The Pandora spectrometer system uses a temperature-stabilized (1 ∘C) symmetric Czerny–Turner system with a 50-micron entrance slit and 1200 lines mm-1 grating. Unlike the Brewer instruments, which only measure intensities at selected wavelengths, the Pandora instruments, with a 2048×64 back-thinned Hamamatsu CCD detector, record spectra from 280 to 530 nm at 0.6 nm resolution (Herman et al., 2015). The spectra are analysed using the differential optical absorption spectroscopy (DOAS) technique (Noxon, 1975; Platt, 1994; Platt and Stutz, 2008; Solomon et al., 1987), in which absorption cross sections for multiple atmospheric absorbers (including ozone, NO2, SO2, HCHO, and BrO) are fitted to the spectra (Tzortziou et al., 2012). The Daumont, Brion, and Malicet (DBM) (Daumont et al., 1992; Brion et al., 1993, 1998) ozone cross section at an effective temperature of 225∘ K is used in the Pandora retrievals (Herman et al., 2015). Additional information on Pandora calibrations and operation can be found in Herman et al. (2015).

Two commercial Pandoras (nos. 103 and 104) were used in this study with no modifications to operational and processing algorithms (available from SciGlob, http://www.sciglob.com/). Pandoras nos. 103 and 104 were deployed in Toronto in September 2013, and in this work all available Pandora data from these instruments are used. Pandora no. 104 was moved to the Canadian oil sands region in August 2014. Following the work of Tzortziou et al. (2012), the Pandora ozone dataset is filtered to remove data from which the normalized root mean square (RMS) of weighted spectral fitting residuals is greater than 0.05, and the Pandora-calculated standard uncertainty (Tzortziou et al., 2012) in TCO is greater than 2 DU.

The Brewer instruments use a holographic grating in combination with a slit mask to select six channels in the UV (303.2, 306.3, 310.1, 313.5, 316.8, and 320 nm) to be detected by a photomultiplier. The first and second wavelengths are used for internal calibration and measuring SO2 respectively. The four longer wavelengths are used for the ozone retrieval. The total column of ozone is calculated by analysing the relative intensities at these different wavelengths using the Bass and Paur (1985) ozone cross sections at a fixed effective temperature of 228.3∘ K (Kerr, 2002).

Most of the instruments in the BrT (nos. 8, 14, and 15) and BrT-D (no. 145, nos. 187, and 191) have been in operation since Pandora instruments were deployed. However, there are a few measurement gaps for some of the Brewers. For example, Brewers nos. 14 and 15 were recalibrated at Mauna Loa, Hawaii, in October 2013, and Brewer no. 145 was in Spain in March 2014 for an intercomparison. We also had to exclude some periods due to instrument malfunction and repairs. The coincident measurement periods for the instruments are shown in Table 1. The data from Brewer and Pandora instruments are both time-binned (3 min) for the comparison. Following the work of Tzortziou et al. (2012), the Brewer dataset is filtered to remove data with calculated standard uncertainty in TCO greater than 2 DU. In addition, the Brewer dataset is filtered for clouds by removing data for which the logarithm of the signal at 320 nm is less than the mean value minus 2 standard deviations (4 % of data were removed with this filter).

The Ozone Monitoring Instrument (OMI) is a nadir-viewing, near-UV–Vis spectrometer aboard NASA's Earth Observing System (EOS) Aura satellite (launched in July 2004). The OMI instrument measures the solar radiation backscattered by the Earth's atmosphere and surface between 270 and 500 nm with a spectral resolution of about 0.5 nm (Levelt et al., 2006). The OMI TCO data are retrieved using both the Total Ozone Mapping Spectrometer (TOMS) technique (developed by NASA (Bhartia and Wellemeyer, 2002) and based on a retrieval using four wavelengths at 313, 318, 331, and 360 nm) and the DOAS technique (developed by KNMI (Veefkind et al., 2006; Kroon et al., 2008) and based on the spectrum measured in the wavelength range 331.1–336.6 nm). The OMI TCO validation done by Balis et al. (2007) shows a globally averaged agreement of better than 1 % for OMI–TOMS data and better than 2 % for OMI–DOAS data in comparison with Brewer and Dobson measurements.

