how well individual long-term station changes represent regional or global variations. Combining data from sparse and widely separated ozonesonde sites involves implicit assumptions about their representativeness. With meteorological trajectory mapping, each original ozonesonde measurement is assigned a trajectory which describes its representativeness, and the TOST averages are therefore weighted according to the representativeness of each measurement. While this is subject to trajectory errors and the fact that coverage is incomplete (Table S3), unless trajectory errors are non-random, it should produce a better result than simple averaging of sonde station data by geographic region.

Figure 12 shows the annual mean of ozone anomalies at 21–22 and 24–25 km from 1970 to 2021; the area-weighted averages were taken over grid cells from 30–70° N all with valid data throughout all years, i.e., ∼70% of grid cells in the latitudinal zone. The 3-year running means are also shown with the time series. The ozone time series at both levels captures the clear ozone depletion before the early 1990s and the slow recovery in the latter part of the 1990s. In addition, these updated TOST time series show that stratospheric ozone has changed little since 2000. There are non-significant trends in the ozone concentrations at 21–22 km (0.5±0.6 % per decade) and 24–25 km (-0.2±0.9 % per decade) from 1998 to 2021, indicating little change of lower stratospheric ozone, despite the fact that 25 years has passed since peak stratospheric chlorine. Recent studies using merged satellite data suggested that the decrease in the lower stratospheric ozone is offsetting the increase in the upper stratosphere (Ball et al., 2018, 2019; Szeląg et al., 2020; Li et al., 2023), which is responsible for the flat trend in the total column ozone since the late 1990s. However, in the Northern Hemisphere midlatitudes, TOST indicates no significant trend in the lower stratospheric ozone after the late 1990s. The difference between the TOST and satellite-based data calls for further in-depth studies on the stratospheric ozone trend, especially in the lower stratosphere. Such observations of the variation in stratospheric ozone are essential to verifying the expected stratospheric ozone recovery under the Montreal Protocol and to understanding the feedbacks among dynamical, thermal and ozone variability.