Introduction
Measurements of soluble impurity species in polar ice cores provide important
high-resolution proxies of past climatic phenomena, including past changes in
sea-ice extent, marine and terrestrial productivity, volcanism, biomass
burning, atmospheric cycling, and anthropogenic pollution (e.g., Legrand and
Mayewski, 1997). A foundational premise, however, is that these species
undergo negligible post-depositional redistribution in the ice column, an
assumption unsupported by numerous ice core records from Greenland and
Antarctica. Processes acting within the upper firn layer – including wind
pumping, diffusion, photolysis, volatility, sublimation, and melt
(Wolff,
1996) – can affect the stability of chemical species soon after deposition and
undermine the climatic interpretation of these records down-core (Wagnon et
al., 1999; Weller et al., 2004). Deeper in the ice column, both observation (e.g., Barnes
et al., 2003b) and theory (Nye, 1991; Rempel et al., 2001, 2002) indicate the
potential for solid and liquid-state chemical migration, impacting the
stability of chemical species much later after deposition. In this study, we
focus on one species particularly susceptible to vertical migration in polar
ice, methanesulfonic acid, or MSA (CH3SO3H; Pasteur and Mulvaney,
2000).
The processes leading to the production, transport, and deposition of MSA
onto an ice sheet are complex (e.g., Abram et al., 2013). The progenitor
compound of MSA, dimethylsulfoniopropionate, or DMSP
((CH3)2S+CH2CH2COO-), is produced by certain
marine algae as an osmotic regulator (Dickson and Kirst, 1986). Planktonic
life cycle processes ultimately release DMSP to the water column, whereupon
the ensuing bacterial-mediated cleavage of the compound promotes the
formation of dimethylsulfide, or DMS ((CH3)2S), a highly insoluble
gaseous compound (Yoch, 2002). Once freed to the atmosphere, DMS is rapidly
photo-oxidized (Saltzman et al., 1983), branching to form either non-sea-salt
sulfate (nssSO4-2) or, to a lesser extent, MSA. Unlike
nssSO4-2, however, DMS production appears to be the exclusive source
of MSA (Abram et al., 2013).
Early studies on DMS and DMSP production in the Southern Ocean (Curran and
Jones, 2000) and in Arctic waters (Leck and Persson, 1996) reported the
greatest fluxes of DMS near the marginal sea-ice zone at the onset of
spring–summer decay (Turner et al., 1995; Curran et al., 1998). Since
concentrations of atmospheric MSA rapidly decrease with increasing altitude
and distance from their marine source (the mean atmospheric lifetime of MSA
is estimated to about 7 days; Hezel et al., 2011), deposition of MSA at
coastal ice sheet localities near-ubiquitously exhibits well-defined annual
peaks during the late-spring to summer months. Conversely, the relatively low
wintertime MSA deposition may be jointly attributed to (1) limited marine
productivity during polar darkness; (2) increased wintertime sea-ice extent
and, accordingly, atmospheric transport distances; and (or) (3) diminished
atmospheric OH radical concentrations, the primary oxidant of airborne DMS
(Jourdain and Legrand, 2001). The strong seasonality and unique marine source
of MSA in ice cores have led to its predominant use as a high-resolution
proxy for past sea-ice cover (e.g., Welch et al., 1993; Abram et al., 2013).
Mulvaney et al. (1992) appear to be the first authors to report migration of
MSA in polar ice, using data from Dolleman Island, Antarctic
Peninsula. In the shallow portions
of the Dolleman Island core, concentrations of MSA exhibited well-defined
summer maxima, as expected. With increasing depth in the ice column, however,
a distinctive shift to predominantly winter [MS-] maxima was found
(hereafter, MSA is denoted as MS- when referring to its anionic form,
CH3SO3-, as measured by ion chromatography). Concluding that a
change in the seasonality of peak MSA production and (or) deposition was
unlikely, the authors postulated this shift to result from post-depositional
vertical migration. Since then, numerous ice core studies from both
Antarctica and Greenland have reported the migration phenomenon over a wide
range of depths, temperatures, and ionic concentrations in the ice column
(Table 1 and references therein).
Ice core sites where MSA migration (or lack thereof) has been
reported (“∼” denotes unavailable data and “n/a” denotes a
non-applicable field).
Ice core name
Lat/long
Year
Depth reached/
Elevation,
Distance to
SAT,
b˙,
MSA
zfo, m
ρfo,
[MS-‾],
[Na+‾],
Reference
collected
reported,
m
coast, km
∘C
m w.e. yr-1
migration
(year)c
kg m-3
µg L-1
µg L-1
m (years)
reported?a
West Antarctic MSA records
Dyer Plateau
70.65∘ S, 65.02∘ W
1988–1989
56 m w.e. (103)
1943
190
-21.7
0.48
U
n/a
∼
∼
∼
Mulvaney et al. (1992),
Pasteur and Mulvaney (2000)
Dolleman Island (1)
70.58∘ S, 60.93∘ W
1985–1986
96 m w.e. (297)
398
20
-16.8
0.34
Y
10 (10)
∼
16.6
382
Mulvaney et al. (1992)
Dolleman Island (2)
70.58∘ S, 60.93∘ W
1992–1993
18.5 m w.e. (45)
398
20
-16.8
0.34
Y
8.5 m w.e.
∼
∼
∼
Pasteur and Mulvaney (2000)
(19)
Gomez Nunatak
74.02∘ S, 70.63∘ W
1980–1981
37 m w.e. (42)
1130
135
-17
0.88
N
n/a
n/a
∼
∼
Mulvaney and Peel (1988),
Pasteur and Mulvaney (2000)
Beethoven Peninsula
71.88∘ S, 74.57∘ W
1992–1993
30 m w.e. (28)
580
16
-12.5
1.20
N
n/a
n/a
∼
∼
Pasteur and Mulvaney (2000)
Berkner Island north (1)
78.30∘ S, 46.28∘ W
1989–1990
11 (21)
730
50
-22.5
0.22
Y
9 (16)
560
19.0
583d
Wagenbach et al. (1994)
Berkner Island north (2)
78.30∘ S, 46.28∘ W
1994–1995
39 m w.e. (174)
730
50
-22.5
0.20
Y
∼
∼
∼
∼
Pasteur and Mulvaney (2000)
Berkner Island south
79.60∘ S, 45.62∘ W
1989–1990
11 (28)
940
150
-24.5
0.17
Y
6 (16)
520
16.0
317d
Wagenbach et al. (1994)
Siple 94-1
81.65∘ S, 148.8∘ W
1994–1995
148 (1150)
621
400
-25
0.13
Y
2 (6)
∼
21.7
147
Kreutz et al. (1998)
DIV2010
76.80∘ S, 101.7∘ W
2010–2011
112 (216)
1329
180
-24
0.41
Y
26 (38)
640
7.7
37.6
Criscitiello et al. (2014),
Criscitiello (2014)
THW2010
77.0∘ S, 121.2∘ W
2010–2011
62 (145)
2020
340
-28
0.28
Y
17 (32)
610
9.0
27.5
Criscitiello et al. (2014),
Criscitiello (2014)
Bruce Plateau
66.03∘ S, 64.07∘ W
2009–2010
448 (∼)
1976
30
-14.8
1.98b
Y
395 (560)
∼
∼
∼
Goodwin (2013),
Porter et al. (2016)
Byrd NBY-2
80.02∘ S, 119.5∘ W
1989–1990
164 (629)
1530
650
-28
0.11
Y
2.6 (13)
∼
6.7
37
Langway et al. (1994)
Filchner-Ronne D235
77∘ S, 64∘ W
1987–1988
4.3 m w.e. (20)
∼
125
∼
0.18
Y
1.8 m w.e.
∼
14.4
361c
Minikin et al. (1994)
(9)
Ferrigno
74.57∘ S, 86.90∘ W
2010–2011
136 (309)
1354
475
-24.7
0.35
Y
25 (30)
620
5.9
88
Thomas and Abram (2016)
East Antarctic MSA records
Law Dome: W20k
66.77∘ S, 112.35∘ E
1997
45 (191)
1370
110
-22
0.15
Y
∼
∼
∼
∼
Curran et al. (2002)
Law Dome: DSS
66.77∘ S, 112.42∘ E
1997; 2000
124 (156)
1370
120
-21.8
0.64
U
n/a
n/a
7.0
85.5
Curran et al. (2002, 2003)
Law Dome: DE08
66.72∘ S, 113.18∘ E
1986
196 (145)
∼
100
-19
1.27
N
n/a
n/a
∼
∼
Curran et al. (2002)
WHG – Victoria Land
72.90∘ S, 169.08∘ E
2006
105 (130)
400
12
-15
0.61
N
n/a
n/a
22
1901
Sinclair et al. (2012, 2014)
Greenland MSA records
Summit2010
72.33∘ N, 38.28∘ W
2010
87 (268)
3213
360
-29.5
0.22
Y
43.7–46.9
710–720
3.4
5.1e
Maselli et al. (2017)
(120–130)
D4
71.4∘ N, 44.0∘ W
2004
145 (270)
2710
300
∼
0.42
Y
54.3–59.4
760–770
2.5
5.3d
MSA data unpublished
(90–100)
2Barrell
76.94∘ N, 63.15∘ W
2011
21.3 (21)
1685
100
∼
0.51
N
n/a
n/a
∼
∼
Osterberg et al. (2015)
a Y = yes; N = no; U = unclear.b Bruce Plateau annual mean accumulation rate appears to be
highly variable over the core-depth; listed value represents the AD
1750–2010 estimate (Goodwin, 2013). c See Supplement Sect. S1 and Table S1 for more information on
how zfo is defined at each site. d [Na+‾] estimated using the reported
site value for [Cl-‾] and converted assuming a
site-ratio [Cl-‾] / [Na+‾]=1.8,
the mean sea-water ratio (e.g., Chesselet et. al, 1972).e [Na‾] measurements
made using continuous-flow inductively coupled plasma mass spectrometry
(ICP-MS), as opposed to [Na+‾] measurements made
using ion chromatography (IC). As ICP-MS measures both the soluble andinsoluble mass content, [Na‾]
values are likely slightly higher than IC-based estimates of
[Na+‾].
Despite the importance of [MS-] records in paleoclimatic studies, there
have been few systematic evaluations of the environmental and (or) chemical
conditions promoting MSA migration from summer to winter layers in polar ice.
Furthermore, aspects of this migration process exhibit behavior distinct from
other post-depositional processes and are important to understand
mechanistically. First, the [MS-] maxima that are formed in winter are
converse to what would be expected from typical (Fickian) diffusion, which
would instead weaken the amplitude of summertime [MS-] peaks. Second,
MSA movement has been reported to occur in the up-core direction (Curran et
al., 2002), ruling out gravitational forcing as the sole mechanism for
migration. These observations, corroborated by evidence for highly
concentrated regions of sulfuric acid at the interface of individual ice
crystals (Mulvaney et al., 1988), led to speculation that liquid migration of
soluble impurities could occur along the boundaries of individual ice
crystals, likely along concentration gradients (Mulvaney et al., 1992).
