ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus GmbHGöttingen, Germany10.5194/acp-15-13895-2015Post-bubble close-off fractionation of gases in polar firn and ice cores:
effects of accumulation rate on permeation through overloading pressureKobashiT.kobashi@climate.unibe.chhttps://orcid.org/0000-0003-4153-8272Ikeda-FukazawaT.SuwaM.SchwanderJ.KamedaT.LundinJ.HoriA.MotoyamaH.https://orcid.org/0000-0003-2533-320XDöringM.LeuenbergerM.https://orcid.org/0000-0003-4299-6793Climate and Environmental Physics, University of Bern,
Bern, SwitzerlandOeschger Center for Climate Change Research, University of
Bern, Bern, SwitzerlandNational Institute of Polar Research, Tokyo,
JapanDepartment of Applied Chemistry, Meiji University,
Kanagawa, JapanThe World Bank, Washington D.C., USADepartment of Civil and Environmental Engineering, Kitami
Institute of Technology, Kitami, JapanDepartment of Earth & Space Sciences, University of
Washington, Seattle, USAT. Kobashi (kobashi@climate.unibe.ch)16December20151524138951391427April201511June201516October201527November2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/15/13895/2015/acp-15-13895-2015.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/15/13895/2015/acp-15-13895-2015.pdf
Gases in ice cores are invaluable archives of past environmental changes
(e.g., the past atmosphere). However, gas fractionation processes after
bubble closure in the firn are poorly understood, although increasing
evidence indicates preferential leakages of smaller molecules (e.g., neon,
oxygen, and argon) from the closed bubbles through the ice matrix. These
fractionation processes are believed to be responsible for the observed
millennial δO2/N2 variations in ice cores, linking ice
core chronologies with orbital parameters. In this study, we investigated
high-resolution δAr/N2 of the GISP2 (Greenland Ice Sheet
Project 2), NGRIP (North Greenland Ice Core Project), and Dome Fuji ice cores
for the past few thousand years. We find that δAr/N2 at
multidecadal resolution on the “gas-age scale” in the GISP2 ice core has a
significant negative correlation with accumulation rate and a positive
correlation with air contents over the past 6000 years, indicating that
changes in overloading pressure induced δAr/N2 fractionation
in the firn. Furthermore, the GISP2 temperature and accumulation rate for the
last 4000 years have nearly equal effects on δAr/N2 with
sensitivities of 0.72 ± 0.1 ‰ ∘C-1 and
-0.58 ± 0.09 ‰ (0.01 m ice year-1)-1,
respectively. To understand the fractionation processes, we applied a
permeation model for two different processes of bubble pressure build-up in
the firn, “pressure sensitive process” (e.g., microbubbles: 0.3–3 % of
air contents) with a greater sensitivity to overloading pressures and
“normal bubble process”. The model indicates that δAr/N2 in
the bubbles under the pressure sensitive process are negatively correlated
with the accumulation rate due to changes in overloading pressure. On the
other hand, the normal bubbles experience only limited depletion
(< 0.5 ‰) in the firn. Colder temperatures in the firn induce
more depletion in δAr/N2 through thicker firn. The pressure
sensitive bubbles are so depleted in δAr/N2 at the bubble
close-off depth that they dominate the total δAr/N2 changes in
spite of their smaller air contents. The model also indicates that δAr/N2 of ice cores should have experienced several per mil of
depletion during the storage 14–18 years after coring. Further understanding
of the δAr/N2 fractionation processes in the firn, combined
with nitrogen and argon isotope data, may lead to a new proxy for the past
temperature and accumulation rate.
Introduction
Atmospheric gases trapped in the firn layer (unconsolidated snow layer;
∼ 70 m at the Greenland summit and preserved in the underlying ice sheets
provide precious and continuous records of the past atmosphere and
environments (Petit et al., 1999; Spahni et al., 2005; Ahn and Brook, 2008;
Kobashi et al., 2008a). However, to reconstruct the original environmental
records, it is important to understand the processes of air trapping in the
firn and how the air is retained in the ice until it is analyzed in
laboratories. There are two well-known processes that change air composition
before the air is trapped within bubbles in the firn. First, gravitational
fractionation separates gases according to their mass differences and
diffusive column height of the firn layer (Craig et al., 1988; Schwander,
1989). Second, a temperature gradient (ΔT) between the top and bottom
of the firn layer induces thermal fractionation generally pulling heavier
gases toward the colder end (Severinghaus et al., 1998). In this study, we
investigate a third process that occurs after the bubbles are closed
(post-bubble close-off fractionation) and that preferentially affects gases
with smaller molecular sizes (< 3.6 Å; for example, helium, neon,
oxygen, and argon) but also gases with larger molecular sizes in smaller
magnitudes (Ikeda-Fukazawa et al., 2005; Huber et al., 2006; Ikeda-Fukazawa
and Kawamura, 2006; Severinghaus and Battle, 2006; Ahn et al., 2008). This
fractionation continues deep in ice sheets smoothing signals (Ahn et al.,
2008; Bereiter et al., 2014), and the process continues during/after coring
(Ikeda-Fukazawa et al., 2005; Kobashi et al., 2008b; Suwa and Bender, 2008b;
Bereiter et al., 2009; Vinther et al., 2009).
Clear evidence of the diffusive gas loss from ice cores through ice crystals
has been observed in the oxygen content in ice cores as a depletion of oxygen
relative to nitrogen (Bender et al., 1995; Ikeda-Fukazawa et al., 2005; Suwa
and Bender, 2008b). Depletion of air content by ∼ 10 % was observed
for the Camp Century ice core after storage for 35 years, although possible
analytical differences between early and late measurements cannot be rejected
(Vinther et al., 2009). The process is highly temperature dependent, and the
gas loss is induced by the pressure gradients between the bubbles and the
atmosphere (Ikeda-Fukazawa et al., 2005). In ice sheets, the concentration
gradients at different depths drive the gas diffusion through ice crystals,
which smooth climate signals (Bereiter et al., 2014). Firn air studies showed
that smaller molecules such as helium, neon, oxygen, and argon preferentially
leak out from the closed bubbles, leading to enrichments of these gases in
open pores near the bubble-close-off depth, which leads to depletions of
these smaller gases in the closed bubbles (Huber et al., 2006; Severinghaus
and Battle, 2006; Battle et al., 2011). However, the mechanisms creating
δAr/N2 or δO2/N2 variations in the time
domain (i.e., ice cores) are still poorly understood.
δAr/N2 vs. accumulation rates or air contents in
GISP2 over the past 6000 years. Note that δAr/N2 are corrected
values for the post-coring fractionation (1.5 ‰ added). A spline
with a 21-year cut-off period (blue line) was applied to the δAr/N2 data. Two σ error bounds are shown, which were
estimated by 1000 iterations of Monte Carlo simulations. Accumulation rates
(m ice year-1) (black line) were filtered by 21-year RMs. Note that
the y axis for the accumulation rate is reversed. δAr/N2 vs.
accumulation rates are significantly negatively correlated over the past
6000 years (r=-0.35, p=0.03). δAr/N2 and air contents
are significantly positively correlated over the past 6000 years (r=0.38,
p< 0.001 after linear detrending). A slight shift of the air contents
around 3700 BP is probably due to the analytical changes that occurred
between two different periods of measurements (Kobashi et al., 2008b). The
correlations between δAr/N2 and air contents before and after
3700 BP are similar and significant (r=0.30, p=0.002 and r=0.26,
p=0.008, respectively). Therefore, the δAr/N2 variation
can explain 7–14 % of the total variance of the air contents.
On a longer timescale (i.e, orbital), variations in δO2/N2 closely follow local insolation changes (Bender, 2002;
Kawamura et al., 2007; Suwa and Bender, 2008a; Landais et al., 2012). As a
possible mechanism, it has been hypothesized that changes in local insolation
affect physical properties of the snow at the surface and persist into the
bubble close-off depth, controlling the δO2/N2
fractionation (insolation hypothesis) (Bender, 2002; Fujita et al., 2009). In
addition, air content in ice cores is also found to co-vary with δO2/N2 on the orbital timescale, indicating common causes
(Raynaud et al., 2007; Lipenkov et al., 2011). According to this hypothesis,
the orbital signals in δO2/N2 in ice cores are linked to
the ice chronology rather than to the gas chronology, which differ by up to a
few thousand years. Therefore, the precise understanding of the gas loss
process in the firn is essential to determine how climate signals in the
bubbles are placed between the ice ages and gas ages on the orbital timescale.
