2.1 The Dobson spectrophotometer

The Dobson spectrophotometer was designed to measure TCO₃ by the technique of differential optical absorption spectroscopy (Dobson, 1957). The TCO₃ values from direct sun (DS) observations are calculated based on the Beer's law applied to spectral UV solar irradiances for selected wavelengths with strong and weak absorption by the ozone layer. These wavelengths are denoted as A (305.5–325.0 nm), C (311.5–332.4 nm), and D (317.5–339.9 nm). The TCO₃ value is determined from linear combination of the logarithm of the ratios between A pair and D pair irradiances, called the double AD wavelength pair algorithm, to reduce the effects of the aerosols scattering on calculated ozone. It is also possible to use C pair irradiances instead of the A pair, i.e., the so-called double CD pair, to obtain TCO₃ if the solar irradiance at the shorter wavelength of the A pair is too weak because of a large ozone absorption under high air masses (μ>3) and/or during cloudy conditions.

Another option to calculate TCO₃ by the Dobson spectrophotometer is to use scattered sunlight from the zenith sky (ZS) at the same wavelengths as for the DS observations. In this case, the same algorithm is implemented, but the result needs to be reduced by empirical charts. The charts proposed by Rindert (1973) were used throughout Belsk's observations for AD and CD double wavelength pairs. The operational data archived in the PANGAEA database was obtained using the Bass–Paur O₃AC at fixed temperature of −46.3 ^∘C according the recommendation of Komhyr et al. (1993).

Figure 1 shows time series of the number of daily TCO₃ means obtained from DS intraday observations with AD and/or CD wavelength pairs in January and July for the 1964–2019 period. The number of the DS daily means per month is larger in June because of usually less cloudy conditions this month compared to January and longer day length in summer (i.e., greater chance for cloudless conditions). The monthly mean TCO₃ for January is mostly based on ZS observations. It is worth mentioning that a reduced number of DS observations (less than 15 per month) were found in July for the period 1985–1995. During this period, ZS observations under a cloudless sky, i.e., the so-called zenith blue (ZB) observations, replaced DS observations because the solar disk was not clear due to heavy contamination of Belsk's atmosphere with industrial aerosols. The observers were then recommended to choose ZB measurement for a clear sky.

Figure 1Number of TCO₃ daily means based on the direct sun measurements for January and July in the period 1964–2019.

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The TCO₃ values by ZS observations could be calculated for almost all weather conditions (excluding cases with heavy and variable cloudiness), but they are reliable, i.e., close to the DS values, for the air masses up to 2.8 (Fig. 2a). The empirical reduction curves (Rindert, 1973), which were used to convert ZS values to equivalent DS values, did not reflect all possible combinations of cloud types and their positions in the sky. Therefore, the DS–ZS differences can sometimes exceed 5 %. To eliminate the long-term drift of the DS–ZS differences, the following transfer function is used from the regression line fit to the relative differences between DS and ZS TCO₃ subsets for $\mathit{\mu }\subset [\mathrm{2.8},\mathrm{4.0}]$:

where TCO_3, ZS is the TCO₃ value derived from ZS observations, μ is air mass during the Dobson observation, and ${{\mathrm{TCO}}_{\mathrm{3},\mathrm{ZS}}}^{*}$ pertains to the corrected value for μ>2.8. However, the linear correction is not valid if μ>4.0 (Fig. 2a). Only 0.7 % of all TCO₃ observations were made at such high μ values. The fixed correction of 1.015 is applied if μ>4.0, but ${{\mathrm{TCO}}_{\mathrm{3},\mathrm{ZS}}}^{*}$ values should be treated with caution. The smoothed pattern of the DS–ZS differences (Fig. 2b) is close to zero after the application of the transfer function according to Eq. (1).

Figure 2Air mass dependence of differences between daily mean TCO₃ values by DS and ZS measurements as a percentage of the DS TCO₃ values: original data (a) and ZS TCO₃ after the correction using Eq. (1) (b).

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Figure 3Time series of relative differences between daily means of TCO₃: DS–AD vs. DS–CD measurements (a) and DS vs. ZS measurements (b). The black curve shows the smoothed pattern of the data. The blue line is the linear regression line.

