Volume 121, Issue 5 p. 907-924
Research Article
Free Access

Holocene accumulation and ice flow near the West Antarctic Ice Sheet Divide ice core site

Michelle R. Koutnik

Corresponding Author

Michelle R. Koutnik

Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA

Correspondence to: M. R. Koutnik,

[email protected]

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T. J. Fudge

T. J. Fudge

Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA

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Howard Conway

Howard Conway

Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA

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Edwin D. Waddington

Edwin D. Waddington

Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA

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Thomas A. Neumann

Thomas A. Neumann

Cryospheric Sciences Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA

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Kurt M. Cuffey

Kurt M. Cuffey

Department of Geography, University of California, Berkeley, California, USA

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Christo Buizert

Christo Buizert

College of Earth Ocean and Atmospheric Sciences, Oregon State University, Corvallis, Oregon, USA

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Kendrick C. Taylor

Kendrick C. Taylor

Desert Research Institute, Nevada System of Higher Education, Reno, Nevada, USA

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First published: 11 April 2016
Citations: 29

Abstract

The West Antarctic Ice Sheet Divide Core (WDC) provided a high-resolution climate record from near the Ross-Amundsen Divide in Central West Antarctica. In addition, radar-detected internal layers in the vicinity of the WDC site have been dated directly from the ice core to provide spatial variations in the age structure of the region. Using these two data sets together, we first infer a high-resolution Holocene accumulation-rate history from 9.2 kyr of the ice-core timescale and then confirm that this climate history is consistent with internal layers upstream of the core site. Even though the WDC was drilled only 24 km from the modern ice divide, advection of ice from upstream must be taken into account. We evaluate histories of accumulation rate by using a flowband model to generate internal layers that we compare to observed layers. Results show that the centennially averaged accumulation rate was over 20% lower than modern at 9.2 kyr before present (B.P.), increased by 40% from 9.2 to 2.3 kyr B.P., and decreased by at least 10% over the past 2 kyr B.P. to the modern values; these Holocene accumulation-rate changes in Central West Antarctica are larger than changes inferred from East Antarctic ice-core records. Despite significant changes in accumulation rate, throughout the Holocene the regional accumulation pattern has likely remained similar to today, and the ice-divide position has likely remained on average within 5 km of its modern position. Continent-scale ice-sheet models used for reconstructions of West Antarctic ice volume should incorporate this accumulation history.

Key Points

  • Holocene accumulation-rate history is inferred from an ice-core record
  • The inferred accumulation history is validated by radar-detected internal layers
  • Evaluating the model fit to observed internal layers constrains the ice-flow history

1 Introduction

Ice-sheet internal layers that have been accurately dated with the chronology from an intersecting ice core are currently the best data set for constraining both spatial and temporal changes in accumulation rate and ice sheet geometry on multi-millennial timescales. To infer accumulation and ice-sheet histories from these data requires an appropriate ice-flow model and can also be constructed as a geophysical inverse problem [e.g., Waddington et al., 2007; Koutnik, 2009; Steen-Larsen et al., 2010; Nielsen et al., 2015]. Solving this problem is possible because radar-detected internal reflections are assumed to be isochrones, i.e., horizons of constant age, created due to distinctive layered dielectric contrasts within the ice column. These reflections represent past subaerial surfaces that have been subsequently buried by surface accumulation, reshaped by basal melting and/or freeze-on, and displaced and strained by ice flow. Hence, these reflections preserve information about past spatiotemporal changes in those processes and may be the most accessible surviving archive of these changes. Deeper reflections contain information from further back in time, but the cumulative effects of ice flow make them more difficult to interpret.

Although data to constrain the evolution of the West Antarctic Ice Sheet (WAIS) interior are relatively sparse, unraveling the history of the region is important for reconstructing changes in past ice volume and for assessing modern and possible future changes in the ice sheet. Internal reflections detected with ice-penetrating radars provide a spatial complement to the highly resolved temporal records from deep ice cores. However, the effects of ice flow and accumulation on ice-sheet internal structure need to be considered in order to interpret layer shapes. This is especially true in the vicinity of the Amundsen-Ross ice divide in West Antarctica, where there is a strong modern surface accumulation-rate gradient across the divide, with higher accumulation on the Amundsen Sea side transitioning to lower accumulation on the Ross Sea side [e.g., Morse et al., 2002; Neumann et al., 2008]. Conway and Rasmussen [2009] found that the present-day divide is currently migrating toward the Ross Sea at a rate of 10 m yr− 1, faster than the surface velocity of ~3 m yr− 1, and thinning at a rate of 8 cm yr− 1, and they hypothesized that this modern migration is driven by changes in dynamics of the Ross ice streams. In general, fluctuations in the flow speed of Amundsen coast outlet glaciers [e.g., Rignot, 1998; Shepherd et al., 2001, 2002; Mouginot et al., 2014; Rignot et al., 2014] and the Ross ice streams [e.g., Joughin and Tulaczyk, 2002; Catania et al., 2012] may propagate hundreds of kilometers inland to change the ice velocity and ice thickness of the West Antarctic interior [Payne et al., 2004; Pritchard et al., 2009, 2012]; understanding how quickly and under what forcing the reservoir of interior ice may be drawn down is key to comprehending, and potentially anticipating, stability or instability of the entire West Antarctic Ice Sheet [e.g., Joughin et al., 2014]. The purpose of this work is to provide the most realistic estimate of the accumulation rate and ice-flow history near the divide. The accumulation rate is a fundamental parameter of climate and is an important input to ice-sheet models seeking to constrain the magnitude and rate of ice-volume change over time. The ice-flow history, in particular the history of ice-divide thickness and position, is an additional constraint on paleo-ice sheet geometry, and it impacts the interpretation of proxies in the ice core, such as δ18O [e.g., Steig et al., 2013], that may have originated away from the core site at a location with different climate conditions.

Our work stems from previous work to quantify the effect of ice advection and changes in ice geometry on ice-core records [e.g., Steig et al., 2001; Huybrechts et al., 2007; NEEM Community Members, 2013], to understand how ice-sheet internal layers are shaped [e.g., Nereson and Waddington, 2002; Hindmarsh et al., 2006; Parrenin and Hindmarsh, 2007; Martín et al., 2009], and to infer accumulation histories using internal layers and ice-flow models [e.g., Waddington et al., 2007; Leysinger-Vieli et al., 2011; Karlsson et al., 2014]. Since spatial and temporal variations in both accumulation as well as changes in ice flow act to shape internal layers, interpretations of internal-layer shapes often assume that the ice flow is stable [e.g., Leysinger-Vieli et al., 2011] or that the accumulation has not changed through time [e.g., Martín et al., 2009]. Our work is different from previous studies because we use the ice-core record and internal layers together to infer temporal variations in accumulation rate, and then we use the layers to constrain the ice-flow history.