In this paper, encouraged by the observation of a significant negative
correlation between δAr/N2 and the accumulation rate over the
past 6000 years in the GISP2 (Greenland Ice Sheet Project 2) ice core
(Fig. 1), we investigated the processes of multidecadal to centennial δAr/N2 variability in three ice cores (GISP2, NGRIP, and Dome Fuji) as
well as gas loss processes during storage. δAr/N2 variations
are generally highly correlated with δO2/N2 in ice cores,
suggesting similar processes driving these variations (Bender et al., 1995).
As δAr/N2 is nearly constant in the atmosphere over the
relevant period (Kobashi et al., 2010), it is better suited to assess the
permeation processes in the firn and ice cores than δO2/N2 that varied in the atmosphere by ∼ 1.5 ‰
during the glacial–interglacial cycles (Bender et al., 1995). In the
following sections, we first describe the data and investigate the
relationships between δAr/N2 and changes in accumulation rates
and surface temperatures. Then, the fractionation processes are examined by
applying a permeation model to the ice cores and the firn under two
processes: “pressure sensitive processes” (e.g, microbubbles) and “normal
bubble process”. Finally, we discuss our findings, draw conclusions and
mention implications.
Data description
δAr/N2 data from three ice cores covering the past millennia
(NGRIP, Dome Fuji, and GISP2) were used for the analyses. GISP2 and NGRIP
(North Greenland Ice Core Project) data have been published earlier (Kobashi
et al., 2008b, 2015), and Dome Fuji data are new. Importantly, storage
histories of these cores (i.e., temperatures) are known and methods for
measuring δAr/N2 are all comparable. GISP2 and NGRIP ice cores
were drilled from the Greenland ice sheet, and Dome Fuji was drilled from the
Antarctic ice sheet (Table 1). For GISP2, sample resolution varies from 10 to
20 years with high-resolution analyses covering the past 1000 years (Kobashi
et al., 2008b, 2010) and around the 8.2 ka event (8100 ± 500 years
before present (BP), “present” is defined as 1950) (Kobashi et al., 2007).
For NGRIP, sample resolution is about 10 years throughout the past 2100 years
(Kobashi et al., 2015). Both GISP2 and NGRIP have similar annual average
temperatures of approximately -30 ∘C (Table 1). However, the
accumulation rate of NGRIP (∼ 0.19 m ice year-1) is 20 %
less than that of GISP2 (0.24 m ice year-1) over the past 2100 years
and, importantly, its variation (standard deviation after 21-year running
means; RMs) is lower by 40 % than that of GISP2 (see later discussion).
Dome Fuji has a radically different environment from Greenland with the
current annual average air temperature of -54.3 ∘C and a mean
accumulation rate of ∼ 0.03 m ice year-1 (Watanabe et al.,
2003).
For the timescale of GISP2 and NGRIP ice ages, we used the GICC05 (Greenland
Ice Core Chronology 2005; Vinther et al., 2006; Seierstad et al., 2014). To
obtain gas ages, we applied a firn-densification, heat-diffusion model
(Goujon et al., 2003) that calculates firn density structure, close-off
depth, and delta age. The gas age uncertainties relative to ice age were
estimated as ∼ 10 % of the estimated gas age–ice age difference
(Goujon et al., 2003). To investigate the δAr/N2
fractionation, we used reconstructed temperature records from argon and
nitrogen isotopes in the trapped air within the GISP2 ice core for the past
4000 years (Kobashi et al., 2011) and within NGRIP for the past 2100 years
(Kobashi et al., 2015) and layer-counted accumulation rate data for the
Holocene (Alley et al., 1997; Cuffey and Clow, 1997; Gkinis et al., 2014).
Dome Fuji data have neither precise temperatures nor accumulation rates over
the past 2100 years. The annual resolution accumulation rate data were
smoothed with 21-year RMs to correspond to gas diffusion and the bubble
close-off process in the firn (Kobashi et al., 2015). A spline fit (Enting,
1987) was applied to gas data (e.g., δAr/N2) with a 21-year
cut-off period to be consistent with 21 RMs of other parameters and used for
the following analyses to investigate signals longer than the decadal
timescale.
Environmental parameters for GISP2, NGRIP and Dome Fuji.
Temperatures for GISP2 and NGRIP are averages over the past 2100 years
(Kobashi et al., 2015). Accumulation rates (Alley et al., 1997; Cuffey and
Clow, 1997; Gkinis et al., 2014) for GISP2 and NGRIP are averages for the
past 2100 years, and accumulation rate variations are calculated as standard
deviations of accumulation rates in 21-year RMs. Annual average temperature
and accumulation rate for Dome Fuji are from Watanabe et al. (2003).
GISP2 and NGRIP ice cores were analyzed for δAr/N2∼ 14 years after coring, however, with different temperature histories.
GISP2 (82.4–540 m) was drilled in summer 1991. After shipment, they were
stored at -29 ∘C in a commercial freezer until they were moved to
a freezer (-36 ∘C) at the National Ice Core Laboratory (NICL) in
February 1993 (G. Hargreaves, personal communication, 2015). The ice samples
were then cut and moved to the Scripps Institution of Oceanography, where
δAr/N2 was measured in 2005 (Kobashi et al., 2008b). On the
other hand, the NGRIP2 ice cores (one of the two NGRIP ice cores;
64.6 m–445.2 m) were drilled in summer 1999 (Dahl-Jensen et al., 2002).
Shallower parts (64.6–254.4 m) were stored in a freezer at the University
of Copenhagen at around -24 ∘C (J. P. Steffensen, personal
communication, 2015), and deeper parts (255.5–445.2 m) were in a freezer of
a commercial facility rented by the Alfred Wegener Institute (AWI) at
-30 ∘C (S. Kipfstuhl, personal communication, 2015). In fall 2011,
we cut the ice samples and shipped them to a freezer at the National
Institute of Polar Research at -30 ∘C until 2013 when we analyzed
the ice cores (Kobashi et al., 2015). The ice cores from Dome Fuji were
drilled in late 1995 and stored at -50 ∘C, with a short period
(2.5 months) at <-25 ∘C during shipment from Antarctica to
Japan (S. Fujita, personal communication, 2015). The ice core was analyzed in
early 2014.
The conventional delta notation is used to express δAr/N2 as
follows:
δAr/N2=[(Ar/N2)sample/(Ar/N2)standard-1]103(‰),
where the subscript “sample” indicates ice core values, and “standard” is
the present atmospheric composition. For GISP2, mass 40 of argon and 29 of
nitrogen, and for NGRIP and Dome Fuji, mass 40 of argon and 28 of nitrogen
were used to calculate δAr/N2. All δAr/N2 data
presented in this study were corrected for gravitational and thermal
fractionations in the firn using the conventional method based on δ15N (Bender et al., 1995; Severinghaus and Battle, 2006; Severinghaus et
al., 2009) as follows:
δAr/N2corr=δAr/N2-11δ15N.
The coefficient 11 arises because the mass difference of δAr/N2 (40Ar and 29N2) is 11 times larger than that of
the nitrogen isotopes (29N2 and 28N2). This coefficient
is replaced with 12 for the calculation of δAr/N2corr
for NGRIP and Dome Fuji because the mass difference between 40Ar and
28N2 is 12. As the temperature sensitivities of δ15N and
δAr/N2 are slightly different, the correction is not perfect.
However, the variability induced by the gas loss is much bigger than the
uncertainties introduced by the differences of the thermal sensitivities.
After these corrections, the δAr/N2corr variations in
the ice cores can be attributed only to gas loss. δAr/N2corr of the GISP2 data using the mass 28 or 29 leads to
negligible differences (an average difference is
0.4 × 10-3 ‰ and the standard deviation is
0.94 × 10-3 ‰) which are much smaller than the
measurement uncertainty of δAr/N2(1σ< 0.7 ‰). We also note that the standard deviation
(0.07 ‰) of δ15N × 11 in GISP2 is much smaller
than standard deviation of raw δAr/N2 (1.33 ‰) over
the past 6000 years, indicating that the variations of δAr/N2corr mostly originate from the raw δAr/N2
and not from δ15N. For the sake of simplicity, we denote all the
δAr/N2corr as δAr/N2 in later sections.
The significance of correlations were calculated considering the
autocorrelation of time series (Ito and Minobe, 2010; Kobashi et al., 2013).
We consider > 95 % confidence as significant, unless otherwise noted.
All error bounds in figures and texts are 2σ.
Post-coring fractionation
Before evaluating δAr/N2 in ice cores for the changes that
have occurred in the firn, it is necessary to consider the post-coring
fractionation (Ikeda-Fukazawa et al., 2005). For this purpose, we applied a
molecular diffusion model (permeation model) through ice crystals
(Ikeda-Fukazawa et al., 2005). It has been applied to observed depletions of
oxygen in the Dome Fuji and GISP2 ice cores in ∼ 10 ‰ with
respect to nitrogen (Ikeda-Fukazawa et al., 2005; Suwa and Bender, 2008b).