However, critical questions remain. For example, why should MSA in particular
exhibit migration while associated soluble impurities and acids (e.g.,
nssSO42-) do not (Pasteur and Mulvaney, 1999)? How could diffusion
result in clearly defined concentration maxima in winter layers? Could the
“trapping” of migrating MSA in the adjacent winter layer stem any
subsequent “spillover” of MSA into an adjacent annual layer, as assumed in
prior studies (e.g., Kreutz et al., 1998; Pasteur and Mulvaney, 2000; Becagli
et al., 2009; Thomas and Abram, 2016)? Clearly, investigating the
mechanisms(s) responsible for MSA migration in polar ice is necessary if we
are to answer these questions and build confidence in the use of [MS-]
in polar ice as a paleoclimatic indicator.
The overarching goal of this study is to develop a better understanding of
the environmental and physico-chemical processes that are conducive to MSA
migration in cold, polar ice, in order to improve the interpretation of
ice-core [MS-] records. This paper is organized as follows. In Sect. 2, we consider published [MS-] and ancillary measurements from a
variety of Greenlandic and Antarctic ice cores in an effort to identify
site-specific factors that influence MSA migration. In Sect. 3, we present
observations from the high-resolution, precisely dated DIV2010 ice core
(West Antarctica) as a case study for MSA migration. In Sect. 4, we
summarize our current understanding of the physico-chemical processes
leading to MSA migration, utilizing an existing model describing soluble
impurity transport along ice grain boundaries (Rempel et al., 2002). We
derive a simplified version of this model to illuminate these processes and
to test the ability of different values of MSA diffusivity to reproduce the
down-core change in phase relationship between the concentrations of MSA
(deposited primarily in summer) and Na+ (deposited primarily in winter)
observed along the DIV2010 core. In Sect. 5, we assess the integrity of
the DIV2010 [MS-] record and discuss the broader implications of our
results for the interpretation of [MS-] records across a wide range of
polar conditions. Section 6 concludes with an overview of our results and
suggestions for future research.
Compilation of data for Antarctic (circles) and Greenland (diamonds)
ice cores for which [MS-] records meet the criteria of this study.
(a) Annual mean accumulation rate versus annual mean surface air
temperature. (b) Core-averaged [MS-] versus distance to the
coast. (c) Core-averaged [Na+] versus distance to the coast.
The colors indicate whether MSA migration has been reported, deemed as
unclear, or not reported in the original publications. The numbers indicate
ice core sites with b˙ > 0.45 m w.e. yr-1:
1. Bruce Plateau (length of record: 448 m), 2. DS08 – Law Dome (196 m,
corresponding to a time span of 145 years), 3. Beethoven
Peninsula (47 m, 28 years),
4. Gomez Nunatak (56 m, 42 years), 5. WHG – Victoria Land (106 m,
130 years), 6. DSS – Law Dome (124 m, 156 years), and 7. Dyer Plateau
(80 m, 103 years).
MSA migration in ice cores
In this section, we use observations to evaluate the relative importance of
site-specific variables for MSA migration in polar ice. We compiled 22 ice
core [MS-] records originating from 20 sites in Greenland and Antarctica
(see Supplement), taken from both the literature and unpublished datasets
(Table 1). The following criteria are adopted for selection of the records:
(1) high temporal resolution and dating accuracy (annually resolved and
dating uncertainty < 3 years); (2) multi-decadal
record length (20 years minimum); and (3) documented changes in seasonality
in the [MS-] record and (or) an explicit mention of MSA migration from
summer to winter layers. Post-depositional surficial losses of MSA may occur
via gaseous diffusion in the top 1–2 m of the firn at low-accumulation
sites (Wagnon et al., 1999; Delmas et al., 2003; Weller et al., 2004). As a
result, we exclude records from sites where annual mean accumulation rate is
less than 100 kg m-2 yr-1 and assume that vertical
redistribution of MSA via gas-phase diffusion (Kuo et al., 2011) is
negligible at all considered sites and depths. Also excluded are records from
sites subject to moderate to severe melt, which, through percolation, can
also rapidly redistribute MS- along the firn (Moore et al., 2005).
Of the 20 sites, 13 indicate MSA migration, 5 do not indicate migration, and
at 2 sites migration is deemed unclear at the greatest depths sampled
(Fig. 1). The sites and records cover a wide range of climatologic and
glaciological conditions, as represented by annual mean surface air
temperature (SAT), annual mean accumulation rate, distance inland, and
impurity concentrations in the ice (Table 1 and Fig. 1). Figure 1a
illustrates the range of annual mean accumulation rates (b˙) and
annual mean surface air temperatures of all sites. A strong, nonlinear
relationship is apparent between both variables, as expected (Cuffey and
Patterson, 2010). Similarly, for the 14 sites where glaciochemical data are
available (Table 1), Fig. 1b and c show, respectively, the depth-averaged
concentrations of Na+ ([Na+‾]; see Table 1 for
proper symbolic representation of Na+ concentration), an ionic species
whose relevance we expound upon in Sect. 2.2, and MS-
([MS-‾]). Both [Na+‾] and
[MS-‾] are taken here as rough measures of winter and
summer deposition, respectively, across sites. While impurity deposition
largely covaries with distance inland (Fig. 1b and c), with higher
[Na+‾] and [MS-‾] at sites
nearer to the coast, this pattern does not always hold true, likely due to
effects associated with seasonal atmospheric transport and (or) local
differences in the production of the progenitor aerosols of both ions (Iizuka
et al., 2016). There is also a notable geographic difference: Greenland
values of [Na+‾] and [MS-‾]
(observed at the high-elevation, inland Summit2010 and D4 sites) are lower
than those reported for all Antarctic ice cores. In the following
subsections, we explore in detail the effects of snow accumulation, ice
impurity concentration, surface air temperature, and ice density on MSA
migration.
Snow accumulation
Previous work has suggested that high snow accumulation acts as the primary
deterrent for MSA migration (Pasteur and Mulvaney, 2000), which is a result
of (i) the longer distance
required for an ion to travel from the summer to winter layer, (ii) the
corresponding suppression of summer–winter layer ionic concentration
gradients at higher accumulation sites, or (iii) both (Curran et al., 2002).
General support for this suggestion is illustrated in Fig. 1a, showing that
sites with b˙> 0.45 m w.e. yr-1 (meter of water equivalent
per year) appear less likely to exhibit clear signs of MSA migration than
sites with lower accumulation rates. This consideration, however, does not
take into account the depth required for migration to occur. As such, we
consider below whether MSA migration invariably occurs across the full range
of accumulation rates, given sufficient depth within the firn column.
At low-to-moderate accumulation rate sites (b˙= 0.1–0.45 m w.e. yr-1), MSA migration seems to universally occur,
with the shallowest reported depth
of migration showing a positive relationship with accumulation rate (Table 1
and Fig. 2). Data from sites characterized by moderately high accumulation
rate (b˙= 0.45–0.65 m w.e. yr-1) are not as straightforward to interpret.
For example, in the Dome Summit South (DSS; Law Dome, Antarctica) and Dyer
Plateau ice cores, signs of MSA migration were noted in the original studies.
At DSS (b˙= 0.64 m w.e. yr-1), moderate indications of
[MS-] annual maxima extending into adjacent autumn layers were reported
at depths greater than about
40–50 m (Curran et al., 2002). Similarly, at Dyer Plateau
(b˙= 0.48 m w.e. yr-1) [MS-] showed suppressed,
localized maxima in both winter and summer layers throughout a core section
from ∼ 51–54 m depth, indicating, perhaps, initial or transitory
stages of migration (Pasteur and Mulvaney, 2002). On the other hand, two
[MS-] records at sites characterized by annual mean accumulation rates
similar to DSS and Dyer Plateau, the 2Barrell (b˙= 0.51 m w.e. yr-1) and WHG ice cores (b˙= 0.61 m w.e. yr-1), respectively, showed no signs of migration.
However, neither WHG nor the 2Barrell records extend as deep as their
counterparts, suggesting WHG and 2Barrell may be of insufficient length and
thus may also show migration at similar depths. Finally, of the four sites
characterized by high accumulation rates
(> 0.65 m w.e. yr-1), three [MS-] records – the
Gomez Nunatak (b˙= 0.88 m w.e. yr-1), Beethoven Peninsula
(b˙= 1.2 m w.e. yr-1), and DE08
(b˙= 1.27 m w.e. yr-1) ice cores – did not present signs of
migration. The exception is the highest accumulation site, Bruce Plateau
(b˙= 1.98 m w.e. yr-1), where clear evidence of
summer-to-winter migration was reported at ∼ 395 m depth (Porter et
al., 2016). Notably, Bruce Plateau is also the deepest drilled record among
the high accumulation rate sites of our compilation.
(a) Shallowest depth of MSA migration, zfo,
versus annual mean accumulation rate (b˙) for Antarctic (circles) and
Greenland sites (diamonds). The dashed line is the least-squares fit
zfo = 125 ⋅ b˙1.77 through the
Antarctic data with b˙ < 0.45 m. w.e. yr-1
(n = 10; r2 = 0.82) and used to predict zfo at
sites where MSA migration was not reported (grey and blue). At two of these
sites (WHG and DE08; grey), maximum sampling depth exceeds the predicted
zfo. The solid black line is the fit when including the Bruce
Plateau data (b˙ = 1.98 m. w.e. yr-1).
(b) Expanded view of panel (a) (rectangle bounded with
dashed lines). Error estimates for zfo are generally crude
(Supplement Sect. S1). Some are based on unit conversion from m w.e. to m
using a firn densification model (Harron and Langway, 1980) constrained by
site diagnostic observations (Table 1) and an assumed surface snow density
range of 300–400 kg m-3. The dashed line is the same as in
panel (a).
We use these observations to determine the relationship between b˙
and the depth of first occurrence of MSA migration, zfo, defined as the
shallowest reported depth where [MS-] consistently shows its annual
maximum in winter (see Supplement for details about the
estimation of zfo for each site). We first consider just Antarctic sites
reporting MSA migration (Fig. 2a). A least-squares fit of a power law of
zfo against b˙, with the intercept fixed to the origin, yields
r2=0.99 (Fig. 2a). To ensure that the fit is not dominated by the
data pair with the highest b˙ value (Bruce Plateau), zfo is
regressed against b˙ using only those records with accumulation rates
< 0.45 m w.e. yr-1, which yields r2=0.82 (Fig. 2b).
Remarkably, extension of the latter fit to the Bruce Plateau data point
produces a value of zfo that is within ∼ 15 m of the
reported value (Fig. 2a). The ability of the power law to describe the data
in both scenarios suggests that, at least at Antarctic sites, the annual
mean rate of snow accumulation has a strong (nonlinear) influence on the
shallowest depth of MSA migration in the ice column.
