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**Atmospheric Measurement Techniques**
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**Research article**
18 Jan 2019

**Research article** | 18 Jan 2019

The effect of instrumental stray light on Brewer and Dobson total ozone measurements

^{1}Department of Earth and Space Science and Engineering, Lassonde School of Engineering, and the Centre for Research in Earth and Space Science, York University, Toronto, ON, Canada^{2}Air Quality Research Division, Environment and Climate Change Canada, Toronto, ON, Canada^{3}Global Monitoring Division, NOAA Earth System Research Laboratory, Boulder, CO, USA^{a}now at: Institute of Space and Atmospheric Studies, Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK, Canada

^{1}Department of Earth and Space Science and Engineering, Lassonde School of Engineering, and the Centre for Research in Earth and Space Science, York University, Toronto, ON, Canada^{2}Air Quality Research Division, Environment and Climate Change Canada, Toronto, ON, Canada^{3}Global Monitoring Division, NOAA Earth System Research Laboratory, Boulder, CO, USA^{a}now at: Institute of Space and Atmospheric Studies, Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, SK, Canada

**Correspondence**: Omid Moeini (omidmns@yorku.ca)

**Correspondence**: Omid Moeini (omidmns@yorku.ca)

Abstract

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Dobson and Brewer spectrophotometers are the primary, standard instruments for ground-based ozone measurements under the World Meteorological Organization's (WMO) Global Atmosphere Watch program. The accuracy of the data retrieval for both instruments depends on a knowledge of the ozone absorption coefficients and some assumptions underlying the data analysis. Instrumental stray light causes nonlinearity in the response of both the Brewer and Dobson to ozone at large ozone slant paths. In addition, it affects the effective ozone absorption coefficients and extraterrestrial constants that are both instrument-dependent. This effect has not been taken into account in the calculation of ozone absorption coefficients that are currently recommended by WMO for the Dobson network. The ozone absorption coefficients are calculated for each Brewer instrument individually, but in the current procedure the effect of stray light is not considered. This study documents the error caused by the effect of stray light in the Brewer and Dobson total ozone measurements using a physical model for each instrument. For the first time, new ozone absorption coefficients are calculated for the Brewer and Dobson instruments, taking into account the stray light effect. The analyses show that the differences detected between the total ozone amounts deduced from Dobson AD and CD pair wavelengths are related to the level of stray light within the instrument. The discrepancy introduced by the assumption of a fixed height for the ozone layer for ozone measurements at high latitude sites is also evaluated. The ozone data collected by two Dobson instruments during the period of December 2008 to December 2014 are compared with ozone data from a collocated double monochromator Brewer spectrophotometer (Mark III). The results illustrate the dependence of Dobson AD and CD pair measurements on stray light.

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Moeini, O., Vaziri Zanjani, Z., McElroy, C. T., Tarasick, D. W., Evans, R. D., Petropavlovskikh, I., and Feng, K.-H.: The effect of instrumental stray light on Brewer and Dobson total ozone measurements, Atmos. Meas. Tech., 12, 327–343, https://doi.org/10.5194/amt-12-327-2019, 2019.

1 Introduction

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Routine atmospheric total column ozone measurements started in the mid-1920s with a Féry spectrophotometer (Dobson, 1931). Following the International Geophysical Year (1958) a worldwide network was developed with a number of Dobson instruments that were installed around the world to monitor total ozone variations. In the early 1980s the automated Brewer became commercially available (Kerr et al., 1981). A network was also introduced for the Brewer as observing organizations started to use these instruments alongside the Dobson for long-term measurements. Although the principle behind the measurements of the Brewer and Dobson instruments is generally the same, seasonal and systematic differences in respective TOC (total ozone column) products became evident after long-term co-incident measurements had accumulated (Staehelin et al., 1998; Vanicek, 2006). The adoption of the Bass and Paur (1985) ozone cross sections (BP) for the Dobson instrument in 1992 put both instruments on the same reference scales (the Brewer uses BP) and reduced the difference to 4 % (Kerr et al., 1988) but it did not resolve the seasonal and nonseasonal differences (Vanicek, 2006).

Temperature corrections to the ozone absorption cross sections may reduce the systematic errors of Dobson ozone data by up to 4 % (Bernhard et al., 2005). The seasonal differences between the measurements by the two instrument types are related to the ozone effective temperature, which affects the ozone absorption measured by the Brewer and Dobson instruments differently (Bernhard et al., 2005; Kerr et al., 1988; Scarnato et al., 2009; Van Roozendael et al., 1998; Vanicek, 2006) because of the different wavelengths employed for the measurements. The impact of different laboratory-determined ozone cross sections has also been investigated and showed up to a 3 % change for the Brewer and 1 % for Dobson data (Redondas et al., 2014).

To facilitate the replacement of Dobson instruments with Brewers, statistical methods have been developed to derive transfer functions for converting Dobson measurements to the Brewer scale (Staehelin et al., 2003). These methods have been partly successful, but they cannot entirely explain the differences between the measurements of the two instruments (Scarnato et al., 2010). Scarnato et al. (2010) found an unexplained 3 % drift over a 10-year period (1988–1997) between Arosa's Dobson and Brewer total ozone series.

Analysis of the data obtained by the Dobson at the South Pole showed that the assumption of the ozone layer being at a fixed height leads to an error in the air mass calculation. The errors caused by this assumption may exceed 4 % in ozone measurements when the ozone distribution is distorted by the ozone hole (Bernhard et al., 2005).

Stray light has been demonstrated to affect measurements by both instrument types (Bais et al., 1996). Basher (1982) used a mathematical model to estimate stray light levels present in the measurements of a particular Dobson instrument. According to Basher (1982), errors of 1 %, 3 %, and 10 % may be present at air mass values of 2.5, 3.2, and 3.8, respectively, for direct sun AD measurements. Christodoulakis et al. (2015) employed Basher's model to estimate the stray light level of Dobson no. 118 at the Athens Dobson station using direct sun AD wavelength pair measurements collected over a large range of solar zenith angles (SZAs). The result showed that the mean underestimation of ozone was 3.5 DU (or about 1 % of the station's mean total ozone column value) for measurements with air mass values of up to 2.5. However, a single-pair parameter was not found for Basher's model that succeeded in calculating the stray light correction for all experimental days. Christodoulakis et al. (2015) concluded that Basher's model cannot quantify the effect of stray light on TOC measurements made by the Dobson instrument under all conditions and that further study was needed. This was also noted by Basher (1982) and Evans et al. (2009).

Karppinen et al. (2014) employed the method suggested by Kiedron et al. (2008) to correct the data collected by a single monochromator Brewer during the Intercomparison/Calibration campaign for Nordic Brewers and Dobsons held at Sodankylä from 8 to 24 March 2011 and a follow-up campaign at Izaña Observatory, Tenerife, between 28 October and 18 November 2011. The method suggested relies heavily on the dispersion information for the instrument which is not available for all instruments, especially in the historical record.