We use the high-resolution WAIS Divide Core (WDC) [e.g., WAIS Divide Project Members, 2013] to date radar-detected internal layers that intersect the ice-core site and extend tens of kilometers upstream in Central West Antarctica. Before the WDC timescale was available, Neumann et al. [2008] used the same radar data and a different modeling approach, but they were able to interpret only select internal reflections that could be dated from the more-distant Byrd ice core (~160 km away; Figure 1). Our new work uses all 39 radar-detected Holocene internal reflections that we dated using the WD2014 chronology (depth-age scale presented in Sigl et al. [2015] and Buizert et al. [2015]). We focus on the last 9.2 kyr of the Holocene because the available geophysical data are not suitable to constrain the ice-flow history further back in time. Using ice-flow models, we determine a Holocene accumulation history for the WDC site, rather than for the varying locations upstream where ice at depth in the core was deposited. This history is spatially and temporally consistent with the ice-core data and with the observed ice-sheet internal structure. By evaluating the mismatch of modeled to observed internal layers we establish bounds on ice-divide stability and ice-flow history upstream of the WDC site.

Details are in the caption following the image
Context map of the West Antarctic Ice Sheet (WAIS; see Antarctic continent inset in left corner). Modern ice-flowlines (thin black lines; provided by the Byrd Polar and Climate Research Center) extend from the interior to the grounding lines (thick black lines [Bindschadler et al., 2011]). Study area near the WAIS Divide Core (WDC) site (star) is boxed and spans the ice divide (red lines) and the black dot marks the location of the Byrd ice core. Subsequent figures refer to the Amundsen Sea side (map left) or Ross Sea side (map right) of the ice divide. Color shading indicates ice thickness from Bedmap2 [Fretwell et al., 2013], where warmer colors represent thicker ice. Major outlet glaciers and ice streams in this region are named.

2 Data

The geophysical data and the ice core data used in our modeling are summarized below. The locations of the data sets are shown in Figures 1 and 2.

Details are in the caption following the image
(a) Locations of radar data near the WDC site discussed in this study, shown in polar stereographic coordinates. The gray contours are the surface elevation, and the vertical dashed line shows the modern location of the ice divide. The black lines crossing the divide are the surface transects defined for WDC-site selection; location of the primary ground-based radar data used in this study is along the thick black line. The red lines show the location of Operation IceBridge (OIB) airborne data in this area from 2011 [Gogineni, 2012]. The brown lines show the location of a CReSIS ground based survey from 2006 [Laird et al., 2010]. (b) Surface-velocity vectors from Conway and Rasmussen [2009] are used to estimate flowband width variations from the divide to the core site (blue lines). The available radar transect (thick black line in Figure 2a) deviates from the flowline (solid blue dots and black circles) approximately 15 km upstream of the WDC. There is significant along-ridge flow prevalent in this area that affects the flowline near the divide. Since this deviates from the radar transect, the part of the model domain used in our analyses only includes the part of the flowline shown with black circles. Width variation is shown along the entire flowline, but in our model we only use width values along the locations of the black circles. The locations of the WDC deep-core site (plus sign) and the ITASE-001 shallow-core site (multiplication sign) are also shown.

2.1 Geophysical Data

Ground-based geophysical data collected in support of the WDC site selection during the 2002–2003 and 2003–2004 austral summer field seasons are the primary geophysical data used in this study. We introduce other available ground-based and airborne data but we do not use these data in our study.

2.1.1 Surface Velocity Field

Repeat surveys (13 months apart) of a network of 98 poles using the Global Positioning System (GPS) were used to map surface topography and calculate the surface velocity field [Conway and Rasmussen, 2009]. Observed surface velocities are approximately 3 m yr− 1 near the WDC site, and the mean uncertainty in the velocity components is 0.04 m yr− 1 [Conway and Rasmussen, 2009]. The network of poles was aligned perpendicular to elevation contour lines on both sides of the divide. Here we use the surface-velocity field to determine the convergence and divergence of ice flow along the flowline to the core site (Figure 2b). The data show that flow converges from the modern divide toward the WDC site; this is incorporated into our flowband model as a width function, which is discussed further in section 4.2.1. More than approximately 15 km upstream of the WDC site, the ice-flowline from the core site to the modern divide does not follow the transect where radar data were collected. For our Holocene study we do not analyze the portion of the radar transect that deviates from the flowline (Figure 2).

2.1.2 Internal Stratigraphy and Ice Thickness

Impulse-radar systems operating at center frequencies of 1 MHz (wavelength in ice of 180 m) and 7 MHz (wavelength in ice of 24 m) were used to map internal layers and ice thickness across the region [Conway and Rasmussen, 2009]. Here we use 7 MHz and 1 MHz radar data collected along a transect that is aligned with a flowline that intersects the WDC site (Figure 2a, thick black line). Data were recorded at an average spacing of 28 m along the profile. Each record consists of several hundred stacked waveforms to improve the signal-to-noise ratio; records were located using GPS. Additional data processing includes band-pass filtering, accounting for the distance between the transmitter and receiver, and a correction for surface topography. Continuous internal reflections were traced as a function of radar two-way travel time. Two-way travel time values were converted to depth by assuming a wave speed of 168.5 m µs−1 in ice and 300 m µs−1 in air. To estimate the radar wave speed in the firn we used the measured WDC depth-density relationship and Looyenga's mixing equation [Glen and Paren, 1975] to calculate the dielectric constant of the ice/air mixture. The depth-density relationship was also used to convert geometric depths to ice-equivalent depths by calculating the height of the air column in the firn. The ice-equivalent depth of each layer at the WDC site was dated using the ice-equivalent WDC timescale (WD2014 [Sigl et al., 2015]); depths reported in all figures are ice-equivalent values. This is the same radar-processing strategy used in Neumann et al. [2008] but here we use the ice-core data from the WDC.

Figure 3 shows 7 MHz (Figure 3a) and 1 MHz (Figure 3b) echograms as a function of two-way travel time along the surface transect shown in Figure 2a (thick black line). Figure 3c shows depth profiles of traced internal layers (39 total) and the bed topography traced from these radar data. Figure 3d shows the age of layers determined from the WD2014 timescale [Sigl et al., 2015].