Applying this power law to the five sites where MSA migration was not
observed or reported (Fig. 1), we find that three of these sites did not
reach the predicted zfo. The exceptions are (i) the WHG core, where
little information on MSA migration in the deepest portions of the core is
provided in the original study (Sinclair et al., 2014); and (ii) the Law
Dome DE08 core, where the largest depth reported by Curran et al. (2002)
remains within ∼ 15 m of the predicted zfo. These results
suggest that MSA migration may be more general than commonly thought and
that records for which MSA migration was not reported either may have not
reached the requisite depth or they did not have the necessary resolution
required to observe the phenomenon. The two high-elevation records from
inland Greenland, which have low overall impurity concentration relative to
the coastal Antarctic records, appear anomalous (Fig. 2a). This anomaly may
result from the effect of ice impurities – in particular cationic sea salts
– on MSA migration, a point we investigate in more detail below.
Ice impurities
Earlier studies hypothesized that the presence of well-defined [MS-]
peaks in winter layers reflects interaction with sea salts, which are
preferentially deposited during winter months at most coastal locations
(Legrand and Mayewski, 1997). The attributed mechanism, first hypothesized by
Mulvaney et al. (1992) and echoed by subsequent studies (Wolff, 1996; Kreutz
et al., 1998; Pasteur and Mulvaney, 2000; Curran et al., 2002), posits that
an MSA molecule rejected to and dissolved in the undercooled liquid veins
present at the interface of ice grains (Mulvaney et al., 1988) would be
transported by diffusion along a concentration gradient. This mechanism could
transport MS- in either the down or up gradient direction and would not
necessarily conform to the concentration gradient measured on bulk ice
samples (Sect. 4). Mulvaney et al. (1992) further proposed that, upon contact
with a cation, the precipitation of a stable cation salt through a metathesis
reaction could effectively remove MS- from solution, thus sequestering
the resultant precipitate in the winter layer.
Here we evaluate whether observations support this mechanism, by comparing
zfo to the bulk concentrations of winter-deposited cations at
sites showing evidence of MSA migration. Our evaluation is premised by the
notion that higher ionic concentrations have a greater ability to regulate
the chemical composition of liquid veins, when in situ temperatures exceed
the eutectic temperatures of the dominant progenitor salt species of those
ions (Nye, 1991; Sect. 4). We constrain our analysis to the relationship
between MSA and Na+ concentrations for the
following reasons. First, at coastal localities, the most abundant
winter-maximum cation is typically Na+, though the relative abundance of
Mg2+, Ca2+, and K+ may vary from site to site (Legrand and
Mayewski, 1997). Second, past studies have noted that MSA concentration peaks
tend to coincide with Na+ concentration peaks down-core (Pasteur and
Mulvaney, 2000; Kreutz et al., 1998). Finally, Na+ is considered to be
relatively nonreactive within the ice column (Barnes et al., 2003a, b;
Legrand and Mayewski, 1997), while less abundant cations, such as Mg2+,
appear to be more susceptible to post-depositional effects (Kreutz et al.,
1998; Wolff, 1996).
In Fig. 3, zfo is plotted against the core-averaged concentration
of Na+ ([Na+‾]) for the 11 sites where
[Na+] data are available. These sites have comparable annual mean
accumulation rates, within 0.13–0.42 m w.e. yr-1, so that the effect
of [Na+‾] on MSA migration could be isolated with
some confidence. We find that as [Na+‾] decreases,
MSA migration tends to be observed at greater depths in the firn or ice
column (Fig. 3). The depth zfo appears to be particularly
sensitive to [Na+‾] for low concentrations of
Na+‾, as can be seen most prominently for the two
Greenland cores showing migration, D4 and Summit2010. This result conforms to
the suggestion that, as the concentration of Na+ is reduced, the
concentration gradient of MS- existing in the liquid vein network
between the winter and summer layers is also reduced, thereby decreasing the
rate at which MSA migration occurs. Another possibility is that the reduction
of [Na+] closes off the liquid vein network within winter layers,
inhibiting the vertical transport of ions along grain boundaries, although
data are lacking to explore this further.
Temperature
Temperature may influence MSA migration in at least two ways. First, the rate
of diffusion of MS- along grain boundaries may depend on temperature,
with higher rates occurring at warmer sites, as suggested by Pasteur and Mulvaney (1999). Such dependence would
imply that sites characterized by lower in situ temperatures would tend to
exhibit larger values of zfo. Second, the precipitation of an
MS- sea salt from solution may be required to sequester MS- in the
winter layer, as proposed by Mulvaney et al. (1992). If effective, the
formation of winter-layer [MS-] annual maxima would be inhibited at
sites where in situ temperature exceeds the eutectic temperature(s) of the
dominant precipitated MS- sea salt(s). We can test both of the foregoing
thermal influences with the available observations. However, due to a lack of
firn temperature profiles, we substitute the more widely available annual
mean surface air temperature as a surrogate for in situ temperature. This
approach appears justified, as vertical thermal gradients in polar ice sheets
are typically small below 10 m and their magnitude is dictated primarily by
local annual mean SAT (Cuffey and Patterson, 2010). We note that, deeper in
the ice, thermal gradients could be important (Rempel et al., 2001),
particularly near the bedrock due to geothermal fluxes and (or) frictional
heat dissipation, but we do not consider those cases here.
Shallowest depth of MSA migration versus core-averaged [Na+]
for different core sites in Antarctica (circles) and Greenland (diamonds).
The dashed line is the least-squares fit
zfo = 142 ⋅ [Na+]-0.58 through all the
data (n = 11, r2 = 0.85).
As a rough test of a thermal influence on MSA migration, we regress
zfo against SAT (not shown). Unlike the relationships between
zfo and b˙ or [Na+‾], no
significant relationship between zfo and SAT is observed.
Likewise, no significant relationship is found between the zfo
residuals of the relationship between zfo and b˙
(arguably, the best predictor for zfo) and SAT (also not shown).
These results suggest that temperature has a negligible influence on MSA
migration, at least for the sites considered (Table 1).
Similarly, available observations do not indicate that sites reporting MSA
migration can be discriminated on the basis of SAT. Although sites
presenting no evidence for MSA migration tend to experience high SAT
(-19 to -12.5 ∘C, Fig. 1a), two sites where MSA
migration has been reported are also characterized by equal or higher SAT.
We interpret this observation as an artifact of the strong relationship
between SAT and accumulation rate in polar regions (Fig. 1), whereupon
b˙ is deemed to be the most relevant variable in driving zfo
(Sect. 2.1). This conclusion, in turn, indicates that either precipitating
MS- salts may not drive MSA migration (Mulvaney et al., 1992) or the
eutectic temperature(s) of the dominant MS- sea salt(s) is (are) less
than -29.5 ∘C, the lowest SAT reported in Table 1. We return to
this discussion in Sect. 5.1, after incorporating recent estimates of the
eutectic temperatures of the dominant MS- sea salts.
Firn or ice density
The mechanism of MSA migration described above, involving diffusion along
liquid grain boundaries, relies on the assumption that the ice grains are
sufficiently well compacted to form interconnected premelted veins between
the summer and winter layers. This mechanism seems to imply there should be a
relationship between the onset of MSA migration and ice density (ρ),
yet to our knowledge such possible relationship has not been investigated.
Here, we consider the firn or ice densities (ρfo) observed at
the shallowest depth of MSA migration again using our
compilation of Greenland and Antarctic data.
In Fig. 4, zfo is plotted against ρfo for the
seven sites where available data permit (Table 1). A weighted least-squares
fit to the data, with the weighting provided by the errors in the
zfo estimates, shows a positive relationship between
zfo and ρfo (p < 0.01), as expected.
Data for low-accumulation Berkner Island sites, where annual mean b˙=0.18–0.22 m w.e. yr-1, indicate the occurrence of MSA migration
at densities exceeding about 515–560 kg m-3 (Wagenbach et al., 1994),
while higher accumulation sites, including THW2010, Ferrigno, and DIV2010
(b˙=0.28–0.41 m w.e. yr-1), show ρfo
values in the range of 610–650 kg m-3. The highest ρfo
values, in the range 710–760 kg m-3, are found for the Greenland
cores, D4 and Summit2010.
Interestingly, the firn or ice densities at the shallowest depths of MSA
migration (∼ 500 to ∼ 800 kg m-3, Fig. 4), are all
comparable to or higher than the critical value of 550 kg m-3 that
corresponds to the theoretical closest random packing of spherical ice grains
(Benson, 1962). Densities greater than 550 kg m-3 can be achieved only
by bond formation, or sintering, at the contact of individual grains (Cuffey
and Patterson, 2010). Persistent vertical transport of undercooled liquid at
the grain boundaries (Mulvaney et al., 1992) requires reaching or exceeding
this effective critical density. The compiled data also indicate that the
critical density for MSA migration may vary between sites (Fig. 4), which
might be due to variability in grain shape, grain size, and (or) impurity
content. For example, firn samples with densities of 350–400 kg m-3
can typically be cut into blocks (Cuffey and Patterson, 2010), which suggests
that bond formation in the upper firn pack can begin at densities below
550 kg m-3. Furthermore, at the lowest accumulation sites – Byrd
Station, Siple Dome, and the Filchner-Ronne Ice Shelf – MSA migration was
reported in the shallowest ∼ 5 m of the firn (zfo=2.6,
2, and 3–4 m, respectively). Although density data are not available for
these specific records, this observation suggests that MSA migration may
begin at bulk densities substantially lower than 550 kg m-3, perhaps
through high-density microlayers, such as wind-blown crusts, which are
features commonly found at lower accumulation sites (Cuffey and Patterson,
2010). While more data are needed, available evidence presented here supports
the notion that a density of at least 500 kg m-3, comparable to the
theoretical value of 550 kg m-3, is needed for MSA migration.
Shallowest depth of MSA migration versus firn or ice density for
different core sites in Antarctica (circles) and Greenland (diamonds). The
vertical bars are error estimates (Supplement Sect. S1); the dashed line is
the weighted least-squares fit zfo=-956+0192ρ through
the data (n = 7; r2 = 0.89), with the weighting provided by
the zfo error estimates; and the shaded region is the region
of 95 % confidence.
Synthesis
Our data analysis suggests that the annual mean rate of snow accumulation
appears to have a strong influence on the shallowest depth at which MSA
migration is observed. The concentration of Na+ in the ice or firn
appears to also be an important factor, especially at sites characterized by
low [Na+‾]. Annual mean SAT appears to play a less
important role in determining zfo, at least in the SAT range
where data are available (-29.5 to -12.5 ∘C). Lastly, the onset
of migration appears to be associated with a critical density near
450–550 kg m-3, though this may not hold true for all
low-accumulation sites. Overall, our analysis suggests that MSA migration may
be more common than usually thought and that existing [MS-] records not
exhibiting evidence for migration may not be deep enough, or have the
necessary (sub-annual) resolution, to observe the phenomenon.