The errors caused by stray light are particularly significant at high latitudes in the late winter and early spring when measurements are made at large SZA and large TOC. Such errors are of considerable importance if those data are to be used for trend analysis or satellite data validation. In particular, if such data are used in cases where Dobsons or single monochromator Brewers are replaced by instruments with a significantly lower level of stray light, such as double monochromator Brewers (Mark III), a significant false positive trend in ozone may result.

The main goal of this study is to investigate and document these sources of error in total ozone as measured by the Dobson and Brewer instruments at high latitudes.

2 Method

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According to the Beer–Lambert law, the spectral irradiance *I*(*λ*)
from a direct solar spectrum at the Earth's surface can be expressed as

$$\begin{array}{}\text{(1)}& I\left(\mathit{\lambda}\right)={I}_{\mathrm{0}}\left(\mathit{\lambda}\right)\mathrm{exp}(-\mathit{\tau}\left(\mathit{\lambda}\right)),\end{array}$$

where *τ*(*λ*) is the optical thickness of the incident path and
*I*_{0}(λ) is the extraterrestrial irradiance at
wavelength *λ*

$$\begin{array}{}\text{(2)}& \mathit{\tau}\left(\mathit{\lambda}\right)=\mathit{\alpha}\left(\mathit{\lambda}\right)X\mathit{\mu}+\phantom{\rule{0.125em}{0ex}}\mathit{\beta}\left(\mathit{\lambda}\right){\displaystyle \frac{{P}_{\mathrm{s}}}{{P}_{\mathrm{0}}}}{m}_{\mathrm{R}}+\mathit{\delta}\left(\mathit{\lambda}\right){m}_{\mathrm{a}}\end{array}$$

and *α*(*λ*) is the monochromatic ozone absorption coefficient at wavelength *λ*, *X* the total ozone column (TOC), *μ* the relative optical air mass corresponding
to ozone absorption, *β*(*λ*) the Rayleigh optical depth for a one-atmosphere
path, *P*_{s} the station pressure, *P*_{0} the mean sea level pressure
(101.325 kPa), *m*_{R} the relative optical air mass corresponding to
Rayleigh scattering (extinction), *δ*(*λ*) the aerosol optical
depth, and *m*_{a} the relative optical air mass corresponding to aerosol scattering (extinction).

The Dobson spectrophotometer does not measure the intensity of sunlight at a single wavelength but instead determines the ratio between the irradiance at two wavelengths, one strongly absorbed and the other more weakly affected by ozone. Several wavelength pairs are used by the Dobson algorithm for calculating total column ozone. In order to minimize the effect of aerosol and other absorbers, two wavelength pairs are used such as AD, AC or CD where the A pair is 305.5–325.4 nm, C is 311.5–332.4 nm and D is 317.6–339.8 nm (Evans and Komhyr, 2008; Komhyr et al., 1993). For example, the total ozone using AD wavelength pair observations is retrieved using the following expression:

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}X=\left({N}_{\mathrm{A}}-{N}_{\mathrm{D}}-K-\mathrm{\Delta}{\mathit{\beta}}_{\mathrm{AD}}{\displaystyle \frac{{P}_{\mathrm{s}}}{{P}_{\mathrm{0}}}}{m}_{\mathrm{R}}-\mathrm{\Delta}{\mathit{\delta}}_{\mathrm{AD}}{m}_{\mathrm{a}}\right)\\ \text{(3)}& {\displaystyle}& {\displaystyle}/\left(\mathit{\mu}\mathrm{\Delta}{\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}_{\mathrm{AD}}\right)\text{(4)}& {\displaystyle}& {\displaystyle}{N}_{\mathrm{A}}=\mathrm{ln}\left[{I}_{\mathrm{0}}\left(\mathrm{305.5}\right)/{I}_{\mathrm{0}}\left(\mathrm{325.4}\right)\right]-\mathrm{ln}\left[I\left(\mathrm{305.5}\right)/I\left(\mathrm{325.4}\right)\right]\text{(5)}& {\displaystyle}& {\displaystyle}{N}_{\mathrm{D}}=\mathrm{ln}\left[{I}_{\mathrm{0}}\left(\mathrm{317.6}\right)/{I}_{\mathrm{0}}\left(\mathrm{339.8}\right)\right]-\mathrm{ln}\left[I\left(\mathrm{317.6}\right)/I\left(\mathrm{339.8}\right)\right]\text{(6)}& {\displaystyle}& {\displaystyle}\mathrm{\Delta}{\mathit{\beta}}_{\mathrm{AD}}=\left[\mathit{\beta}\left(\mathrm{305.5}\right)-\mathit{\beta}\left(\mathrm{325.4}\right)\right]-\left[\mathit{\beta}\left(\mathrm{317.6}\right)-\mathit{\beta}\left(\mathrm{339.8}\right)\right]\text{(7)}& {\displaystyle}& {\displaystyle}\mathrm{\Delta}{\mathit{\delta}}_{\mathrm{AD}}=\left[\mathit{\delta}\left(\mathrm{305.5}\right)-\mathit{\delta}\left(\mathrm{325.4}\right)\right]-\left[\mathit{\delta}\left(\mathrm{317.6}\right)-\mathit{\delta}\left(\mathrm{339.8}\right)\right]\text{(8)}& {\displaystyle}& {\displaystyle}\mathrm{\Delta}{\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}_{\mathrm{AD}}=\left[\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left(\mathrm{305.5}\right)-\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left(\mathrm{325.4}\right)\right]-\left[\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left(\mathrm{317.6}\right)-\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left(\mathrm{339.8}\right)\right],\end{array}$$

where $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}$ is the effective differential ozone
absorption coefficient at −46.3 ^{∘}C and *K* is the
instrument constant. Other double wavelength pairs such as CD can be used
for the ozone calculation by modifying Eq. (3) accordingly
(Komhyr et al., 1993).

The basic measurement principle for the Brewer instrument is the same as the Dobson. However, the Brewer measures the intensity of four operational wavelengths quasi-simultaneously. The total ozone is calculated using the following equation:

$$\begin{array}{}\text{(9)}& X=\left(\mathrm{MS}\mathrm{9}+\mathrm{\Delta}\mathit{\beta}{\displaystyle \frac{{P}_{\mathrm{s}}}{{P}_{\mathrm{0}}}}{m}_{\mathrm{R}}-\mathrm{ETC}\right)/\left(\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\mathit{\mu}\right),\end{array}$$

where $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}$ and ETC are the effective differential
ozone absorption coefficient at −45 ^{∘}C and extraterrestrial constant
(ETC), respectively. Both are obtained from a linear weighted combination of
the logarithms of their individual values at the four wavelengths used for
the total ozone retrieval (Kerr, 2002). MS9 is
calculated from a linear combination of the logarithms of the intensities
(*I*(*λ*_{i})) measured at the four wavelengths *λ*_{i} = (310.0,
313.5, 316.8, 320.0), multiplied by weighting coefficients *w*_{i}.