The OMI TCO products used in the present study are the Level-3 Aura/OMI daily global TCO gridded product (OMTO3e) retrieved by the enhanced TOMS Version 8 algorithm (Balis et al., 2007). The OMTO3e data (Bhartia, 2012) are generated by the NASA OMI science team by selecting the best pixel (shortest path length) data from the good-quality Level-2 TCO orbital swath data (for example, L2 observations with SZA < 70∘; details can be found in Bhartia, 2012) that fall in the 0.25∘×0.25∘ global grids. The OMTO3e data that come from the grid point over the ground-based site are used in this work to validate our correction method for Pandora TCO data.

In this work, the ozone-weighted effective temperature was used to assess the temperature sensitivity of Pandora ozone retrievals. Temperature and ozone profiles were extracted from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim data for 2013–2015 (Dee et al., 2011) with 0.5∘×0.5∘ spatial resolution on 37 standard pressure levels, available from http://apps.ecmwf.int/datasets/. The ozone-weighted effective temperature (Teff) is calculated based on daily ozone and temperature profiles (at 18:00 UTC) over Toronto, defined as Teff=∑i=630weff,i⋅Ti,weff,i=ni∑j=630nj=MMRi⋅pi/Ti∑j=630MMRj⋅pj/Tj, where weff is the weighting function, Ti is the temperature, ni is the ozone number density, MMRi is the ozone mass mixing ratio, and pi is the pressure at pressure level i. In this work, profile data on ECMWF standard pressure levels from no. 6 to no. 30 (10–800 mbar) were used to decrease the noise from variable surface temperatures.

We define the two types of measured TCO (denoted as MB and MP, for Brewer and Pandora respectively) as simple linear functions of the true TCO value (X) and instrument random uncertainties (δB and δP), and assume that there is no multiplicative or additive bias between Pandora and Brewer, giving MB=X+δB,MP=X+δP. If we assume that the instrument random uncertainties are independent of the measured TCO, the variance of M is the sum of the variances of X (around the mean of the dataset) and δ: σMB2=σX2+σδB2,σMP2=σX2+σδP2. If the difference between Pandora and Brewer does not depend on X (no multiplicative bias), and the random uncertainties of the two instruments are not correlated, then the variance of the difference is equal to the sum of the variance of the random uncertainties: σMB-MP2=σδB2+σδP2. Since we have the measured TCO and the difference between the Pandora and Brewer datasets, the variance of the TCO and instrument random uncertainties can be solved by σX2=σMB2+σMP2-σMB-MP2/2,σδB2=σMB2-σMP2+σMB-MP2/2,σδP2=σMP2-σMB2+σMB-MP2/2. Equation (6) can be used to estimate the standard deviation (SD) of instrument random uncertainties (σδB and σδP) and the SD of ozone variability (σX). We do not actually know the variances σMi2 and σMB-MP2; we can only estimate them, with some uncertainty, from the available measurements. It can be shown that the uncertainties in the σX2, σδB2, and σδP2 estimates depend on the sum of all three variances (σMB2, σMP2, and σMB-MP2) and can be high even if the estimated variance itself is low (but one or more of the variances σMB2, σMP2, and σMB-MP2 are high). The estimates are thus only as accurate as the least accurate of these parameters. The variance estimates can be improved by increasing the number of data points or by reducing variances of X by removing some of the daily variability. To remove the variability in X, the residual ozone here is defined as the difference between the high-frequency TCO and the low-frequency TCO measured by an instrument: dMres=Mhigh-f-Mlow-f. For example, the Brewer residual ozone could be the Brewer TCO measurements minus the Brewer ozone daily mean for that day, whereas the corresponding Pandora residual ozone would be the Pandora TCO measurements minus the Pandora ozone daily mean. By subtracting the low-frequency signal, we remove most of the ozone variability. In addition, as proposed in Fioletov et al. (2005), to improve the removal of the bias, we can use the following statistical model to calculate the low-frequency signal: Mlow-f=AB⋅IB+AP⋅IP+B⋅t-t0+C⋅t-t02, where t is the time of the measurement and t0 is the time of local solar noon. IB is an indicator function for the Brewer instrument; it is set to 1 if the TCO is measured by the Brewer and to 0 otherwise. IP is the indicator function for the Pandora. The coefficients AB, AP, B, and C are estimated by the least-squares method for each day (for example, the calculated low-frequency signal for Brewer and Pandora will share the same B and C terms, but they have their own offsets AB and AP). In the following, we will refer to the residual ozone calculated by subtracting the daily mean value as residual type 1 and that obtained by subtracting this second-order function as residual type 2. The present work is focused on evaluating the high-quality TCO data. Thus to avoid the stray-light effect, in the statistical uncertainty estimation, we only use Pandora and Brewer data with ozone air mass factor (AMF) less than 3 (see Sect. 4 for more details about the stray-light effect).