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DS–AD observations provide the most accurate TCO₃ values (Dobson, 1957) when μ<2.5. However, these observations are not possible for northern sites, such as Belsk, where the noon air masses above 2.5 appear in the period from 3 November up to 9 February, and the yearly maximum air mass at noon on 23 December is 3.75. Therefore, DS–CD observations are recommended for these periods (Dobson, 1957). Additional intraday TCO₃ values, especially after 2005, were calculated using the nearly simultaneous DS–AD and DS–CD observations to find a relationship between these TCO₃ values. Figure 3a shows that the relationship is quite stable in the 1963–2019 period, i.e., the smoothed differences (black curve) are within the [0 %,1 %] range, and the linear regression line (blue line) is trendless. A similar comparison between DS and ZS observations, after application of the transfer function (1), ensures that the smoothed differences are close to the zero line throughout the observation period (Fig. 3b).

The monthly mean TCO₃ differences between various subsets of the TCO₃ data over the period 1963–2019 are shown in Fig. 4. The differences are derived from the monthly averaging of the daily mean TCO₃ values for the following subsets: DS–AD, DS–CD, ZB, ZS, and for less reliable ZS observations, when the zenith was obscured by clouds, i.e., the so-called zenith cloudy (ZC) observations. For all ZS intraday values if μ≥2.8, the correction function according to Eq. (1) was applied. The TCO₃ differences shown in Fig. 4 are in the range of ±1 % almost all year round, excluding autumn/early winter months (October–November–December). Moreover, for each selected month, from January to September, the spread between the monthly mean differences is about ∼1 % for the all considered subsets of the Dobson observations. The maximum spread is 4 % in December based on the difference of −1 % for DS–AD vs. DS–CD and 3 % for DS vs. ZC.

Figure 4The monthly mean relative differences between daily TCO₃ means derived from different types of the Dobson measurements. The bar denotes the range: mean ± standard deviation.

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2.2 Calibrations of the Dobson spectrophotometer

The Dobson spectrophotometer serial no. 84 at Belsk has been operated continuously since 23 March 1963 in the same place with only a few breaks in observations (up to several weeks) due to the international calibration campaigns with other Dobson instruments. The frequent comparisons of Belsk's Dobson with the world standard instrument in combination with the recalibration of the optical wedge of the instrument and the calculation of the resulting R–N tables were of key importance for maintaining the quality of Belsk's Dobson. The R–N table is used to convert the dial reading (the so-called R value) obtained by the Dobson observer into the logarithm of the ratio between the light intensities in a pair of the UV wavelengths with weak and strong absorption by ozone (the so-called N value). N values are used in theoretical formulas to calculate TCO₃ (e.g., Dobson, 1957).

The first DI intercomparison was held at Belsk in June/July 1974. The participating Dobsons were compared against the world primary standard (WPS) Dobson spectrophotometer no. 83 and the optical wedge of Belsk's Dobson was recalibrated (Dziewulska-Łosiowa and Walshaw, 1975). The next DI intercomparison was held in Potsdam (Germany) in June 1979 also with the attendance of the same WPS. During the comparison the new R–N tables were obtained, which only slightly differed from those calculated earlier at Belsk's intercomparison (Dziewulska-Łosiowa et al., 1983). The subsequent campaigns were in Arosa (1986, 1990, and 1995) with the WPS Dobson no. 83. The next intercalibrations (2001, 2005, 2009, and 2014) were organized at the European regional Dobson calibration center, the Meteorological Observatory Hohenpeissenberg, Germany. The local European sub-standard, DI no. 64, was used as the reference instrument for comparisons at the center. After the intercomparisons, the new R–N tables were obtained and used immediately, i.e., after the instrument arrived at the observing site, as input to the TCO₃ calculation algorithm. The retrieval software has not been changed since its first operational use in 1978 (Degórska et al., 1978). Table 1 summarizes the intercomparison campaigns with Belsk's Dobson.

Table 1The intercomparison campaigns with the Dobson instrument from Belsk.