The shallowest depth of MSA migration (zfo) appears most readily
predictable from b˙ in coastal Antarctica. This result appears in part
attributable to the comparably higher concentrations of Na+ in the
coastal Antarctic cores than in the two Greenland cores showing evidence of
migration (Table 1). The joint effect of annual mean accumulation rate and
depth-averaged Na+ concentration on the shallowest depth of MSA
migration is illustrated in Fig. 5, which shows MSA migration tends to occur
deeper in the firn or ice column for larger values of b˙ and lower
values of [Na+‾]. Notably, Antarctic sites with
comparably low concentrations of Na+ tend to occur further inland and at
higher elevations, and thus also tend to have lower accumulation rates than
considered in this study (i.e.,
b˙ < 0.1 m w.e. yr-1). Greenland, in contrast,
experiences comparably large accumulation rates even at its highest-altitude,
inland locations (e.g., Summit2010). For a recent overview of
Greenland-wide [Na+] deposition, see Rhodes et al. (2017).
A case study: the DIV2010 MSA record
In this section, we use a well-dated multi-century ice core record from
DIV2010, an intermediate accumulation rate site in coastal West Antarctica
(Table 1), to document in detail the phenomenon of MSA migration. Prior
studies have investigated aspects of the DIV2010 core, including variability
in accumulation (Medley et al., 2013, 2014) and chemical composition
(Criscitiello et al., 2013, 2014; Pasteris et al., 2014). As this is the
first report of the DIV2010 [MS-] record below the zone of MSA
migration, however, we describe the record in more detail here. Inorganic
salt ions (e.g., Na+) and MS- concentrations were measured on discrete samples at a constant sampling interval
Δz=5 cm using standard suppressed ion chromatography methods
(Curran and Palmer, 2001). The age-depth relationship of the core was
established independently by identifying summer maxima in three parameters –
[nssS], [H2O2], and δ18O – measured at ∼ 2 cm
resolution (Pasteris et al., 2014). Here, we examine data from the top
60.4 m of DIV2010 (AD 1905–2010) covering the zone of progressive migration
of MSA. Dating uncertainty over this depth interval is estimated to be less
than 1 year based on tie points to well-known volcanic events (Pasteris et
al., 2014), and the sampling frequency (∼ 10–15 samples per year)
allows for seasonally resolved records throughout this depth interval
(Criscitiello et al., 2013; Criscitiello, 2014). At a depth of 60.4 m in the
core, annual layer thinning estimated using a thinning model assuming frozen
basal conditions and a linear vertical strain rate (Nye, 1963) is
considerably less than the distance required for a chemical species to
migrate from the summer to the winter layer (∼ 30 cm). As a result, no
correction for thinning is applied.
Core-averaged [Na+] versus annual mean accumulation rate for
different core sites in Antarctica and Greenland. The different colors
correspond to different values of the shallowest depth of MSA migration.
The migration of MSA from summer to winter layers in the DIV2010 ice core
appears to be progressive. To document this progression and contrast the
behavior of Na+ and MS-, the month of the annual maximum of
[MS-] (mMS-) and the month of the annual maximum of [Na+]
(mNa+) are each plotted versus age (Fig. 6). The month of the annual
maximum of [MS-] tends to change down-core from summer to predominantly
winter, as revealed by the significant linear trend of mMS- between
AD 1905 and 1999 (r=0.75; p < 0.001). In contrast, [Na+]
consistently shows maxima in the winter layers; i.e., mNa+ portrays
no significant trend over this period (r=0.09, p = 0.41). Similarly,
[nssSO42-] displays its annual maximum consistently in the summer
layers during this period (not shown). Note that no significant decrease in
annual mean [MS-] is found deeper than 10 m, suggesting
post-depositional losses are negligible at the DIV2010 core site.
Timing of annual maximum of [MS-] (red) and annual maximum of
[Na+] (blue) versus calendar age (year AD) for the DIV2010 core. No
obvious sign of migration in the up or down-core direction is observed in
DIV2010. As such, the timing of annual maximum [MS-] and annual maximum
[Na+] is defined in terms of the number of degrees out of phase from
1 January (0∘), where 180∘ indicates an annual maximum on
1 July. The two dashed lines are the least-squares fits for [MS-] and
[Na+] over the period AD 1999–1905, corresponding to depths below which
ρ = 550 kg m-3. The fit is highly significant for [MS-]
(n = 95, r = 0.75, p < 0.001) and not significant for
[Na+] (n = 95, r = 0.09, p = 0.41).
Records of [MS-] (red) and [Na+] (blue) from the DIV2010
ice core. (a) The entire record considered in this study, with a
depth scale at the top and a timescale (year AD) at the bottom (raw data).
(b–d) The 11-year long portions of the records within the shallow
zone (b), the transition zone (c), and the deep
zone (d). Three-point running averages are displayed for each zone.
Dashed vertical lines denote 1 January of each year.
Monthly mean concentration of Na+ and MS- in the
shallow (a), transition (b), and deep (c) zones of
DIV2010. The shaded regions indicate ±1 standard error of the mean.
(a–c) Correlograms of [MS-] and [Na+] in the
three zones of the DIV2010 ice core. The horizontal dashed lines show the
95 % confidence interval for a time series with no autocorrelation (white
sequence). (d–f) Cross-correlation between [MS-] and
[Na+] in the three zones of the DIV2010 ice core. The horizontal dashed
lines show the 95 % confidence interval for two uncorrelated time
series.
Identification of DIV2010 migration zones
Notwithstanding the progressive nature of MSA migration in the DIV2010 core,
we identify three distinct zones in the [MS-] record for this core
(Fig. 7). First, a shallow zone is defined as the depth interval where density is
less than 550 kg m-3; at DIV2010, this depth occurs at approximately
9.1 m (Medley et al., 2014). The upper 9.1 m of the core appears to contain
the original (unaltered by migration) [MS-] variations, to the extent
that annual maxima of [MS-] are found in the summer layers and are out
of phase with winter [Na+] maxima. Second, a transition zone is defined further
down-core, where the [MS-] record exhibits no consistent seasonality.
Finally, a deep zone is defined as the deepest portion of the record considered,
where [MS-] and [Na+] annual maxima appear to be broadly in phase
(Fig. 7). In order to facilitate our analysis, we linearly interpolated the
[MS-] record onto a monthly scale, with the three zones defined to
entail an equal number of data points (n=132 months, or 11 years).
To better reveal the variable phase relationship between [MS-] and
[Na+] in the shallow, transition, and deep zones, monthly mean values
of [MS-] and [Na+] are calculated and the standard error of the
monthly means are computed for each zone (Fig. 8). In all three zones,
Na+ shows concentration maxima in winter, albeit with broad variation
between April and September. In contrast, MS- exhibits concentration
maxima during summer (January) in the shallow zone but during winter
(broadly, May to August) in the deep zone. In the transition zone, the
monthly mean [MS-] values are not significantly different between summer (DJF)
and winter (JJA), though local maxima in both spring (MAM) and fall (SON)
are apparent.
Cross-correlation analysis
Cross-correlation coefficients are calculated to quantify the degree of
linear relationship
between the monthly mean [MS-] and [Na+] at different lags in the
three zones. Due to the finite length of the records, only the coefficients
from lag 1 to lag 24 (2 years) are calculated (Fig. 9). In the shallow zone,
[MS-] and [Na+] show a negative correlation at lag 0 and a positive
correlation at lag 6 (i.e., 6 months); both correlations appear significant
at the 5 % level compared to two uncorrelated series (Chatfield, 1996).
These results reflect MSA and Na+ being deposited primarily during
summer and winter, respectively. In contrast, in the transition zone, and
more prominently in the deep zone, the [MS-] and [Na+] records show
a positive correlation at lag 0 and a negative correlation at lag 6; in the
deep zone the correlations at lags 0 and 6 are both significant at the
5 % level. The positive correlation at zero lag in the transition and
deep zones indicates that positive deviations in [MS-] tend to coincide
with positive deviations in [Na+]. The distinct phase relationships
between the two species in the shallow and deep zones are consistent with MSA
migration.
Towards a mechanistic understanding of MSA migration
In this section, we discuss the physico-chemical processes that may be
responsible for MSA migration using an existing model of soluble impurity
transport. We then derive a linearized version of the model in order to
further illuminate the processes that lead to the movement of MSA from
summer to winter layers.
The impurity transport model of Rempel et al. (2002)
The physical mechanisms responsible for the presence of a liquid phase in ice
cores, even well below the freezing point of pure water, are well documented
(e.g., Nye and Frank, 1973; Nye, 1991) and attributed to two distinct
physical processes. The first relates to the fact that the atomic radii of
most impurity species (not including requisitely small ionic species, e.g.,
F-, Cl-, and NH4+; Wolff, 1996) possess a misfit strain
energy that inhibits their incorporation into the tightly packed, crystalline
ice lattice. During densification, these impurities are thus preferentially
expelled to the boundaries of individual grains of ice. This process has been
observed using optical measurements (Mulvaney et al., 1988; Bartels-Rauch et
al., 2014). As the concentration of impurities at the grain boundary is
increased, the local equilibrium temperature is decreased, depressing the
freezing point of the water-impurity mixture. At temperatures greater than a
system's eutectic point, premelted aqueous solutions are assumed to exist at
equilibrium as interconnected, submicron veins at the grain boundaries. The
second process responsible for the presence of a liquid phase in polar ice
pertains to the interstitial curvature occurring at the interface of three
(i.e., triple junctures) or four (i.e., nodes) ice grains. Known as the
Gibbs–Thompson effect, this thermodynamic phenomenon is related to the
deviation in chemical potential of a vapor surrounding a curved surface from
that of the same vapor at equilibrium with a flat liquid surface. In effect,
it allows smaller (more curved) ice grains of a given composition to melt at
lower temperatures than larger (less curved) ice grains of the same
composition (Wettlaufer and Worster, 2006).
Importantly, both of the foregoing processes should respond collaterally to a
temperature change, although they may not have the same importance in the
maintenance of a liquid phase: scaling arguments suggest that the curvature
effect required to reach a given volume of premelted liquid is negligible in
ice sheets in comparison to the effect of impurity-driven undercooling
(Rempel et al., 2001). Focusing on the latter process, Rempel et al. (2002) developed an elegant model describing
the movement of soluble impurities along crystal grain boundaries. They
considered impurity migration due to (1) temperature gradients (Rempel et
al., 2001), which vary gradually down-core (typically
< 1 ∘C per 100 m in ice sheet interiors; Cuffey and
Patterson, 2010); and (2) impurity concentration gradients, which are
characterized by length scales typically on the order of centimeters (Rempel
et al., 2002). They derived the following impurity migration equation,
referred to below as the RWW model:
∂∂tcB,k=-∇⋅(v+vk)cB,k,
where,
vk=Dk∇TTm-T+Dk∑Γi∇cB,i-∇cB,kcB,k∑ΓicB,i∑ΓicB,i.
Here cB,k is the bulk concentration of the kth impurity
species, i.e., the mass of the kth impurity species per unit ice volume as
measured during standard chemical analyses; t is time; and vk is an
effective velocity of the kth impurity species relative to the surrounding
ice. The ice velocity, v, would arise, for example, from a vertical strain
rate and appears to have a small influence on MSA transport on timescales of
years to decades (Nye, 1963). As a result, it is systematically neglected in
this paper (see also, Rempel et al., 2002).
