We estimate mean accumulation rates for the past Accumulation rates were 18 % higher during the mid-Holocene compared to
modern rates over the Amundsen–Weddell–Ross Divide. Spin-up of regional and continental ice-sheet models should include
time-varying changes in Holocene accumulation rates from the WAIS Divide ice core to generate more realistic grounding-line evolution and past sea-level rise contribution across this region.
Improving our knowledge of past climatic changes over the Antarctic Ice
Sheet is required if we are to understand its present evolution and model
its future under increasingly rapid climatic changes (IPCC, 2021). Most
studies of past ice-sheet behaviour over Antarctica have focused on
modelling changes in ice volume and grounding-line retreat following the
Last Glacial Maximum (LGM,
Many numerical ice-sheet models that aim to predict Antarctica's long-term (past and future) contribution to sea-level rise use past ice-sheet reconstructions from after the LGM to guide and evaluate their models (Chavaillaz et al., 2013; DeConto and Pollard, 2016; Bracegirdle et al., 2019). However, even well-used ice-sheet reconstructions assume that the ice sheet retreated continuously throughout the Holocene (e.g. RAISED Consortium, 2014), a finding that has been challenged recently for the WAIS (e.g. Kingslake et al., 2018). Further, significant discrepancies between model simulations and the paleoproxy record currently impede our ability to confidently predict how the ice sheet will respond to future changes in the climate (e.g. Johnson et al., 2021). While improvements in model parameterizations are needed to close this gap (Bracegirdle et al., 2019; Sutter et al., 2021), considerable improvement in the availability and quality of paleoproxy records, particularly during the Holocene, is also needed to provide better constraints for ice-sheet models and ultimately better resolve past ice-sheet changes (Kingslake et al., 2018; Jones et al., 2022). Paleoproxy data have traditionally come from point-based measurements, such as ice cores (e.g. Petit et al., 1999; Parrenin et al., 2007; WAIS Divide Project Members, 2013; Buizert et al., 2021), sediment cores (e.g. Hillenbrand et al., 2013; Arndt et al., 2017; Hillenbrand et al., 2017; Kingslake et al, 2018; Venturelli et al., 2020; Neuhaus et al., 2021; Sproson et al., 2022), or surface-exposure dating (e.g. Stone et al., 2003; Suganuma et al., 2014; Johnson et al., 2014; Hein et al., 2016; Nichols et al., 2019; Johnson et al., 2020; Braddock et al., 2022). A complementary and spatially extensive alternative data source for inferring past climate across an ice sheet is provided by internal reflecting horizons (IRHs) detected by RES. They primarily result from englacial acidity contrasts and are often detected for hundreds of kilometres on RES data (Harrison, 1973; Bingham and Siegert, 2007). When employed in combination with ice-core stratigraphies, IRHs can be used to extend age–depth relationships away from an ice core by following peaks in electromagnetic return power in the radar data (e.g. Beem et al., 2021; Bodart et al., 2021a; Cavitte et al., 2016; Jacobel and Welch, 2005; MacGregor et al., 2015; Whillans, 1976; Winter et al., 2019).