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The first homogenization of Belsk's TCO₃ data for the period 1963–1981 by Dziewulska-Łosiowa et al. (1983) was based on Potsdam's R–N tables, extraterrestrial constants determined at Belsk in 1974 during the first DI intercomparison, and the O₃AC by Vigroux (1967). The zenith sky irradiances (for AD and CD observations) were reduced to the DS equivalent values using the empirical charts according to Rindert (1973). The next homogenization was in 1991 by Degórska and Rajewska-Więch (1991). All data collected before 1992 were re-evaluated on a reading-by-reading basis using the Bass–Paur O₃AC (at a fixed temperature of −46.3 ^∘C) that has been recommended for processing Dobson TCO₃ measurements since 1 January 1992.

Optical wedge calibrations performed during the entire period of ozone observations at Belsk had only a slight effect on the TCO₃ values. Figure 5 shows the comparison of TCO₃ calculated for the first 2-year period (1963–1964) and last 2-year period (1980–1981) of the time series after the first homogenization in 1983. Original TCO₃ values from DS–AD observations presented by Dziewulska-Łosiowa et al. (1983), which were based on the Vigroux O₃AC, are converted to the values obtained using the Bass–Paur O₃AC (i.e., multiplied by 0.9743, as recommended by the International Ozone Commission in 1992) and then compared with the corresponding values obtained from the current retrieval based on the Bass–Paur O₃AC and R–N tables obtained in the last intercomparison in 2014. There is almost one-to-one correspondence between the two TCO₃ datasets, i.e., the slope of linear fit is 0.9999 and 0.9962 for the periods 1963–1964 and 1980–1981, respectively. The maximum difference between TCO₃ values is less than 1 %. Small differences (<1 %) are also found after comparison of the DS–AD subset of TCO₃ values in August 2020 calculated using different R–N tables that were operationally used in the 1990s and 2020s (Fig. 6).

Figure 5TCO₃ daily means by AD–DS measurements in the periods 1963–1964 and 1980–1981 calculated with the present (2019) calculation algorithm (R–N tables based on the 2014 intercomparison) vs. those by the same algorithm using old (1979) R–N tables.

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Figure 6Daily means of TCO₃ in August 2020 from DS–AD measurements as calculated with different R–N tables obtained during intercomparisons in the 1990s and 2000s (see Table 1).

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From these comparisons of the DS–AD measurements, it can therefore be concluded that Belsk's Dobson demonstrated stable performance throughout the measurement period. A linear approximation of TCO₃ values in periods between the calibration campaigns was not necessary to account for changes in R–N values and instrument aging.

2.3 Adjustment to the Brewer spectrophotometer

The ozone monitoring with the Brewer spectrophotometer serial no. 64 (BS64) mark II (single monochromator) was launched at Belsk in 1991. Like other Brewers, the BS64 is a fully automated, self-testing, PC-controlled instrument intended for continuous, long-term observations in all weather conditions (e.g., Fioletov et al., 2005). The quality of BS64 measurements has been supported by regular (yearly or at least every 2 years) comparisons with the international travel reference instrument provided by the International Ozone Services Inc. (https://www.io3.ca/index.php, last access: 2 September 2021). The BS64 instrument constants re-defined after each comparison were immediately incorporated into the operating retrieval.

The Brewer TCO₃ is derived from a weighted linear combination of solar irradiances at five wavelengths (306.3, 310.0, 313.5, 316.8, and 320.0 nm) to eliminate noise due to SO₂ absorption in the UV range (Kerr et al., 1988). The Brewer TCO₃ retrieval uses the Bass–Paur O₃AC at −45 ^∘C for two types (DS and ZS) of observations. There are many daily BS observations regardless of weather conditions. Cycles of five observations, which are performed in ∼3–4 min, are repeated every 5 to 20 min throughout the day depending on the instrument's schedule. The mean TCO₃ value, averaged over five observations, is calculated if the scatter of these TCO₃ values is small, i.e., standard deviation is less than 2.5 Dobson units (DU). The Dobson spectrophotometer provides instantaneous TCO₃ values, while the Brewer instrument gives the average of five observations, so this may be an additional source of differences between the spectrophotometers.

