Introduction

The ozone layer is crucial for sustaining life on Earth’s land surface. Its destruction by man-made chemicals was and still is a major environmental concern, as the expected recovery remains difficult to detect1,2,3. For a century, scientists have measured total column ozone (see Box 1)4,5,6, which mainly represents stratospheric ozone. Today, the resulting long column ozone records could help us to assess ozone recovery and separate it from the effects of atmospheric circulation changes. Open questions concerning the contributions of ozone depleting substances, changes in ozone precursor gases, and climate change to changes in column ozone are mostly addressed with the help of models7, but long records could help in the analysis. The record from Arosa, Switzerland, which starts in 1926, is the world’s longest ozone record8. Another long record exists for Tromsø, Norway, reaching back to 19359. In this contribution, I present a new, century-long ozone record for Oxford that reaches as far back as 1924. This series is based on existing segments10, complemented with a new segment digitised from original data sheets from the 1970s (Fig. 1) and further extended to the present using series from neighbouring stations (see Methods).

Fig. 1: Total column ozone observations sheets from Oxford.
figure 1

a Original observations sheet from Oxford, June 1976. b R-N table for the A pair, dated 1974 (excerpt).

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Fig. 2: The first total column ozone measurements.
figure 2

a Ozone measurements in Paris, May-June 1920 by Fabry and Buisson58 (purple circles, given in their original units) and 200 hPa GPH from the CERA-20C reanalysis33 (green lines, reverse scale, 10 ensemble members). b Photographed spectra in the UV region from which Dobson derived total column ozone by measuring the spectrum at wavelengths in which ozone absorbs relative to nearby wavelengths that are not absorbed (from Dobson and Harrison59).

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The new series from Oxford is then analysed together with that from Arosa with respect to multiannual and long-term variability. Specifically, I use the long time series to better constrain ozone recovery and address trends in column ozone in the era prior to the onset of ozone depletion by chlorofluorocarbons.

Results

Comparison with other series

Figure 3 shows the new, centennial series from Oxford together with the series from Arosa as well as a 50-year long series of zonal mean total column ozone at 52.5°N from satellite instruments11. Note that the series are offset for visualisation (Arosa, 1000 km away from Oxford and at 1850 m asl has a lower ozone column than Oxford and both deviate from the zonal average). The two station series are in very good agreement. Both show the same long-term evolution, and they also show concurrent, strong spikes such as in the early 1940s or in 2010. The zonal average series also agrees well with the two station series. It shows less variability as zonally asymmetric effects of changes in the planetary wave structure and thus tropopause height partly cancel out. What remains are zonally symmetric, dynamical effects and chemical changes.

Fig. 3: Long-term total column ozone series.
figure 3

Annual mean total column ozone at Oxford (homogenised series), Arosa (continued with data from Davos after Feb 2021) as well as annual mean zonal mean total column ozone at 52.5°N from the SBUV merged data set MOD v2 from 1924 to 2021 (note the offsets). For historical reasons, I also plot the first data for Oxford, 1924 (blue circle) and Paris, 1920 (olive dashed line, qualitative), although requirements for annual averaging are not met.

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Inter-and multiannual variability

The value of long records is that they capture a wider range of dynamical variability that affects the ozone layer. In the following, I focus on the two most prominent spikes in the two records, in the early 1940s and in 2010, and show that both can explained be exceptional, but different, atmospheric circulation. During the years 1940–42, total column ozone was exceptionally high over both stations. In fact, column ozone was also high at other locations in Europe, and also at stations on other continents (New York, Shanghai), as found in a previous study12. Here I add three further series, namely from Oxford, Table Mountain, California13, and Montezuma, Chile (the latter two series are very sparse and based on spectroscopy in the visible wavelength range, i.e., the Chappuis band, which is much less accurate, see Methods). All extratropical series confirm the increase in 1940–1942 relative to the neighbouring years (Fig. 4), which is the expression of an increased transport of ozone from the tropics to the extratropics through a stronger Brewer–Dobson circulation. We would then expect an ozone decrease in the tropics. There is only one series from the tropics: Montezuma, Chile. Despite its very large uncertainty, it is interesting that this series shows a decrease concurrent with the increase in the extratropics.