The model was also implemented with modifications for gas permeation
processes in the firn (Severinghaus and Battle, 2006) and in ice cores
(Bereiter et al., 2009). The gas permeation in ice cores is driven by the
pressure gradients between two spaces isolated by ice walls (e.g., between
bubbles or between bubbles and the atmosphere). The concentration (Um;
mol molice-1) of species m (i.e., nitrogen, oxygen, and
argon) in bubbles in 1 mol of ice after a time t can be described as
follows (Ikeda-Fukazawa et al., 2005):
Um=Um0-kmXmPiZmi-PaZmsS/Vt,
where Um0 (mol molice-1) is the original
concentration of species m. km (m s-1) is the mass transfer
coefficient, and it is equal to
Dm/Δl, where Dm (m2 s-1) is the diffusion
coefficient of the species m and Δl (m) is the thickness of the
surface layer of ice (Ikeda-Fukazawa et al., 2005). Xm
(mol molice-1 M Pa-1) is the solubility of
species m in ice. Pi and Pa are the pressures in the bubbles and
in the atmosphere, respectively. Zmi and Zms are molar
fractions of species m in the bubbles and in the atmosphere, respectively.
S (m2) and V (m3) represent the surface area and the volume of
an ice sample such that S/V can be understood as specific surface area
(m-1), an important variable for the gas exchange between the atmosphere
and the ice (Matzl and Schneebeli, 2006).
For Eq. (3), we assumed an initial air content of
6.53 × 10-5 mol in 1 mol of ice (a typical air content in ice
cores). Um0 for each gas is calculated from the total air content
multiplied by the atmospheric molar ratio of each gas. In this case,
Zmi and Zms are set to the atmospheric partial pressures for
each molecule. Another factor that affects the gas loss is the specific
surface area. The GISP2 ice core has a larger diameter (0.132 m) and longer
length (1 m) during the storage than the NGRIP core (0.098 m diameter and
0.55 m length). Dome Fuji core has a diameter of 0.093 m and length of
0.50 m. Therefore, the specific surface areas (S/V) were calculated to be
32.3, 44.5, and 47.0 m-1 for GISP2, NGRIP, and Dome Fuji, respectively.
It is noted that these specific surface areas are approximations given that
ice cores during storage often have different shapes from earlier sampling shapes and because we shaved the ice surface by ∼ 5 mm
before the analyses (Kobashi et al., 2008b, 2015). However, we also note that
shallow late Holocene ice cores often had nearly intact shapes (no sampling)
at the time of our sampling from ice cores.
Diffusivity (DAr) and solubility (XAr) for argon in ice
are less known than for nitrogen and oxygen. Therefore, we attempted to
estimate two possible functions (Ar(I) and Ar(II)) for
kArXAr (i.e., DAr/Δl⋅XAr) in
relation to those for nitrogen and oxygen (Fig. 2).
KN2XN2 and kO2XO2 in
different temperatures can be estimated using Eqs. (4) and (2) with Δl=12 and 7 mm for nitrogen and oxygen in Ikeda-Fukazawa et al. (2005) for
the Dome Fuji core (Fig. 2), which were consistent with various observations
(Ikeda-Fukazawa et al., 2005; Severinghaus and Battle, 2006; Suwa and Bender,
2008b; Bereiter et al., 2009).
km⋅Xm for oxygen, argon, and nitrogen for different
temperatures. Ar(I) and Ar(II) were calculated from Eqs. (4) and (5) and Eqs. (6),
respectively (see text).
The first estimate of Ar(I) uses a diffusion coefficient (DAr;
4.0 × 10-11 m2 s-1) of argon at 270 K calculated
from molecular dynamic simulations with those of nitrogen (DN2;
2.1 × 10-11 m2 s-1) and oxygen (DO2;
4.7 × 10-11 m2 s-1) (Ikeda-Fukazawa et al., 2004).
Owing to the molecular–size-dependent fractionation, argon permeation occurs
slower than oxygen but faster than nitrogen (Fig. 2), which cannot be
explained by their mass differences (Huber et al., 2006; Severinghaus and
Battle, 2006). Then, temperature-dependent kAr and XAr
were estimated assuming that the geometrical relationship between
DN2,DAr, and DO2 at 270 K from the
molecular dynamics simulations holds for kAr and XAr at
different temperatures as follows:
kAr=kO2-(DO2at 270K-DArat 270K)/(DO2at 270K-DN2at 270K)(kO2-kN2),XAr=XO2-(DO2at 270K-DArat 270K)/(DO2at 270K-DN2at 270K)(XO2-XN2).
Second, we estimated Ar(II) from an observation that δAr/N2 in
ice is often depleted about half of δO2/N2 in ice cores
(Bender et al., 1995). To satisfy this condition, kArXAr
can be written as
kArXAr=(kN2XN2+kO2XO2)/2.
Estimated kArXAr for Ar(I) and Ar(II) are higher than
kN2XN2 and increase with temperatures, resulting in a
general depletion of δAr/N2 in ice compared to the atmospheric
composition, and the depletion is faster in warmer temperatures (Fig. 2). The
use of Ar(I) induces faster depletion of δAr/N2 than that of
Ar(II) owing to faster permeation of argon. With the two estimates of
kArXAr, we explore the range of uncertainties associated
with argon permeation.
(a) Estimated post-coring fractionation on δAr/N2. The values are averages over the past 2100 years for GISP2 and
Dome Fuji. NGRIP shallow and deep are averages of the corresponding depths
defined in the text. (b)kN2XN2 and
kArXAr
(m s-1 mol molice-1 MPa-1) at various
temperatures. See also Fig. 2.
In a pioneering study by Bender et al. (1995), δAr/N2 in a
shallow core of GISP2 was analyzed after 1 week, 3 months, and 7 months of
drilling in 1989 to study the time-dependent gas loss process (Fig. 3). As
the data from three different periods are not significantly different, we
treat Bender's data as the true Ar/N2 values before coring. By
comparing the data (Bender et al., 1995) with our data set analyzed 14 years
after the coring (Kobashi et al., 2008b), we estimated the post-coring
fractionation of δAr/N2 in GISP2 to be
-1.5 ± 0.6 ‰, a difference of the two data sets for common
depths (124–214 m) (Fig. 3). Using this value, we derived an unknown
parameter (i.e., bubble pressure) in Eq. (3). The bubble pressures are
calculated as 0.6 ± 0.2 MPa and 0.8 ± 0.3 MP for two different
estimates of kArXAr of Ar(I) and Ar(II), respectively,
which agree with the normal bubble pressure at 150–200 m depths in Vostok
(Lipenkov, 2000). Using the estimated bubble air pressure and aforementioned
parameters, the amounts of depletion in δAr/N2 after coring
are estimated as -3.0 ± 1.2, -2.5 ± 1.0, and
1.5 ± 0.7 ‰ for NGRIP shallow, NGRIP deep, and Dome Fuji,
respectively (Table 2). As a result, it is possible to derive the original
δAr/N2 values before coring for GISP2, NGRIP shallow, and
NGRIP deep, and Dome Fuji as -2.4 ± 0.6, -3.3 ± 1.2,
-3.4 ± 1.0, and -6.3 ± 0.8 ‰, respectively
(Table 2).
Comparison of δAr/N2 for shallow GISP2 cores
(124–214 m) measured in different periods. Color data points (blue
triangles, orange squares, and green diamonds) are individual data from
Bender et al. (1995), and black data points with error bounds are from
Kobashi et al. (2008b). We did not use shallower data of Bender et al. (1995)
as they exhibit depletions similar to our shallow NGRIP data (Fig. 8); an
anomalous value (-16.91 ‰ at 145.4 m) in the Bender data set was
also excluded. Squares, diamonds, and triangles represent the data measured
after 1 week, 3 months, and 7 months of coring, respectively (Bender et al.,
1995). The average difference between the Kobashi and Bender data sets is
-1.51 ± 0.58 ‰, which we interpret as the post-coring
fractionation for GISP2.
δ15N, δ40Ar/4, and δAr/N2 from
the GISP2 ice core over the Holocene (Kobashi et al., 2008b). The grey arrow
indicates the brittle zone (Gow et al., 1997).