In contrast to East Antarctica and Greenland, the IRH extension of WAIS ice
cores has been challenging so far due to fewer deep ice cores there and,
until recently, the lack of well-dated IRH datasets. However, efforts have
intensified in recent years to improve our understanding of ice stratigraphy
over this sector. In particular, four recent studies using airborne RES data
(Karlsson et al., 2014; Muldoon et al., 2018; Ashmore et al., 2020a; Bodart
et al., 2021a) all identified a distinct and bright IRH dated using the Byrd
and WD14 ice-core chronologies to
Despite their potential wide-ranging applications, the incorporation of IRHs into ice-sheet models has been limited so far compared to other types of paleoproxy data, primarily because the inference of accumulation-rate or ice-flow history from IRHs is an ill-posed inverse problem (Waddington et al., 2007). Previous applications using IRHs to inform regional and continental models include the following: (a) constraining decadal-scale surface mass balance (SMB) estimates from atmospheric models using annually resolved IRHs found in the shallow firn (Medley et al., 2013, 2014; Van Wessem et al., 2018; Dattler et al., 2019; Kausch et al., 2020; Cavitte et al., 2022); (b) inferring past accumulation rates going back further in time (i.e. hundreds to thousands of years) with the aim of comparing past accumulation estimates with modern times (e.g. Leysinger Vieli et al., 2004; Siegert and Payne, 2004; Neumann et al., 2008; MacGregor et al., 2009, 2016; Leysinger Vieli et al., 2011; Cavitte et al., 2018); or (c) integrating both their characteristics (e.g. elevation in the ice) and the information inferred from them (e.g. accumulation or basal-melt rates) to evaluate the output from regional and continental ice-sheet models (Leysinger Vieli et al., 2011, 2018; Holschuh et al., 2017; Sutter et al., 2021). Promisingly, Sutter et al. (2021) recently showed that spatially extensive Antarctic IRHs can provide unique benchmarks for constraining ice-sheet model parameterizations (i.e. climate forcing and simulated ice flow), which are then used to simulate paleo-ice-sheet evolution. Together, these studies indicate multiple avenues for ice-sheet models to assimilate IRHs to further improve estimates of past, current, and future ice-sheet changes.
Here, we estimate mid-Holocene accumulation rates across the WAIS from first-order calculations using a one-dimensional (1-D) model, constrained by the spatially extensive 4.72 ka IRH. We first describe the data, the model used and their limitations and uncertainties (Sect. 2). We then present our accumulation-rate estimates and compare them to observed and modelled modern accumulation rates to reveal a longer-term perspective on changes between the mid-Holocene and the present (Sect. 3). Finally, we place our results in the context of previous studies that consider WAIS evolution during the Holocene (Sect. 4).
We used data from extensive (
Map of the datasets and key locations in this study. The three
datasets that contain the 4.72 ka IRH are colour-coded as IMIS (green), PIG
(blue), and THW (pink). IRH data where
These RES surveys were used to track and date six IRHs spanning the Late
Pleistocene and Holocene (25.7–2.3 ka BP) that collectively cover much of
the WAIS, including IMIS (Ashmore et al., 2020a), PIG (Karlsson et al.,
2014; Bodart et al., 2021a), and THW (Muldoon et al., 2018). Here, we only
consider the 4.72 ka IRH mapped in all four studies and shown in Fig. 1,
as it is by far both the most spatially extensive and the only commonly
traced IRH across all studies. We first merged all data points from the 4.72 ka IRH across the three catchments, resulting in a cumulative distance of
Characteristics of each IRH dataset used in this study that contain the 4.72 ka IRH. “Reflector 1” in Muldoon et al. (2018) is abbreviated here as “R1”.
To infer accumulation rates from the 4.72 ka IRH, we used the Nye model, a
1-D ice-flow model widely used for estimating accumulation rates and
age–depth relationships over relatively slow-flowing parts of an ice sheet
(Nye, 1957; Fahnestock et al., 2001a). This model invokes the local-layer
approximation (LLA), i.e. it assumes that the time-averaged accumulation
rate that the IRH has experienced since its upstream inception at the
surface can be adequately represented by its depth where it is observed
presently. Other 1-D models exist, including the Dansgaard–Johnsen
(Dansgaard and Johnsen, 1969) and the shallow-strain rate model (MacGregor
et al., 2016), but were less suitable for estimating accumulation rates here
due to uncertainty in the basal shear layer thickness across our survey area
and because we are limited to only one IRH to constrain the ice-flow model,
respectively. The Nye model assumes that ice thickness is constant and
therefore that the ice sheet has been in a steady state since the deposition
of the IRH, an acceptable assumption for the period under investigation
here. The Nye model states:
To quantify the suitability of the LLA which is used here to estimate accumulation rates, we calculated the effects of horizontal gradients in modern ice thickness and accumulation rates along particle paths in their ability to affect IRH depths across our grid, as per Waddington et al. (2007). Where these gradients are large, estimates of accumulation rates from IRHs likely require a more complete treatment of ice flow and its effect upon IRH depths, which multi-dimensional models and more physically complete models can better resolve (e.g. Waddington et al., 2007; Leysinger Vieli et al., 2011; Karlsson et al., 2014; Nielsen et al., 2015; Koutnik et al., 2016). However, such models are significantly more computationally expensive over such a larger area and depend on well-constrained boundary conditions from along-flow radar profiles which are not often available at an ice-sheet level (MacGregor et al., 2009).