Details are in the caption following the image
(a) Segment of the 7 MHz radar echogram of the upper few hundred meters of the ice sheet. (b) Segment of the 1 MHz radar echogram of middepth layers and the bed reflector (traced in black). (c) Traced layers from 7 MHz data (gray layers) and the 1 MHz data (black layers) and the smoothed bed topography (solid gray line) that we use here. The deepest imaged layer (black dash-dot) is known as “Old Faithful” with an age ~17,650 kyr B.P., but is not used in this analysis; the age of the deepest layer used in this study is ~9,165 kyr B.P. (discussed as ~9.2 kyr B.P.). The dashed vertical line is the modern divide position, and the solid vertical line is the WDC site. (d) All 39 radar-traced layers were dated using the WD2014 timescale. Elevation is relative to the deepest bed value set at zero, and elevations above the bed are in kilometers of ice-equivalent values.

Interpreting the depths of radar-detected internal layers requires an estimate of the uncertainty in measured layer depths. The depth resolution (~1/4 wavelength) is approximately 6 m for 7 MHz data and approximately 45 m for the 1 MHz data. There is some uncertainty in the separation distance between the transmitter and the receiver during radar-data collection, which we estimate can result in a layer-depth uncertainty of up to ±2 m. There is uncertainty in picking layers from the waveform. Tracing travel time values of internal reflections was done manually using the MATLAB graphical interface “RadarGUI4” (developed by K. Matsuoka, K. Liu, and M. Yamamoto). Comparison of the same layer picks from multiple users indicated that the traced layer depth difference was less than ±6 m. High tracing uncertainty was primarily in cases where the strength of an individual reflection changed along the profile, making it a challenge to consistently pick. There is also uncertainty in the wave speed through the ice column, a necessary value in order to convert travel-time measurements to depth values. We assume that the uncertainty in wave speed through ice is ±2 m µs−1, which is equivalent to about 1.2% of the depth of the reflection. Summing these contributions in quadrature yields a total uncertainty that increases from ±8 m near the surface to ±32 m at approximately 1800 m (the maximum depth of the 9.2 kyr B.P. layer). A realistic estimate of the uncertainty is necessary to avoid overinterpreting layer structure. Uncertainty in the ages of internal reflections can be obtained directly from the depth uncertainty and using the WD2014 timescale. In modeling this portion of the ice sheet we use a smoothed version of the measured bed that may neglect kilometer-scale topographic variations of tens of meters, but captures multi-kilometer-scale bed variations of up to hundreds of meters. This was done because topographic variations on a scale less than a kilometer could not be confidently picked in the radar data, but topographic variations over multiple kilometers are reliably picked and are the scale of topography that is important for modeling layer shapes.

2.1.3 Spatial Gradient in Accumulation Rate

Neumann et al. [2008] used radar-detected internal layers from the upper 100 m of the ice sheet, dated with the ITASE 00-01 ice core, to show that snow accumulation is 25% higher at 25 km upstream from the WDC and that the divide position does not affect the accumulation gradient. This significant spatial gradient in accumulation rate is also inferred from near-surface layers observed by the National Aeronautics and Space Administration (NASA) Operation IceBridge (OIB) snow radar, which resolves annual layering in the firn [Medley et al., 2013]. The OIB data also show a similar accumulation gradient for the past three decades (Brooke Medley, personal communication). We use a linear approximation of the pattern inferred by Neumann et al. [2008] so as not to over-fit kilometer-scale features in the radar data (Figure 4a).

Details are in the caption following the image
(a) Modern accumulation rate and pattern (thin line [Neumann et al., 2008]) and linear approximation (thick line) used in our study. (b) Modeled ice-flow particle paths in steady state that reach a modeled 9.2 kyr layer (thick black line) calculated using our flowband model with the accumulation pattern in Figure 4a. Holocene ice in the WDC likely originated less than 15 km upstream, as indicated by following the path of a 9.2 kyr particle. The modern divide (vertical dashed gray line) is currently located 24 km upstream from the WDC (vertical solid gray line). Elevations are measured relative to the deepest point of the bed in the domain. Elevation is relative to the deepest bed value set at zero, and elevations above the bed are in kilometer of ice equivalent.

2.1.4 Additional Ground-Based and Airborne Data

Figure 2a shows the locations of all the available and relevant geophysical data in relation to the primary surface transect of radar data that we use here. These additional data provide a contextual complement to our analyses but are not used directly in this work because the radar-profile locations or the quality of imaged reflections were not sufficient.

Prior to ground-based geophysical investigations for ice-core site selection of the WDC, airborne geophysical surveys were conducted across Central West Antarctica. The Support Office for Aerogeophysical Research (SOAR) at University of Texas radar systems [e.g., Blankenship et al., 2001] collected data along multiple transects in this area [Morse et al., 2002; Matsuoka et al., 2010]. The radar profile we use in this study was collected on the ground along the same airborne SOAR line that crossed the WDC site, but the airborne data did not resolve internal reflections as well as ground-based profiles. Additional ground-based data were collected by the University of Kansas Center for Remote Sensing of Ice Sheets (CReSIS), where they imaged detailed deep stratigraphy and bed topography in the 2005–2006 austral summer field season during testing of a newly developed coherent radar system [Laird et al., 2010]. However, this gridded survey was not designed to follow flowlines and adjacent survey lines did not intersect at 90° to give crossovers, so we could not use these data in our study. Most recently, CReSIS radars on board a NASA OIB mission targeted a transect following the flowline upstream of the WDC site toward the divide [Gogineni, 2012]. Starting approximately 10–15 km upstream from the WDC site the flowline deviates from the transect where data used in this study were collected; defining a flowline across the divide in this area is a challenge due to along-ridge flow. While new information about the bed topography tens of kilometers upstream of the WDC was obtained from the OIB data following the flowline, internal reflections were not sufficiently resolved for use in our study. Since Holocene ice in the WDC likely originated less than 10–15 km upstream, the existing ground-radar transect follows the flowline to this distance from WDC and therefore can be used in our study.

2.2 Ice Core Data

The WDC site is located approximately 24 km west of the modern Ross-Amundsen ice-flow divide (Figures 1 and 2) and approximately 160 km east of the Byrd ice core site. The WDC, with drilling completed in 2011, reached a depth of 3405 m [e.g., WAIS Divide Project Members, 2013]. The ice-core record is highly resolved because the relatively high accumulation rate and deep ice result in thick annual layers. The borehole temperature gradient near the bottom of the borehole indicates that the bed is melting [Clow et al., 2012; WAIS Divide Project Members, 2013]. The oldest ice from the WDC is ~68 kyr B.P. (thousands of years before present, taken as 1950 [Buizert et al., 2015]), and annual layers are resolved for the past 31 kyr B.P. [Sigl et al., 2015]. For this Holocene study we use the layer-counted section of the WD2014 timescale [Sigl et al., 2015] to date internal layers back to 9.2 kyr B.P..

