Auxiliary material for COS hydrolysis in Antarctic ice cores
Introduction
This auxiliary material contains: 1) a description of the thermal history calculations
for different ice core, 2) a description of the ice flow assumptions that are used for the
thermal history calculations, and 3) ice core data pairings used in the minimizations and
their impact on the results. There are four supplemental figures (Figures S1 through S4)
and three supplemental tables (Tables S1 through S3) that accompany this readme file.
1.
Ice thermal history calculations
Calculating thermal histories for the ice samples is an under-constrained problem.
Many pairs of an accumulation-rate history and an ice-flow strain history will produce
the same depth-age relationship [e.g. Waddington et al., 2005]. Similarly, many pairs of
a surface-temperature history and a geothermal flux will match the modern borehole
temperature profiles reasonably well (Figure S1 and S2). The ice-flow histories can be
constrained by using internal layers imaged by radar [e.g. Nereson et al., 1998], geologic
and topographic constraints [e.g. Morse et al., 1998], and glaciological modeling [e.g.
Price et al., 2007]. We use the ice-flow parameterizations suggested in previous work
and described in section 2.
To assess the uncertainty in the inferred thermal histories, we vary the isotope
calibration factors that we use to calculate the surface-temperature histories. The
geothermal flux that minimizes the misfit with the modern borehole temperature profiles
for the different isotope calibration was found. At a site like WAIS Divide, the thick ice
and high accumulation rate preserve information about past temperature changes [Cuffey
et al., 1995; Dahl-Jensen et al., 1998; WAIS Divide Project Members, 2013]. For the
thinner and lower accumulation sites like Siple Dome and Taylor Dome, there is little
memory of past temperature changes. Therefore, a wide range of combinations of
isotope calibration factors and geothermal fluxes match the modern borehole temperature
profile sufficiently well. We use upper and lower limits on the isotope calibration factors
and then test the sensitivity of the corrections for COS loss to hydrolysis under these
conditions.
For Taylor Dome, the recommended isotope calibration was 0.5‰ per ˚C with an
uncertainty of 0.2‰ per ˚C [Steig et al., 1998]. We also calculated the thermal histories
for isotope calibration factors of 0.3 ‰ per ˚C and 0.7 ‰ per ˚C (Table S1). In all three
cases, the borehole fits for Taylor Dome agree with the measured borehole temperature
profile within 0.6˚C at all measurement depths (Figure S2a). The COS records corrected
with the different thermal histories from the three different scenarios display only minor
differences (Figure S3a), indicating the thermal histories of the Taylor Dome samples
from last 8 ky are well-constrained with the available borehole temperature data.
For Siple Dome, the recommended isotope calibration is 0.7‰ per ˚C with an
uncertainty of 0.2‰ per ˚C [Taylor et al., 2004]. We also calculated the thermal histories
for isotope calibration factors of 0.5 ‰ per ˚C and 0.9 ‰ per ˚C (Table S1). The 0.7‰
per ˚C and 0.9‰ per ˚C cases both match the measured temperatures within 0.6˚C while
the 0.5‰ per ˚C has a maximum misfit greater than 1˚C regardless of what geothermal
flux is used (Figure S2b). The differences between the COS hydrolysis corrections for
the different isotope calibrations are larger at Siple Dome than the Taylor Dome (Figure
S3b). However, the differences are still small over the last 5 ky, especially between the
two cases that provide a better fit to the borehole temperature measurements.
2.
Ice-flow Assumptions
Calculating the thermal histories requires different assumptions at each ice core site.
The WAIS Divide site is located 25 km from the divide and the ice flow is best
approximated as a flank site. We use the same ice-flow model inputs as described in
WAIS Divide Project Members [2013].
Siple Dome is a complicated site because there have been changes in the ice
thickness and the development of an ice-flow divide at the core site. We assume constant
ice thickness during the Holocene and the onset of divide flow occurring between 4 and 3
ky [Nereson et al., 1998]. We use a Dansgaard-Johnsen kink height of 20% for flank
flow and 70% for divide flow [Waddington et al., 2005]. We also prescribe 200 m of
thinning between 15 and 12 ky based on results of Price et al. [2007]. The accumulation
rate is derived from depth-age relationship for these ice-flow assumptions.
The rough basal topography beneath Taylor Dome makes it difficult to observe if a
Raymond Bump is present [Morse et al., 1998]. The Taylor Dome ice core was drilled 1
km (approximately two ice thicknesses) away from the topographic high [Morse et al.,
1998]. We use a Dansgaard-Johnsen kink height of 30% of the ice thickness because the
vertical ice-flow will be similar to a flank site, but with a small influence from the divide
[Nereson and Waddington, 2002]. We assume no changes in ice thickness.
3.
Ice core data pairings used in the minimizations and their impact on the
results
In the main body of the paper, equation (6) and figure 5 are based on minimization
results using six different ice core pairings: Siple Dome (SDM) – WAIS Divide (WAISD), SDM – Byrd, SMD – Taylor Dome (TDM), WAIS-D – South Pole (SPO), WAIS-D –
Byrd, and WAIS-D – TDM (Min-1 in Table S2). The cost function (C) used in the
minimization is the sum of the differences in mean COS levels between the pairs, with
one exception that it also includes a slope comparison for the SDM – WAIS-D pair:
C  c1 c2  c3  c4  c5  c6  c7
(1)
where:

c1  abs(SDM  WAIS  D)
c2  abs(SDM slope  WAIS  Dslope)
c3  abs(SDM  Byrd )
c4  abs(SDM  TDM )
c5  abs(WAIS  D  SPO)
c6  abs(WAIS  D  Byrd )
c7  abs(WAIS  D  TDM )
Several additional searches were conducted using varying combinations of pairings

between different ice cores (i.e. different variations of C) to explore the impact of the
chosen minimization criteria on the search results (Table S2). Minimizations 2, 3, 4, and
6 focus specifically on the impact of having the Byrd and the Taylor Dome measurements
as part of the search criteria. These data sets have comparatively larger uncertainties
regarding the measurements, the chronology, and the model-derived thermal histories.
The results demonstrate that the sensitivity of our results to whether or not the Byrd and
the Taylor Dome measurements are used in the minimizations is fairly low (Figure S4a,
Table S3).
In minimization 5, we removed the slope equality constraint on the SDM – WAIS-D
pairing, and in minimization 6, we eliminated the WAIS-D – SPO pairing replacing it
instead with the SDM – TDM and the WAIS-D – TDM pairings (Table S2). Neither had
a considerable impact on the results (Figure S4b, Table S3). These tests demonstrate that
the slope in equation (6) (in the main body of the paper) is not sensitive to the changes in
the parameterization of equation (1) (shown here) as long as the SDM – WAIS-D pair is
included in C. There is seemingly more than one term in (1) that imposes this
requirement. For example, the requirement that both SDM and WAIS-D agree with Byrd
also requires that SDM and WAIS-D agree with each other. However, the time periods
of overlap between pairings are not exactly the same and each pairing places some
independent constraint on the minimization.
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