Post-bubble close-off fractionation in firn: empirical evidenceGISP2 δAr/N2 variation over the Holocene
The δAr/N2 record over the Holocene in the GISP2 ice core
exhibits relatively constant values of around -3 ‰, except for a
prominent rise of up to 10 ‰ around 7000 years BP (Fig. 4). The rise
is located within the depths of the brittle zone (650–1400 m), where air in
the bubbles changes to clathrate inducing anomalously high pressure (Gow et
al., 1997). The dissociation pressure of nitrogen in the clathrate phase is
higher than that of argon (or oxygen) so that nitrogen is enriched in the gas
phase in relation to the clathrate (more stable state), resulting in a
preferential leakage of nitrogen and thus argon (or oxygen) enrichments in
these depths (Ikeda et al., 1999; Ikeda-Fukazawa et al., 2001; Kobashi et
al., 2008b). As the dissociation of gases from the clathrate depends on
various factors, δAr/N2 in these depths are highly variable
(Fig. 4). It is noted that δ15N and δ40Ar exhibit little
influences from the anomalous δAr/N2 fractionation, indicating
that the processes are mass independent in first order (Huber et al., 2006;
Severinghaus and Battle, 2006) (Fig. 4).
Changes in the surface temperatures and accumulation rates are the dominant
controlling factors for the state of firn layers (e.g., density profile,
bubble close-off depth, and firn thickness) (Herron and Langway, 1980;
Schwander et al., 1997; Goujon et al., 2003). Therefore, we investigated if
changes in surface temperature or accumulation rate have any controls on the
δAr/N2 variations. We found a significant negative correlation
(r=-0.35, p=0.03) between δAr/N2 on the gas-age scale
and the accumulation rate for the past 6000 years, a time interval in which
the abnormal δAr/N2 fractionation is not observed (Figs. 1, 4).
This negative correlation is opposite of what an earlier study
(Severinghaus and Battle, 2006) suggested for the permeation fractionation in
the firn (positive correlation). In addition, the significant correlation was
found for δAr/N2 on the “gas ages” scale rather than the
“ice ages” that the insolation hypothesis predicts; an indication that new
processes need to be considered for the gas loss processes in the firn.
Observed and modeled δAr/N2, surface temperatures, and
accumulation rates from the GISP2 ice core over the past 4000 years. Note that
the observed δAr/N2 is corrected for the post-coring
fractionation (1.5 ‰ added). (a)δAr/N2 and
surface temperatures (Kobashi et al., 2011). Ages of the temperatures were
adjusted for the lag (68 years). (b)δAr/N2 and
accumulation rates in 21-year RMs (Alley et al., 1997; Cuffey and Clow,
1997). Ages of the accumulation rates were adjusted for the lag (38 years)
(c) Observed and modeled δAr/N2 from multiple linear
regression (see text). (d) Observed and modeled δAr/N2 of multiple linear regression using δ18Oice
as a temperature proxy (see text).
The subset of the GISP2 data covering the past 4000 years provides a unique
opportunity to investigate δAr/N2 variations because precise
temperature (Kobashi et al., 2011) and accumulation rate by layer counting
(Alley et al., 1997; Cuffey and Clow, 1997) are available. Using these data,
we applied a linear regression and lag analysis on δAr/N2. It
is found that the surface temperature is positively correlated with δAr/N2 on the gas ages (r=0.47, p=0.04; r=0.28, p=0.001 after linear detrending) with a 68-year lag (Fig. 5a), indicating that
cooler (warmer) temperatures induced more (less) depletions in δAr/N2 with a multidecadal lag. On the other hand, the accumulation
rate is negatively correlated with δAr/N2 on the gas ages (r=-0.47, p=0.12; r=-0.26, p=0.01 after
linear detrending) with a 38-year lag (Fig. 5b), indicating that high (low)
accumulation rates induced more (less) depletions in δAr/N2
over the past 4000 years. We note that the surface temperature and
accumulation rate have a negative but insignificant correlation (r=-0.32,
p=0.13; after linear detrending r=-0.11, p=0.2) over the past
4000 years.
To estimate the relative contribution of the accumulation rate and the
surface temperature changes on δAr/N2, we applied a multiple
linear regression, which finds the best linear combination of variables
(i.e., temperature and accumulation rate) for a response variable (i.e.,
δAr/N2). Before the regression is applied, the temperature and
accumulation records were shifted toward younger ages to account for the lags
(38 and 68 years for accumulation rate and temperature, respectively), and
δAr/N2 is corrected for the post-coring fractionation
(1.5 ‰ added). As ordinary least squares including the multiple
linear regression underestimate the variance of target time series when the
data are noisy (Von Storch et al., 2004), we used “variance matching” by
linearly scaling regression coefficients according to the ratio between the
variance of the target and model time series. Figure 5c shows the original
and modeled results of δAr/N2 over the past 4000 years. As
expected, the model of the multiple linear regression captures the δAr/N2 variations better than the individual variables do (Fig. 5a–c)
with a correlation coefficient of r=0.58, p=0.09 (r=0.36, p< 0.001 after linear detrending). For the centennial variations, the model
captures nearly half of the total variance of the observed δAr/N2 variations with a 95 % confidence (r=0.71, p=0.05
after linear detrending with 200-year RMs). The high and significant
correlation between the model and observed δAr/N2 indicates
that changes in the surface temperature and accumulation rate play important
roles in controlling the δAr/N2 variations. From the multiple
linear regression, δAr/N2 on the gas ages in GISP2 can be
expressed by temperature (∘C) and accumulation rate
(m ice year-1) as a function of time after adjusting for the lags:
δAr/N2(t)=A×temperature(t+ttemp)+B×accumulation(t+taccm)+C,
where A=0.72±0.06 ‰ ∘C-1, B=-58.8±4.3 ‰ (m year-1)-1, C=32.7±1.8 ‰, and t,ttemp, and taccm are time, lag for temperature, and lag for
accumulation rate, respectively (all in years).
Next, we attempted to use oxygen isotopes of ice
(δ18Oice) as a temperature proxy for the same regression
analyses of δAr/N2 since we do not have the N2/Ar
isotope-based temperature information before 4000 years BP. Temperature
records derived from δ18Oice can be quite noisy but
stacking several δ18Oice records can improve the derived
temperature histories (White et al., 1997; Kobashi et al., 2011). Thus, we
stacked three oxygen isotope records (GISP2, GRIP, and NGRIP) over the
Holocene in the 20-year RMs (Stuiver et al., 1995; Vinther et al., 2006). The
stacked record was calibrated to temperatures using the relation obtained
from borehole temperature profiles (Cuffey and Clow, 1997). Using the
regression coefficients obtained in Fig. 5c, a δAr/N2 model
was calculated from the oxygen-isotope-based temperature and the accumulation
rate (Fig. 5d). We found that the correlation between the model and the
observed δAr/N2 performs not as well as the one with the
temperature and accumulation rate records for the last 4000 years based on
Ar/N2 isotope values (Fig. 5c) but does slightly better than the
correlations with the temperature or accumulation rate individually (Fig. 5a,
b).
Observed and modeled δAr/N2 over the Holocene, and
decomposition of δAr/N2 into the effects of accumulation rates
and temperatures. Note that the observed δAr/N2 are corrected
values for the post-coring fractionation (1.5 ‰ added).
(a) Observed and modeled δAr/N2.
(b) Decomposition of δAr/N2 into the effects of
temperatures and accumulation rates using multiple linear regression (see
text).
The δAr/N2 regression model with the δ18Oice-based temperatures and accumulation rates can span the
entire Holocene, including the periods when the observed δAr/N2 are highly variable owing to the post-coring fractionation as
discussed earlier. Except for the time interval around 7000 years BP, the
model and observed δAr/N2 exhibit rather constant values of
-1 to -3 ‰ during the Holocene (Fig. 6). Interestingly, the
model indicates that the constant δAr/N2 during the early
Holocene is the result of a cancellation between the effects of the
accumulation rate and the temperature, both of which were rapidly rising in
the early Holocene (Fig. 6). The observed δAr/N2 variations
remained higher or noisier from the early Holocene to ∼ 6000 BP than
for the later period, which probably make it difficult to decipher the
original multidecadal to centennial signals in δAr/N2
(Fig. 6).
Surface temperatures, accumulation rates, δ15N, δAr/N2 for GISP2, NGRIP, and Dome Fuji over the past 2100 years.
(a) Surface temperatures for GISP2 (black) and NGRIP (blue) (Kobashi
et al., 2015). (b) Accumulation rates in 21-year RMs for GISP2
(black: Alley et al., 1997; Cuffey and Clow, 1997) and NGRIP (blue: Gkinis et
al., 2014). (c) Raw δ15N and spline for NGRIP and GISP2
(Kobashi et al., 2010, 2015). (d–f)δAr/N2
and the values corrected for the post-coring fractionation for GISP2, NGRIP,
and Dome Fuji. Blue and black lines are the raw and corrected values for the
post-coring fractionations, respectively. A red point with error bounds
(2σ) indicates estimated δAr/N2 for Dome Fuji using
Eq. (7).