Fig. 4: Stratospheric ozone during the early 1940s.
figure 4

a Total column ozone (standardised anomalies with respect to 1938–1944) at nine stations smoothed with a 12-month moving average (see Methods)12. b Zonally averaged ozone concentrations from HISTOZ14 in 1940–1942 (annual means of ensemble mean) relative to the annual averages of 1938, 1939, 1943, and 1944. The long arrows qualitatively indicate the strengthening of the Brewer–Dobson circulation, the short arrows the wave-driving of stratospheric circulation, the dotted black line indicates the tropopause.

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The global view is analysed in a two-dimensional (latitude-height) ozone data set based on off-line assimilation of historical total column observations into a chemistry-climate model (HISTOZ14). Contrasting 1940–1942 with the neighbouring years, I find a decrease of ozone in the tropical lower stratosphere concurrently with the increase in the northern extratropics (Fig. 4, right), consistent with a large change in the Brewer–Dobson circulation (qualitatively depicted by long arrows in the figure), which was also found in model simulations12,15. Thus, historical total column ozone data, on an interannual time scale, can help to shed light on the variability of the stratospheric circulation.

The underlying cause of the strong Brewer–Dobson circulation, in this case, was an El Niño event, which was accompanied by a strong positive Pacific North American pattern and a negative phase of the North Atlantic Oscillation (NAO)16. These two variability modes might have contributed to enhanced wave-driving of the stratospheric circulation during this El Niño event12,15 (short arrows in Fig. 4b). A weakened polar vortex17 and increased poleward ozone transport during El Niño18,19 was also found in other studies20 (see also the review by ref. 21). Conversely, the weak polar vortex caused by enhanced wave activity could have contributed, via downward propagation, to the cold European winters from 1940 to 1942.

This example shows that amplifications of the Brewer–Dobson circulation over 2–3 year are possible. This is relevant for assessing ozone trends, but also for better understanding stratospheric trace gas transport and the lifetime of stratospheric aerosols.

An even more prominent, but shorter change in total column ozone at the two stations occurred in 2010. This year’s climate was also remarkable at the Earth surface in the North Atlantic-European sector. The NAO index reached the lowest recorded winter value, and Western Europe was in the grip of cold waves16. The stratospheric polar vortex (Fig. 5 shows 200 hPa height and anomalies with respect to 1991–2020, from ERA531) started with many disturbances in November and December, but then was strong in early January22. A strong planetary wave number one event in the second half of January then led to a displacement of the vortex. From 22–26 January the situation developed into a sudden stratospheric warming due to a polar vortex split. The effects of this event (reversal of zonal mean wind in the stratosphere) lasted well into March, and polar-cap averaged temperatures of the stratosphere were high22. Monthly geopotential height anomalies at the tropopause over the polar cap remained positive (Fig. 5). The NAO index remained strongly negative during the entire year (with the exception of July, where the index reached +0.0616). Extremely low values were noted again in November and December of 2010. According to Steinbrecht et al.23 the negative Arctic (or North Atlantic) Oscillation contributed ca. two thirds to the 2010 peak at Hohenpeissenberg, Germany. One third was attributed to an easterly wind-shear phase of the Quasi–Biennial Oscillation (QBO).

Fig. 5: Upper-level circulation and ozone in 2010.
figure 5

200 hPa geopotential height (lines) and anomalies (shading) from the 1991–2020 mean in each month of 2010 (ERA5 data). Also shown are total column ozone anomalies at Arosa and Oxford (filled circles).

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Oxford and particularly Arosa are near the southern centre of action of the NAO and therefore ozone anomalies are expected in relation to NAO excursions24. Monthly anomalies at Oxford (i.e., Reading) and Arosa relative to 1991–2020 were positive in each month of 2010, strongest in December (Fig. 5). This is a different situation than in the early 1940s as it is rather connected to an unusual persistence of the geopotential height anomaly pattern.

Very strong variations such as 1940–1942 and 2010 need to be understood for assessing ozone trends24 and for detecting ozone recovery. In the next section, a regression model is used to capture these effects and separate them from chemical effects.

Long-term trends

Both series, Arosa and Oxford, exhibit their lowest values in 1992 or 1993, after the Pinatubo eruption and at a time with high stratospheric chlorine loading (Fig. 3). Ozone recovery was then expected. However, almost 30 years later, ozone columns have not increased strongly. Since 1997, when stratospheric chlorine concentration peaked25, column ozone increased only 1–2 DU until 2021, similar numbers are found for the period since 2000 (Table 1; note the Oxford column ozone data 2002–2021 are from Reading, those before 2002 are from Camborne and adjusted to Reading; the effect of this change on the trend since 2000 is likely small).