We quantified the effect of horizontal gradients on an IRH of age
For our study area,
One of the main limitations of the Nye model is that it assumes that gradients in sliding velocity are mostly concentrated in a thin layer at the ice–bed interface and that the ice column deforms by pure shear only (Nye, 1957; Fahnestock et al., 2001a). For this reason, the Nye model is generally only appropriate for IRHs found in the upper part of the ice column, as is the case here. Additionally, the use of the model is restricted to areas where ice flow is relatively slow and horizontal strain rates are also relatively low.
Here, we focus on a shallower IRH situated in the upper part of the ice column (median: 40 %; 25th quartile: 30 %; 75th quartile: 50 %; Fig. 2b and c), for which we can reasonably assume that the ice sheet has remained close to a steady state and where IRHs are likely shallow enough not to have experienced appreciable flow disturbances that would affect the Nye model assumptions. Additionally, due to the inherent nature of tracking IRHs through RES data, our coverage is limited to areas where ice-flow speeds are relatively low and IRHs are undisturbed. In some portions of our study area, the IRH is found deeper in the ice column or in faster-flowing sections of the ice sheet (e.g. in the downstream sectors of our grid, Figs. 1 and 2b, c), both of which challenge the assumptions that the 1-D model is based upon and thus where uncertainties in accumulation estimates are likely to be higher.
Estimating uncertainty in accumulation rates from the Nye model is non-trivial. Previous studies have used the misfit between the accumulation rate calculated using multiple proximal IRHs in the ice column (e.g. Fahnestock et al., 2001a, b; Leysinger Vieli et al., 2004; MacGregor et al., 2016). Unfortunately, this method is not suitable here due to the dearth of spatially extensive IRHs younger than 4.72 ka over our model domain.
Instead, uncertainty in the Nye-inferred accumulation rates were calculated
using (a) the lowest and highest possible accumulation rates from Eq. (1)
using the age uncertainty (
This calculation provides lower and upper bounds for the IRH-inferred
accumulation rates (Fig. S4a and b), which were then averaged to generate a
relative uncertainty (Fig. S4c). From this assessment, we estimate a median
relative uncertainty in the Nye-inferred accumulation rates for the 4.72 ka
IRH of 14 % across our grid. This uncertainty is higher in the downstream
edges of our grids, particularly over the PIG, THW, and IMIS catchments, and
generally low over the Amundsen–Weddell–Ross Divide (Fig. S4), reflecting
the effect of spatially variable strain rates on the inferred accumulation
rates. When combined with the assessment of the suitability of the LLA and
exclusion of IRHs where the
Once IRH depths and accumulation rates for the 4.72 ka IRH were obtained at
regular 500 m points along RES flight paths, we filtered the results using a
moving-average Gaussian filter of length 30 samples (equivalent to
To compare our inferred accumulation estimates for the past 4.72 ka with modern values (defined here as 1651–2019), we derived information on modern accumulation rates from two sources, one modelled (gridded) and one from a series of observational (point-based) datasets.