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}\mathrm{MS}\mathrm{9}=\sum _{i=\mathrm{1}}^{\mathrm{4}}{w}_{i}\cdot \mathrm{ln}I\left({\mathit{\lambda}}_{i}\right)=\mathrm{ln}\left[I\left(\mathrm{310.0}\right)\right]-\mathrm{0.5}\mathrm{ln}\left[I\left(\mathrm{313.5}\right)\right]\\ \text{(10)}& {\displaystyle}& {\displaystyle}-\mathrm{2.2}\mathrm{ln}\left[I\left(\mathrm{316.8}\right)\right]+\mathrm{1.7}\mathrm{ln}\left[I\left(\mathrm{320.0}\right)\right]\text{(11)}& {\displaystyle}& {\displaystyle}\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}=\sum _{i=\mathrm{1}}^{\mathrm{4}}{w}_{i}\cdot \stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left({\mathit{\lambda}}_{i}\right)\text{(12)}& {\displaystyle}& {\displaystyle}\mathrm{\Delta}\mathit{\beta}=\sum _{i=\mathrm{1}}^{\mathrm{4}}{w}_{i}\cdot \mathit{\beta}\left({\mathit{\lambda}}_{i}\right)\end{array}$$

The weighting coefficients, *w*_{i} = (1.0, −0.5, −2.2 and 1.7), have been
selected to minimize the absorption of SO_{2} and suppress any variations
that change linearly with wavelength. Hence, the aerosol scattering effect,
which is approximately linear with wavelength over a narrow wavelength
range, is suppressed in the calculation. The *w*_{i} sum to zero, the
requirement for the absorption function to be independent of absolute
intensity. The ETC of a primary standard instrument is determined using
observations made at Mauna Loa Observatory (MLO) and are calculated using zero
air mass factor extrapolation (Langley plot method). It can be transferred
to other instruments by comparisons with a traveling standard instrument
(Fioletov et al., 2005).

To calculate the effective ozone absorption coefficients, the
laboratory-determined ozone cross sections at an effective atmospheric ozone
layer temperature must be convolved with the instrument slit function,
weighted by the solar flux. The BP ozone cross sections were recommended by
the International Ozone Commission (IO_{3}C) in 1992
(http://www.esrl.noaa.gov/gmd/ozwv/dobson/papers/coeffs.html, last access: 10 June 2017) for the Brewer
and Dobson networks. The calculation of the absorption coefficients, which
are currently recommended by the World
Meteorological Organization (WMO) for Dobson instruments, is described by
Komhyr et al. (1993) (K93 hereinafter) and the
reevaluation is described by Bernhard et al. (2005) (B05
hereinafter). Recently the IO_{3}C has recommended the ozone
cross sections measured by Serdyuchenko et al. (2014) (SC hereinafter), as they reduce the Dobson temperature sensitivity.
In this study, for consistency with previous work and to be relevant and
comparable to modern work, both the BP and SC cross sections are used. A
correction factor

$$\begin{array}{}\text{(13)}& {f}_{\mathrm{c}}=\mathrm{1.0112}-\mathrm{0.6903}/\left[\mathrm{87.3}-(T-{T}_{\mathrm{0}})\right]\end{array}$$

based on the results of Barnes and Mauersberger (1987), as
suggested by K93, is used to adjust the BP cross sections. *T* is the
temperature in kelvin and *T*_{0} is 273.15 K. For this study all BP
cross sections are multiplied by this factor and calculated at −46.3 for
both instruments to be consistent. This correction has been implemented in
the Dobson network. For wavelengths longer than 340 nm, where BP data are
not available, the Brion et al. (1993),
Daumont et al. (1992), and
Malicet et al. (1995) (BDM) data are used.
These data sets are available at individual temperatures and also with the
associated quadratic coefficients of temperature dependence on the IGACO
(Integrated Global Atmospheric Chemistry Observations) web page. For this
study the quadratic coefficients in the file “Bp.par” are used for BP
cross sections and the Liu et al. (2007)
quadratic approximation which excludes −273 ^{∘}K data from the
quadratic temperature dependence fitting is used for BDM cross sections. For
SC cross sections the quadratic temperature dependence fitting is also used.
The temperature dependence of the cross sections is expressed as

$$\begin{array}{}\text{(14)}& \mathit{\sigma}\left(\mathit{\lambda},T\right)={C}_{\mathrm{0}}\left(\mathit{\lambda}\right)+{C}_{\mathrm{1}}\left(\mathit{\lambda}\right)T+{C}_{\mathrm{2}}\left(\mathit{\lambda}\right){T}^{\mathrm{2}},\end{array}$$

where *σ*(*λ*,*T*) is the ozone absorption
cross sections at wavelength *λ* and temperature *T*, and *C*_{0},
*C*_{1}, and *C*_{2} are the quadratic coefficients at wavelength *λ*.
The absorption coefficients are calculated from the ozone cross sections
*σ*(*λ*,*T*) and the ozone number density *ρ*(z):

$$\begin{array}{}\text{(15)}& \mathit{\alpha}\left(\mathit{\lambda}\right)={\displaystyle \frac{\mathrm{1}}{X}}\underset{{z}_{\mathrm{0}}}{\overset{\mathrm{\infty}}{\int}}\mathit{\sigma}\left(\mathit{\lambda},\phantom{\rule{0.125em}{0ex}}T\left(z\right)\right)\mathit{\rho}\left(z\right)\mathrm{d}z,\end{array}$$

where *z*_{0} is the altitude of the station and *T* is the temperature in
kelvins. The total ozone column, *X* (in Dobson units equal to 2.69×10^{16} ozone molecules per square centimeter), is defined as

$$\begin{array}{}\text{(16)}& X={\displaystyle \frac{k{T}_{\mathrm{0}}}{{P}_{\mathrm{0}}}}\underset{{z}_{\mathrm{0}}}{\overset{\mathrm{\infty}}{\int}}\mathit{\rho}\left(z\right)\mathrm{d}z,\end{array}$$

where *T*_{0} is 273.15 K and *k* is the Boltzman constant. (It
should be noted that *X* is used in the equations, whereas TOC is used in the
text.) In order to account for the finite bandwidth of the Brewer and Dobson
slit functions, the effective ozone absorption coefficient $\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left(\mathit{\lambda}\right)$ is used instead of *α*(*λ*) in the Brewer and Dobson
retrieval algorithms (Basher, 1982; Vanier and Wardle,
1969):