Table 1 Changes in column ozone in different periods (in DU over the entire period) in observations and in different terms of the regression model (linear least-squares fit with 95% confidence intervals; for uncertainty of regression coefficients see Fig. 7).
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In order to detect recovery, long records are vital26 not only because they reach back into the “pre-CFC” period, but also because they cover, compared to short series, a larger range of circulation-related anomalies such as those in the early 1940s and 2010. Long-term trends such as those arising from ozone depleting substances or those due to climate change or changing emissions of ozone precursor gases can then be better isolated. I formulated multiple linear regression models to explain the time series of annual mean column ozone, with predictor variables that capture chemical as well as dynamical effects (though a strict separation is not possible). Five chemical variables were considered. Ozone depletion is measured by the Equivalent Effective Stratospheric Chlorine (the variable is termed EESC)27. The time series for the midlatitudes, starting in 1960, is backward extended asymptotically to plateau out in 1950 and updated after 2008 based on ref. 25. The concentration of methane28 is used as a proxy for chemical ozone formation from precursor gases. The CO2 concentration28 is taken as a measure of upper-stratospheric cooling, causing higher ozone concentrations. The global aerosol optical depth28,29 (VOL) is used to measure ozone depletion due to volcanic aerosols. Finally, spectral solar irradiance in the 240–280 nm band represents the chemical effect of solar UV changes30. All data were used in the form of annual mean values.

In addition to chemical variables, I considered three dynamical variables. The QBO was incorporated as the May-to-October average zonal mean zonal wind at 50 hPa, which was found to give the best fit. QBO data were taken from ERA531 after 1979 and from a reconstruction32, adjusted to ERA5 based on the 1979–2010 overlap, for 1925–1978 (this reconstruction is itself based on ERA40 between 1957 and 1978). I also included the strength of the polar vortex at 200 hPa (POL, defined as the difference between geopotential height at 75–90°N and 45–55°N32) from ERA5 back to 1950, backward extended with CERA-20C data33 (adjusted to ERA5 based on the 1950–1956 overlap), averaged from December (of the preceding year) to April. This is the season when the large-scale stratospheric circulation is most active and ozone most variable and when the polar vortex is most closely related to the Brewer–Dobson circulation34. In this way, the state of the polar vortex can imprint on the entire year as anomalies at the end of the winter tend to persist for several months35. I also considered local 200 hPa height (Z200) as a measure of local tropopause height. A low tropopause is associated with a larger fraction of stratospheric air in the column and therefore higher column ozone, exactly as found by Dobson in 1924 (shown in Fig. 2) and in the extreme year 2010 (Fig. 5). This is a year-round, instantaneous effect and hence the annual mean is chosen. Data are taken from ERA5 back to 1950, backward extended with a reconstruction based on upper air observations36 (individual missing months were complemented with CERA-20C, all data were adjusted to ERA5 based on the 1950–1956 overlap). This replaces the use of an NAO index as in other approaches37; in fact, including an annual mean NAO16 in addition to Z200 does not improve the result, using it instead of Z200 makes results clearly worse. Finally, in line with other regression approaches37, I also tested a predictor for the effect of El Niño (ENSO), namely the NINO3.4 index from HadSST1, averaged from September of the previous year to February38. However, as for the NAO, the effect is sufficiently well captured by the other dynamical variables. Unfortunately, eddy heat fluxes or similar measures of the strength of the Brewer–Dobson circulation are not available back to 1924. Note that only Z200 is different between Arosa and Oxford. Due to tropospheric warming, Z200 has a trend that might affect column ozone partly dynamically39 but might not separate well from chemical variables in the regression.

Regression results (least-squares fit) show that most of the variables have coefficients that are significantly different from zero at Arosa or Oxford. Exceptions are CO2, which also has an unexpected negative sign at both locations (arguably due to collinearity with CH4) and is highly collinear with the other variables, and solar UV. Therefore, I excluded CO2 but kept solar UV (termed SOL) as it has the correct (positive) sign and collinearity is not a problem. Note that methane (termed GHG) and EESC, though both significant, still have a high degree of collinearity.