NGRIP and Dome Fuji δAr/N2 variation over the past
2100 years
The δAr/N2 data of NGRIP ice cores allows for a good
comparison with the GISP2 data (Fig. 7). The averages of δAr/N2 for the past 2100 years are -3.36 and -2.40 ‰ for
NGRIP and GISP2, respectively (Fig. 7). The δAr/N2 variability
in NGRIP (1σ=0.91 ‰) over the past 2100 years is 24 %
smaller than that of GISP2 (1σ=1.19 ‰) after correcting for
the post-coring fractionation (Table 2), likely owing to the smaller
variations of the accumulation rate at NGRIP than that of GISP2 (Fig. 7). The
pooled standard deviations of replicated samples are 0.94 ‰ for
NGRIP over the past 2100 years and 0.66 ‰ for GISP2 over the past
1000 years (replicates are available only for the past 1000 years in GISP2)
(Kobashi et al., 2008b). The noisier data for NGRIP than for GISP2 should not
be analytical as the mass spectrometer used for the NGRIP had better
precision on δAr/N2 than the one used for GISP2 (Kobashi et
al., 2008b, 2015). δAr/N2 for GISP2 and NGRIP are weakly but
significantly correlated with a correlation coefficient of r=0.24 and p=0.02 (after linear detrending) for the past 1000 years of the
high-resolution part of GISP2 but not for the deeper part, likely owing to
the difference of sampling densities between the two periods (Kobashi et al.,
2015). The surface temperatures at NGRIP were only weakly correlated with
δAr/N2 in the deeper part of NGRIP (r=0.20, p=0.06
after linear detrending) and were uncorrelated in the shallower part. No
significant correlations were found between δAr/N2 and the
accumulation rate for NGRIP, probably due to the lower variation of the
accumulation rate at NGRIP than that of GISP2. It is consistent with the fact
that the signal to noise ratio (SNR = variance of signals/variance of
analytical errors = 1.2) for NGRIP is about one-fifth of that for GISP2
(6.1) estimating the NGRIP signals from Eq. (7).
From the relationship between δAr/N2 and the temperature or
accumulation rate of GISP2 in Eq. (7), we can calculate expected δAr/N2 for NGRIP and Dome Fuji. Using the past 2100 years of
temperatures and accumulation rates for NGRIP (Fig. 7a, b) and the current
observation (Table 1) for Dome Fuji, the expected δAr/N2 from
Eq. (7) were calculated as 0.3 ± 1.3 and -6.4 ± 1.2 ‰,
respectively. The value for NGRIP is significantly higher than the observed
value of -3.3 ± 1.2 ‰ corrected for the post-coring
fractionation (Table 2). For Dome Fuji, the value is similar to the observed
-6.3 ± 0.8 ‰ corrected for the post-coring fractionation
(Fig. 7, Table 2). This may indicate that the relationship of δAr/N2 with the temperature and accumulation rate becomes non-linear
when the firn thickness becomes thinner than that of GISP2 as δAr/N2 is not expected to be positive without the existence of
clathrate (see later discussion).
δAr/N2 ice core data of NGRIP from the depth range 64.6–80 m
exhibit some interesting features (Fig. 8). The depth from ∼ 60 to
78 m corresponds to the lock-in zone in NGRIP, where vertical mixing of gas
is limited so that δ15N stays nearly constant in these depths
(Huber et al., 2006; Kawamura et al., 2006). Therefore, the shallowest data
at 64.6 m are located in the lock-in zone. Generally, gas data from the
lock-in zone are not used owing to possible contamination (Aydin et al.,
2010). However, a recent study (Mitchell et al., 2015) demonstrated that
δ15N can be used to estimate the amount of ambient air
contamination using ice samples in the lock-in zone, and the original methane
concentration in the firn was reconstructed with a range of uncertainties.
Therefore, we interpret the observed rapid decreases of δ15N and
δ40Ar toward shallower depths in the lock-in-zone as the result of
mixing with ambient air (Fig. 8d). Based on isotope mass balance, we
calculated the original δAr/N2 values, which exhibited highly
depleted values as low as -50 ‰ (Fig. 8e). The depleted δAr/N2 in the lock-in zone provides a clue to the processes of gas
loss in the firn (see later discussion).
δ15N, δ40Ar/4, and δAr/N2 in the
NGRIP ice core from shallower depths (60–100 m). (a)δ15N, (b)δ40Ar/4, (c)δAr/N2,
(d) estimated original air fractions, and (e) estimated
original δAr/N2. The estimated original air fractions relative
to the value at 75.6 m were calculated with a mass balance calculation,
assuming that δ15N in the lock-in zone is constant with the value
of 0.289 ‰ at 75.6 m and δ15N of the ambient air is
0.0 ‰. From the calculated original air fraction, the original
δAr/N2 were estimated again by the mass balance calculation,
assuming that the ambient δAr/N2 is 0.0 ‰. The green
shaded area indicates the lock-in zone. Black dotted lines in δ15N,
δ40Ar, and the estimated original air fraction are the values at
75.6 m (red dotted line).
Post-bubble close-off fractionation in firn: process study
Air bubbles in the polar firn or ice can be categorized into two types
(Lipenkov, 2000): normal bubbles and microbubbles (< 50 µm).
They can be distinguished as a bimodal distribution in ice cores (Lipenkov,
2000; Ueltzhöffer et al., 2010; Bendel et al., 2013). The air volume
contribution of the microbubbles to the total air content is estimated to be
0.3 % in the Vostok ice core (Lipenkov, 2000), but the value is not known
for Greenland ice cores. Importantly, the two types of bubbles have
significantly different bubble pressure histories in the firn. The normal
bubbles form at the bubble close-off depth. Most of the air in ice cores is
captured as normal bubbles, and the air-trapping processes are relatively
well known (Schwander et al., 1997; Goujon et al., 2003; Mitchell et al.,
2015). Normal bubble pressures build up according to increasing density
(normal bubble process; Severinghaus and Battle, 2006). On the other hand,
the microbubbles are believed to form near the surface (Lipenkov, 2000); so,
they are highly pressurized and have a rounded shape by the time when the
bubbles reach the bubble close-off depth (Lipenkov, 2000; Ueltzhöffer et
al., 2010). As a result, the microbubbles are more sensitive to changes in
the overloading pressure at the bubble close-off depth (pressure sensitive
process).
Owing to the different bubble pressure histories in the firn, δAr/N2 or δO2/N2 in the microbubbles and normal
bubbles are expected to be different due to the differential permeation of
each molecule. In this study, we attempted to quantify two types of the gas
loss processes – pressure sensitive process (microbubble) and normal bubble
process – in the firn using a permeation model (Ikeda-Fukazawa et al., 2005)
combined with the inputs from firn-densification, heat-diffusion models
(Schwander et al., 1993; Spahni et al., 2003; Goujon et al., 2003).
Pressure sensitive process (microbubbles)
We first look into the pressure sensitive process as exemplified by the
microbubbles. Microbubbles are believed to form in the shallow firn by
sublimation–condensation processes (Lipenkov, 2000). These bubbles have
smaller sizes, smoothed spherical surfaces, and can generally be found in the
interior of the ice crystals (Lipenkov, 2000). The bubble pressure reaches a
near-overloading pressure at the bubble close-off depth, so it is sensitive
to changes in the overloading pressure. As the actual contribution of
microbubbles and air content involved in the pressure sensitive processes is
not known, we consider a 2 % contribution of air to the total air. As it
will be discussed later, more air fractions than simply from microbubbles
(0.3 % in Vostok) are likely involved in the pressure sensitive process.
Therefore, we conducted additional calculations with 0.3, 1, and 3 %
microbubble contributions, and assessed the impacts to the total δAr/N2.
To model the gas permeation process from the microbubbles, we assumed a
steady state with given surface temperatures and accumulation rates and
calculated the ages, firn densities, porosities, and overloading pressures at
given depths, using a firn-densification, heat-diffusion model (Schwander et
al., 1993; Spahni et al., 2003). Then, they are interpolated for annual
layers in the firn for the following calculation.
Changes in the concentrations of species m were calculated according to
Eq. (8), similar to Eq. (3).
Um(l+1)=Uml-kmXmPilZmil-PaZms⋅SV(l)so/s(l)tC(l)
Zmil=Um(l)UArl+UO2l+UN2(l),
where l is an annual layer from the surface to below the firn layer (e.g.,
l=1 to 2000), and so/s(l) in a layer l is the open porosity
ratio. s,sc, and so are the total, closed, and open
porosities (so=s-sc), respectively (Spahni et al., 2003;
see also Sect. 5.2). In a steady state, l can be considered as a time
variable. At l=1, the microbubbles in an annual layer are at the surface,
although they are not active in terms of permeation at these depths (Fig. 9).