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left({\mathit{\lambda}}_{i}\right)={\displaystyle \frac{-\mathrm{1}}{X\mathit{\mu}}}\\ \text{(17)}& {\displaystyle}& {\displaystyle}\mathrm{ln}\left({\displaystyle \frac{\int {I}_{\mathrm{0}}\left(\mathit{\lambda}\right)S(\mathit{\lambda},{\mathit{\lambda}}_{i})\mathrm{exp}\left(-\mathit{\alpha}\left(\mathit{\lambda}\right)X\mathit{\mu}-\mathit{\beta}\left(\mathit{\lambda}\right)\frac{{P}_{\mathrm{s}}}{{P}_{\mathrm{0}}}{m}_{\mathrm{R}}\right)\mathrm{d}\mathit{\lambda}}{\int {I}_{\mathrm{0}}\left(\mathit{\lambda}\right)S\left(\mathit{\lambda},{\mathit{\lambda}}_{i}\right)\mathrm{exp}\left(-\mathit{\beta}\left(\mathit{\lambda}\right)\frac{{P}_{\mathrm{s}}}{{P}_{\mathrm{0}}}{m}_{\mathrm{R}}\right)\mathrm{d}\mathit{\lambda}}}\right),\end{array}$$

where *S*(*λ*,*λ*_{i}) is the slit function for a nominal
wavelength *λ*_{i}.

The Brewer operational method employs a simpler approximation, which is identical to the approximation method of B05 and the simplest approach of K93, and also used by Redondas et al. (2014), Van Roozendael et al. (1998), Scarnato et al. (2009), and Fragkos et al. (2015):

$$\begin{array}{}\text{(18)}& {\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}^{\mathrm{apx}}\left({\mathit{\lambda}}_{i}\right)={\displaystyle \frac{\int \mathit{\alpha}\left(\mathit{\lambda}\right)S\left(\mathit{\lambda},{\mathit{\lambda}}_{i}\right)\mathrm{d}\mathit{\lambda}}{\int S\left(\mathit{\lambda},{\mathit{\lambda}}_{i}\right)\mathrm{d}\mathit{\lambda}}}.\end{array}$$

Both Brewer and Dobson retrievals assume a fixed height for a thin layer of
ozone to calculate the ozone air mass. The following expression is used by
both instruments to calculate relative optical air mass at a solar zenith
angle of *θ*:

$$\begin{array}{}\text{(19)}& \mathit{\mu}\left(\mathit{\theta}\right)=({R}_{\mathrm{e}}+h){\left[{\left({R}_{\mathrm{e}}+h\right)}^{\mathrm{2}}-{\left({R}_{\mathrm{e}}+r\right)}^{\mathrm{2}}{\mathrm{sin}}^{\mathrm{2}}\mathit{\theta}\right]}^{\mathrm{0.5}},\end{array}$$

where *R*_{e} is the radius of the Earth, *r* is the altitude of the station, and *h* is
the height of the ozone layer. Using the mean Earth radius for *R*_{e} instead of
the actual Earth radius at the station does not introduce a significant
error in *μ*. However, it is important that the correct values for the
station altitude and the height of the ozone layer are used in Eq. (19). The
Dobson community has adopted a variable ozone layer height with latitude
which, to some extent, is in agreement with ozone climatology, while a fixed
height of 22 km is used in the Brewer network.

Stray light is unwanted radiation from other wavelengths that arrives at the detector during measurements at a selected wavelength. Scattering by instrument optical elements and inefficient out-of-band (OOB) rejection of the light by dispersive elements, e.g., the grating, are the main sources of stray light in the spectrometers. Particulate scattering within the instrument and radiation scattered from the atmosphere within the field of view of the instrument can also contribute a stray light effect (Josefsson, 1992). Generally, holographic gratings with higher line densities generate lower stray light. The Mark II and IV versions of the Brewer demonstrate higher levels of stray light compared to the Mark III as the Mark III instruments utilize a double monochromator with higher line density gratings that leads to significantly better rejection of the OOB light.

Since the gradient of ozone absorption is large in the ultraviolet spectral region, the stray light contribution from longer wavelengths can make up a significant fraction of the signal measured at shorter wavelengths where the intensity is reduced by ozone absorption. As the light path (air mass and ozone path) increases, stray light effects in the measurements also increase. Stray light results in an underestimated ozone column at larger ozone slant column amounts.

To characterize the stray light in an instrument it is necessary to measure
the instrument slit function. The Brewer Mark III and IV can measure the
wavelength range of 286.5 to 363 nm with 0.5 nm resolution. The Brewer slit
function is characterized as using a narrow band line source such as a laser as
input source and scanning through all wavelengths. Measurements at 350 nm
(not reported) have shown the slit function to be similar at all wavelengths
in the Brewer measurement range. The slit function is reversed in wavelength
space to account for the reciprocal nature of scanning the instrument versus
scanning the wavelength of the line source. A He-Cd laser is commonly used
to measure the slit function of the Brewer (Karppinen et al.,
2014; Kiedron et al., 2008; Pulli et al., 2018). For this study a
He-Cd laser (single line at 325.029 nm) was used as well to measure the slit
functions of Brewers no. 009 and no. 119. Figure 1
shows the measured slit functions of Brewer Mark IV no. 009 (single
monochromator) and Mark III no. 119 (double monochromator) located at Mauna
Loa Observatory. Several Brewer Mark IV, Mark II, and Mark III slit
functions have been measured during intercomparison campaigns (e.g., the
Fourth North American Interagency Intercomparisons of Ultraviolet Monitoring
near Boulder, Colorado, in 1997 and published by Lantz et
al., 2002, and Intercomparison Campaigns of the Regional Brewer Calibration
Center for Europe, RBCC-E). The slit function consists of a core (band-pass),
the shoulders, and the extended wings (Fig. 1). The stray light measured
from nearby wavelengths (the wings of the slit function) is typically below
10^{−6} times that of the primary wavelength in the Mark III double
Brewers as compared to 10^{−4} in the Mark II and Mark IV single Brewers.
To reduce the effect of stray light, the Brewer Mark II uses a cutoff filter
which strongly attenuates wavelengths longer than 345 nm. A solar blind
filter (SBF) made of nickel sulfate hexahydrate (NiSO_{4}.6H_{2}O)
crystal sandwiched between two UV colored glass filters (similar to Schott
UG5 or UG11) is also used in the Mark IV. Figure 2
shows the transmission of a typical UG11-NiSO_{4} filter measured by a
Cary 5E spectrophotometer. The stray light level depends on the optical and
mechanical configuration which is unique for each instrument, and thus two
identically configured instruments can have somewhat different OOB light
rejection.