2.2.1 Ice Core-Derived Accumulation Rate History

The ice-core timescale can be used to infer the ice core accumulation rate if the amount of layer thinning over time is known. This accumulation rate (in meters ice equivalent per year) as a function of time t is given by urn:x-wiley:21699003:media:jgrf20539:jgrf20539-math-0001, where Λ is the layer-thinning function calculated using an appropriate ice-flow model and λ is the layer thickness measured from the ice core. The thinning function is defined as Λ(t) = 1 − ε(t), where ε(t) is the cumulative strain history of the ice layer.

A summary of the method and results for the WDC-derived accumulation history used here are given in Buizert et al. [2015]; here we provide only a brief synopsis of that work. A one-dimensional (1-D) thermomechanical ice-flow model was used to determine the amount of thinning experienced by layers in the ice core and that thinning function was then used to infer the accumulation rate from the ice-core timescale. The accumulation-rate history and thinning function were constrained with additional data from the ice core. First, the accumulation history must be consistent with the borehole temperature profile and the surface temperature history based on the water stable isotope record. Second, the δ15N isotopic ratio of N2, a proxy for firn thickness [Sowers et al., 1992], was used with a thermomechanical firn-densification model to estimate past accumulation rates given the surface temperature history [Buizert et al., 2015]. Ice-flow model parameters were optimally inferred by minimizing the misfit between the modeled and measured borehole-temperature profiles, and between the accumulation rate inferred from the ice-flow model and the accumulation rate inferred from the firn-densification model.

The accumulation-rate history inferred in this way is termed the ice core accumulation rate because it is the amount of ice accumulation at the surface location where ice in the core originated upstream (as in Figure 5) at the time that the snow was deposited. This is different from the climate accumulation rate, which refers to the amount of ice accumulation at a fixed location on the ice surface (e.g., the WDC site). Since there is an accumulation gradient upstream of the WDC site, and because the core was drilled on the flank of the modern ice divide, the ice core and the climate accumulation rates are not the same. In the next section we discuss how to infer the climate accumulation rate at the WDC site from the ice core accumulation rate.

Details are in the caption following the image
Ice-core layers record accumulation rate at a point that moves across the ice sheet surface through time, but we want to learn about climate at a fixed location. (a) Annually resolved accumulation-rate history inferred from the high-resolution annual WDC record (gray). Values are in m yr−1 ice-equivalent (ice-eq). Smoothing with a 100-year moving-average filter produced the “ice-core accumulation rate” history (thin black line). This curve gives accumulation rate through time along the trajectory of origin points for ice samples recovered in the core. (b) A 1-D ice-flow model that included a correction factor for advection of ice from upstream was used to derive the “advection-corrected climate accumulation” history (thick black line) at the WDC ice core site.

3 Methods

3.1 Advection Correction

As an example of why the ice core accumulation rate history differs from the climate accumulation rate history at the WDC site, Figure 4b illustrates modeled paths of Holocene ice particles reaching the core for an ice sheet in steady state with the modern accumulation rate shown in Figure 4a. Over the past 9.2 kyr, ice particles in the core likely originated 10–15 km upstream, where the accumulation rate is different from that at the core site. Over this 15 km distance the modern accumulation rate varies from ~22 cm yr− 1 at the WDC to ~25 cm yr− 1 upstream. Deriving a climate accumulation rate history from the WDC data and a 1-D ice-flow model requires a correction for the advection of climate conditions from where the ice in the core originated upstream. We make an initial advection correction using three simplifying assumptions: (1) the relative spatial gradient in accumulation has not changed through time, (2) the modern ice-flow pattern has not changed through time, and (3) the ice in the upper half of the ice sheet moves at the same speed as the measured surface velocity.

To determine the advection correction, we first estimate the location on the surface where ice in the WDC originated. Using the surface-velocity measurements [Conway and Rasmussen, 2009], the upstream origin of ice at 1000 year timesteps is shown as blue dots in Figure 2b. Then we need to determine the ratio of the accumulation rate at the origin location to the accumulation rate at the core site; the ratio is the advection correction factor. The climate accumulation rate is determined by dividing the ice-core accumulation rate by the advection correction. The ice core accumulation rate and climate accumulation rate smoothed with a 100 year moving-average filter are shown in Figure 5a, and the advection correction that we used is shown in Figure 5b. As expected, the magnitude of the advection increases with age as older (deeper) ice originated progressively further upstream from the core site where accumulation rates are higher. The advection correction provides an initial estimate of the climate accumulation rate (Figure 5a, red line) but may be inaccurate if the three simplifying assumption are invalid. The advection correction is commonly used to obtain a climate record from an ice core record, but for the first time we test the validity of this assumption at the WDC site by using a multi-dimensional (flowband) ice-flow model.

3.2 Flowband Ice-Flow Model

In previous work we developed and applied a time-varying flowband model that efficiently balances the capability and simplicity necessary for this problem [Koutnik and Waddington, 2012]. This flowband model is a 1.5-D representation of the ice surface and a 2.5-D representation of the ice-flow field, where the half dimension is a parameterization to account for transverse strain rates along the flowline. Model-domain boundaries are defined by two adjacent flowlines, and the distance (width) between these two flowlines is represented by the width function. The model volume is bounded vertically beneath these flowlines. The extent of our flowband model domain is limited to the interior of the ice sheet where data to constrain the model exist and where internal reflections that we want to match have been observed by radar.

The bed topography is determined from the radar data, and the width function is determined from the surface velocity field; the choice of width function is discussed in section 4.2.1. The ice-temperature field is prescribed by applying the borehole-temperature profile from the WDC site [Clow et al., 2012; WAIS Divide Project Members, 2013], including the multicentennial average surface temperature at the core site (approximately −30 °C [e.g., Orsi et al., 2012]), spatially across the model domain as a function of the thickness.

Ice flow is described by the Shallow Ice Approximation [e.g., Cuffey and Paterson, 2010, pg. 322], which applies broadly in the ice-sheet interior except within the divide zone a few ice thicknesses from the divide where the stress regime is different [Raymond, 1983]. While our study domain includes flow near the divide, we do not compare modeled with observed internal structure in the divide zone. The oldest Holocene-aged ice particles that reach the WDC site started on the ice surface approximately 10–15 km upstream from the core site (shown for steady state in Figure 4b), which is still at least 10 km from the modern divide position. Also, internal reflections imaged by the 1 MHz radar do not show arched stratigraphy beneath the modern divide (or elsewhere in the area) that would be indicative of stable divide flow, and Conway and Rasmussen [2009] showed that the modern divide is migrating and thinning. Uncertainty in the history of divide position complicates modeling paths of particles that originated in the divide zone.