We used modelled gridded accumulation rates from the Regional Atmospheric
Climate Model 2.3p2 (hereafter RACMO2) 1979–2019 SMB product forced at its
margin with the ERA-Interim product (native resolution: 27 km) as an
estimate for modern accumulation rates (Van Wessem et al., 2018). Although
SMB is not technically equivalent to the accumulation rate, runoff and
sublimation are negligible in our survey area (Medley et al., 2013), so we
assume that SMB is equal to accumulation rate in this region. We converted
modelled values from kilograms per square metre per annum (kg m
Observational point-based measurements were obtained from a series of snow, firn and ice cores from the ITASE (Mayewski and Dixon, 2013), MED14 (Medley et al., 2014), SAMBA (Favier et al., 2013), and SEAT-10 (Burgener et al., 2013) datasets, as well as from a network of centennially-averaged modern accumulation rates derived from shallow IRHs traced on ground-based RES data over the central divide and dated using a shallow ITASE Ice Core (Neumann et al., 2008) (Fig. 1). This resulted in 79 point-based accumulation measurements from cores covering the period 1651–2010 CE (Common Era) and spread across our model domain (see Fig. 1). Further detail on these datasets can be found in the above references.
To compare the Holocene gridded product with the point-based measurements, we first calculated the average value of the accumulation rate at the point measurement for the entire period. We converted these values to ice-equivalent accumulation rates and then extracted two paired values, i.e. the value for the point measurement for modern accumulation rates and the value for the nearest grid cell in the gridded 4.72 ka-to-present accumulation estimates to this measurement.
The final grids for depth and accumulation rates for the 4.72 ka IRH are
shown in Figs. 2 and 3. In total, these grids are made of
Gridded depths for the 4.72 ka IRH across the model domain
covering the PIG, THW, and Institute and Möller ice-stream catchments.
Figure 3 shows a comparison of the ice-equivalent accumulation rates we
inferred for the 4.72 ka IRH (Fig. 3a) and modern SMB estimates from RACMO2
(Fig. 3b). We observe that the IRH accumulation rate pattern for the last
4.72 ka is similar to the modern pattern of accumulation rates for the
Amundsen Sea sector of the WAIS, which is dominated by higher coastal
accumulation rates that progressively decrease inland to reach their lowest
rates over the Ross side of the divide (Fig. 3a and b). Differences in
accumulation rates between the 4.72 ka-to-present estimates and modern
values are mainly observed directly upstream of the main trunks of PIG and
THW, where modern rates are much higher (up to 0.2 m a
Gridded estimates of ice-equivalent accumulation rates for the
last 4.72 ka and modern times.
Comparison between our 4.72 ka-to-present accumulation-rate estimates and 79
core-derived point-based accumulation measurements for modern times
(1651–2010 CE) are shown in Figs. 3, 4, and S6. This evaluation shows that
the 4.72 ka-to-present accumulation-rate estimates for the nearest grid cell
to each point measurement are, on average, 22 % higher for cores situated
across the entire grid (
Summary statistics for the modern (modelled and observational) and
4.72 ka-to-present ice-equivalent accumulation rates at the catchment-scale
and over the Amundsen–Weddell–Ross Divide (abbreviated CD for Central Divide
here). Values for the Amundsen–Weddell–Ross Divide are for all points that
fall within 100 km of either side of the divide (see dashed line in Fig. 4).
Relative change in accumulation rates between the 4.72 ka-to-present estimates and modern rates. The points on the map represent
the relative change in ice-equivalent accumulation rate between the nearest
grid cell in the 4.72 ka-to-present grid and the 79 modern observations from
cores (Figs. 1 and S6; Sect. 2.4). The dashed black outline line represents
the 100 km boundary on either side of the Amundsen–Weddell–Ross Divide used
to provide the summary statistics in Sect. 3.1 and Table 2. The dashed
blue line shows the contours of the upper limit of the interquartile range
for the
While Figs. 3 and 4 help to assess potential differences in patterns and
rates across spatial scales, considering accumulation-rate differences in
terms of elevation can inform how topography influences accumulation and
whether this has changed over time. We binned the ice-equivalent
accumulation values by 50 m elevation bands across the three main catchments
covering our grid (Amundsen, Weddell, and Ross) for both the 4.72 ka-to-present estimates and modern model rates and calculated the mean
accumulation rate and the total accumulation rate for each bin over the
entire elevation gradient (Fig. 5). We again find that the accumulation-rate
estimates for the period since 4.72 ka are lower at low elevations
(
Comparison of ice-equivalent accumulation rates between the 4.72 ka-to-present estimates and modern rates (RACMO2) binned by 50 m elevation
bands across the three main catchments considered here (Amundsen, Weddell,
and Ross).