In the Brewer operational wavelength calibration, the individual slit functions are characterized separately through dispersion analysis (Gröbner et al., 1998). For this study, a symmetrical trapezoid is fitted to the measured slit functions of Brewer no. 009 (single – Mark IV) and Brewer no. 119 (double – Mark III) (Fig. 1). The model slit function fit to the data (red line) includes three parts: a trapezoid with a nominal full width half maximum (FWHM; Table 1) at the core band-pass, the shoulders which are modeled by fitting a Lorentzian function (Table 1) to the measured data, and two horizontal straight lines for the outer parts (wings). To investigate the effect of stray light, an ideal slit function, which is a trapezoid shape with a flat top at 0.87 of the full height and two straight lines to zeros with a nominal FWHM, has been used (Fig. 1, top left).

The slit functions of the world standard Dobson no. 83 were experimentally
measured by Komhyr et al. (1993) and recently
verified by Köhler
et al. (2018) using a tuneable light source. However, the published slit
functions are restricted to the core band-passes. It has been assumed that
the Dobson instrument restricts OOB light from entering the slit. The
extended wings have not been measured for the Dobson instrument.
Basher (1982) attempted to estimate the level of stray light
within the Dobson instrument by fitting a mathematical model to the AD pair
direct sun measurements and analyzing the total column ozone changes with
solar zenith angle. His analysis suggested that for most Dobson instruments
the level of stray light is 10^{−4} based on the nonlinearity of the
AD direct sun measurements beyond an air mass factor of 3.

Another approach has been used by Evans et al. (2009) to measure the stray light entering the Dobson instrument. They used a filter that is opaque to the C-pair nominal short wavelength band-pass, and transparent outside of this range (Fig. 6 in Evans et al., 2009). The idea is that the filter would remove the desired band-pass from the signal and any current remaining is from OOB light. This method was used to estimate the contribution of stray light in zenith sky measurements of Dobson no. 65 in Boulder, Colorado. They also used a model approach for the stray light contribution in zenith sky measurements and concluded that the level of stray light in Dobson no. 65 is likely 2$\times {\mathrm{10}}^{-\mathrm{5}}$.

The Dobson slit functions for short and long wavelengths are approximately a triangle with a FWHM of 1.06 nm and a trapezoid with a FWHM of 3.71 nm, respectively (Fig. 3). For this study, symmetrical trapezoids centered at the nominal Dobson wavelengths were fitted to the experimentally determined slit functions of Dobson no. 83 and used as ideal slit functions. The characteristics of these trapezoids are given in Table 1. In order to account for stray light, for this study two horizontal straight lines were added to the outer parts of the ideal slit functions.

3 Discussion

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To calculate the ozone absorption coefficients, the standard values defined
in Tables 1 and 2 are employed. To validate the calculations, the
$\mathrm{\Delta}{\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}^{\mathrm{apx}}$ is calculated for the double Brewer
using an ideal trapezoid slit function and BP cross sections at
−45 ^{∘}C without the Barnes and Mauersberger (1987) correction.
Redondas et al. (2014) have calculated the ozone absorption coefficients for
the nominal Brewer which is identical in terms of slit functions, nominal
wavelengths, and slit FWHMs with the double Brewer of this work using ideal
trapezoid slit functions. The IGQ4 cross sections used in Redondas et
al. (2014) are the same as the BP cross sections employed in this work. The
value 0.3367 calculated using IGQ4 cross sections at −45 ^{∘}C
(Redondas et al., 2014, Table 6) has a difference of
0.06 % to the value 0.3365 calculated here with the same cross sections
at the same temperature (−45 ^{∘}C) (Table 3).

To be consistent with Dobson calculations, the Barnes and Mauersberger (1987) correction is applied to BP cross sections. Both BP and SC
cross sections at −46.3 ^{∘}C are used for the calculation of $\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left({\mathit{\lambda}}_{i}\right)$ and ${\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}^{\mathrm{apx}}\left({\mathit{\lambda}}_{i}\right)$ presented in Tables 4 and 5 for the single and double Brewers.

The contribution of stray light in determining the ozone absorption coefficients can be seen from comparing the $\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}$ calculated using ideal slit functions (without stray light) with the values ($\mathrm{\Delta}\stackrel{\mathrm{\u203e}}{\mathit{\alpha}})$ calculated using modeled slit functions (including stray light). For the single Brewer the results show a difference of 0.7 % (modeled slit functions including stray light are less than that of the ideal slit functions) using both BP and SC cross sections, while for the double Brewer the difference is less than 0.01 %.

The values of $\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left({\mathit{\lambda}}_{i}\right)$ and ${\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}^{\mathrm{apx}}\left({\mathit{\lambda}}_{i}\right)$ calculated for the Dobson instrument using the modeled slit functions are provided in Table 6. ${\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}^{\mathrm{adj}}\left({\mathit{\lambda}}_{i}\right)$ is the adjusted set of coefficients which are recommended by WMO to be used for the Dobson network. After applying the K93 data set to the observations made by the World Standard Dobson instrument no. 083 at Mauna Loa Observatory, 0.8 % for AD pair differences and 2.2 % for CD pair differences in the calculated total ozone values were detected. K93 realized that increasing $\mathrm{\Delta}{\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}_{\mathrm{D}}$ by 2 % would decrease the discrepancies to below 0.5 %. Thus, the adjusted values were recommended by WMO to be used for the Dobson instruments.

The values of ${\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}^{\mathrm{apx}}\left({\mathit{\lambda}}_{i}\right)$ calculated using ideal slit functions and BP cross sections agree with the corresponding values of K93 to within ±2.0 %. In the case of $\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left({\mathit{\lambda}}_{i}\right)$, the comparison indicates agreement to within ±3.4 % except for $\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left(\mathrm{339.9}\right)$ where the difference is about 67 %. Approximately the same difference was reported by B05 for the same wavelength compared to K93. B05 have investigated this discrepancy by using Molina and Molina (1986) cross sections to extend the BP data sets for Dobson calculations and concluded that the K93 value for $\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left(\mathrm{339.9}\right)$ is unreasonably high. As in B05, the calculated value, $\mathrm{\Delta}{\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}_{\mathrm{D}}$ , presented in this study agrees better with the empirically adjusted value, $\mathrm{\Delta}{\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}}_{\mathrm{D}}^{\mathrm{adj}}$. The comparison shows agreement to within ±1.6 % between the values calculated for this work and the K93 adjusted values.

Generally, the differences between values presented here and those from K93 are slightly higher than the difference between B05 and K93. However, it should be noted that the slit functions and the parameters used in the calculations presented here are slightly different from those used by K93 and B05 (Tables 1 and 2).