Assuming that the ice sheet begins in steady state at the first model timestep, required initial and boundary conditions for the flowband ice-flow model include (1) the ice flux entering or leaving the domain at one boundary at the first model timestep, (2) externally forced changes in ice flux across the model-domain boundaries (see Koutnik and Waddington [2012] for additional details), (3) the spatial and temporal accumulation rate, and (4) the ice-surface elevation at one point along the domain at the first model timestep. Initial conditions 1, 2, and 4 are chosen so that the modeled steady state ice sheet geometry is consistent with the observed modern ice sheet geometry where ice thickness at the divide is the same as our best estimate of the modern divide thickness (~3300 m) and divide position is the same as the modern position (at ~15.5 km along our model flowband). Changes in ice flux over time due to significant ice-sheet change originating external to our limited-domain model of the ice-sheet interior are not included because we do not have a good way to quantify how near-margin changes during the Holocene affected the ice-sheet interior. While it is possible that near-margin changes in the late glacial and early Holocene have influenced interior flow, in section 4.2.2 we show that on average it is likely that the Holocene divide has remained within a few kilometers of the modern position. Therefore, changes in ice flux that can drive changes in divide position and ice thickness were likely relatively small.

Time variation in accumulation rate is inferred from the WDC record (Figure 5), and we assume that the pattern of accumulation across the divide (Figure 4a) has not changed significantly in the Holocene. We scale the climate accumulation rate inferred from the WDC record (Figure 5a) to the modern accumulation pattern (shown in Figure 10a). Using these initial conditions and boundary conditions the flowband model calculates the time-varying ice surface and ice-velocity fields; if the accumulation rate changes in time then the surface elevation will also change in time (Figure 10b). Internal layers are generated by tracking ice particles through the time-varying ice sheet by integrating the velocity field over an amount of time equal to the prescribed age of each layer. Modeled layer ages have the same ages as observed layers, and the modeled layer depths are compared to observed depths in order to evaluate the prescribed accumulation rate history and the values of select flow-model parameters.

4 Results

The methods presented above generate an estimate of the climate accumulation-rate history from the high-resolution WDC record (section 3.1) that is needed as a boundary condition to drive our flowband model (section 3.2); finding the best estimate of the climate accumulation history is a goal of this work. By comparing flowband-modeled internal layers to observed internal layers we can evaluate the correctness of the climate accumulation rate history derived from the ice-core record. To do this we analyze results from targeted flowband model runs. We do not infer the climate accumulation-rate history directly from the flowband model by solving an inverse problem because the accumulation history cannot be uniquely constrained by matching modeled to observed internal layers when ice-flow conditions over time are also unknown (see section 5.3).

4.1 History of Holocene Accumulation Rate

We quantify the correctness of our estimates of the accumulation history based on the ability to match observed internal structure within the layer-depth measurement uncertainties. To do this we prescribe an accumulation-rate history as a boundary condition in our flowband model to generate modeled internal layers with the same ages as the observed internal layers dated from the ice core. The only time-varying parameter that we consider is the accumulation rate. For these cases we assume that there is 1 cm yr− 1 of basal melting, which is consistent with the upper estimate of the basal-melt rate inferred from WDC observations [Clow et al., 2012; WAIS Divide project members, 2013]. Assuming that our ice-flow model adequately represents the flow field (sections 3.2 and 4.2), we can evaluate if a particular accumulation rate history is consistent with internal structure by evaluating the mismatch between modeled and observed internal layers. We want to fit layers within the observed layer uncertainty of ±8 m for the shallowest layer to ±32 m for the deepest layer (section 2.1.2).

Interpreting the fit to observed layers at the divide and on the Amundsen Sea side is challenging due to uncertainties in the flowline location. To realistically model ice flow near the divide requires accounting for a significant component of along-ridge flow and knowing the bed topography along the flowline from the divide to the core site. We do not currently have the necessary data available to do this well (see Figure 2), and the divide position may not have been stable over the past tens of thousands of years. Since we are focusing on the Holocene, we interpret mismatches in a portion of our study domain from the WDC site to approximately 15 km upstream where Holocene ice in the core originated. This is the region where our flowband model can best represent the flow field.

The simplest assumption about the Holocene history of accumulation rate in the vicinity of the WDC site is that the modern accumulation rate and pattern remained the same over the past 9.2 kyr B.P.; the ice sheet in this region is in steady state. However, we do not expect the steady-state assumption to produce a good match to the internal layers based on the accumulation history inferred by Neumann et al. [2008]. Figure 6a shows the contoured mismatch between modeled and observed layer depths assuming that the accumulation rate remained in steady state over the past 9.2 kyr, where negative mismatch (cool colors) means that the modeled layers are too shallow and positive mismatch (warm colors) means that the modeled layers are too deep in all panels. Indeed, the fit is not good; mismatches across the domain are up to 175 m and mismatches 10–15 km upstream of the WDC are up to 95 m. The thick dashed line in Figure 6 shows the approximate path of a 9.2 kyr particle that reaches the WDC site (from Figure 4b) and highlights the portion of the domain over which we want to minimize the mismatch between modeled and observed layers to within the layer-depth uncertainty.

Details are in the caption following the image
Contoured layer-depth mismatch between modeled and measured layer depths; the value of layer mismatch goes from −180 m to +180 m, the warm colors mean that modeled layers are too deep, and the cool colors mean that the modeled layers are too shallow compared to observed layers. The thick dashed line is path of 9.2 kyr particle that reaches the WDC site in steady state (as in Figure 4b) and designates the portion of the domain that we analyze the mismatch. (a) Accumulation rate is assumed to be steady at the modern rate with the same spatial pattern (Figure 4a) over the 9.2 kyr period. (b) Accumulation rate is assumed to vary in time following the accumulation history inferred directly from ice-core data (Figure 5a), with the same spatial pattern (Figure 4a) over the 9.2 kyr period. (c) Accumulation rate is assumed to vary in time following the accumulation history inferred from ice-core data but corrected for advection (Figure 5a), with the same spatial pattern over the 9.2 kyr period. In this case, modeled and measured layer depths match within the uncertainty, which increases from ±8 m for shallow layers to ±32 m for the deeper layers in our study across the study region, and also through all depths at sites upstream of the WDC where Holocene ice originated. However, mismatch near the modern divide and on the Amundsen Sea side of the divide remains large; as expected, our model assumptions do not apply in these areas.

Next, we use the ice-core accumulation rate history and then the climate accumulation rate history inferred from the WDC record (Figure 5a) to force the flowband model. Figure 6b shows the contoured mismatch between modeled and observed layers using the ice-core accumulation-rate history. While the fit to observed layers improves at shallower depths, the mismatches at greater depths and near the WDC site remain high. Figure 6c shows that using the climate accumulation rate history further improves the match, especially in the vicinity of the WDC site. This shows that neglecting the advection correction results in modeled Holocene layers upstream of the WDC that are too deep by up to 110 m. The profile of the layer-depth mismatch at the WDC site using these three different accumulation-rate histories is shown in Figure 7.