Previous studies of past accumulation rates over the WAIS have shown that
accumulation varied temporally during the Holocene. Using a single airborne
RES profile over the Amundsen Sea sector, Siegert and Payne (2004) showed
that accumulation rates were approximately the same at 3.1 ka compared with
modern rates, but
These studies together point to a period of increasing accumulation observed
at the WD14 from
We also find that accumulation estimates for the 4.72 ka-to-present are
smaller than modern rates in the lowest elevation bands (
We suggest that future ice-sheet modelling studies investigate the difference in accumulation rates inferred from our 1-D model using multi-dimensional flow-band models to assess effects of divergent and convergent flow on IRH depth and ultimately accumulation rates, as previously considered elsewhere in Antarctica (MacGregor et al., 2009). This could be conducted along a flowline transitioning from the slow-flowing regions directly downstream of the Amundsen–Weddell–Ross Divide to the coastal margins of our grid, particularly over THW where we observe the largest uncertainties in accumulation rates. In addition, we suggest that future modelling studies use the accumulation-rate variability from the WD14 as a climate forcing in their ice-sheet models. Koutnik et al. (2016) previously showed that the WD14 record is unique in that it provides a reliable record of accumulation-rate variability during the Holocene, which other East Antarctic ice-core records, often used to reconstruct the evolution of the WAIS, do not possess. We found that these higher accumulation rates are spatially extensive across nearly one third of the WAIS, further suggesting that the WD14 is indeed representative of the wider WAIS and can be used in regional or continental ice-sheet models as a reliable climate forcing for the region. Future regional and continental ice-sheet models should make use of this record to adjust their climatic boundary conditions to provide improved estimates of ice-elevation change and grounding-line evolution over Antarctica.
Model results from Steig et al. (2001) suggest that the maximum elevation of
the WAIS was most likely reached during the early to mid-Holocene (around
Using a flow-band model, Koutnik et al. (2016) suggested that an increase of
up to 40 % in accumulation rates for the period 9–2 ka would likely
have led to an increase in ice thickness of tens of metres during the
mid-Holocene. Although this finding was warranted by physical assumptions
around the response time of the ice-sheet interior to adjust to an increase
in accumulation in the model, it points to the potential for the divide to
have thickened by several metres over a relatively short period of time from
increased accumulation rates alone. Because the WAIS is also sensitive to
ice-dynamical changes at the ice-sheet margins (e.g. grounding-line retreat
or calving), an increase in accumulation rates in the upper part of the ice
sheet may not necessarily result in enough thickening to counteract
potential dynamical losses farther downstream (Jones et al., 2022). Conway
and Rasmussen (2009) reported that the Amundsen–Ross Divide is currently
thinning and migrating towards the Ross Sea at a speed of 10 m a
The lack of an ice-dynamical component in the model used here precludes us from evaluating any ice-surface-elevation change associated with changing accumulation rates. However, 18 % higher accumulation rates during the mid-Holocene relative to the present across 30 % of the WAIS could be consistent with an elevation increase of several tens of metres in ice thickness, according to Koutnik et al. (2016). Even if tens of metres of ice-surface-elevation change occurred, it is still unlikely to significantly affect the steady-state assumption of the 1-D model used here (constant ice thickness over time), because such changes are small (a few percent of the ice thickness) and that ice thickness exceeds 3500 m in places over our survey area.