2.3.1 Correction for the effective temperature

Figure 7a shows the time series of the differences between Brewer and Dobson TCO₃ daily means (Brewer minus Dobson TCO₃ as percent of the Dobson TCO₃ value) calculated for the period 2002–2019. This period was selected because more DS–AD and DS–CD observations were performed during the day (see Fig. 3a) to construct a transfer function from the Dobson TCO₃ to the Brewer equivalent TCO₃ before the predicted change in monitoring policy to less frequent measurements during the day, i.e., only a few observations around noon in perfect weather conditions. The well-known seasonality of the Brewer–Dobson (BD) differences, i.e., underestimation of the Dobson TCO₃ in the cold period of the year, could be observed after applying a low-pass filter, the locally weighted scatterplot smoothing (LOWESS, Cleveland, 1979), to the time series of BD differences.

Figure 7The differences between the Brewer and Dobson TCO₃ daily means as a percentage of the Dobson TCO₃ value: original data after application of the correction function, according to Eq. (1), to the Dobson ZS data (a) and the Dobson and Brewer TCO₃ corrected for the effective temperature (b). The red curve represents the smoothed pattern by the LOWESS filter.

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To reduce the BD seasonal differences, the temperature-dependent O₃AC is applied instead of the operational O₃AC assuming fixed temperature T₀, i.e., $T_{\mathrm{0}}=-\mathrm{46.3}$ ^∘C (Dobson) and $T_{\mathrm{0}}=-\mathrm{45.0}$ ^∘C (Brewer). Here we use the temperature correction factor, α, calculated by Redondas et al. (2014), i.e., α=0.104 % K⁻¹ (for Dobson) and α=0.009 % K⁻¹ (for Brewer). These values are based on the O₃AC dependence on temperature obtained by the Institute of Experimental Physics (IUP), University of Bremen (Serdyuchenko et al., 2014). The correction function to account for the actual effective temperature is as follows:

$$\begin{array}{}\text{(2)}& {\mathrm{TCO}}_{\mathrm{3},\mathrm{NEW}}=(\mathrm{1}+\mathit{\alpha }(T_{\mathrm{0}}-T_{\mathrm{eff}}\left)\right)\times {\mathrm{TCO}}_{\mathrm{3},\mathrm{OLD}},\end{array}$$

where T_eff is the effective (weighted by the ozone vertical profile) temperature, TCO_3, OLD is the TCO₃ value at the fixed temperature, and TCO_3, NEW is the temperature-corrected value. Prior to the application of Eq. (2), TCO₃ values by ZS Dobson observations need to be converted to the DS TCO₃ equivalent using transfer function according to Eq. (1). The effective temperature at noon is taken after the Tropospheric Emission Monitoring Internet Service (TEMIS) overpass data (https://www.temis.nl/climate/efftemp/overpass.php, last access: 2 September 2021), based on the European Centre for Medium-Range Weather Forecasts (ECMWF) model estimates. Koukouli et al. (2016) found that the ECMWF effective temperature was in good agreement with that from the ozone sounding in Northern Hemisphere midlatitudes.

Figure 7b shows the time series of the BD differences after applying the correction function according to Eq. (2). The visible seasonality in Fig.7a disappears, but there are still limited seasonal variations. To find out the range of these oscillations, the monthly mean BD differences are calculated averaging the daily differences. The results are shown in Fig. 8a (DS subset) and Fig. 8b (ZS subset). A comparison of the original DS and ZS data (not accounting for T_eff seasonal variability) ensures that the seasonal BD difference is ∼4.5 % as calculated using the monthly mean difference values of ∼3.5 % and −1 % for January and July (or August for ZS data), respectively. After the application of Eq. (2), the BD difference is smaller, i.e., ∼2.5 % (DS) and 3 % (ZS). The smoothed curve in Fig. 7b ensures that the Dobson TCO₃ values were ∼1 % lower (2002–2004) and ∼1 % higher (2018–2019) compared to the Brewer values. Such discrepancies may be related to the Brewer ZS TCO₃ values because they may be influenced by clouds (the Brewer ZS algorithm is based on a statistical relationship with parallel DS observations), which in some years results in overestimation (or underestimation) in relation to the Dobson TCO₃ values.