As indicated by Eq. (2), the relative velocity vk has two distinct
contributions. The first is due to the motion of molecules in the liquid
along a temperature gradient and leads to solute transport, even in the
absence of concentration gradients. It is proportional to the diffusivity of
the kth impurity in the liquid, Dk, and inversely proportional to
the difference Tm-T between the melting point of pure ice (Tm) and the
temperature of the liquid (T). The second contribution to vk arises from
the concentration gradients of all solutes present in the liquid veins,
including the kth impurity. As with the first contribution, it is
proportional to the diffusivity of the kth impurity in the liquid, but
it would occur in the absence of a temperature gradient. It also depends on
the slope of the liquidus curve, Γi, of the various solutes
that are present in the liquid veins. Scaling arguments suggest that vk is often well approximated by the second contribution in Eq. (2), at least in
portions of the ice column where temperature gradients are small (Rempel et
al., 2002). The small effect of the first contribution on MSA migration is
further supported by observations made in Sect. 2.3.
Comparison between the RWW model and the linearized model.
(a) Profiles of [MS-] and [Na+] simulated by the RWW model
with DMS=DNa=10-11 m2 s-1 and
ΓMS=ΓMS=6.5 K M-1.
(b) Profiles of [MS-] simulated by the linearized model with an
effective velocity based on the [Na+] profile shown in the panel and
with DMS=10-11 m2 s-1 (see text and
Supplement for details).
A binary mixture provides the simplest context to discuss the mechanisms of
MSA migration in the RWW model. In a mixture comprising MS- and
Na+, Eqs. (1)–(2) reduce to (for negligible v)
∂∂tcMSA=-∇⋅vMScMS,∂∂tcNa=-∇⋅(vNacNa),
where,
vMSA=DMSΓNaΓMScMS+ΓNacNa∇cNa-cNacMS∇cMS,vNa=DNaΓMSΓMScMS+ΓNacNa∇cMS-cMScNa∇cNa.
In this case, the model implicitly assumes that an appreciable amount of the
MSA and Na+-containing impurities are rejected from the crystalline
lattice of individual ice grains during firnification. The postulated
expulsion would concentrate impurities at the grain boundaries, depressing
the freezing point of the intergranular medium to form submicron, undercooled
liquid veins. In general, higher impurity concentrations would lead to higher
abundance of premelt liquid. Thus, more premelt liquid is predicted to occur
in winter layers, where [Na+] is typically maximum, than in summer
layers, where the comparatively low (bulk) concentration of MSA shows a
maximum. The ensuing network of liquid veins would allow the ionic impurities
to diffuse under their own concentration gradients, such that a large
proportion of the MS- from the MS--rich summer layer migrates to
the MS--poor winter layer. Conversely, a comparatively small proportion
of Na+ migrates to the summer layer, because the Na+ concentration
difference between the summer and winter layers is reduced by the larger
amount of premelt liquid in the winter layer than in the summer layer. The
net result of the different transport rates of MS- and Na+ is that
variations in [MS-] ultimately become in phase with variations of
[Na+] (Fig. 10a).
Physico-chemical parameters of MSA migration
The RWW model as applied to the system containing MS- and Na+
(Eqs. 3–4) includes four parameters: the slopes of the liquidus curve
for relevant MS-- and Na+-containing soluble impurity species
(ΓMS and ΓNa), and the grain-boundary diffusivities of
MS- and Na+ (DMS and DNa). Below, we review the existing
literature on each of these quantities.
Grain boundary diffusivity of MS- and Na+
We first consider the grain boundary diffusion coefficient of MS-,
DMS. Lacking empirical constraints, Rempel et al. (2002)
approximated the diffusivity for ionic constituents in Eq. (2) as one-third
the molecular diffusivity of a bulk liquid (i.e., DMS=5×10-10 m2 s-1), scaled so as to account for the random
orientation of premelted liquid veins in the ice (Lemlich, 1978). Smith et
al. (2004) reported a value of DMS=2×10-13 m2 s-1 for solid ice, estimated by measuring variations
in [MS-] across horizontal sections of an ice core from Law Dome,
Antarctica, following nearly 15 years of freezer storage at
-20 ∘C. Using a similar ice substrate and experimental setup,
Roberts et al. (2009) revised this estimate to (4.1×10-13±2.5×10-14) m2 s-1 at -20 ∘C, which was
interpreted by the authors to represent diffusive losses of volatile MSA
occurring during extended periods of freezer storage. Notably, this estimate
is 1–3 orders of magnitude larger than that reported for solid-state
diffusion of HCl (Thibert and Dominé, 1997), HNO3 (Thibert and
Dominé, 1998), HCHO (Barret et al., 2011), and
deuteriorated water (Lu et al., 2009) determined in
single ice crystals, despite the molecular radius of MSA greatly exceeding
that of each of these species (Roberts et al., 2009). In fact, subsequent
studies have contended that the DMS estimate of Roberts et
al. (2009) is unlikely to represent pure solid-state diffusion of MSA in firn
or ice and suggested that at least some of the
storage-related losses of MSA occurred
via liquid transport along grain boundaries (McNeil et al., 2012;
Bartels-Rausch et al., 2014). We thus consider the two values of
DMS as suggested by Rempel et al. (2002) and Roberts et
al. (2009) as potential extrema.
Although the grain boundary diffusion coefficient for Na+,
DNa, is also under-constrained, empirical evidence supports a
relative immobility of Na+ in polar ice. For example, Barnes et
al. (2003a) noted no detectable changes in the amplitude of [Na+] peaks
over the past ∼ 11 000 years (top 350 m) in the low-accumulation Dome
C ice core record (East Antarctica), while the amplitudes of both [Cl-]
and [SO42-] peaks were found to change over the same period.
Furthermore, optical measurements at Dome C suggest a predisposition for
Na+ to be situated at grain boundaries and for Cl- to be located
preferentially within the crystalline structure (Barnes et al., 2003b). The
importance of these findings is twofold: (i) Na+ appears to be situated
in the requisite location to favor the presence of premelt liquid at the
grain boundaries, enabling MS- migration as envisioned in the RWW model
to occur; and (ii) Na+ shows greatly reduced mobility relative to
MS- (or similar sulfur-based acidic species).
Liquidus relationships for relevant sea-salt species
The slopes of the liquidus curves, ΓMS and
ΓNa, represent linear approximations of the undercooling as
a function of impurity concentration in the liquid phase present near the
grain boundaries, c, i.e., Tm-T=Γc, where T is the
in situ temperature and Tm is the melting point for pure ice
(see Supplement, Fig. S2). Knowledge of Γ requires knowledge of the
dominant precursor (bonded) molecular state(s) of the MS- and Na+
ions present in the ice (thus, ΓMS and ΓNa
should be viewed as shorthand notations for ΓMS∗ and
ΓNa∗, where ∗ represents some unknown
cationic–anionic pair). Unfortunately, such data remain sparse beyond those
reported in a few notable studies (e.g., Barnes et al., 2003b; Sakurai et
al., 2010; Iizuka et al., 2016).
It is generally assumed that all measured MS- present in polar firn or
ice samples derives solely from MSA (Sakurai et al., 2010). In the binary
system MSA–H2O, MSA reaches its eutectic temperature at
-75 ∘C (Stephen and Stephen, 1963). Thus, any MSA molecules
expelled to and concentrated at grain boundaries are expected to exist in
liquid solution with H2O. By contrast, Na+ in polar ice may have a
number of precursors. For coastal ice cores, however, it seems reasonable to
expect that the majority of Na+ is deposited either as NaCl derived
primarily from sea spray during storm activity (Legrand and Mayewski, 1997)
or as sodium-sulfate salts such as mirabilite, Na2SO4 ⋅ 10H2O, derived from brine rejection in sea ice or from atmospheric
sea-salt sulfatization (Rankin et al., 2002; Iizuka et al., 2016). While the
NaCl–H2O system reaches its eutectic at -21.3 ∘C (Stephen
and Stephen, 1963), the eutectic of the Na2SO4–H2O system is
-1.6 ∘C (Hougen et al., 1954), suggesting that Na+ deposited
as Na2SO4 should be relatively immobile at most polar ice core
sites. Consequentially, the majority of Na+ relevant to grain boundary
migration is likely derived from NaCl. At DIV2010, for example, the molar
ratio Cl:Na in the top 60.4 m of the core averages 1.806, similar to the
mean molar ratio Cl : Na = 1.8 of seawater (e.g., Chesselet et al., 1972). This indicates a primary
marine source of NaCl aerosols at DIV2010, as both brine rejection and sea
salt sulfatization in the atmosphere would tend to produce an offset in the
amount of Cl- deposited (Iizuka et al., 2016).
Slopes of the liquidus curves (Γ) estimated for various
binary mixtures composed of impurity species of likely relevance and water.
All values listed in columns prior to the Γ column are required for
calculation of Γ (see Supplement Sect. S2).
Species
Mol. mass
Eutectic
Eutectic
Density at
Γ
Reference
(g mol-1)
temperature (∘C;
composition (wt %;
eutectic (g mL-1;
(K M-1)
binary with H2O)
binary with H2O)
∗ = approximated)
CH3SO3H
96.11
-75.0
51.1
1.20
11.7
Stephen and Stephen (1963)
Na(CH3SO3)
119.11
-29.3
47
1.15∗
6.5
Sakurai et al. (2010)
Mg(CH3SO3)2
214.50
-5.0
14.2
1.15∗
6.6
Sakurai et al. (2010)
Ca(CH3SO3)2
230.27
-32.6
47
1.20∗
12.9
Sakurai et al. (2010)
NaCl
58.44
-21.3
23.3
1.16
4.6
Stephen and Stephen (1963)
MgCl2
95.21
-33.0
21.6
1.13
12.9
Stephen and Stephen (1963)
CaCl2
110.98
-51.0
30
1.19
15.9
Stephen and Stephen (1963)
H2SO4
98.08
-62.0
35.6
1.19
14.3
Hornung et al. (1956)
Na2SO4
142.04
-1.6
4.0
1.12
5.5
Hougen et al. (1954)
MgSO4
120.37
-3.6
17.3
1.22
2.3
Marion and Farren (1999)
CaSO4
136.14
-0.7
18.0
1.23
0.4
Rolnick (1954)
Although the annual mean surface air temperature at most sites showing MSA
migration is observed to be well below -21.3 ∘C (Sect. 2.3), the
upper firn (< 10–20 m) undergoes seasonal temperature fluctuations
that may exceed this value during summer months (Cuffey and Paterson, 2010),
thereby providing a potential mechanism to temporarily free Na+ from its
bonded state with Cl-. When premelted liquid solutions containing
Na+ and Cl- refreeze, Cl- may thus be preferentially allocated
within the ice structure (Tokumasu et al., 2016; Barnes et al., 2003b).
With Na+ and MS- both situated at the grain boundaries, the
resulting binary system is the sodium-salt of MS-,
CH3SO3Na ⋅ nH2O, and water (Mulvaney et al., 1992).