With l increasing in a 1-year step, the microbubbles move deeper in the
firn with l annual layers overlying. C(l) is a coefficient defining the
gas concentration in annual layer l relative to the total air in ice. It is
assumed that the pressure Pi(l) in the microbubbles starts increasing
with overloading pressure from the depth at which the normal bubbles
generation initiates (firn density of around 0.7 g cm-3) (Fig. 9c) and
that pressure changes were considered to be negligible above that depth
(Lipenkov, 2000). Initial Pi(0) was set at 0.065 MPa, similar to the
atmospheric pressure at the Greenland summit (Schwander et al., 1993)
with a 0.3 MPa lag from overloading pressure as in Fig. 9 (Lipenkov, 2000).
We estimated the specific surface area (S/V(l)) in a layer l from the
linear relationship between the specific surface areas (m-1) and
densities ρ from the Greenland summit (Lomonaco et al., 2011)
with an equation: S/V(l) (m-1) =-16 799 ρ(l)
(g cm-3) + 14 957. The initial gas content in the microbubbles was
set at 0.3–3 % of the air content
(6.53226 × 10-5 mol × 0.01) per 1 mol of ice, and it
is composed of nitrogen (78.084 %), oxygen (20.9476 %), and argon
(0.934 %). The specific surface area S/V was multiplied by the open
porosity ratio so/s(l) (Spahni et al., 2003; Fig. 9a), as the gas
loss occurs toward open pores. kmXm was calculated as for the
post-coring fractionation, and we used the estimate Ar(II) for argon.
Simulated δAr/N2 vs. depth relationship in the
microbubbles with a temperature of -31 ∘C, accumulation rate of
0.24 m ice year-1, and microbubble contribution of 2 %.
(a) Density and closed porosity (sc). (b)δAr/N2 and δO2/N2. (c) Air content and
air pressure in the microbubbles. (d) Nitrogen and argon
concentrations.
Figure 9 shows model results with a temperature of -31 ∘C, an
accumulation rate of 0.25 m ice year-1 (similar to GISP2 condition),
and 2 % microbubble contribution. It shows that the gas permeation from
the microbubbles starts soon after the pressure was applied in the
microbubbles (Fig. 9c, d). As oxygen has a larger permeability than of argon,
δO2/N2 depletion is larger than δAr/N2
(Fig. 9b). At the temperature of -30 ∘C and accumulation rate of
0.25 m ice year-1, the depletion reaches up to 133 ‰ for
δAr/N2, and 243 ‰ for δO2/N2 in
the model, which corresponds to a 12 % gas loss from the original air
content of the microbubbles (Fig. 9c).
Normal bubble process
Most of the air in ice cores is trapped as normal bubbles near the lock-in
depth. As a result, bulk air pressure in the normal bubbles does not build up
as high as the microbubbles in the lock-in zone (Lipenkov, 2000). We used
Eq. (8) to model the permeation process for the normal bubbles. As for the
microbubbles, we assumed a steady state with the given temperatures and
accumulation rates. The general characters of the firn in various depths
(ages, densities, porosities, loading pressures, bubble close-off depths)
were calculated using the firn-densification, heat-diffusion model (Schwander
et al., 1993; Spahni et al., 2003), and they were interpolated for annual
layers as for the microbubbles. We first calculated how much bubble air is
generated in each annual layer according to the increase in the closed
porosity (sc) with depth as the following equation:
V0(l+1)=asc(l+1)-sc(l)(ρice-ρ(l+1))/(ρice-ρ(l))/ρ(l+1),
where V0(l) is newly trapped air in an annual layer l,
ρice is the density of ice, and ρ(l) is the density at
depth l. sc(l) is the closed porosity in an annual layer l,
and a is a scaling coefficient. sc can be written as (Schwander,
1989; Spahni et al., 2003)
sc=s⋅exp75⋅ρlρco-1,0<ρl<ρco,s,ρl>ρco,
where ρco is the density at the depth in which the air is
totally enclosed in bubbles. The sum of all the newly generated air
(∑l=12000V0(l)) is set to have the air content of
6.53×10-5 mol per mole of ice. Then, V0(l) was scaled
accordingly using the coefficient a and converted to the volume (m3)
with the atmospheric pressure (0.065 MPa) as in Fig. 10a.
Traces of simulated δAr/N2 changes for each annual
layer for the normal bubbles. The model calculates bubble generation for each
annual layer, gas permeation into open air, and finally trapping into ice
(see text). The model is calculated assuming an equilibrium state with a
temperature of -31 ∘C, accumulation rate of
0.24 m ice year-1, and microbubble contribution of 2 % (same as
for Fig. 9). (a) Changes in the volumes of the normal bubbles for
each annual layer induced by density changes with depth.
(b) Nitrogen concentrations as in (a). (c) Argon
concentrations as in (a). (d)δAr/N2 as
in (a). (e) Air contents with depth, δAr/N2,
and C(l) for the bulk of the normal bubbles (sum of the values in annual layers
for each depth). Different colors (a–d) indicate values for each annual layer, showing how the bubbles
generated in different annual layers evolve with time.
The normal bubbles start forming at approximately 40 m depths and the
formation is maximum around the bubble close-off depth of 60–75 m at
-31 ∘C and 0.24 m ice year-1 in the model (Fig. 10a).
Then, the permeation from each annual layer was calculated according to
Eq. (8). The difference from the microbubble permeation process is that the
volume of the normal bubbles decreases according to increasing
modeled density towards deeper depth, leading to a generally smaller pressure
build-up and total permeation from the bubbles in the firn than that of the
pressure sensitive process for the microbubbles (Fig. 10a). C(l) in Eq. (8)
was calculated from V0(l) for each annual layer l by setting the sum
of C(l) as 1-0.02=0.98 (if microbubble contribution is 2 %)
(Fig. 10e). Other parameters in Eq. (8) were set to be the same as for the
microbubbles.
Figure 10 shows the evolution of the normal bubble volumes, the nitrogen and
argon concentrations, the δAr/N2 in each annual layer, and the
air content and bulk δAr/N2 with depth at a temperature of
-31 ∘C and an accumulation rate of 0.24 m ice year-1 as
for the microbubbles for Fig. 9. A new generation of closed pore volumes in
annual layers generally increases towards deeper depths (Fig. 10a). When open
pore space disappears completely, we assume the gas permeation to the open
pore stops. As argon (oxygen) permeation in ice is faster than nitrogen by
289 (479) % at -31 ∘C (Ar(II), Fig. 2), δAr/N2
(δO2/N2) within the bubbles decreases when the permeation
proceeds. At the temperature of -31 ∘C and accumulation rate of
0.24 m ice year-1, the δAr/N2 depletion can reach
about -5 ‰ for those bubbles formed at shallow depths (Fig. 10d).
However, the amount of air contained in these bubbles is so small (Fig. 10a)
that the influence on the total δAr/N2 is limited (Fig. 10e).
The depth vs. δAr/N2 relationship of the total air from the
normal bubbles (Fig. 10e) indicates that the total δAr/N2
reaches the minimum of -0.39 ‰ at the middle of the bubble
close-off depth of 73.2 m. Then, the total δAr/N2 increases
to -0.29 ‰ as a large amount of ambient air with δAr/N2= 0 is trapped in these depths (Fig. 10a, d, e).
Modeled and observed δAr/N2 in various conditions
with microbubble contribution of 2 %. In the first column, T indicates
temperature (∘C) and A indicates accumulation rate
(m ice year-1). Duration is the time that bubbles experience from the
depth of 20 % bubble closure to the depth of complete bubble close-off.
Average pressure is the average overloading pressure between the depths of
the 20 % bubble closure and complete bubble close-off. The average depth
is the middle depth between the 20 % bubble closure and complete bubble
close-off. Depth width is the depth range from 20 to 100 % bubble
closed. Microbubbles, normal
bubbles, and total δAr/N2 are the values after all the bubbles
are closed (i.e., in ice cores). Observed δAr/N2 are the
values corrected for the post-coring fractionation in Table 2.
The permeation models for the normal and microbubbles were run for various
firn conditions with different surface temperatures, accumulation rates, and
microbubble contributions to investigate their effects on the δAr/N2 in the bubbles (Fig. 11, Table 3). The resultant air content
(i.e., nitrogen, argon, and oxygen) for each annual layer from the microbubbles and
normal bubbles was added to calculate the combined effects of the
accumulation rates and temperatures on total δAr/N2 (Fig. 11).
Results show that the normal bubbles experience only limited δAr/N2 depletion (>-0.5 ‰) by the different
temperatures or accumulation rates we considered (Table 3). On the other
hand, δAr/N2 in the microbubbles varies with temperatures
through thickening of the firn, leading to higher pressures in the bubbles
and longer exposure to the gas loss in the firn (Table 3). A higher
accumulation rate with the same temperatures induces more depletion as it is
primarily controlled by the changes in loading pressure (Fig. 11c,
Table 3). As a result, the total δAr/N2 generally reflects the
variation of δAr/N2 in the microbubbles (r=0.95, Table 3).