Figure 8The monthly means of the Brewer–Dobson differences for the operational data (Bass–Paur O₃AC at fixed temperature) after application of the correction, according to Eq. (2), for the dependence of O₃AC on temperature based on IUP measurements and after adjustment of the Dobson TCO₃ to the Brewer TCO₃ equivalent by Eq. (3) accounting for the stray light effect differences between the spectrophotometers. The results are for DS measurements (a) and ZS measurements (b). Bar denotes the range: mean ± standard deviation.

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It is worth mentioning that the monthly BD differences for the temperature-corrected data are out of the ±1 % range only in January and December (DS subset) and additionally in November for the ZS subset. To the authors' knowledge, the BD differences for a less precise ZS subset have not yet been discussed by other authors. It seems that the stray light effect, which may be different in the Dobson and Brewer instruments (Belsk BS64 is a single monochromator spectrophotometer), is responsible for greater differences between these spectrophotometers during low-solar-elevation periods.

2.4 Uncertainty of the Brewer-adjusted Dobson TCO₃

Typically, daily TCO₃ averages were archived based on a few measurements around local noon with nominal best quality. The AD–DS observation shows the highest accuracy of all possible combinations of the double wavelength pairs (AD and CD) and observation type (DS, ZB, and ZS). This kind of observation is not always possible because of weather conditions (clouds) and during low solar elevation. At the beginning of the TCO₃ observations at Belsk, a decision was made to increase the number of daily observations for selected days in each month in order to assess the uncertainty of TCO₃ observations. On such days, there were many, almost simultaneous observations with different instrument settings. For example, Fig. 9 shows the TCO₃ measurements at Belsk on 8 August 2017, planned to calculate differences between successive TCO₃ values. During the day, 46 observations were made for the following instrument settings: AD–DS, AD–ZS, and CD–DS.

Figure 9The Brewer-adjusted TCO₃ values measured at Belsk on 8 August 2017 with different settings of the Dobson spectrophotometer.

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The difference between two consecutive TCO₃ values sometimes exceeded 10 DU even if the measurements were taken within 10 min. It is impossible for TCO₃ to change rapidly over such a short timescale, taking into account natural variability in ozone in the stratosphere. The statistics of TCO₃ differences between the almost simultaneous Dobson measurement allows us therefore to estimate the uncertainty of the Brewer-adjusted Dobson TCO₃ values.

The statistics were obtained for various selected maximum ranges between the successive measurements, i.e. less than 1, 5, and 10 min. It was found that the statistical parameters did not depend on these ranges, which proved a reliable estimation of the uncertainty. This uncertainty combines the instrumental uncertainty associated with the differences between various types of Dobson measurements with the uncertainty resulting from the observer's skill to perform the measurements. Table 2 presents the statistics of the differences between TCO₃ values obtained almost simultaneously for different data subsets.

Table 2The statistics of the differences between the Brewer-adjusted Dobson TCO₃ values from two successive measurements taken at an interval of no longer than 10 min for the period 1963–2019. The differences (in % of the mean of the two compared values) are shown for different sub-classes of the data and μ ranges. SD and n denote standard deviation and number of the measurement pairs used in the calculations, respectively.

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The uncertainty of the Dobson observations for the subset with the nominal highest accuracy (DS–AD) is $[-\mathrm{1.15}\mathit{\%},\mathrm{1.09}\mathit{\%}]$, calculated as the range from the 5th to 95th percentile. The uncertainty increases with decreasing solar elevation, and the largest value, $[-\mathrm{4.58}\mathit{\%},\mathrm{4.04}\mathit{\%}]$, is for the ZS subset when air mass is between 3 and 4. The greatest uncertainty for this type of observations seems to be due to the cloud variability over the site as the ozone retrieval for non-DS observations is based on a statistical relationship with nearly parallel DS measurements, not taking into account the specific cloud configuration and optical properties.