Recent experimental data indicate that the eutectic temperature for the
CH3SO3Na ⋅ nH2O–H2O system occurs at
approximately -29.3 ∘C (Sakurai et al., 2010). For comparison, the
eutectics for the binary systems
Ca(CH3SO3)2 ⋅ nH2O–H2O and
Mg(CH3SO3)2 ⋅ nH2O–H2O amount to -32.6
and -5.0 ∘C, respectively (Sakurai et al., 2010). Table 2 lists
the slopes of the liquidus curves for these MS- salts in addition to
those for alternative relevant sea salts containing Ca2+, Mg2+,
and (or) SO42- (see also
Supplement Sect. S2). For the system
CH3SO3Na ⋅ nH2O–H2O the slope amounts to
6.5 K M-1.
A simplified model of MSA migration
Although the RWW model provides significant insight into the mechanisms of
MSA migration, the system of nonlinear partial different Eqs. (3)–(4) does
not permit a straightforward analysis (e.g., no closed form solution of these
equations with general initial and boundary conditions is available to our
knowledge). In this section, we develop a linearized version of the model for
the binary system comprising CH3SO3Na and H2O (Eqs. 3–4) in
order to further our understanding of MSA migration. Of course, the insight
to be gained is only as reliable as the assumptions upon which the linearized
model relies.
Consider the governing Eq. (3a–b), making it explicit that concentration
gradients are strictly vertical,
∂cMS∂t=-∂∂zwMScMS,∂cNa∂t=-∂∂zwNacNa,
where,
wMS=DMSΓNaΓNacNa+ΓMScMS∂cNa∂z-cNacMS∂cMS∂z,wNa=DNaΓMSΓNacNa+ΓMScMS∂cMS∂z-cMScNa∂cNa∂z.
Here, wMS and wNa are the vertical components of
MS- and Na+ migration velocity, respectively, and z is depth.
Three assumptions are made (see also Rempel et al., 2002). First, the slope
of the liquidus curve is taken to be the same for the two ionic species,
i.e., ΓNa=ΓMS (Sect. 4.2.2). This assumption
appears plausible if the MS- salt species
CH3SO3Na ⋅ nH2O dominates in the premelt liquid
present near the grain boundaries. With this assumption, the slopes of the
liquidus curves cancel out in the defining relationships for wMS
and wNa (Eq. 6a–b). Second, the concentration of MS- is
taken to be much smaller than the concentration of Na+ in the liquid
veins, i.e., cMS≪cNa. This assumption is generally
supported by [MS-] and [Na+] measurements on ice core samples
originating from most coastal sites (Sect. 2.3; Table 1). Under the two
assumptions above, relation (6a) becomes
wMS=DMS1+0cMScNa1cNa∂cNa∂z-1cMS∂cMS∂z,
upon expansion of the denominator in a Taylor series. Thus, to the first
order in cMS/cNa, the speed of MS- migration can be approximated
as
wMS=DMS1cNa∂cNa∂z-1cMS∂cMS∂z.
A similar development for wNa leads to
wNa=DNa1cMS∂cMS∂z-1cNa∂cNa∂zcMScNa,
which is also first order in cMS/cNa. The ratio of the migration
speeds for the two ionic species is thus
wNawMS=DNaDMScMScNa.
If DMS is comparable to or higher than DNa, then
Na+ would migrate much more slowly than MS-. In this case, Na+
would be quasi-immobile and its concentration at a given depth would vary
only slowly with time (compared to MS-). This consideration suggests the
following third assumption. The concentration of Na+ at a given depth in
the ice column and at a given time is decomposed into a mean value,
c‾Na(z), and a fluctuation, cNa′(z,t):
cNaz,t=c‾Naz+cNa′z,t.
Assuming that cNa′(z,t)≪c‾Na(z), as
suggested by the relatively small mobility of Na+, the vertical speed
of MS- migration along the ice column can be further approximated as
wMS=DMS1c‾Na∂c‾Na∂z-1cMS∂cMS∂z.
The insertion of Eq. (11) into Eq. (5a) yields
∂cMS∂t+∂∂zw∗cMS=∂∂zDMS∂cMS∂z,
where w∗ is an effective velocity of MS- induced by vertical
gradients in [Na+],
w∗=DMSc‾Na∂c‾Na∂z.
Thus, under the three stated assumptions, MSA migration can be described by a
single, linear partial differential equation (Eq. 12) with the MS-
diffusivity as a single parameter. In this model (Eq. 12), MSA migration
arises from two fundamental processes: (1) the convergence or divergence of
MS- driven by Na+ concentration gradients and (2) the diffusion of
MS- along its own concentration gradient. Albeit physically distinct,
both processes depend on the diffusivity of MS- in the intergranular
liquid.
It is instructive to consider the character of the steady state distribution
of [MS-] according to the linearized model. With the tendency term
∂cMS/∂t set to zero, Eq. (12) reduces to
∂∂zcMSc‾NaDMS∂c‾Na∂z=∂∂zDMS∂cMS∂z,
given the defining relation for w∗ (Eq. 13). If DMS is uniform
along the ice column (∂DMS/∂z=0), and at depths
where Na+ shows an extremum (∂c‾Na/∂z=0),
Eq. (14) becomes
cMSc‾Na∂2c‾Na∂z2=∂2cMS∂z2.
Since concentrations are positive quantities, the concentration ratio on the
left-hand side of Eq. (15) is always positive, implying that the two
second-order derivatives should always have the same sign. Thus, minima
(maxima) of MS- concentration will coincide with minima (maxima) of
Na+ concentration. The [MS-] profile, regardless of its initial
(i.e., unaltered) character, will evolve so as to become eventually in phase
with the [Na+] profile. Figure 10 illustrates this evolution of the
[MS-] profile to steady state as simulated by the linearized model and
compares it with the evolution simulated with the RWW model (see Supplement
Sect. S3 for details about the numerical solutions of these two models).
The following example illuminates the respective roles of the effective
velocity, w∗, and of the diffusivity, DMS, in the MSA
migration process. Consider a locally Gaussian profile of [Na+],
c‾Na∝exp-z-z02/2σ2,
where z0 is the depth at which [Na+] is maximum and σ
describes the spread of Na+ on each side of the maximum (Fig. 11). In
this case, the effective velocity w∗=-DMS-(z-z0)/σ2
is positive above z0 and negative below z0, and the migration
Eq. (12) becomes
∂cMS∂t-DMSσ2z-z0∂cMS∂z=DMS∂2cMS∂z2+DMSσ2cMS,
where it has been again assumed that DMS is vertically uniform.
Interestingly, the migration Eq. (17) has the familiar form of an
advection–diffusion–reaction equation. The second term on the left-hand
side corresponds to downward advection of MS- above z0 and to
upward advection of MS- below z0, i.e., it tends to accumulate
MS- at z0. On the right-hand side, the first term represents
Fickian diffusion, and the second term is a “reaction” term that stems from
the vertical variation of w∗. The second term is always positive,
effectively leading to MS- production throughout the ice column at a
rate proportional to the amount of MS- initially present. As time
progresses, all [MS-] maxima that may be present in the ice section
where [Na+] is distributed according to Eq. (16) will be gradually
shifted toward z=z0. At steady state, the [MS-] profile will be
maintained by a balance between MS- advection to the [MS-] maximum
and effective production on the one hand, and the diffusion of MS- away
from the [MS-] maximum on the other hand (Fig. 11).
Evolution of [MS-] simulated by the linearized model assuming
(i) an effective velocity based on a Gaussian profile of [Na+] (blue)
and (ii) DMS=10-11 m2 s-1. The dashed,
dotted-dashed, and solid red lines show, respectively, the initial,
transient, and steady state profiles of [MS-]. The different symbols and
arrows show the two transport processes affecting the steady state profile of
[MS-]: MS- convergence toward the [Na+] maximum and MS-
diffusion away from the [Na+] maximum (see text and Supplement for
details).
Assessment of MS- diffusivity
We next aim to constrain a range of values for MS- diffusivity along
ice grain boundaries consistent with observed MS- concentrations in
polar ice. To this end, the simplified model of MSA migration (Eq. 12),
which includes DMS as the sole parameter, is solved for different
values of DMS and model results are compared with data from the DIV2010
ice core.
The model is solved numerically using finite differences (Supplement
Sect. S3; Figs. S5 and S6). The model domain, with an upper boundary situated
at z=9.1 m and a lower boundary at z=60.4 m, is intended to
represent the present-day shallow zone at the DIV2010 site. The model grid
has a uniform spacing (Δz=0.05 m), with grid points coinciding
with the sampling depths of the DIV2010 core. The grid cell interfaces
coincide with the upper and lower boundaries of the domain. With this
configuration of the grid, the boundary conditions of the model consist of a
vanishing flux of MS- prescribed at the upper and lower boundaries of
the domain:
w∗cMS-DMS∂cMS∂z=0,atz=9.1 and 60.4m.
The initial conditions of the model consist of an idealized [MS-]
profile obtained by linearly interpolating, at the model grid points, the
(unaltered) monthly mean [MS-] values for the shallow zone (Fig. 5).
The vertical profile of [Na+], which determines the effective velocity
of MS- (w∗), is directly derived from the measured profile of
[Na+] in the shallow zone (since model grid points coincide with
sampling depths, no interpolation is necessary).
Cross-correlation between [Na+] and [MS-] at different
vertical spacings (a) and different time lags (b). In each
panel, the red line shows the cross-correlations calculated from the DIV2010
data below the shallow zone (z > 9.1 m), the blue lines show
the cross-correlations calculated from the linearized model for different
values of DMS, the solid black line shows the
cross-correlations corresponding to the initial conditions of the model, and
the horizontal dashed lines show the 95 % confidence interval for two
uncorrelated time series (see text and Supplement for details).
The model is integrated over a time interval that approximates the time it
would take for the shallow zone to be buried by a layer of equal thickness
through surface accumulation (see Supplement Sect. S4 for details). This
final time, denoted as tf, is taken as 95 years, based on the
difference between the ages of the samples at z=9.1 and 60.4 m. At the end of the model integration (t=tf), the cross-correlation between the [MS-] and [Na+]
profiles simulated by the model between z=9.1 and 60.4 m is calculated
and compared to the cross-correlation between the measured [Na+] and
[MS-] profiles over the same depth interval. This procedure is repeated
for four different values of DMS – 10-10, 10-11,
10-12, and 10-13 m2 s-1 – encompassing the values
assumed or suggested in prior studies (e.g., Rempel et al., 2002; Roberts et
al., 2009). A “good” value of DMS is expected to lead to a
“good” agreement between the simulated and observed cross-correlations, at
least at small lags.
Consider first the model solution with DMS=10-13 m2 s-1. At t=tf, the simulated [MS-]
profile has not significantly deviated from its initial profile, which is
negatively correlated at zero lag with the [Na+] profile (Fig. 12a).
This result suggests that the value of DMS=10-13 m2 s-1 is too small to account for the down-core change
in phase relationship between [Na+] and [MS-] observed at DIV2010.