In this work, we calculate two different types of residual ozone (see Eq. 7) as defined in Sect. 3.1 and then use them to calculate the instrument random uncertainty with the statistical variable estimation method (Eq. 6; more details can be found in Fioletov et al., 2006). For example, we use Eqs. (7) and (8) to calculate two type 2 residuals for both Brewer and Pandora (dMb-res2 and dMp-res2), and then calculate their difference (dMb-res2-dMp-res2). Next, we calculate their variances values σ2(dMb-res2), σ2(dMp-res2), and σ2(dMb-res2-dMp-res2). Those variance terms are used in Eq. (6) to estimate the random uncertainties. The residual types and relevant terminologies are summarized in Table 2.

Figure 2 shows the Brewer-estimated random uncertainties obtained using the two types of residual ozone data (Fig. 2a for residual type 1, Fig. 2b for type 2). For example, in Fig. 2a, the estimated random uncertainty for Brewer no. 8 using Pandora no. 103 data (residual type 1, derived from MP103) is shown as a black square in the column for Brewer no. 8, while its estimated random uncertainty using Pandora no. 104 data (residual type 1, derived from MP104) is shown as a red triangle in the same column. Figure 2 demonstrates that type 1 (Fig. 2a) and type 2 (Fig. 2b) residual ozone data provide comparable results and confirm that Brewer instruments have random uncertainties of 1–2 DU.

Figure 2 also shows the Pandora-estimated random uncertainties using the two types of residual ozone data (Fig. 2c for residual type 1, Fig. 2d for type 2). For example, in Fig. 2c, the estimated random uncertainty for Pandora no. 103 using Brewer no. 8 data is shown as a black square in the column of Brewer no. 8, while its estimated random uncertainties using other Brewer data are shown by respective Brewer columns. Figure 2 demonstrates that the Pandora instruments have estimated random uncertainties less than 1.5 DU. Slight differences in the estimated Pandora random uncertainties were found using different Brewer instruments. This is due to the sample size; when the sample size is large (> 1200 coincident points; see Table 1), the Pandora-estimated random uncertainties from different instruments are more consistent. For example, in Fig. 2c, one of the estimated random uncertainties for Pandora no. 103 (black square in Brewer no. 187 column) is below 0.5 DU. This result is undesirable (the value is ∼ 0.5 DU lower than the other values) but not unusual. Dunn (2009) describes this issue in detail and points out that the low (even negative in some cases) variance estimate is due to small sample size. In general, Dunn (2009) concludes that, even with the correct model, the comparisons and estimation of precision are only viable with large sample sizes. Figure 3c shows that the low variance was indeed from the smallest sample size (608 coincident points for Pandora no. 103 vs. Brewer no. 187 and 397 for Pandora no. 104 vs. Brewer no. 187). In addition, when using the data from the same pair of Brewer and Pandora instruments, the estimated random uncertainty for Pandora is consistently lower than that for Brewer by ∼ 0.5 DU.

Fioletov et al. (2006) estimated natural ozone variability (σX) using Eq. (6). However, because we are using the residual ozone instead of the TCO in the statistical analysis, the σX calculated from our method is not the estimated natural ozone variability but the estimated residual ozone variability for the measurement period. It can be used to characterize the difference between residual types 1 and 2. Figure 3a shows the estimated residual ozone variability using residual type 1 data, while Fig. 3b shows the variability using residual type 2. Figure 3a and b demonstrate that residual type 1 data have larger variability than type 2 data, indicating that using the daily mean value as the low-frequency signal did not fully remove the natural ozone variability. Ideally, the random uncertainty estimate should only contain random noise caused by the instrument and no natural ozone variation. Scatter plots of Brewer vs. Pandora residual ozone (Fig. 4) illustrate the same results. Figure 4 shows that the correlation coefficients for residual type 1 (R=0.813 for Brewer no. 8 vs. Pandora no. 103, see Fig. 4a; 0.909 for Brewer no. 8 vs. Pandora no. 104, see Fig. 4b) are higher than the ones for residual type 2 (0.333 for Brewer no. 8 vs. Pandora no. 103, see Fig. 4c; 0.688 for Brewer no. 8 vs. Pandora no. 104, see Fig. 4d). The low correlation coefficients for ozone residual type 2 data indicate that the ozone variability has been largely removed from Pandora and Brewer data. Thus when we use residual ozone type 2, even with relatively small sample size, the estimated uncertainties for Pandoras are still consistent with those obtained from comparisons with other Brewers having larger sample sizes (see Fig. 2c and d, Brewer no. 187 column).