Overall, the total δAr/N2 have a higher correlation with
temperatures (r=0.97) than with accumulation rates (r=0.57) in the
model (Table 3).
The simulated δAr/N2 fractionation with depth in the
firn for the normal bubbles and microbubbles with different temperatures and
accumulation rates. Microbubble contribution was set to 2 % except in
(d); see also Table 3. (a)δAr/N2 changes in
the normal bubbles. (b)δAr/N2 changes in the
microbubbles. (c) Total δAr/N2 changes (changes in
the sum of the microbubbles and normal bubbles). (d) Total δAr/N2 changes as in (c) but with different microbubble
contributions (0.3 to 3 %) with a temperature of -30 ∘C and
accumulation rate of 0.25 m ice year-1.
The modeled δAr/N2 agrees with the observed δAr/N2 corrected for the post-coring fractionation and is
within their uncertainty ranges (Table 3).
The extremely cold temperature in Dome Fuji with low accumulation rate
induces a long (274 years) bubble exposure to the permeation in the firn,
leading to a large depletion of δAr/N2 in the microbubbles and
in the total air (Table 3). The variations of δAr/N2 in normal
bubbles are limited and, clearly, microbubbles (or the pressure sensitive
process) play a critical role for the variation of δAr/N2 in
ice cores. The δAr/N2 minima in the firn ranges from -14 to
-83 ‰ depending on the temperatures and accumulation rates. The
most depleted δAr/N2 with a temperature of -30 ∘C
and accumulation rate of 0.2 m ice year-1 in Fig. 11c capture the
highly depleted observation-based estimates of δAr/N2 in the
NGRIP ice core (Fig. 8e). As the normal bubble process alone does not produce
such depleted values in the firn (Fig. 11a), the observed highly depleted
δAr/N2 (Fig. 8e) is an evidence for the involvement of the
microbubble process (or pressure sensitive process). The total δAr/N2 at the bubble close-off depth increase to less depleted values
from the minimum owing to the rapid inclusion of the ambient air (Fig. 11c).
The calculated dependencies of the δAr/N2 variations on the
temperature (0.24 ‰ ∘C-1 for an accumulation rate of
0.25 m ice year-1) and accumulation rate
(-0.05 ‰ (0.01 m ice year-1)-1 at -30 ∘C)
with the 2 % microbubble contribution (Table 3) are lower than those of
the observed ones in GISP2 ice cores
(0.72 ± 0.1 ‰ ∘C-1 and
-0.58 ± 0.09 ‰ (0.01 m ice year-1)-1),
respectively. Considering a possibility of larger volume contributions on the
pressure sensitive process, we calculated the permeation model with
microbubble volume contributions of 0.3–3 % to the total air. The
3 % microbubble contribution induces more depletion in the total δAr/N2 (Fig. 11d). Also, the dependencies of δAr/N2 on
temperatures and accumulation rates linearly increase to
0.38 ‰ ∘C-1 with an accumulation rate of
0.25 m ice year-1, and
-0.11 ‰ (0.01 m ice year-1)-1 with a temperature at
-30 ∘C, respectively. The fact that they are still lower than
those of the observations indicates the involvement of larger air content as
microbubbles and/or normal bubbles influenced by the pressure sensitive
process. This is plausible considering the inhomogeneity of firn (Hörhold
et al., 2012) and resultant differential pressurization of
bubbles at the same depth.
Evidence of the larger air involvement in the pressure sensitive process
is the significantly positive correlation between δAr/N2 and
air contents over the past 6000 years in GIPS2 (Fig. 1). This correlation
indicates that the bubble air was squeezed out before close-off, resulting in
smaller air contents when overloading pressure was higher, eventually
inducing higher pressure in the bubbles and thus enhanced δAr/N2
depletions. This observation is also consistent with recent findings that
abrupt increases of accumulation rate at abrupt warming during the last
glacial period induced reductions in air contents (Eicher et al., 2015). In
addition, artificial sintering of snow with higher pressure has been shown to
contain much smaller air content than ice cores, owing to the lack of time to
develop spherical cavities by vapor transport (B. Stauffer, personal
communication, 2015). These lines of evidence indicate that higher
overloading pressures at the lock-in zone have impacts on normal bubbles and
microbubbles. The inclusion of this process in the model is beyond the scope
of the current paper, and we leave it for future studies.
We also investigated the observed lags of 68 and 38 years, respectively, for
the δAr/N2 variations in GISP2 from the changes in the surface
temperatures and accumulation rates (Fig. 5). Presumably, the lags are
introduced during the process of transferring surface temperature and
accumulation rate signals into overloading pressure at the bubble close-off
depths. Therefore, two transient simulations were conducted using a
firn-densification and heat-diffusion model (Goujon et al., 2003). First, the
model was run with a constant temperature (-30 ∘C) and
accumulation rate (0.2 m ice year-1) over thousands of years to reach
an equilibrium state. Then, surface temperature and accumulation rate
anomalies of -35 ∘C and 0.26 m ice year-1 for 20 years
were introduced, separately (Fig. 12a). The surface anomalies of the
temperature and accumulation rate were set to induce similar δAr/N2 changes of 3.5 ‰ from the relationship obtained by the
multiple linear regressions on the δAr/N2 of GISP2.
Two model experiments for the effects of surface temperatures and
accumulation rates on the overloading pressure at the bubble close-off depth.
(a) Input data for the accumulation rate (0.2 m ice year-1)
and surface temperature (-30 ∘C) with 20-year anomalies
(+0.06 m year-1 and -5 ∘C) for the years 1000–981 BP,
respectively. When one input was used for an experiment, the other was set
constant. Zero in (a) indicates the central year (model year
990 BP) of the anomalies. (b) Temperatures at the bubble close-off
depth. (c) Firn thickness. (d) Overloading pressures at the
bubble close-off depth. The orange line is the accumulation rate experiment,
and the blue line is the temperature experiment. Numbers on peaks
in (b–d) are the lag in years from the central year of the
initial anomalies in (a).
We found that the surface temperature anomaly takes 20 years to reach the
minimum temperature at the bubble close-off depth (Fig. 12b). The cooling
induces maximum firn thickening after 56 years. The accumulation rate anomaly
also induces firn thickening with an 11-year lag (Fig. 12c). Overloading
pressures at the bubble close-off depth reach similar maximum values with 85-
and 21-year lags from the surface temperature and accumulation rate
anomalies, respectively (Fig. 12d). Apparently, the surface temperature
anomaly takes longer to reach the maximum increase in the overloading
pressure than the accumulation rate anomaly, which is consistent with the
observations (68 and 38 years, respectively). The accumulation rate anomaly
is almost instantaneously and increasingly felt by the bubble close-off depth
through overloading pressure, as compared to the temperature anomaly that
takes decades to reach the bubble close-off depth. In addition, we note that
similar magnitudes of the overloading pressure anomalies were induced by the
temperature and accumulation rate anomalies (Fig. 12d). Therefore, we
conclude that the overloading pressure is the carrier of the surface
temperature and accumulation rate signals, linking the δAr/N2
variations through the permeation.
Discussions
The processes responsible for the δAr/N2 variations should
also play similar roles on the variations of δO2/N2 in
ice cores but with larger magnitudes owing to the larger permeability of
oxygen (Bender et al., 1995; Huber et al., 2006; Severinghaus and Battle,
2006; Battle et al., 2011). In earlier studies, causes of the δO2/N2 variation were attributed to the metamorphisms of surface
snow induced by local insolation changes (Bender, 2002; Kawamura et al.,
2007). The altered snow properties remain until the snow reaches the bubble
close-off depth and affects the preferential oxygen loss (Bender, 2002). Our
work demonstrates that the permeation processes in the firn can be induced by
changes in the surface temperature and the accumulation rate through the
changes in overloading pressure, indicating a possibility that the δO2/N2 variations in the orbital scale are also a result of the
surface temperature and accumulation rate changes. We note that δAr/N2 in GISP2 also shows a significant positive correlation (r=0.38, p< 0.001 after linear detrending) with the air
content (Kobashi et al., 2008b) over the past 6000 years, indicating a
similar link between δO2/N2 and air content in the
orbital timescale (Raynaud et al., 2007; Lipenkov et al., 2011). As the timescale we considered in this study is different from the orbital scale
variation, other mechanisms may play a role in controlling the δO2/N2 variations in ice cores. However, the mechanisms discussed
here must be considered in future studies.
Although the gas permeation from ice is generally believed to be a mass-independent process (no effects on isotopes), there is some evidence of
isotopic fractionation (Bender et al., 1995; Severinghaus et al., 2003, 2009;
Severinghaus and Battle, 2006; Kobashi et al., 2008b; Battle et al., 2011).
