1 Supporting Material.
2 1.
Modeled Absorption Cross-sections at different Instrument Function Resolutions.
3 The goal of the model presented in main text is to find correct for errors that may be
4 introduced because the instrument cannot fully resolve the rovibrational features of the
5 measured sample. In order to do this we need to compare a fully resolved spectrum
6 against several instrument functions of different resolutions. In this study we took the
7 measurements of Koplow et al.
[1998] which are the only report in the literature in
8 which all rovibrational lines for a very small segment of the spectrum are fully resolved.
9 The model assumes an instrument function of a Gaussian type ( exp [−( x
− b )
2
/2 c
2
]) where
10 the instrument resolution “ c
” is assigned to several values and the center of the function
11 is at 215.221783 nm. A comparison of the instrument function and the reported data by
12 Koplow et al.
[1998] is presented in fig. S1 A. The literature data extend from 215.21
13 nm to 215.235 nm; instrument function of 5, 1, 0.1 and 0.01 cm
-1
are overlapped with
14 the literature data. For resolutions larger than 0.1 cm
-1
the width of the instrument
15 function is too broad to capture the detailed spectral features of the measured spectra.
16 The spectral band of SO
2
extends beyond the range of the data of Koplow et al.
[1998]
17 and in order to account for the lack of spectral resolution for an instrument function of
18 25 cm
-1
the experimental data was repeated 25 times as a starting point for analyzing the

19 impact of resolution (Fig. S1 B.). Once this pseudo-spectra and the instrument function
20 were established the ratio of the areas were compared according to equations 12 to 14 in
21 section 3.1 in the main text. Fig. S1 C. shows the modeled data at different values of c .
22 By comparing the different results it becomes quite clear, as shown in Fig. 2, that
23 conventional under-resolved cross-sections (
σ
P
) change as a function of column density.
24 Panel C shows the pressure dependence of
σ
P
as a function of various c (resolution) of
25 the instrument function.
σ
P
depends strongly on column density when resolution is
26 lower than 0.1 cm
-1
.
27
28 Reference
29
30
31
32
Danielache, S. O., C. Eskebjerg, M. S. Johnson, Y. Ueno, and N. Yoshida (2008),
High-precision spectroscopy of 32 S, 33 S, and 34 S sulfur dioxide: Ultraviolet absorption cross sections and isotope effects, J. Geophys. Res.
, 113 (D17), D17314, doi:10.1029/2007JD009695.
33
34
35
Koplow, J. P., D. a Kliner, and L. Goldberg (1998), Development of a narrow-band, tunable, frequency-quadrupled diode laser for UV absorption spectroscopy., Appl.
Opt.
, 37 (18), 3954–60.
36
37
Rottman, G. J., T. N. Woods, and W. McClintock (2006), SORCE solar UV irradiance results, Adv. Sp. Res.
, 37 (2), 201–208, doi:10.1016/j.asr.2005.02.072.
38
39

40
41
42
43
Table S1, Isotopic distribution (%) of S 0 samples used in the production of SO
2
samples.
This data has been provided by the vendor, Isoflex USA, with certificate numbers,
16-01-32-1372, 16-01-33-3017, 16-01-34-3740 and 16-01-36-3895. According to the vendor the samples qere analized with a scientific-research mass-spectrometer Ml1201.
44
32 S Sample
33 S Sample
34 S Sample
36 S Sample
32 S
99.99
0.2
<0.1
0.07
33 S
<0.01
99.8
1.1
0.05
34 S
<0.001
<0.01
98.8
0.64
36 S
<0.001
<0.01
0.05
99.24

45
46
47
48
49
Table S2, chemical admixtures (ppm) of S
0
samples used in the production of SO
2 samples. This data has been provided by the vendor, Isoflex USA, with certificate numbers, 16-01-32-1372, 16-01-33-3017, 16-01-34-3740 and 16-01-36-3895.
According to the vendor the samples were analized with a scientific-research mass-spectrometer Ml1201.
50
51
36 S
Sample
32 S
Sample
33 S
Sample
34 S
Sample
C
750
F
530
Mg
<30
Si
100
Fe
<30
Al
<30
Mn Cu
<30 <30
B Cr Cu Mg Fe Al Ni Zn Si P
<10 30 <10 <15 70 <10 <10 <10 180 <10
Al B Cr Cu Fe Mg Mn
<10 <10 30 <10 80 <10 <10
Ni
<10
P
<10
Si
200
Mn
<30
<10
Co
Zn
<10
Al Ni P Co Cr Fe Zn Mg B Si Pb Mn Ag Cu
30 <20 <10 <5 <20 70 <10 <20 <10 180 <10 <10 <10 <10

52
C
53
58
59
60
61
54
55
56
57
Fig. S1. Panel A, Experimental cross-sections of natural abundance SO
2
reported by
Koplow et al.
[1998] (light green line) and instrument function of different resolutions expressed as a c constant for a Gaussian function centered at 215.221783 nm. Panel B,
Pseudo-spectra created as repetition of the experimental values reported by Koplow et al.
, 1998 (light green line) and compared to different work functions. Panel C, pressure dependence of
σ
Conventional
as a function of various FWHM (resolution) of the instrument function.
σ
Conventional
depends strongly on column density when resolution is lower than
0.1 cm
-1
.

62
63
68
69
70
71
64
65
66
67
72
73
Fig. S2. Absorption cross-sections calculated using the algorithm presented in Fig. 3,
Panel A shows which case was employed for each wavelength of 32 SO
2
. For comparison panel B shows the segment of the spectra of 32 SO
2
(200-205 nm). From this comparison it is clear that most of the wavelengths fulfill the conditions for the case 2 (a quadratic fitting with R
2
> 0.7) obtained from measurements that are within the 5-95% absorbance range. Wavelengths near the minima of absorption fulfill the conditions for the case 1 (a quadratic fitting with R
2
< 0.7). On the other hand, wavelengths near the maxima of absorption (such as 200.5nm, 202.2 nm and 203.7 nm) fulfill case 3 because absorption is too large. Panel C shows which case was employed for each isotopologue. The algorithm doesn’t cause significant bias for each isotopologue.

78
79
80
81
74
75
76
77
82
83
84
Fig. S3 Comparisons of 33 SO
2
spectra presented in this report with literature from
Danielache et al.
, [2008] measured by vacuum FTUV spectrometer at the same resolution. The wavelengths of absorption peaks are in good agreement with previously published spectra, but the amplitudes in the previous study of the vibrational structure were underestimated because of difference of the methodology employed to calculate cross-sections.

85
90
91
92
93
94
86
87
88
89
Fig. S4 Comparisons of 34 SO
2
spectra presented in this report with literature from
Danielache et al.
, [2008] measured by vacuum FTUV spectrometer at the same resolution. The wavelengths of absorption peaks are in good agreement with previously published spectra, but the amplitudes in the previous study of the vibrational structure were underestimated because of difference of the methodology employed to calculate cross-sections.

95
100
101
102
96
97
98
99
Fig. S5. The 3 x J ( x = 2, 3, 4 and 6) values calculated by equation 14 using solar spectra measured at the top of atmosphere by Rottman et al.
, [2006] as actinic flux. The d 3 x J values are defined as 3 x J values in an infinitesimal wavelength. In this study, wavelength is divided into 0.02 nm for integration. Wavelength near 212 nm give the largest contributions to the 3 x J values.