To summarize, we tested two different methods for calculating residual ozone and applied them in the statistical uncertainty estimation. The comparison of two residuals helps us understand more details about the variable estimation method. Although using the daily mean value as a low-frequency signal (as in the residual type 1 calculation) has some shortcomings, it is more straightforward than using the complex second-order statistical model (Eq. 8). By showing the consistency of results from both type 1 and 2 in Fig. 2, we validated the use of the second-order statistical model (Eq. 8) and proved some of the advantages when using type 2. For example, the residual type 2 could work with smaller data size than the residual type 1 (without making the estimated variance unrealistic, too low, or even negative). In general, Fig. 2 demonstrates that the Pandora TCO data have ∼ 0.5 DU smaller estimated random uncertainties than the Brewer TCO data. The mean estimated random uncertainties for BrT and BrT-D are in the range of 1–2 DU (∼ 0.6 %). The mean estimated random uncertainties for Pandora nos. 103 and 104 are in the range of 0.5–1.5 DU (∼ 0.4 %). These results confirm the quality of the TCO data, with all eight instruments meeting the GAW requirement for a precision better than 1 % to measure ozone (WMO, 2014).

When comparing Pandora and Brewer TCO data, we can see a clear seasonal structure and a bias in the difference and ratio. Figure 5a shows the time series of Brewer no. 14–Pandora no. 103 TCO difference; the seasonal amplitude is 3–4 DU, and the mean bias is 10.81 DU. Figure 5b (which uses the corrected data) will be discussed in Sect. 4.2. The locally weighted scatter plot smoothing (LOWESS(x)) fit (the dashed line) is based on local least-squares fitting applied to a specified x fraction of the data (Cleveland and Devlin, 1988). The bias between Pandora and Brewer TCO is mainly due to the fact that both retrievals depend on the choice of ozone absorption cross section (Scarnato et al., 2009; Herman et al., 2015). The Brewer TCO in this work was retrieved using the standard Brewer network operational ozone cross section (Bass and Paur, 1985), while the Pandora TCO was retrieved using the standard Pandora network operational ozone cross section (the DBM ozone cross section). Redondas et al. (2014) reported that changing the Brewer operational ozone cross section from Bass and Paur (1985) to that of Daumont et al. (1992) (DBM) will change the calculated TCO by -3.2 %. In addition to the offset caused by the use of different ozone cross sections, the seasonal difference between Pandora and Brewer TCO data is due to their differing temperature dependence, which varies from instrument to instrument because of the differences in ozone retrieval algorithm and instrument design. Moreover, even for the same type of instrument, the temperature sensitivity can be different due to imperfections in the wavelength settings and slit function for each individual instrument. We will study these differences (offset and temperature effect) by using the standard TCO products from Pandora and Brewer instruments.

In this work, we use ECMWF ERA-Interim ozone and temperature profiles to calculate daily ozone effective temperature (described in Sect. 2.4). Then we use the following simple linear regression model to find the temperature dependence factor for Pandora instruments: MBMP=a⋅Teff-225+b, where a is the temperature dependence factor for Pandora, b is the (systematic) multiplicative bias between Pandora and Brewer, and 225 refers to effective temperature of 225∘ K for ozone cross sections used in the Pandora retrievals. Here, the MB and MP are TCO daily means measured by the Brewer and Pandora respectively. To increase the number of coincident data points, the MB dataset is formed by merging all measurements from the six Brewers (see Table 1). A successfully merged MB data point has coincident measurements from at least two Brewers, to avoid domination by a single instrument. The coincident time period of the MB and MP103 datasets is from October 2013 to December 2015 with 272 coincident days (points). Figure 6 shows the linear regression results for Pandoras nos. 103 and 104. We found the “relative temperature dependence factor” (RTDF) for Pandora no. 103 to be 0.247 ± 0.013 %  K-1 (from the term a in Eq. 9), with a 2.2 ± 0.1 % multiplicative bias (from the term b in Eq. 9). Although Pandora no. 104 only has measurements from January to April 2014 (53 coincident days), the linear regression still results in a similar temperature dependence factor (0.255 ± 0.040 % K-1) and the same bias as Pandora no. 103. The correlation coefficients for those two linear regressions are 0.91 and 0.89 respectively.