For 10-12
m2 s-1 < DMS < 10-11 m2 s-1,
the simulated cross-correlation at zero lag between [Na+] and [MS-]
switches from negative to positive. For values of DMS≥10-11 m2 s-1, it is positive but much stronger than observed,
suggesting that these values may be too large. Thus, DMS values
that best explain the DIV2010 data would be in the range from 10-12 to
10-11 m2 s-1, i.e., greater than the value of (4.1×10-13±2.5×10-14) m2 s-1 reported by Roberts et
al. (2009) and lower than the value of 5×10-10 m2 s-1
assumed by Rempel et al. (2002). We stress that this result is immune to
potential dating errors in the sense that the cross-correlation coefficients
are calculated for different vertical spacings along the core, not for
different time lags; calculating cross-correlations at different time lags
leads to a similar result (Fig. 12b; see also Supplement Figs. S5 and S6).
While the DMS range estimated by a comparison to DIV2010 data is
instructive, we note it is not necessarily universal, as diffusivities in
polar ice are expected to vary in response to multiple glaciological factors.
For example, the experimental results of Kim and Yethiraj (2008) show that
the diffusion coefficients of ions in undercooled mixtures are a function of
both ionic concentration and temperature. Additionally, physical properties
of the firn and ice, including porosity, grain-boundary density, and crystal
size, may affect the partitioning of chemical impurities between the liquid
premelt and the ice lattice (Dominé et al., 2008; Spaulding et al.,
2011), thereby affecting the amount of impurities subjected to anomalous
diffusion as well as the interconnectivity of the liquid
premelt or vein network. While the RWW
model can account for this partitioning (Rempel et al., 2002), the
proportions of total MS- and Na+ that are present in liquid form
remain poorly constrained (Sakurai et al., 2010). Even at a given site,
seasonal and interannual variations in impurity concentrations may lead to
down-core changes in DMS. Finally, DMS does not take
into account whether MS- migration is dominated by diffusion at
two-grain boundaries, or at triple junctures and node networks (Wettlaufer
and Worster, 2006; Riche et al., 2012). As a result of all these complicating
factors, DMS, as defined in the RWW model and constrained here,
should probably be viewed as an effective diffusivity.
Paleoclimatic implications
Revisiting the effect of temperature on grain boundary migration
In Sect. 2.3, we tested the hypothesis that post-depositional formation of
winter [MS-] maxima occurs solely as a result of the precipitation of
MS- salts from their grain boundary solutions in sea-salt-rich winter
layers (Mulvaney et al., 1992; Wolff, 1996; Kreutz et al., 1998; Pasteur and
Mulvaney, 2000; Curran et al., 2002). This hypothesis, denoted below as the
“Mulvaney model”, suggests that MS- in undercooled solutions should
migrate along its concentration gradient via Fickian diffusion until reaching
Na+-rich layers, where crystallization of CH3SO3Na removes
MS- from the premelt solution, thereby perpetuating an [MS-]
gradient between summer and winter layers in the residual premelt.
Importantly, it suggests MSA migration would be inhibited at sites where in
situ temperatures are greater than the eutectic temperature of the binary
system CH3SO3Na ⋅ nH2O–H2O
(-29.3 ∘C), since CH3SO3Na in this case would not be precipitated from the premelt liquid. However,
such an inhibition is not apparent in our data compilation (Sect. 2.3).
The RWW model (Sect. 4) is fundamentally different than the Mulvaney model.
The RWW model does not represent crystallization and metathetic removal of
constituents from the liquid phase (Sect. 2). Rather, in the RWW model,
MS- is implicitly assumed to remain dissolved in the premelt liquid
following migration from the summer to winter layers, provided in situ
temperatures exceed the eutectic temperature of the binary system
CH3SO3Na ⋅ nH2O–H2O.
The foregoing assumption can be evaluated using our data compilation. At 19
of the 20 sites considered (Table 1), the ice temperature as estimated from
the annual mean SAT exceeds the eutectic temperature of the binary system
CH3SO3Na ⋅ nH2O–H2O, suggesting MSA migration
could occur according to the RWW model at these sites. The only site where
ice temperature is estimated to be less than -29.3 ∘C is the
Summit2010 record from Greenland (Maselli et al., 2017), where MSA migration
is also observed but not predicted to occur based on this model. We offer a
few explanations for this sole discrepancy. First, ice temperatures may
depart significantly from annual mean SAT. The annual mean SAT at
Summit, Greenland, is -29.5 ∘C (Giese and Hawley, 2015), just below
but very close to the eutectic temperature for the system
CH3SO3Na ⋅ nH2O–H2O. It is therefore
conceivable that ice temperatures may in fact slightly exceed the eutectic
temperature of this system, at least along some portions of the ice column
and (or) during some time intervals in the past. Another possibility is that
the Ca2+ salt of MS-, Ca(CH3SO3)2, which is a
component of the system
Ca(CH3SO3)2 ⋅ nH2O–H2O with a lower
eutectic of -32.6 ∘C, may be more efficient than the Na+ salt
of MS-, CH3SO3Na, in driving MSA migration at Summit2010,
given the much higher abundances of Ca2+ in inland Greenland ice
compared to coastal Antarctica (Iizuka et al., 2008).
A currently poorly constrained situation arises for sites characterized by
in situ temperatures less than ∼ -30 ∘C and greater than
-75 ∘C (Table 2). In this temperature regime, MSA
should remain in solution while Na+
is presumably immobile, either as solid-state NaCl, CH3SO3Na, or
Na2SO4 (Table 2). MSA migration as envisioned in the Mulvaney
model, but not in the RWW model, may operate under such conditions. On the
other hand, the Mulvaney model may not apply should summer concentrations of
Na+ be high enough to sequester a large fraction of the [MS-] as
CH3SO3Na(s) in summer layers. This
sequestration process appears supported by the lack of discernable MSA
migration in the sub-annually resolved portion (i.e., down to
∼ 10.5 m) of the [MS-] record from the South Pole (SP-95), where
annual mean SAT is -51 ∘C (Meyerson et al., 2002). While SP-95 is
not considered in our data compilation due to the site's low b˙
(0.08 m w.e. yr-1), the lack of clear MSA migration at SP-95 departs
from the expected relationship found between b˙ and zfo in
Antarctica (Sect. 2.1; Fig. 2). This observation leads us to speculate that
MS- at SP-95 may be immobilized in the summer layers through a
metathesis reaction with Na+ allocated to the grain boundaries.
Extent of MSA migration in the DIV2010 ice core as estimated from
the linearized model. (a) Top: DIV2010 [Na+] record (five-point
smoothed). Middle: (i) annual means of [MS-] (black line) and standard
deviations of [MS-], σ (gray band, representing ±1σ
about the means) for the initial conditions (ICs) of the model experiments;
and (ii) annual means of [MS-] (blue line) and standard deviations of
[MS-] (blue band) for the terminal conditions (TCs, ∼ 95 years) of
the model experiments for DMS=10-11 m2 s-1.
Bottom: same as panel (a), middle (blue band), but for DMS=10-12 m2 s-1. (b) Probability density of the
absolute difference between the annual mean [MS-] for the ICs and TCs,
normalized to the annual mean [MS-] of the ICs, for all model
experiments with DMS=10-11 m2 s-1 (blue) and
10-12 m2 s-1 (red). (c) Absolute difference between
the annual mean [MS-] for the ICs and TCs, normalized to the annual mean
[MS-] of the ICs, for all model experiments with DMS=10-11 m2 s-1 (blue) and 10-12 m2 s-1 (red),
as a function of the data averaging interval. The shaded regions illustrate
the dispersion (±1 standard deviation) of the normalized absolute
differences among the model experiments.
In sum, we propose that MSA migration operates at most sites through
anomalous diffusion as described in the RWW model. This migration process
would occur if in situ temperatures exceed the relevant eutectic
temperatures, so that MS- can occur in solution in the presence of Na+ and Ca2+ situated at
the grain boundaries. The relevant eutectic temperatures are inferred here to
range from -29.3 to -32.6 ∘C, depending on the binary system
considered (Sakurai et al., 2010). Importantly, most coastal ice core
locations, despite their paleoclimatic significance, are susceptible to MSA
migration given their relatively high SAT (Table 1), although high
accumulation rates will mitigate this phenomenon to some degree (Sect. 2.1).
One coastal region of exception may be northeastern Greenland, where
relatively cold conditions (SAT of approximately -30 to 33 ∘C;
Weißbach et al., 2016) may keep the ice below the eutectic temperature of
the primary MS- salts.
Vertical extent of MSA migration
A reigning question in the use of [MS-] in polar ice as a paleoclimate
proxy is the extent of MSA migration along the core. Past studies have
circumvented this potential issue by assuming either that (1) MSA migration
is confined within an annual layer (Kreutz et al., 1998; Curran et al., 2003;
Thomas and Abram, 2016) or (2) multiyear averages of [MS-] are largely
unaffected by migration (Wolff, 1996). While (2)
appears a more conservative approach, the requisite averaging period, and
thus the maximum resolution that can be achieved in a paleoclimatic
reconstruction given MSA migration, remains unknown. In this section, we
examine assumptions (1)–(2) using DIV2010 data and the linearized model of
MSA migration.
In an effort to account for a range of initial (i.e., unperturbed) [MS-]
profiles in the shallow zone of DIV2010 (Sect. 3.1), a large number (10 000)
of numerical experiments of MSA migration are conducted. The initial
[MS-] profile of a given experiment is obtained by adding, to the
monthly mean [MS-] values observed in the shallow zone, a normal noise
with a mean of zero and a variance equal to that of the mean monthly values
in the shallow zone. If a negative concentration value arises in the initial
profile, the procedure is repeated until all values in the profile are
positive. Using this approach, interannual variability in the initial
[MS-] profile is emulated, such that no 2 years should contain the same
mean [MS-] in a given experiment, nor should a given year display the
same mean [MS-] for different experiments. In contrast, all experiments
rely on the same [Na+] profile measured at DIV2010. Given the
uncertainties in MS- diffusivity (Sect. 4.4), two sets of experiments
are considered: a first set with DMS=10-12 m2 s-1 and a second with DMS=10-11 m2 s-1 (so that 2×10000=20000
experiments are actually performed). For all experiments, the model is
subjected to a condition of no MS- flux at both the upper and lower
boundaries of the domain and is integrated for
tf=95 years (Sect. 4.4).
Figure 13a shows (i) the [Na+] profile observed at DIV2010 and used to
constrain the effective velocities w∗ in the model, and (ii) the
annual mean [MS-] profiles simulated by the model at t=tf.
For DMS=10-11 m2 s-1, the changes in annual mean
[MS-] relative to the initial [MS-] profile are much larger than
for DMS=10-12 m2 s-1 (Fig. 13b), particularly
prior to AD 1975 (t=25 years). In some sections of the simulated
profiles, dramatic positive or negative changes in annual mean [MS-]
occur, depending on the magnitude of the local [Na+] gradients. In some
individual years (e.g., AD 1954), relative changes in the annual mean
[MS-] reach 60 to 100 %, clearly negating the assumption (1) above
– that MSA migration is confined within an annual layer.