The final models have seven predictor variables. The explained variance amounts to 69% for Oxford and 79% for Arosa; coefficients are given in Supplementary Table S1. The correlation between the two column ozone time series decreases from 0.87 in the observations to 0.62 in the residuals. This implies that there is common unexplained variability that could possibly be explained with better or additional predictor variables or more complex, monthly models, which however would come at the cost of simplicity (also, observations at Oxford were taken irregularly, such that monthly means could often not be calculated). Errors and uncertainties in the ozone data and in the predictor data contribute to unexplained variance.

The residuals of both models (Fig. 6a) show no specific patterns, apart from a high value at Oxford in 1934 (which is based on very few observations, but fulfils the criteria defined). The two prominent excursions in the 1940s and in particular in 2010 are greatly reduced in the residuals, indicating that the model well captures dynamical effects (for the 2010 case, Z200 and QBO explain roughly equal proportions of the anomaly at Oxford and Arosa relative to the neighbouring years, comparable to the results of ref. 40). No long-term trend is visible in the series and there is no autocorrelation. I can therefore interpret the model.

Fig. 6: Components of the regression fit for Oxford and Arosa.
figure 6

a Residuals and b sum of chemical and dynamical variables as well as observations and model fit. For visualisation, series are centred around their 1924–1960 mean value. The dotted black line marks the year 1997.

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The chemical and dynamical contributions, each centred around the period 1924–1960 (pre-CFC era) for visualisation, are shown in Fig. 7. Oxford (solid) and Arosa (dashed) agree well. The contribution with the largest amplitude in both models is EESC, followed by methane. Volcanic eruptions also had a marked impact. The dynamical contributions (Fig. 7b) have smaller amplitudes than the chemical ones, obviously varying strongly from year to year. The magnitude of all three dynamical contributions is similar, and they are almost identical for Oxford and Arosa.

Fig. 7: Components of the regression fit for Oxford and Arosa.
figure 7

a Chemical variables and b dynamical variables. For visualisation, series are centred around their 1924–1960 mean value. Error bars indicate ±1 standard error of the coefficients, multiplied with (and shown at the location of) the maximum absolute anomaly from the mean over the time series of the corresponding predictor variable. The dotted black line marks the year 1997.

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The fitted values (Fig. 6b) track the observations well. They also show a small but non-significant increase since 1997 (Table 1, for comparison with the LOTUS37 (Long-term Ozone Trends and Uncertainties in the Stratosphere) activity the Table also provides trends since 2000, which yields very similar results). This is however not true for the chemical and dynamical contributions individually. The sum of the chemical contributions reaches a minimum after the Pinatubo eruption and shows a clear increase afterwards. Since 1997, column ozone would have increased by 8 DU (1% decade−1) (Table 1, 7 DU since 2000) until 2021 due to a decrease in stratospheric chlorine and an increase in methane or other ozone precursors and upper-stratospheric recovery. Conversely, the sum of the dynamical contributions shows a decrease of ca. 4–5 DU or 0.5% decade−1 (Table 1, 6 DU since 2000). This negative dynamical trend, whose coefficient is not statistically significant at the 95% significance level, hides the increase expected from the chemical contribution.

Finally, I also performed the same analysis for the periods 1926–1960 and 1926–1970, i.e., periods during which the effect of stratospheric chlorine was weak. For the former period I find an increase of ca. +3 DU (0.25% decade−1) in the observations, which is reproduce in the regression model (ca. 4 DU) and is due to chemistry (3.5 DU). The latter period shows no trend in observations, +2.5 DU in the model with contributions of chemistry and dynamics of 1 DU. These trends are all very small and not significant.

Discussion

Column ozone monitoring has a century-long history (see Box 1). However, up to now only two long records have been available8,9. All other long series start in 1957 or later (see ref. 41 for an overview of ground-based measurements and their role in studying ozone recovery). The new Oxford series is therefore a welcome addition and provides support for the Arosa record, which is arguably of higher quality. Together, the two series allow us to analyse past variability and to better assess trends.