We applied the Pandora temperature dependence factors to the Pandora TCO to remove its bias and seasonal difference relative to Brewer TCO data. Similar to the correction function used in Herman et al. (2015) for Pandora no. 34, we used the following function to correct Pandora TCO data: Mcorr=MP⋅a⋅Teff-225+b, where Mcorr is corrected Pandora TCO, and other terms are as defined for Eq. (9). For the Pandora no. 103 dataset, this becomes Mcorr=MP103⋅0.00247⋅Teff-225+1.022, where MP103 is the TCO data from Pandora no. 103. The temperature dependence factor (0.247 ± 0.013 % K-1) and the multiplicative bias (1.022) are found in Fig. 6. The same regression model and method give a 0.255 ± 0.040 % K-1 temperature dependence factor with a 2 % multiplicative bias to Pandora no. 104, and hence Mcorr=MP104⋅0.00255⋅Teff-225+1.022, where MP104 is the Pandora no. 104 TCO. For comparison, Herman et al. (2015) derived the correction function for Pandora no. 34 as Mcorr=MP34⋅0.00333⋅Teff-225+1, where the 0.00333 (0.333 % K-1) is the temperature dependence factor for Pandora no. 34. Note that this value was determined by applying retrievals using ozone cross sections from 215 to 240 K and then obtaining a linear fit to the percent change (Herman et al., 2015). However in this work, the factors for Pandora nos. 103 and 104 were found by statistical analysis (comparison) of the Pandora and Brewer TCO datasets. Thus our temperature dependence factor combines the temperature sensitivity from both Pandora and Brewer instruments, and describes the relative temperature sensitivity between the Pandora and Brewer standard TCO products. We call it a “relative temperature dependence factor” (RTDF), while that from Herman et al. (2015) is an absolute temperature dependence factor (ATDF). Although the RTDF is a non-linear combination of ATDF from both Pandora and Brewer (note that the Pandora used an ozone cross section at an effective temperature of 225 K, while the Brewer used that at 223.8 K), we can still make a simple linear estimation of the RTDF from reported ATDFs. In fact, the reported ATDF for Pandora no. 34 (0.333 % K-1; Herman et al., 2015) minus the reported ATDF for Brewer nos. 8 and 14 (0.07 and 0.094 % K-1; Kerr et al., 1988; Kerr, 2002) gives relative numbers (0.26 and 0.24 % K-1) that are close to our model-calculated RTDF (∼ 0.25 % K-1). In our correction functions (Eqs. 11–12), we have a constant b term of 1.022 given 0.001 uncertainty, which indicates a multiplicative bias of ∼ 2 % (not caused by the temperature effect) between the Pandora and Brewer instruments due to their different selection of ozone cross sections.

Merging data from all six Brewers could lead to variation of the Brewer temperature dependence, so we performed sensitivity tests on the dataset. Table 3 summarizes the tests; the combined Brewer data are merged from all available Brewer data during the data period indicated in the table. Figure 7 shows the RTDFs, multiplicative bias, correlation coefficient, and number of data points for the 13 sensitivity tests. Tests 1 and 2 are the results adapted from Fig. 6. Due to the small data size, the RTDF for test 2 has larger error bars than test 1. Test 3 shows Pandora no. 103 RTDF using combined Brewer data for the same time period as Pandora no. 104. Pandora no. 103 has a measurement gap from August to December 2014 due to instrument failure (see Fig. 1); hence, tests 4 and 5 use combined Brewer data for 2013–2014 (∼ 1-year coverage, before the instrument failure of Pandora no. 103) and 2015 (1-year coverage, after Pandora no. 103 was repaired) separately. Brewer no. 191 was one of the most reliable Brewer instruments during the comparison period. Thus tests 6–8 use only Brewer no. 191 data; test 6 uses all available data (2013–2015), test 7 uses only 2013–2014 data (before the instrument failure of Pandora no. 103), and test 8 uses 2015 data (after Pandora no. 103 was repaired). Tests 9–13 use individual Brewer data (all available data for each individual Brewer). For the 13 tests, the RTDFs (see Fig. 7a) are in the range of 0.24–2.9 %, and the multiplicative biases (see Fig. 7b) are in the range of 1.7–2.5 %. The correlation coefficients (see Fig. 7c) for most tests are above 0.8. In general, the RTDFs found for the Pandora instruments are stable when derived from combined Brewer data or reliable individual Brewer data. For this 2-year data period, the derived RTDFs from BrT-D instruments are lower (0.241–0.246 % K-1) than the ones from BrT instruments (0.262–0.290 % K-1). However, with the large uncertainties on the estimated RTDFs and the bias, we could not conclude whether this is due to the different instrument designs or a sampling issue.