Clearly, the stray light level within each instrument has an effect on the
ozone absorption coefficient calculations. This effect is negligible for
instruments with a stray light level on the order of 10^{−5}. But the
difference could be up to 4.0 % for AD pair coefficients ($\stackrel{\mathrm{\u203e}}{\mathit{\alpha}}\left({\mathit{\lambda}}_{i}\right)$ ) and 6.9 % for CD pair coefficients using BP
cross sections, and up to 4.6 % and 6.4 % using SC cross sections, for
instruments with levels of stray light on the order of 10^{−4} when
compared with the values calculated using ideal slits. These differences
translate to an underestimation of ozone values through Eq. (3). However, by
scaling the data using the Dobson calibration procedure, the difference
between the AD measurements of the standard instrument and a calibrated one
is reduced to less than 0.7 % (Evans and Komhyr,
2008). In the Dobson AD pair calibration, scale factors are calculated for
different ranges of air masses. The data from the instrument being
calibrated are scaled to the data from the reference instrument. Then, using
the quasi-simultaneous measurements of AD and CD pairs of the calibrated
instrument, a scaling factor is also calculated to reduce the CD measurements
to the AD level.

To illustrate the effect of stray light on low-sun measurements, the
percentage difference between ozone derived using Brewer and Dobson
retrievals with assumed constant ozone in the atmosphere is depicted as a
function of ozone slant path (OSP, total ozone times air mass) in Fig. 4. As
the selection of the cross sections has an insignificant effect on the results
shown and discussed in this section, only BP cross sections are plotted.
Equation (1) along with parameters indicated in
Table 2 are used to model the atmosphere and
calculate the solar spectrum at the surface. To retrieve the ozone values,
the BP absorption coefficients calculated in Sect. 3.1 are used. To
calculate the ETC values, the instrument absorption function is calculated
and plotted as a function of ozone slant path, using the solar spectrum
(Chance and Kurucz, 2010), Eqs. (1) and (2), and retrieval algorithm of the
Brewer (or Dobson) for an assumed constant amount ozone (325 DU in this
study). The best fit to the data with air mass less than 2 (less than 3 for
the Dobson instruments) is found and extrapolated to zero air mass.
Figure 5 shows the best fit to data from a single
Brewer. For the single Brewer the ETC is calculated as 1945.4 for a modeled
trapezoid slit function with stray light, which is close to the value of
2020 calculated by Kiedron et al. (2008), noting the slight differences in
slit functions and solar spectrum. Karppinen et al. (2015) have reported
3218 for an ETC value for slit functions with stray light. However, they
used the LibRadtran 1.6-beta radiative transfer model to scale their modeled
data to be matched with real data. For Dobsons, the ETC values calculated
using ideal slits are used for other models (i.e., with 10^{−4} and
10^{−5} levels of stray light). Two versions of the Brewer are compared
with the Dobson instrument measurements with two levels of stray light. AD
measurements with 10^{−4} order of stray light show approximately 25 % discrepancy at 2000 DU OSP (air mass 6.2 in this case). The difference is
about 5 % for a typical single Brewer at the same OSP. The
underestimation of total ozone as measured by the AD pair of a Dobson
instrument with 10^{−5} level of stray light could be up to 6 % at
2000 DU OSP. It has to be noted here that AD pair measurements are conducted
for air mass factors less than 2.5 and thus, during the ozone hole period
(total column ozone is less than 300 DU), Dobson data will only be reported
for OSP less than 750 DU (Evans and Komhyr, 2008).

Evidently, the CD pair is less influenced by scattered light than the AD
pair because of the smaller ozone cross sections at the CD wavelengths and
the consequent smaller gradient with respect to wavelength in the spectrum
measured. For a Dobson instrument with a minimum level of stray light
(10^{−5}) the difference for the CD pair could be up to 1.8 % at 2000
DU OSP, while it is less than 0.8 % for a typical double Brewer at the
same OSP. Dobson CD total ozone is reported for air mass values between
2.4 and 3.5; thus for the total ozone (TCO) of 300 DU or less, the maximum reported OSP would be 1100 DU (Evans and Komhyr, 2008).

For decades the Dobson community has faced a discrepancy between the ozone
values deduced from quasi-simultaneous AD and CD pair measurements. As
indicated by the Dobson operational handbook, AD observations are the
standard for the Dobson instrument and all other observations must,
therefore, be scaled to the AD level by determining a multiplying factor.
For example, the ozone values deduced from measurements on CD wavelengths
should be multiplied by the factor of *X*_{AD}∕*X*_{CD} (where *X*_{AD} and
*X*_{CD} are the average ozone measurements retrieved from AD and CD pairs
derived from a large number of quasi-simultaneous observations covering a
broad range of *μ* values greater than 2.0) to be scaled to those deduced
from AD measurements.

Figure 6 illustrates the discrepancy in total ozone reduced from AD and CD pairs for two modeled Dobson instruments with different levels of stray light using two different ozone cross sections (BP and SC) as a function of OSP. The ratio of the AD to the CD pair is also shown. The adjusted coefficients calculated by K93 and recommended by WMO are used to derive the total ozone amounts for this model. The ETC values that were calculated using the Langley method for an ideal instrument are used here as well. It can be seen that, as the level of stray light increases, the difference between the AD and CD values increases, indicating the role of stray light in the observed discrepancy between AD and CD values. The results suggest that the difference between the AD and CD values also depends on the selected cross sections. It is apparent that the increase of the AD–CD difference as a result of increasing the level of stray light is larger for BP cross sections than for SC cross sections. This is consistent with Redondas et al. (2014) analysis, indicating the role of ozone cross sections in the difference detected between AD and CD measurements.

Clearly, the difference varies between Dobson instruments as it depends on the level of stray light, which is unique for each individual instrument. Moreover, as discussed in Sect. 3.1, these discrepancies are reduced during calibration using simultaneous measurements with a well-maintained, standard instrument.

To retrieve total ozone from direct sun measurements, it is required that the
ozone air mass value be calculated. For measurements at the South Pole, the
following values are used by the Dobson community in Eq. (19): *R*_{e}=6356.912, *r*=2.81 km, and *h*=17 km. Figure 7
shows the ratio of total ozone retrieved using air mass values calculated
with four different sets of assumptions for *R*_{e}, *r*, and *h* to ozone values retrieved
using the air mass factor calculated for the South Pole employing the Dobson
community's values for *R*_{e}, *r*, and *h* as a reference. Any discrepancy in the air
mass is directly reflected in the Dobson and Brewer retrieved ozone via Eqs. (3) and (9), respectively. It is obvious that the fixed ozone layer height of
22 km, as used by Brewer retrieval, can cause up to a 2.2 % difference at
an air mass of 5.4. In addition, the altitude of the site can introduce a
significant difference at high solar zenith angles.