In particular, poor quality ice cores often exhibit isotope fractionation
(e.g, δ18O and δ40Ar) with highly depleted δO2/N2 or δAr/N2 (Bender et al., 1995;
Severinghaus et al., 2009). This mass-dependent fractionation is explained by
the existence of microcracks in poor quality ice samples that permit a
relatively large air flow. On the other hand, slowly occurring gas
permeations through ice crystals in good quality ice cores (e.g, NGRIP,
GISP2, and Dome Fuji) appear to have small or non-existent effects on
isotopes (Kobashi et al., 2008b; Suwa and Bender, 2008b). As small mass-dependent fractionation of δ15N and δ40Ar during the gas
loss are similar to the gravitational fractionation (Kobashi et al., 2008b),
the removal of the gravitational components also cancels the post-coring
isotopic fractionation. As a result, the estimated temperature gradients in
the firn are little affected by the gas loss (Kobashi et al., 2008b).
Another sign of isotopic fractionation during the gas loss is δ40Ar enrichment in ice cores, which produces calculated temperature
gradients in the firn to be lower than expected from firn modeling (Kobashi
et al., 2010, 2011, 2015). The systematically higher δ40Ar is
believed to be caused by processes during the bubble close-off; however, so far no
clear evidence has been found in firn air studies (Huber et al., 2006;
Severinghaus and Battle, 2006) except δ18O of O2 (Battle et
al., 2011). If the enrichment of δ40Ar occurs in the firn, it
should be correlated with δAr/N2. Therefore, the corrections
for the δ40Ar enrichment have been applied using δAr/N2 (Kobashi et al., 2010, 2011, 2015), δKr/Ar
(Severinghaus et al., 2003), or a constant value (Orsi, 2013; Kobashi et al.,
2015). All these methods of correction generate similar surface temperature
histories (Kobashi et al., 2010, 2015). Other possible causes for the
systematic offset are related to the standardizations to the atmosphere (in
this case both nitrogen and argon isotopes can be affected) or
methodological differences during the extraction from ice samples (Kobashi et
al., 2008b). In these cases, a constant shift should be a better solution.
Some uncertainties remain regarding the bubble air pressures for the modeling
of post-coring fractionation. First, Lipenkov (2000) reported that bubble air
pressure increases toward deeper depths through the increase of ice loads,
which should have induced a decrease in δAr/N2 toward deeper
depths. However, the δAr/N2 data do not exhibit any trends
with depth (Fig. 7), indicating that some other processes (e.g, changes in
bubble diameters, S/V, and relaxation of ice after coring especially at
depths deeper than 300 m; Gow and Williamson, 1975) may have canceled the
depth effect. At even deeper depths, where the bubbles exist as clathrate,
the pressure between ice and clathrate boundaries can be estimated from the
dissociation pressures of clathrates and should be independent of depth
(Ikeda-Fukazawa et al., 2005). In future studies, it will be necessary to
consider changes in each parameter in ice cores and investigate post-coring
fractionation. Second, we identified that overloading pressure at the bubble
close-off depth plays an important role in the post-bubble close-off
fractionation in the firn. These pressure anomalies should also remain in ice
cores and play some roles for the post-coring fractionation. For example, the
relationship of δAr/N2 with temperatures and accumulation
rates in GISP2 may have been overestimated by the imprints of differential
post-coring fractionations owing to the different bubble pressures induced by
temperatures and accumulation rates at the time of the bubble close-off. Of
course, the imprints of the post-coring fractionation increase if the
duration of storage is longer at warmer temperatures, emphasizing the need
for colder storage temperatures and the timing of measurements to recover the
original signals.
For future studies on δAr/N2 or δO2/N2 in
ice cores, the following suggestions should be taken into account. First, the
solubility and diffusivity of argon, oxygen, and nitrogen in ice are not well
constrained (Salamatin et al., 2001; Ikeda-Fukazawa et al., 2005; Bereiter et
al., 2014). As precise δAr/N2 or δO2/N2
data from various ice cores are building up, the reanalyses from these cores
could provide stronger constraints on the permeability. Second, although
δAr/N2 is less susceptible to the post-coring gas loss than
δO2/N2, we have shown that ice core preservation is
critical to retrieve the original δAr/N2 signals. To preserve
original signals, ice cores need to be stored at low temperatures (ideally
<-50 ∘C) (Ikeda-Fukazawa et al., 2005; Bereiter et al., 2009;
Landais et al., 2012) and/or to be analyzed soon after the coring. Third, we
also found that the use of large ice samples (600–700 g) for each analysis
reduced the noise in δO2/N2 and δAr/N2
substantially (Headly, 2008), compared to the data from smaller samples in
GISP2 (Suwa and Bender, 2008b). This observation emphasizes the importance of
the sample size. Fourth, observations of the bubbles in the firn and ice
cores, especially of the microbubbles (e.g., numbers, volume contributions,
pressure, and gas composition), are lacking, which are critical for further
advances in understanding permeation in the firn and ice cores. Fifth, we
have shown that δAr/N2 could be estimated from local
temperatures and accumulation rates. Therefore, combined with nitrogen and
argon isotopes, it may be possible to retrieve the information of past
temperatures and accumulation rates from δAr/N2 in ice cores.
Finally, the high-resolution analyses (10–20 years) provided key
observations for the effects of the accumulation rates and temperatures on
the permeation, which warrants further similar studies along with surface
temperature reconstructions.
Conclusions
Gas fractionation after bubble close-off in the firn is complex and the
associated processes are poorly understood, especially in ice cores. In this
study, we investigated the gas permeation processes in the firn and ice cores
using high-resolution δAr/N2 data from the GISP2, NGRIP, and
Dome Fuji ice cores for the past few millennia. We found that δAr/N2 on the gas age in the GISP2 ice core is significantly
negatively correlated with the accumulation rate and positively with air
contents over the past 6000 years. Furthermore, the precise surface
temperatures (Kobashi et al., 2011) and accumulation rates (Alley et al.,
1997; Cuffey and Clow, 1997) over the past 4000 years from the GISP2 ice core
have nearly equal control on the δAr/N2 variations over the
past 4000 years with the sensitivities of
0.72 (‰ ∘C-1) and
-0.58 (‰ (0.01 m ice year-1)-1). To understand the
processes of the δAr/N2 fractionation, we applied a permeation
model (Ikeda-Fukazawa et al., 2005) in which air in the bubbles leaks out by
steric diffusion through ice crystals, driven by the pressure gradients
between the bubbles and the atmosphere. The permeation model in the firn was
applied considering two processes on the bubbles: pressure sensitive process
(e.g., microbubbles) and normal bubble process. Microbubbles are believed to
form near the surface. Therefore, by the time the microbubbles reach the
bubble close-off depth, they develop pressures as high as overloading ice
pressure that are strongly associated with changes in the accumulation rates
at the surface. Several lines of evidence indicate that the pressure
sensitive process occurs on a larger air fraction than that only from the
microbubbles. On the other hand, the normal bubbles develop slightly higher
pressures than that of the atmosphere at the bubble close-off depth such that
the permeation in the firn is limited (>-0.5 ‰). The model
also indicates that δAr/N2 of the microbubbles is negatively
correlated with changes in accumulation rates through increases in the
overloading pressures, although it underestimates the magnitude observed in
the GISP2 ice core. Colder temperatures are found to induce more depletions
in δAr/N2 through higher overloading pressure (thicker firn)
and longer exposure time to the permeation, which explains a larger depletion
in the Dome Fuji ice core. Further understanding of the gas permeation
processes in the firn may lead to a new tool for estimating the past
accumulation rates and/or surface temperatures.
Acknowledgements
We are grateful to G. Hargreaves at the US National Ice Core Laboratory,
J. P. Steffensen at the Center for Ice and Climate, S. Kipfstuhl at the Alfred
Wegener Institute, and S. Fujita at the National Institute of Polar Research for
supplying ice core information. We thank T. Uchida, and B. Vinther for
discussions, and R. Spahni for help on firn modeling. This project is
supported by KAKENHI 23710020, 25740007, 22221002, 21221002, and 21671001,
and a EU Marie Curie fellowship for T. Kobashi. The NGRIP and Dome Fuji ice
cores were analyzed at the National Institute of Polar Research by T. Kobashi
supported by the Senshin project and NIPR ice core center. The GISP2 ice core
was analyzed by T. Kobashi at Scripps Institution of Oceanography, supported
by J. Severinghaus. The early version of the paper was written when
T. Kobashi was visiting the Centre for Ice and Climate (CIC), University of
Copenhagen, in spring 2015 hosted by T. Blunier and B. Vinther. Finally, we
thank two anonymous reviewers, whose comments substantially improved this
manuscript. Edited by: W. T. Sturges
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