Neither series shows a significant trend since the peak of stratospheric chlorine. This is in agreement with several other studies37,42,43,44. Coldewey-Egbers et al.44 find regionally different trends (1995–2020) that are positive (1.5 ± 1.0% decade−1) over the North Atlantic and negative (−1.0 ± 1.0% decade−1) over Eastern Europe and are modulated by long-term changes in tropopause pressure. My study suggests that, for an unchanged circulation, ozone over Oxford and Arosa would possibly have increased by 8 DU since 1997, which is in agreement with changes found in chemistry-climate models40,45. This trend is masked by a negative trend of −5 DU induced by atmospheric circulation. This is consistent with Weber et al.43, who found a positive trend after 1996 only when properly accounting for dynamical changes. All three of our predictors (local tropopause height, polar vortex strength, and the Quasi–Biennial Oscillation) contribute to this negative trend; the first contributed the most. Together they offset almost two thirds of the chemically induced increase over the past 25 years. The warming troposphere and the poleward shift of atmospheric circulation might contribute to the trend in Z200 and continue into the future. However, the trend in the dynamical contribution is not statistically significant in my model and thus could also partly reverse in the future. The recovery of the ozone layer is a slow process, the amplitude over the past quarter century is likely small and thus circulation variability – random or not – can hide the trend at a given location3. Long time series can help to better address and put into perspective the dynamical contributions.

However, the statistical model used in this study has uncertainties. Calibrating statistical models mainly in the phase of ozone depletion can lead to misleading results46. By taking a century-long perspective, the regression in this study should be more robust, but stationarity is still assumed. The fact that we now have two long records, whose coefficients are very similar, and that all coefficients have the theoretically expected sign also suggests that the results are robust. The regression model could possibly be further improved37 by including seasonally varying factors or allowing for non-linear relations. Furthermore, the predictor variables themselves have uncertainties, particularly in the early decades.

Some factors need additional study. The trend in column ozone is affected by changes in tropospheric ozone. At temperate latitudes surface ozone increased by 30–70% between the historical period (1896–1975) and the present (1990–2014)47, the increase in the tropospheric column is however difficult to estimate. In the regression model, this trend would be captured by the increasing methane concentrations. However, these contribute only to a small chemical column ozone increase from the 1920s to the 1960s, amounting to ca. 2–4 DU. Interestingly, an increase in total column was noted by ozone scientist at that time48. In CMIP6 models column ozone at 30°–60°N increases by ca. 4–5% (ca. 12 DU) from the 1920s to 1960s40, which is considerably more than in my regression model (0–1% or 0–4 DU, Table S1) and cannot be explained with uncertainties in the regression coefficients. An increase of ca. 3% from pre-industrial to present day due to increasing precursor gases is found in another study7. These different numbers point to the need of reconciling climate model simulations with historical observations. Specific model studies would be needed to clarify these important discrepancies. With respect to chemical processes in the stratosphere, recent studies show that there can still be surprises49. Long time series are required for better addressing these questions. Although long series are only available for the northern midlatitudes and do not allow conclusions on global recovery, they allow testing the results from chemistry-climate model simulations. This study shows a good agreement for the recovery period (1997–2021), but a worse agreement for the pre-CFC era (1926–1970).

Historical ozone data also serve as a diagnostic for past atmospheric circulation changes, as shown on behalf of the 1940–1942 anomaly. They have been used for that purpose since the early years (see Box 1). The Brewer–Dobson circulation was discovered in the context of studies on the global ozone distribution. Total column ozone played a role in our understanding of the Quasi–Biennial Oscillation from the very start50. More recently, total column ozone data were used in one of the first studies on the expansion of the tropical belt51, and historical total column ozone data were used to study the preceding southward shift of the northern tropical belt52.

Therefore, historical ozone data can help us to better understand past weather and climate extremes. Long series cover a broader range of circulation-related anomalies and serve as a background against which ozone trends can be compared. In this study, the analysis of past events suggests that deviations of 20–30 DU over 2–3 years are possible. Even the day-to-day changes could be informative. Historical column ozone measurements could today lead to improved weather reconstructions by assimilating them into reanalyses, thus using them in a similar way as envisaged by Dobson in 1924.

Ozone monitoring has a century-long history that goes back to the work of Fabry in Paris and Dobson in Oxford. The interest in ozone has changed several times – ozone was a meteorological quantity, then a geophysical quantity, a chemical quantity, and a radiative quantity – evidencing the many geophysical relations it has with the atmosphere (the motivation of Dobson back in 1924, see Box 1). For precisely these reasons, historical ozone data are interesting today as a window to the past radiative, dynamical and chemical state of the atmosphere, with relevance for answering currently open questions in science such as constraining ozone recovery.