4 Comparison between Dobson and Brewer measurements at the South Pole

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Total ozone measurements collected by two Dobson instruments (no. 82 and
no. 42) and one double Brewer Mark III, no. 085, collocated and operated
simultaneously at the Amundsen-Scott site (24.80^{∘} W,
89.99^{∘} S; altitude 2810 m), are used for this comparison. Double Brewer no. 085 was
installed at the South Pole station in 2008 and since then it has been in routine
operation. The Brewer data for the South Pole site are available on the
World Ozone and Ultraviolet Data Centre (WOUDC) website. Due to logistic difficulties, Brewer no. 085 was not
replaced or calibrated until 2016.

The Dobson data used for this study are freely available at ftp://aftp.cmdl.noaa.gov/user/evans/York_Omid/ (last access: 10 January 2019). For this study all direct sun Dobson measurements are used, while only one measurement representative of the day is reported to the NDACC or WOUDC. A complete description of the South Pole data set is provided by Evans et al. (2017). The reprocessed data using WinDobson software as described in Evans et al. (2017) are used for the analysis here. Generally, the Dobson instrument at the South Pole site is replaced with a calibrated instrument every 4 years. The instrument replaced is calibrated against the reference Dobson no. 83 and the calibration results are used to adjust and post-process the last 4 years of data collected at the South Pole. The calibration procedure can be found in Evans and Komhyr (2008) and the major calibration or instrument changes regarding the South Pole data set can be seen in Fig. 5 of Evans et al. (2017).

To avoid the impact of ozone hole on the analyses presented here, only the
data with total ozone values larger than 220 DU are used for this study.
Quasi-simultaneous direct sun measurements performed within 5 min during
the period of December 2008 to December 2014 were used in the present
analysis. The air masses calculated by the Brewer retrieval were adjusted
using Eq. (19) by applying the values used by Dobson instruments (*R*_{e}=6356.912 km, *r*=2.81 km, and *h*=17 km) to be consistent with the
Dobson air masses. Figure 8 shows the total ozone
column measured by double Brewer no. 085 and the total ozone retrieved using
the adjusted air masses. The ratio of total ozone columns retrieved using
adjusted air masses to the total ozone columns retrieved using unadjusted
air masses are also shown in the same figure.

The ozone absorption coefficients calculated by Komhyr et al. (1993) and recommended by WMO have been used to retrieve ozone values for the AD and CD pairs. It is necessary to mention that only the data collected with air mass factors less than 2.5 or OSP less than 800 DU would be reported for AD pair measurements to the WOUDC or other institutes for regular research purposes. The range of air mass factor for CD measurements is 2.4 to 3.5 and that means in the case of the South Pole station, the maximum OSP would be about 1100 DU.

Figure 9 presents a comparison of the Brewer total ozone measurements with Dobson ozone observations reduced from the direct sun AD pair as a function of OSP. The ratios between the unadjusted Brewer data and Dobson measurements are also shown in the same plot. The ratio between the Brewer adjusted data and the Dobson values shows some dependence on OSP: the Dobson no. 82 and no. 42 are on average 1 % and 0.46 % higher, respectively, for OSPs below 800 DU. When the OSP is above 800 DU, Dobson measurements gradually become lower by up to 4 % for OSPs up to 1400 DU for Dobson no. 42 and up to 5 % for OSPs up to 1200 DU for Dobson number no. 82 (Fig. 9).

The ratio between Dobson CD pair measurements and the Brewer data also shows a dependence on OSP (Fig. 9). However, CD pair ozone values are on average 3.4 % and 4.5 %, higher for almost the entire measurement set for Dobson no. 82 and no. 42, respectively. It should be noted that the CD pair values are scaled to the AD pair for each individual Dobson instrument. The scaling factors 1.043 and 1.025 were calculated during calibration procedure in 2015 and used for adjusting total column ozone values derived from Dobson no. 82 and no. 42 CD pair measurements, respectively (Robert Evans, personal communication, 2015. Note to the user: the subset of the South Pole station Dobson record used in this paper was reprocessed in June of 2015 using the WinDobson software as described in Evans et al. (2017). The NOAA archived data referenced in Evans et al. (2017) (ftp://aftp.cmdl.noaa.gov/ozwv/Dobson/dobson_toSPO.txt, last access: 20 November 2018) were finalized in 2017. The data contain the same AD TOC, while CD TOC was reprocessed to adjust for AD–CD differences and updates in the air mass factor calculation. The scaling factors were changed to 1.018 and 0.998, respectively, and data were resubmitted to the NDACC archive (ftp://ftp.cpc.ncep.noaa.gov/ndacc/station/spole/ames/dobson/, last access: 20 November 2018) in October 2017 – Glen McConville and Koji Miyagawa, NOAA, personal communication, 2018). The calibration procedures and the method for calculating the scaling factor are described and published by WMO in GAW report no. 183 (Evans and Komhyr, 2008). As illustrated by B05 (Fig. 4 of Bernhard et al., 2005) the temperature dependence of the ozone absorption cross sections may also cause discrepancy in Dobson total ozone measurements. As illustrated by B05 (Fig. 4 of Bernhard et al., 2005) the temperature dependence of the ozone absorption cross sections may also cause deviations in Dobson total ozone column measurements. B05 assessed variability in the effective temperature using ozone profiles measured by the Global Monitoring Division of NOAA (former Climate Monitoring and Diagnostics Laboratory, CMDL) at the South Pole between 1991 and 2003. They found that the temperature-adjusted AD and CD ozone absorption coefficients deviated from nominal values (K93) by up to ±4 %, leading to underestimation or overestimation of the total ozone column through Eq. (3). B05 also found that the 1991–2003 collection of temperature-adjusted CD ozone absorption coefficients exhibited a SZA dependence. The ozone absorption coefficient adjustment is likely magnified at low-sun (large SZA) conditions (preferential for CD over AD measurements) when extreme changes in ozone and temperature profiles are observed during the ozone hole period.

It can be seen from this analysis that Dobson no. 42 TOC values show less
dependence on OSP. Based on the physical model developed in this work, it
appears that this instrument has a significantly lower level of stray light
than Dobson instrument no. 82. As shown in Fig. 10, the physical model
developed in this study suggests a 10^{−3.5} and 10^{−4.1} level of stray
light for Dobson no. 82 and 42, respectively.

Figure 11 shows a box plot of the difference between double Brewer ozone measurements and Dobson values retrieved from AD and CD pairs. The data are binned for 100 DU from 400 to 2000 DU. For each box, the central red line is the median, the edges of the box are the 25th and 75th percentiles, the whiskers extend to the most extreme data points not considered outliers, and outliers are plotted individually. In each bin the values with differences larger than 3 standard deviations from the mean of the bin have been removed from the calculation. The number of simultaneous measurements in each bin is summarized in Table 7.