Details are in the caption following the image
Vertical profiles of layer-depth mismatch at the WDC site are shown from three different model runs: one assumes a steady state accumulation history (as in Figure 6a), another assumes the ice core accumulation history estimated from the WDC (as in Figure 6b), and the third is the climate accumulation history that includes a correction for advection (Figure 6c). The gray band shows the layer-depth uncertainty range (±8 to ±32 m from the shallowest to the deepest layers).

Our primary result is that using the advection-corrected climate accumulation rate history in a simple flowband model can match observed internal layers upstream of the WDC where Holocene ice in the core originated (Figures 6c and 7b). Our 2.5-D model match to the observed internal layers gives confidence that the accumulation rate inferred from the ice-core record that has been corrected for thinning using a 1-D model and also corrected for advection is consistent with the ice sheet internal layers. While the available radar layers in the vicinity of the WDC site are matched within the measurement uncertainties, in section 4.2 we show that different values of flow-model parameters change the mismatch profile. Since we are not trying to match the layers exactly, and since plausible changes in flow-model parameter values lead to meaningful changes in the mismatch, we cannot further reduce the mismatch between modeled and observed layers by only adjusting the accumulation-rate history. Therefore, we consider that the climate accumulation rate history we inferred is a robust estimation that is consistent with the internal stratigraphy and the ice-core record.

We find that the lowest accumulation rates are observed at the beginning of the 9.2 kyr record, after which accumulation increases to a maximum between 4 and 2 kyr B.P.. The accumulation rate then decreases from 2 kyr B.P. to the modern values. The accumulation rate has been greater than today for the past 6 kyr. The maximum accumulation rate was 20% greater than today and was at this rate approximately 2.3 kyr B.P.; the modern accumulation rate at the WDC is ~0.22 m yr−1 and a 20% increase gives ~0.265 m yr−1. This result is similar to Neumann et al. [2008], who found that accumulation rate was 30% higher between 3 and 5 kyr B.P.. The younger ages and lower maximum values are likely due to the more accurate age-scale from the WDC. In contrast with Neumann et al. [2008], we find that the accumulation rate prior to 6 kyr B.P. is lower than modern values, which is also likely due to using a more accurate age scale and more accurate accounting for advection of ice from upstream. Compared to previous estimates of the accumulation history across Central West Antarctica, our new results are derived directly from the high-resolution WDC record and take into account the influence of parameters needed to describe the ice-flow field (section 4.2), and we provide an estimate of the uncertainty (section 4.3).

4.2 Influence of Ice-Flow Model Parameters

While different accumulation-rate histories produce different depths of modeled internal layers, different ice-flow model parameter values also have an influence on the modeled layer depths. Here we explore the independent impact of three different ice-flow model parameters that are not exactly known in this problem: flowband width, ice-divide position, and basal melt rate. These are prescribed using an average value through the Holocene (they do not change as a function of time over the past 9.2 kyr), and the initial ice thickness is set to the modern value and allowed to evolve in response to the accumulation history. The results below all use the climate accumulation rate history and are evaluated with respect to the case using our best estimate of the flowband model parameters (used in Figures 6 and 7).

4.2.1 Flowband Width

There are at least two challenges in adequately prescribing the variations in the width of two adjacent flowlines (the flowband width function) upstream of the WDC: limited surface-velocity measurements are available to define the ice-flow field, and the width function may have changed in time. In particular, we do not have enough surface-velocity measurements to adequately estimate width variations in the vicinity of the ice divide and across the divide toward the Amundsen Sea. In the areas upstream of the core site where width variations could not be estimated we assumed that the problem could be reduced to a flowline (i.e., the flowband width does not vary). Figure 8 (cases 1–3) shows that assuming the flow field is either divergent or has no convergence toward the core site gives a poorer fit to observed layers near the core site. Assuming more convergence of ice flow toward the core site gives a similar fit to observed layers.

Details are in the caption following the image
Eight additional independent model runs (colors) are compared to our run using the climate accumulation rate (Figure 6c; shown with black dots and black line). (a) Vertical profiles of mismatch at the WDC site are compared in order to evaluate model assumptions of flowband width, ice-divide position, and basal melt through the Holocene. The gray band is the layer-depth uncertainty range (±8 to ±32 m). (b) Cases 1, 2, and 3 use different flowband widths. (c) Cases 4 and 5 place the divide 10 km or 5 km farther from the WDC site (toward the Amundsen Sea) for the past 9.2 kyr, compared to its modern position. Cases 6 and 7 place the divide 10 km or 5 km closer to the WDC site (toward the Ross Sea) for the past 9.2 kyr, compared to its modern position. (d) Case 8 has no basal melting, compared to a basal melting rate of 1 cm yr−1 in the preferred run (black dots). Only cases 3 and 8 give a mismatch between modeled layers and observed layers that falls within our measurement uncertainty.

4.2.2 Ice-Divide Position

The divide is migrating today [Conway and Rasmussen, 2009], and it is likely that it has migrated in the past. The Central West Antarctic divide position is controlled by both the spatial pattern of accumulation and by ice dynamics, and near the WDC site the divide may migrate in response to changes in the flow of Thwaites Glacier or Kamb Ice Stream. Figure 8 (cases 4–7) compares model runs where the Holocene divide is assumed to be stationary at a position either 5 km or 10 km closer to or farther away from the WDC site compared to the modern position. To change the modeled divide position we changed the prescribed value of ice flux at the model-domain boundary and the surface elevation initial conditions in order to generate ice sheet geometries with comparable divide elevation, but with different divide position. To achieve this the value of flux entering the domain was changed by up to 30% and the surface elevation at the domain boundary was changed by up to 20 m. A robust conclusion is that the match is significantly worse assuming that the Holocene divide position has been 5–10 km farther away from or closer to the WDC site. Case 5 assumes that the divide is 5 km farther from the WDC site (toward the Amundsen Sea) and indicates that the model-data agreement may be somewhat better assuming that the ice divide has been on average a few kilometer farther from the modern position, but that cannot be robustly determined. If the Holocene divide position was consistently more than 5 km from its modern position then this effect on layer depth must have been compensated by a change in another parameter.

4.2.3 Basal Melt

The ice at the bed beneath the WDC is at the pressure melting point and is likely melting. Optimized models indicate a melt rate of a few mm yr−1, and separate studies estimate a rate of up to 1 cm yr−1 [Clow et al., 2012; WAIS Divide project members, 2013]. We use a melt rate of 1 cm yr−1 in our standard case, and case 8 in Figure 8 shows the impact of excluding basal melt along the entire flowband. Not accounting for basal melting gives a worse fit. It is worth noting that the impact of melting on the layer thicknesses is greatest near the bed, while our study only investigates the upper part of the ice sheet. In addition, the observed depth-age relationship and temperature profile in the WDC deep ice provide more reliable constraints on the basal melt rates than our inference based on internal layers.