Methods

Oxford ozone series

The Oxford record from 1924 to December 1975 has been re-evaluated by ref. 10. These data were obtained by or under the direct guidance of G. M. B. Dobson and they are available from the World Ozone and Ultraviolet Radiation Data Centre (WOUDC, https://woudc.org). Dobson died on 11 March 1976. Here, I add two more years of data that were measured by the staff of the Department, including Robert J. Wells, after Dobson’s death, covering June 1976 to October 1977. The instrument used was still the same – Dobson Spectrophotometer #1. These data were digitised from the original data sheets (Fig. 1) and processed according to the Handbook for Dobson Ozone Data Re-evaluation (see next Section)53. In total, 1209 measurements were digitised. There are some gaps in the extremely hot summer of 1976 as the instrument got too hot.

Most observations used the AD or CD wavelength pairs, some were done with the CC’ pair. Operation modes include the standard modes direct sun (DS), zenith blue (ZB), and zenith cloudy (ZC). In addition, modes MS, FS, and FSF are marked on the data sheets. FS and FSF possibly refer to “focused sun” and “focused sun with filter” observations. The latter were exclusively performed when the sun was very low.

Processing

In Dobson spectrophotometers, ozone x is calculated from the radiation intensities I at two wavelengths λ and λ’ via the relative intensity N:

$$N=\,\log \left(\frac{{I}_{0}}{{I}_{0}^{{\prime} }}\right)-\,\log \left(\frac{I}{I{\prime} }\right)$$
(1)

where I and I0 are the intensities at the surface and outside the Earth’s atmosphere, respectively. N is normally obtained from the dial reading at the instrument, R, via an instrument specific conversion table (R-N table). Observations mostly use the double difference of two wavelength pairs (subscripts 1 and 2), the standard equation for calculating total column T ozone then is:

$${T}_{12}=\frac{({N}_{1}-{N}_{2})-[{(\beta -\beta ^{\prime} )}_{1}-{(\beta -\beta ^{\prime} )}_{2}]\frac{mp}{{p}_{0}}-[{(\delta -\delta ^{\prime} )}_{1}-{(\delta -\delta ^{\prime} )}_{2}]{{\mbox{sec}}}(SZA)}{[{(\alpha -\alpha^{\prime} )}_{1}-{(\alpha -\alpha ^{\prime} )}_{2}]\mu }$$
(2)

where β is the Mie scattering coefficient (primes denote the longer wavelength), α is the absorption coefficient, δ is the aerosols scattering coefficient, m is the relative air mass, μ is the relative path length through the ozone layer, SZA is the solar zenith angle, p is station pressure, and p0 is mean sea-level pressure.

Aerosol scattering can then be neglected and the equation reduces to:

$${T}_{12}=\frac{({N}_{1}-{N}_{2})-[{(\beta -\beta ^{\prime} )}_{1}-{(\beta -\beta ^{\prime} )}_{2}]\frac{mp}{{p}_{0}}}{[{(\alpha -\alpha ^{\prime} )}_{1}-{(\alpha -\alpha ^{\prime} )}_{2}]\mu }$$
(3)

From the observation time I recalculated the solar zenith angle and, assuming a mean ozone layer height of 22 km, the air mass m and the relative path length through the ozone layer μ. I used pressure data from E-Obs54 for p in Eq. 3. In addition to the data sheets, I also have the R-N table for this instrument, dated to 1974 (Fig. 1). The data sheets indicate intermediate steps, allowing in part to reverse engineer the calculations, but the intermediate steps become more sparse as time progresses, and soon only the dial readings R and the final ozone values are noted. From the observations with intermediate steps. I note that the R-N table was not applied directly, but offsets of 0.040, 0.024, and 0.012 were added for the A, C, and D wavelength pairs. However, the ozone values derived in this way (those reduced by the observers as well as my re-calculation) showed quite substantial differences between concurrent (<1 h apart) DS measurements at the AD and CD pairs, amounting to ca. 15 DU. I considered the AD pair as the standard and changed the offset applied to the C pair to 0.034, such that the differences vanished (r = 0.97, RMSE = 12 DU). I then reduced all other operation modes based on their N and μ values according to simultaneous measurements with already reduced data as described below.