Finally, we consider the possibility for Holocene ice thickening at the
divide from increased accumulation rates to affect downstream grounding-line
evolution. Recent evidence from ice-sheet modelling and field measurements
suggest that grounding-line retreat during the Holocene was not monotonic,
particularly at the Ross and Weddell sea sides of the WAIS (Bradley et al.,
2015; Kingslake et al., 2018; Neuhaus et al., 2021). Rather, Kingslake et
al. (2018) showed that the grounding-line position in the Ross and Weddell
sea sectors initially retreated from the LGM inland until
Our results, which provide strong and widespread evidence for higher accumulation along the Amundsen–Weddell–Ross Divide during the mid-Holocene compared with the present, support these hypotheses further, as higher accumulation rates at the divide would likely result in upstream thickening (Sect. 4.2). In the absence of ice-dynamical processes counter-balancing this increase in accumulation rates, the grounding-line should advance in these regions. However, we note that the pattern of grounding-line retreat and readvance has not been observed over the Amundsen Sea sector (Kingslake et al., 2018; Johnson et al., 2020, 2021; Braddock et al., 2022) despite the accumulation-rate increase we also observed along the Amundsen–Weddell–Ross Divide and the recent results from Balco et al. (2022). This complication may indicate that the Amundsen sector is more strongly influenced by coastal changes in ice dynamics, for which even moderate changes in accumulation rate cannot compensate.
Using a ubiquitous internal reflecting horizon found across most of the Pine Island, Thwaites, and Institute and Möller ice-stream catchments, we have estimated mid-Holocene accumulation rates in the relatively slow-flowing parts of West Antarctica, representing 30 % of total surface area of the WAIS.
By comparing our Holocene accumulation-rate estimates with a modern climate
reanalysis model and observational syntheses, we estimated that accumulation
rates across the Amundsen–Weddell–Ross Divide since 4.72 ka were, on
average, 18 % higher than modern values. Our results suggest that spatial
patterns of accumulation across the WAIS have remained stable during this
period, i.e. higher accumulation rates on the Amundsen side of the divide
transitioning to lower accumulation rates on the Ross side of the divide.
The higher accumulation rates reported here for the mid-Holocene compared to
the present agree well with earlier, spatially focused studies of
accumulation rates, all of which indicate higher accumulation rates (
The higher mid-Holocene accumulation estimates inferred here over large sectors of the WAIS occurred at a time of sustained, millennial-scale increase in accumulation rates found at the WAIS Divide ice core. This pattern indicates that the ice core is suitably representative of the climatic conditions of the wider region over time. We suggest that future regional or continental ice-sheet modelling studies base their paleoclimate forcing on modern spatial SMB products that are modulated over time using the WAIS Divide ice core record. This will enable those models to obtain a more realistic climatic forcing representative of the past conditions of the wider WAIS, and ultimately, constrain ice-sheet volume change and grounding-line evolution during the Holocene.
All the codes used to produce the results presented in this paper are
available on the GitHub page of Julien A. Bodart (
The IRH information for each of the three surveys used in this paper are
archived in open-access repositories (
The supplement related to this article is available online at:
JAB designed the study with supervision from RGB, DAY, and DDB. JAB performed the data processing, gridding, and 1-D modelling, with contributions from JAM for the modelling approach. JAB interpreted the results with input from RGB, DAY, DDB, and JAM. JAB wrote the paper, with edits from RGB, DAY, JAM, DWA, EQ, ASH, DGV, and DDB.
At least one of the (co-)authors is a member of the editorial board of
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors would like to dedicate this work to our dear friend and colleague, David G. Vaughan, who recently passed away. This study was motivated by the AntArchitecture SCAR Action Group. UTIG acknowledges the high school students who did the original AGASEA layer interpretation. We would like to thank the editor, Olaf Eisen, as well as Michelle Koutnik and an anonymous reviewer for thorough and constructive reviews, which improved this paper.
Julien A. Bodart was supported by the NERC Doctoral Training Partnership grant
(grant no. NE/L002558/1), hosted in the Edinburgh E
This paper was edited by Olaf Eisen and reviewed by Michelle Koutnik and one anonymous referee.