As an example, Fig. 5 shows the time series of Brewer no. 14–Pandora no. 103 TCO differences, before and after applying the Pandora correction (Eq. 11). A clear seasonal signal is seen due to the variation of Teff before we apply the temperature dependence correction (see Fig. 5a). Figure 8 shows scatter plots of Pandora no. 103 versus Brewer no. 14 TCO. In Fig. 8a, the linear regression (green line, weighted accounting for uncertainties from both measurements; York et al., 2004) between Pandora no. 103 and Brewer no. 14 gives a slope of 1.023, an offset of -18.486 DU, and strong correlation (R=0.9954). Forcing the intercept to 0 gives a slope of 0.969, indicating -3.1 % mean bias. This is consistent with the work of Redondas et al. (2014), which showed that changing the Brewer ozone cross section from Bass and Paur to DBM changed the Brewer TCO by -3.2 %. By colour coding the scatter points, it is obvious that this non-ideal slope and offset are related to Teff . After applying the correction, the seasonal Brewer–Pandora difference disappears as seen in Fig. 5b, and the linear regression (green line) gives a slope of 1.008, an offset of -2.678 DU, and an improved correlation (R=0.9982) (see Fig. 8b). Linear fitting with zero intercept gives a slope of 1.001, indicating that the correction improves the mean bias between Pandora and Brewer TCO from -3.1 to 0.1 %.

To calculate the effective temperature, we use daily temperature and ozone profiles from ECMWF ERA-Interim data at 18:00 UTC for Toronto, but Herman et al. (2015) used monthly averaged temperature and ozone climatology data (interpolating the climatological ozone profile to the observed TCO in order to capture day-to-day variability; see ftp://toms.gsfc.nasa.gov/pub/ML_climatology) for latitudes of 30–40 and 40–50∘ N to form an average suitable for Boulder (40∘ N). To understand the difference due to the selection of Teff, we adapted the climatology data used in Herman et al. (2015) and used the data from 40 to 50∘ N to calculate effective ozone temperature for Toronto (44∘ N). Figure 9 shows the comparison between the ECMWF daily Teff and the NASA monthly climatology Teff. A sudden cooling event happened at Toronto on 29–30 January 2014, for which the difference between the daily and monthly Teff was -10 K. Figure 10 shows the time series of TCO difference (combined Brewer–Pandora no. 103) before and after applying the temperature dependence correction using both the monthly climatology Teff and daily Teff. Because the monthly climatology Teff does not reflect the low temperature during those two days, the correction function (see Eq. 11) overcompensated for the temperature effect (the minimum delta ozone value on 29 January changed from -8 DU in Fig. 10a to -14 DU in Fig. 10b). The low-temperature event was captured by the daily Teff; thus the compensation from the temperature effect was reasonably small when using ECMWF daily Teff (the minimum value was -7 DU; see Fig. 10c). In general, the ECMWF daily Teff can better capture some ozone variation events that are associated with rapid temperature changes.

Figure 11 shows time series of the monthly average TCO difference in percentage before and after applying the temperature dependence correction for eight pairs of instruments (six individual Brewers vs. Pandora no. 103, combined Brewer vs. Pandora no. 103, and combined Brewer vs. Pandora no. 104). Figure 11a shows that both Pandora nos. 103 and 104 have similar offsets relative to the Brewers before applying the correction to Pandora data. In addition, the seasonal variations are consistent when comparing Pandora no. 103 to six individual Brewers (see Fig. 11a). After applying the TCO corrections (Fig. 11b), the seasonal differences decreased from ±1.02 to ±0.25 % for Pandora no. 103 and from ±0.40 to ±0.25 % for Pandora no. 104, as did the offset which decreased from 2.92 to -0.04 % for Pandora no. 103 and from 2.11 to -0.01 % for Pandora no. 104. The 1σ uncertainty in Fig. 11b shows that, statistically, the corrected Pandora datasets have no significant seasonal differences or offsets compared to the Brewer datasets.