4.3 Uncertainty in the Inferred Accumulation-Rate History

Since modeled layer depths are sensitive to inexactly known ice-flow model parameters, it is not straightforward to quantify the uncertainty in the climate accumulation-rate history that we infer from the ice-core record by evaluating the mismatch to internal layers. However, we can roughly estimate the uncertainty by evaluating the assumptions required to infer the climate accumulation-rate history. The two main assumptions are (1) the choice of thinning function used to convert WDC layer thicknesses to the ice core accumulation-rate history and (2) the choice of advection correction used to convert the ice core accumulation rate history to the climate accumulation rate history.

The thinning function applied here [Buizert et al., 2015] was calculated using a 1-D flow model to be consistent with high-resolution WDC records (section 2.2.1). Using the climate accumulation-rate history inferred with this thinning function, we have also calculated the thinning function from the flowband model. Since this calculated ice-flow field, and therefore the thinning function, changes for different flow-parameter values, we evaluate the thinning function only for our best estimate (Figure 6c and black dotted line in Figures 7 and 8) that has width variations, divide position, and basal-melt rate similar to modern conditions. Using this thinning function from the flowband model to convert WDC layer thicknesses to the ice-core accumulation rate history alters the accumulation values by 0–8%, where the difference increases almost linearly back in time from 0 to 9.2 kyr B.P.. We evaluated multiple iterations of calculating a thinning function from the flowband model and using this to update the accumulation-rate history, but in this case differences in the thinning function using iteratively updated accumulation-rate histories were insignificant after three iterations.

We also evaluate the uncertainty in the accumulation-rate history from the advection correction. If the assumptions required to calculate the advection correction (section 3.1) are not valid, the advection correction could overestimate or underestimate the climate accumulation-rate history. We compared the advection correction calculated using the flowband model to our simple estimate and found that the difference was only up to 2% at 9.2 kyr B.P.

Considering the uncertainty in the thinning function and in the advection correction, an uncertainty of up to ±10% at 9.2 kyr B.P. is our rough estimate of the actual uncertainty for our inferred Holocene climate accumulation-rate history. However, for the best estimates of flow-model parameters and using an accumulation-rate history that linearly increased or linearly decreased back in time by 0–10% compared to our inferred climate accumulation-rate history (Figure 5) does not give the same quality of model fit to the observed internal layers. So within our ability to quantify the climate accumulation-rate uncertainty, if the actual accumulation history was 10% higher or 10% lower than our best estimate then a different set of flow-model parameters is needed in order to achieve a comparably good fit to the internal layers as in the case using our best estimates; however, we do not have enough information to discriminate between ice-flow and climate histories at this level.

5 Discussion

5.1 Implications of Changes in Holocene Accumulation Rate

Prior to drilling the WDC, our understanding of accumulation rate change across Central West Antarctica throughout the Holocene was limited. Shallow ice cores (to depths ~100 m) have been drilled across West Antarctica, providing decadal-to-annual resolution for the past century-to-millennia [e.g., Dixon et al., 2004; Kaspari et al., 2004]. Inference of the Holocene accumulation rate from previous deep ice cores from West Antarctica (Byrd and Siple Dome) is challenging because of uncertain ice-flow histories [Steig et al., 2001; Waddington et al., 2005; Price et al., 2007] and less precise timescales [Hammer et al., 1994; Taylor et al., 2004]. Similarly, variability in Holocene accumulation cannot be reliably reconstructed from East Antarctic cores due to the low-precision timescales in which a scaling relationship between accumulation rates and water stable isotopes needs to be assumed [e.g., Bazin et al., 2013; Veres et al., 2013]; the fidelity of the accumulation-rate/stable water isotope relationship is unclear [e.g., van Ommen et al., 2004; Parrenin et al., 2015]. Therefore, the WDC climate accumulation rate provides the most reliable inference of Holocene accumulation in West Antarctica. Validating the accumulation rate history against ice sheet internal layers gives confidence in these values and that they can be used as part of interpretations of Antarctic climate and ice-sheet history [e.g., Frieler et al., 2015; Hall et al., 2015].

A challenge common to all ice-core derived accumulation-rate histories is that they are essentially point measurements, and it is unclear how large of an area they represent. Radar-observed internal layers can be tracked across much of West Antarctica [e.g., Siegert and Payne, 2004], but inferring the accumulation-rate history from these layers can be limited by imaging few continuous layers and complicated flow conditions away from divides. However, our work has the advantage of using the high-resolution WDC record, and by focusing on the Holocene there are numerous internal layers detected in the available radar data. We show that the WDC-derived accumulation history is consistent with layers extending at least 15 km upstream of the ice core site, which indicates that the ice core point record is more generally representative over this portion of Central West Antarctica. Fudge et al. [2016] showed that accumulation rate variations at the WDC site over the past few decades are well correlated with accumulation rate variations across much of Central West Antarctica.

The inferred ~40% increase in accumulation between 9 and 4 kyr B.P. is nearly half of the assumed deglacial increase for Antarctica [e.g., Parrenin et al., 2007] and occurs at a similar rate. As shown in Figure 9, the millennial-scale Holocene variability is also much larger than that inferred from East Antarctic cores where the structure is primarily dictated by the stable-isotope record [e.g., Parrenin et al., 2007; Bazin et al., 2013; Veres et al., 2013]. The Dome C and Vostok ice-core records, which are commonly used to force ice-sheet models [e.g., Huybrechts, 2002; Pollard and DeConto, 2009; Whitehouse et al., 2012], show little variability during the Holocene. We emphasize that the Holocene variability that we inferred near the divide should be accounted for in the boundary forcing used to drive continent-scale ice-sheet models. Important questions are whether the Holocene variations in accumulation rate at WDC also occurred over a wider region of Antarctica, and what was the driver of these changes? This is a new challenge to understand with global climate models. In addition, using our validated accumulation rate history Fudge et al. [2016] showed that the relationship between accumulation rate and temperature from the WDC record is not consistent on centennial to multi-millennial timescales. This is in contrast to the coherent temperature-accumulation relationship currently used in global climate models, which points to the need to better understand how atmospheric circulation drives accumulation across Central West Antarctica.

Details are in the caption following the image
Accumulation rate normalized by the mean of the accumulation rate over the most recent 500 years from the WDC (black), compared to four other Antarctic ice cores: Dome C (blue), EDML (magenta), Talos Dome (green), and Vostok (red); data from Bazin et al. [2013] and Veres et al. [2013]. Holocene accumulation rate at WDC is the highest and the most variable of all these sites.