5 Conclusions

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Physical models of the Dobson instrument and two types of Brewer
spectrophotometer were developed to help better understand the effects of
stray light on ozone measurements and indicate a way forward for correcting
current and past data for the resulting error in the calculated ozone
column. The influence of assuming a fixed ozone layer height on air mass
calculations and the difference caused by this assumption to the ozone
retrieval were also examined. The target accuracy for ground-based ozone
measurements is 1 %, while physical models show that the stray light
effect can cause a discrepancy for a typical single Brewer and Dobson AD
pair at large ozone slant paths of up to 5 % and 25 %, respectively.
At 2000 DU OSP the difference for a double Brewer and a Dobson CD pair with
minimum level of stray light (10^{−5}) is up to 0.8 % and 1.8 %,
respectively. This effect restricts measurements at high latitudes, such as
polar stations, particularly in the late winter and early spring when the
ozone slant column is particularly large. It is considerably important if
those data are to be used for trend analysis. In particular, if such data
are used in the case where Dobsons or single Brewers are replaced by double
Brewers, a significant false positive trend in ozone may result.

Stray light also can affect the calculation of ozone absorption coefficients. Currently, an approximation method is used to calculate the absorption coefficients for Brewer instruments. The analysis shows that using a modeled trapezoid slit function with stray light (instead of an idealized trapezoidal one) and taking into account the solar spectrum leads to a difference of 0.7 % and less than 0.01 % in calculated coefficients for a typical single and double Brewer, respectively.

Absorption coefficients for the Dobson spectrophotometers, taking into account the effect of stray light, have been calculated and compared with the results of similar calculations by K93, which are the coefficients recommended by WMO. The slit functions of Dobson no. 83 have been measured using a tunable light source (K93). Recently, the measured slit functions and calculated coefficients were verified by measuring the slit functions of three Dobsons (no. 74, no. 64, and no. 83) at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig in 2015 and at the Czech Metrology Institute (CMI) in Prague in 2016 within the EMRP ENV 059 project “Traceability for atmospheric total column ozone” (Köhler et al., 2018). Köhler et al. (2018) showed that the optical properties of these three Dobsons deviate from the specification described by G. M. B. Dobson. However, the AD pair ozone absorption coefficients derived from new slit functions lead to less than 1 % deviation in total ozone column values. It is generally assumed that the slit functions of other Dobson spectrophotometers are similar to the standard one (no. 83).

For the study presented here, the slit functions were modeled to examine the
effect of stray light on the calculation of ozone absorption coefficients.
The results show that a 10^{−5} level of stray light has a negligible effect
on absorption coefficient calculations, while the difference could be up to
4.0 % and 4.6 % for AD coefficients and up to 6.9 % and 6.4 % for CD coefficients for an instrument with a 10^{−4} level of stray light
using BP and SC cross sections, respectively.

When quasi-simultaneous measurements are made using Dobson AD and CD wavelengths, the results may not agree. For decades the Dobson community has faced such differences. The AD pair is the standard for Dobson measurements, and the observations using other pairs' data should be scaled to the AD pair before release. Our analysis indicates that the difference between quasi-simultaneous measurements using AD and CD pairs is related to the level of stray light inside each Dobson instrument. Higher levels of stray light lead to larger differences between the values deduced from AD and CD wavelengths. However, this increase in difference between AD and CD values is slightly smaller when the SC cross sections are used than when the BP cross sections are used.

Both Brewer and Dobson retrievals assume a fixed height for the ozone layer to calculate the ozone air mass. A fixed height of 22 km is used by the Brewer network for all sites, while a variable ozone layer height changing with latitude is employed by the Dobson community. The assumption of a 22 km height for the ozone layer at the South Pole, compared to the 17 km height used in the Dobson analysis, leads to a 2.2 % difference in the ozone column at an air mass of 5.4.

Comparisons with total ozone data larger than 220 DU from a double Mark III
Brewer spectrophotometer located at the South Pole indicate some dependence
on OSP for the Dobson measurements. For the OSPs below 800 DU the AD values
are generally 1 % higher. However, for OSPs between 800 and 1400 DU the
Dobson AD measurements are lower by up to 4 %. Using the physical model
developed in this study the stray light levels of Dobson no. 82 and no. 42
are estimated as 10^{−3.5} and 10^{−4.1}, respectively.

Observations made at the CD wavelengths also show some dependence on OSP. Compared to Brewer data, the CD values are, on average, 4 % higher for almost the entire range of measurements. However, as is the case for the AD pair, the CD pair values also decrease at larger OSPs. It should be noted that the Dobson AD and CD pair measurements are not reported for air mass factors above 2.5 and 3.5, respectively, due to the effect of stray light.

Data availability

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Data availability.

The Brewer data can be obtained from the WOUDC Data Centre at http://www.woudc.org (last access: 2 August 2017). The Dobson data used for this study are available at ftp://aftp.cmdl.noaa.gov/user/evans/York_Omid/ (NOAA/ESRL, 2015).

Author contributions

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Author contributions.

OM developed the Brewer and Dobson models and wrote the paper with the support and input of other co-authors. ZV was involved in the model development and analysis of the results. TM, DV, IP, and RE assisted in the writing of the paper and provided valuable discussions about the Brewer and Dobson retrievals and measurements. KF was involved in the analysis and comparison of the South Pole data.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

The authors thank the many NOAA/ESRL technical staff members and officers for
their invaluable efforts to operate the facility year-round at the South Pole
and obtain the data used in this report. The U.S. National Science Foundation
provides the infrastructure and logistics support for the facility at the
South Pole. The Brewer data were obtained from the World Ozone and
Ultraviolet Radiation Data Centre (WOUDC; http://www.woudc.org, last access: 20 August 2017) operated by
Environment and Climate Change Canada, Toronto, Ontario, Canada, under the
auspices of the World Meteorological Organization. The first author is
grateful for support from Environment and Climate Change Canada and the
Natural Sciences and Engineering Research Council of Canada
(NSERC).

Edited by: Mark Weber

Reviewed by: Alberto Redondas and one anonymous referee

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Short summary

This study documents the error caused by the effect of stray light in the Brewer and Dobson total ozone measurements using a mathematical model for each instrument. The errors caused by stray light are particularly significant at high latitudes in the late winter and early spring when measurements are made at large solar zenith angles and large total ozone column. Such errors are of considerable importance if those data are to be used for trend analysis or satellite data validation.

This study documents the error caused by the effect of stray light in the Brewer and Dobson...

Atmospheric Measurement Techniques

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