First, I reduced the MS measurements. In the original calculations offsets of −0.121, −0.076, and −0.025 were applied for the A, C, and D pairs. However, results showed a rather poor agreement with DS measurements (both AD or CD). Therefore, I used a regression model as suggested by ref. 55

$$x={c}_{0}+{c}_{1}N+{c}_{2}\mu +{c}_{3}{N}^{2}+{c}_{4}{\mu }^{2}+{c}_{5}{N}^{3}+{c}_{6}{\mu }^{3}+{c}_{7}N\mu +{c}_{8}N{\mu }^{2}+{c}_{9}{N}^{2}\mu$$
(4)

This regression was calibrated separately for AD-MS vs. AD-DS (R2 = 0.988, RMSE = 5 DU) and CD-MS vs. CD-DS (R2 = 0.977, RMSE = 7 DU) data. The FS observations were reduced using the R-N conversions of the DS values. I found a bias of −7.8 DU (RMSE = 10 DU) for AD-FS and −7.8 (11) DU for CD-FS, which I considered acceptable. Then AD-ZB data were reduced to AD-DS (using Eq. 4) after removing 2 outliers (R2 = 0.991, RMSE = 3.6 DU). AD-FSF and CD-FSF were separately reduced, however, due to the smaller number of simultaneous observations, both were reduced against all AD/CD DS/MS measurements combined (R2 = 0.985, RMSE = 6.3 DU, for AD-FSF and R2 = 0.987, RMSE = 6.1 DU, for CD-FSF).

Then I reduced CC’ ZB (against AD-DS), yielding R2 = 0.908, RMSE = 13 DU. CC’ ZC data could not be reduced in the standard way as no N-values were given for the C’ pair, only R values. Therefore, I used polynomial regression (against all AD/CD DS/MS data as there were too few simultaneous AD-DS observations):

$$x={c}_{0}+{c}_{1}N+{c}_{2}\mu +{c}_{3}{R}_{C^{\prime} }+{c}_{4}N\mu +{c}_{5}N{R}_{C^{\prime} }+{c}_{6}\mu {R}_{C^{\prime} }+{c}_{7}{N}^{2}+{c}_{8}{\mu }^{2}+{c}_{9}{R}_{C^{\prime} }^{2}$$
(5)

This model yields R2 = 0.946, RMSE = 14 DU. Finally, values from different observation modes and wavelengths were then averaged to yield daily ozone data. Given the RMSE values from the comparison above (to which both compared series contribute) and given the fact that daily means typically average ca. 3 values, thus reducing the random error, we can assume that the error of daily values is clearly below 10 DU.

Homogenisation

After 1977, I complemented the Oxford series with data from Bracknell (1967–1989, Dobson Beck #2, 65 km from Oxford), Camborne (1989–2003, Dobson Beck #41, 330 km), and Reading (2002–2021, Brewer MkIV #75, 38 km), all taken from the WOUDC. All series were statistically adjusted to the Reading series by adding offsets based on the overlapping data portions and proceeding backwards (no adjustment was performed for the transition from Bracknell to Camborne, which do not overlap). For annual averaging, to make best use of sparse data, I deseasonalised the data by fitting and subtracting the first two harmonics of the annual cycle and adding back the constant (mean value). This was performed separately for each daily value considering a window of ±500 values (correspondingly shortened at the edges). Then I averaged the data into 5-day intervals. If at least 15 intervals were available in a given year, an annual average was formed. The same procedure was applied to the homogenised series from Arosa. Applying the Craddock test56 revealed a clear break in 1963, the cause could not be identified. The break was corrected by considering 5 years before and after the break. Furthermore, the period 1933–1946 (in this period Dobson used his photoelectric instrument57, but not yet with a photomultiplier) was found to be off and was adjusted to the period 1949–1962 (note that this period is internally rather heterogeneous; further subdivisions would be equally defendable).

Total column ozone in 1938–1944

Three series were added to the figure of Brönnimann et al.12: Oxford, Table Mountain13, and Montezuma. From the monthly means in 1938–1944 in the Oxford series, the mean annual cycle was subtracted, the anomalies were standardised and smoothed with a 12-month moving window. For Oxford, a minimum of 10 daily values per month and 6 monthly means per 12-month average was required. I also added ozone data calculated from transmission in the visible wavelength range at Table Mountain, California (at 574 and 615 nm) and Montezuma, Chile (at 578 nm). As these measurements were very sparse, I processed daily data and subtracted an annual mean cycle based on fitting the first two harmonics of the annual cycle and then standardising the daily anomalies. To produce a 12-month moving average, I required 15 daily values per window (due to the different method the lines are dashed).