Given this finding, we next explore assumption (2) that multiyear averages of
[MS-] data could be used to accurately reflect the original (i.e.,
unaltered) multiyear mean [MS-] signal. To this end, we average the
simulated [MS-] profiles at t=tf in different time
intervals ranging from 3 to 15 years and compare the final (altered) averages
to the initial (unaltered) averages (Fig. 13c). As expected, the difference
between the final and initial averages of [MS-] decreases as the
averaging period increases. Interestingly, the difference shows only modest
reduction as the averaging period increases from 7 to 15 years.
In sum, while our results may pertain only to DIV2010 and rely on a series of
modeling assumptions (Sect. 4.3), two points appear worthy of note. First,
for [MS-] records showing evidence of MSA migration, the assumption that
MSA remained confined within annual layers may not be generally valid, given,
in particular, the high interannual variability in the concentrations of
Na+ and other major impurities potentially conducive to MSA migration,
which is typical of most ice cores originating from coastal sites (Legrand
and Mayewski, 1997). High interannual variability in [Na+], for example,
corresponds to large vertical [Na+] gradients along the core, which tend
to enhance MSA migration. Second,
at least for [MS-] records exhibiting severe MSA migration such as at
DIV2010, averaging the data over a time period of approximately 10 years may
constitute a reasonable compromise between accuracy and temporal resolution
for paleoclimatic reconstruction.
Revisiting the combined influence of snow accumulation and [Na+] on
MSA migration
In Sect. 2, we provided empirical evidence that two local factors appear to
influence the shallowest depth of MSA migration in polar ice cores: annual
mean accumulation rate (b˙) and core-averaged Na+ concentration.
Here, we assess whether the ability to predict zfo from these two
factors is also mechanistically grounded. Since the linearized model is not
valid for small values of [Na+] / [MS-], the original model of
Rempel et al. (2002) is used in an effort to produce results of more general
validity.
(a) Evolution of the phase difference between [MS-]
and [Na+] maxima for (i) two different extents of the model domain, or
“annual layer thickness” (0.1 and 1 m); and (ii) different layer averages
of [Na+] (25–400 µg L-1), as calculated from the RWW
model. Note the two different scales along the horizontal axis: the scale
from 0.1 to 100 years applies to model results with DMS=10-11 m2 s-1, and the scale from 1 to 1000 years applies to
model results with DMS=10-12 m2 s-1.
(b) Time required for approximate alignment of [MS-] and
[Na+] maxima for different values of annual layer thickness and
different layer averages of [Na+], as calculated from the RWW model.
Conditions for the DIV2010 core site are indicated by the cross.
(c) Shallowest depth of MSA migration for different values of annual
mean accumulation rate and different core averages of [Na+] according to
our data compilation, with DIV2010 denoted. Note the logarithmic scales in
all panels.
The time required for approximate alignment of [MS-] and
[Na+] maxima (tφ) as a function of annual layer thickness
(λ) for different layer averages of [Na+] and DMS=10-11 m2 s-1. The various curves are least-squares fits of the form tφ=aλe. The exponent e is estimated to about 2 for all values of
layer-averaged [Na+] (note that the fits for DMS=10-12 m2 s-1, not shown, yield a value of a that is a factor of 10 higher than for
DMS=10-11 m2 s-1).
We first simulate, for a range of layer thicknesses and layer-averaged
[Na+] values, the time it takes for an [MS-] maximum present in the
annual layer, and initially out of phase with the [Na+] maximum in the
layer (φ=180∘), to align with the [Na+] maximum in the
layer (φ=0∘). Given the asymptotic nature of the
concentration evolutions simulated by the model, we approximate this time as
the time at which the phase difference between the [MS-] and [Na+]
maxima drops to φ < 20∘. Experiments are conducted
for different extents of the model domain to represent different values of
annual layer thicknesses (λ). For each experiment, the initial
[MS-] and [Na+] profiles in the layer are sinusoidal functions of
depth, with (i) a period set equal to the layer thickness, (ii) a [MS-]
maximum present in the middle of the layer, and (iii) two [Na+] maxima
present at the top and bottom of the layer (see Supplement Sect. S5 for
details). The model is subjected to a condition of no flux both at the top
and at the bottom of the layer. The model parameters are set to ΓMS=ΓNa=6.5 K M-1 and DMS=DNa=10-11 or 10-12 m2 s-1.
The time required for approximate phase alignment (φ < 20∘) of the simulated [MS-] and [Na+]
profiles is shown for two different values of λ and a range of
layer-averaged [Na+] values (Fig. 14a); this time is referred to as
tφ below. It is seen that tφ increases with λ and decreases with layer-averaged [Na+]. Similar results are displayed
in Fig. 14b in a form that is reminiscent of Figs. 5 (linear scales) and 14c
(logarithmic scales), which both show the combined effect of annual mean
accumulation and core-averaged [Na+] ([Na+‾]) on
the shallowest depth of MSA
migration (zfo) in our data compilation. To the extent that
λ increases with b˙, the model results appear to be
qualitatively consistent with the data, thereby providing a theoretical basis
to the notion that b˙ and [Na+] could be used to predict
zfo.
The nonlinear relationship found between zfo and b˙
(Sect. 2) is also worth further exploration. Results from the RWW model can
be well approximated by the power law tφ∝λ2
(Fig. 15), which is reminiscent of the power law relationship zfo∝λ1.77 derived from our data compilation (Fig. 2). The
observed variation of the shallowest depth of MSA migration with accumulation
rate would thus reflect the mere fact that, similar to Fickian diffusion with
constant diffusivity, the timescale for anomalous diffusion (tφ)
varies quadratically with the thickness over which the diffusion takes place
(λ). Both current observations and the present set of experiments
with the RWW model suggest that [MS-] records from ice cores
characterized by high accumulation and low core-averaged [Na+] should
undergo relatively small alteration by MSA migration.
Conclusions
Polar ice core records of methanesulfonic acid have been used to draw
inferences about oceanic and atmospheric processes at polar latitudes on a
range of timescales. However, both observation and theory suggest that MSA is
mobile in the ice column, leading to uncertainties about its integrity as an
indicator of past climatic conditions. Here, we synthesize existing data from
a range of polar environments and consider an impurity transport model to
study MSA migration in polar ice. Emphasis is placed on (i) the environmental
conditions that favor MSA migration and (ii) the physico-chemical processes
causing the movement of MSA in polar firn and ice.
Our analysis shows that the shallowest depth at which MSA migration occurs in
coastal ice cores varies with annual mean accumulation rate. In Antarctica in
particular, a power law characterizes this relationship accurately. It
suggests that the absence of MSA migration observed in some ice cores from
high-accumulation sites stems from the fact that chemical measurements for
these cores have been conducted on samples that are not deep enough to have
undergone migration. Thus, MSA migration in polar ice may be more general
than commonly thought. Annual mean surface air temperature and the
concentration of the dominant cation, Na+, appear to be less influential than accumulation rate
under most circumstances, at least at most coastal Antarctic sites and in the
temperature range from -29.5 to -12.5 ∘C. A notable exception is
for inland Greenland sites, where MSA migration tends to occur deeper in the
core than would be predicted from surface accumulation alone – an offset
hypothesized to stem from extremely low concentrations of marine-derived
impurities relative to most coastal Antarctic sites. Our analysis further
suggests that MSA migration generally takes place once firn or ice density
reaches a critical value near 550 kg m-3, which corresponds to the
tightest packing of spherical ice grains in the firn and enabling the
formation of premelted liquid veins at grain boundaries. However, at some
low-accumulation sites (b˙=0.1–0.2 m w.e. yr-1), MSA
migration is observed at depths where bulk density is likely to be less than
550 kg m-3. This result suggests that small-scale variability in ice
density is important and (or) that other factors may also determine the onset
of MSA migration along the firn or ice column.
New high-resolution data from the West Antarctic DIV2010 ice core show
annual [MS-] maxima gradually shifting down-core from austral summer,
when MSA deposition is high, to austral winter, when MSA deposition is low
and Na+ deposition is high. As a result, a down-core change in the
phase relationship between [MS-] and [Na+] is observed, whereby
[MS-] and [Na+] are negatively correlated at zero lag in the upper
part of the core and positively correlated at zero lag in the lower part of
the core, providing evidence of the progressive nature of MSA migration.
A linearized version of the impurity transport model of Rempel et al. (2002)
is derived for the binary system
CH3SO3Na ⋅ nH2O–H2O in order to further
understanding of the MSA migration phenomenon in polar ice. In this
linearized model, MS- transport is governed by a single linear partial
differential equation with MS- diffusivity in the undercooled liquid
(DMS) as the sole parameter. In this model, MSA migration arises
from two transport processes: (1) the convergence or divergence of MS-
driven by [Na+] gradients and (2) the diffusion of MS- along its
own concentration gradient. Analysis of this model shows that [MS-]
maxima (minima) are bound to coincide with [Na+] maxima (minima) along
the ice column, regardless of the timing of MSA deposition maxima. The model,
therefore, provides a mechanistic explanation for the tendency for MSA,
deposited mainly during summer, to present concentration peaks in winter
layers in the deepest part of polar ice cores.
Finally, we use the linearized MSA migration model and the DIV2010 data to
gain insight into two poorly constrained yet critically important aspects of
MSA migration. First, we evaluate different values of MS- diffusivities
in polar ice. We find that DMS values in the range from
10-12 to 10-11 m2 s-1 lead to the most accurate
simulations of the down-core change in the phase relationship between
[MS-] and [Na+] observed at DIV2010. Second, using this range of
values, we apply the model to determine the extent to which MSA migration has
altered the original [MS-] record for DIV2010. We estimate the errors
incurred by averaging [MS-] data over annual (and multiyear) intervals,
an approach often adopted to reduce the effect of migration on the
interpretation of [MS-] records. We find that MSA migration may have
lead to significant changes in the annual and multiyear [MS-] averages
at DIV2010. This result suggests that [MS-] records severely perturbed
by MSA migration may best be used to infer decadal
or lower-frequency climate
variability, though a range of [MS-] records and a better constrained
model are needed to investigate this further.
The migration of MSA in cold, polar ice is a fascinating but challenging
phenomenon. This paper covers many, but not all, of its observational and
theoretical aspects. For example, contentions of MSA migrating away from
regions of high acidity in the core, as caused by the deposition of
compounds of volcanic origin (Curran et al., 2002; Delmas et al., 2003), are
not explored here. While the model of Rempel et al. (2002) provides an
important mechanistic framework for understanding MSA migration in polar ice
and perhaps for ultimately correcting its effects for paleoclimatic
reconstruction, its usefulness remains limited by uncertainties about key
physico-chemical parameters. These include most notably the diffusivities of
the relevant migrating species in undercooled liquid, the slope of the
liquidus curves for relevant, interacting species, and the partitioning of
impurities between the ice lattice and the surface of the ice grains.
Laboratory studies under a range of controlled conditions would help
constrain these parameters, improve our understanding of MSA migration in
polar ice, and make full use of the paleoclimatic potential of this
compound.