5.2 Implications of Stable Holocene Divide Position

All the flowband model cases that we analyze include plausible estimates for unknown model parameters but some scenarios improve the modeled match to observed layers, and some scenarios do not; in this case we learn from what scenarios do not improve the model fit. We did not search the entire model-parameter space but instead evaluated select, plausible changes in model-parameter values. While the Holocene history of ice-divide position cannot be resolved in detail, we find that the average position of the ice divide was likely within a few kilometers of the modern position throughout the Holocene. This is broadly consistent with Holocene stability inferred for the Amundsen-Weddell ice divide [Ross et al., 2011] and could imply that centennial-scale fast-flow events from major WAIS outlet glaciers [e.g., Johnson et al., 2014] and/or the Ross ice streams [e.g., Catania et al., 2012] did not significantly alter interior ice geometry during the Holocene. This means that the driver of the large-scale pattern of accumulation across Central West Antarctica (high accumulation at the Amundsen Sea coast transitioning to lower accumulation across the Ross Ice Streams) should be investigated using our new understanding that the Holocene accumulation pattern has likely remained similar to the modern pattern near the Central West Antarctic divide. In addition, we find that modeled layer depths were sensitive to flow convergence, and in general, to ice flux, from near the modern divide toward the core site. Including basal melting improved the match between modeled and observed layers, yet the Holocene layers alone do not constrain the rate of basal melting.

5.2.1 Implications for Ice-Surface Elevation

The ice thickness during the early Holocene is poorly constrained but changes in interior ice thickness since the last glacial are likely to have been on the order of 100 m [e.g., Steig et al., 2001]. Therefore, the simplest assumption is that the ice-surface elevation at 9.2 kyr B.P. is similar to the ice thickness today. Since our inferred accumulation history is lower at 9.2 kyr B.P., in our flowband calculation the interior ice first thins, and then thickens as the accumulation rate increases through the mid-Holocene as shown in Figure 10b. The changes are small (a few percent of the total ice thickness) and do not significantly affect the inferred accumulation rate history. The choice of initial thickness results in a different evolution through the Holocene, indicating that our modeling cannot accurately constrain the Holocene variations in ice thickness. Additionally, the modeling assumes that the flux at the boundaries of the flowband is affected only by the changes in interior accumulation rate and does not account for variations in flux due to changes outside of our limited model domain of the ice sheet [Koutnik and Waddington, 2012]. For these reasons, our calculated thickness history cannot be used as an estimate of what actually occurred during the Holocene. But, an accumulation rate increase of up to 40% in a few thousand years, if spatially extensive, would cause the WAIS to thicken, possibly at a rate comparable to Figure 10b. However, the thickening due to increased accumulation rate may be counteracted by ongoing grounding line retreat and increased discharge related to ice dynamics forced near the ice sheet margin. However, without prescribing changes in ice dynamics, the interior ice thickness must change in response to changes in accumulation rate; with changes in ice dynamics the interior ice may thicken more, thin more, or remain the same.

Details are in the caption following the image
(a) Climate accumulation rate history from Figure 5a, scaled by the modern accumulation rate from Figure 4a (scaling factor equals 1 for the modern). (b) Change in ice thickness calculated using the flowband model with the accumulation history from Figure 10a and assuming that the initial condition for this 9.2 kyr run was a steady state ice sheet with modern accumulation back at that time. Due to this initial condition, the ice immediately thins in response to lower accumulation 9.2 kyr B.P. and then thickens when accumulation rate increases in the late Holocene. Since the ice-sheet configuration in the early Holocene is unknown, other initial conditions cannot be better justified, and we use this simple assumption (see sections 3.2 and 5.2). However, since the accumulation history, the ice-flow history, as well as the ice sheet initial state are all unknown, we cannot determine or bound the actual Holocene surface-elevation history without additional information. This calculation is shown to emphasize that ice-thickness changes as accumulation-rate changes, unless compensated by other controls on interior ice-sheet geometry.

5.3 Solving an Inverse Problem

In this work we solve a suite of forward problems (runs of our ice-flow model) in order to constrain accumulation rate and ice-flow history by testing targeted hypotheses. This was a successful strategy, but, in general, this objective could also be met by solving an inverse problem. In an inverse problem, observable quantities result from known processes that depend on unknown parameter values that we wish to reconstruct. This framework is a powerful tool for understanding geophysical processes [Menke, 1989; Parker, 1994], but issues concerning solution existence, solution uniqueness, and algorithm stability must be evaluated for every problem [Aster et al., 2005]. To jointly infer changes in past ice flow, ice-sheet thickness, and accumulation rate from the shapes of radar-detected internal reflections it is necessary to solve an inverse problem [Waddington et al., 2007; Koutnik, 2009]. Each of these parameters may be better constrained through solving inverse problems: patterns and histories of surface accumulation rate and basal melt/freeze-on rate, history of ice thickness and ice-divide position, history of ice flow and ice rheology, and geothermal flux. However, due to the inherent nonuniqueness of inferring multiple spatiotemporally varying parameters from dated internal reflections, highly reliable assumptions and constraints are required to construct tractable problems.

In previous work, we tried solving the formal inverse problem to infer the history of accumulation, ice thickness, and divide position from layers near the WDC site [Koutnik, 2009]. Finding a unique solution for the jointly unknown accumulation and ice-flow histories is a challenge when accumulation changes and flow changes may both have occurred and may have similarly altered layer shapes. Most importantly, the solution to the inverse problem is only as good as the forward model that is capable of generating realistic estimates of the observed internal layers. The flow field more than 15 km upstream of the WDC, and therefore the flowband model, is poorly constrained. Figure 8 demonstrates the nonuniqueness evident between forward model runs with plausible values of unknown model parameters. In this case, instead of attempting to solve a single inverse problem to infer many or all of the inexactly known flow parameters in addition to the accumulation history, we isolate the key unknowns while prescribing all other values and evaluate targeted forward runs. While probabilistic inverse methods (e.g., Monte Carlo methods) can be used to statistically evaluate a multi-parameter solution space, this effort is most worthwhile if simple estimates of the ice-flow and climate histories cannot match the available internal layers within their uncertainties.

There is an inherent challenge to infer accumulation-rate history from internal layers: the accumulation rate history and the ice-flow history are often both poorly constrained, and both histories may leave an imprint on ice sheet internal structure. Independent data sets (e.g., ice core bubble-number density [Fegyveresi et al., 2011]) may constrain the accumulation-rate history, and other data sets may constrain the ice-flow history, but inferring the accumulation-rate history requires assumptions about the ice-flow history, and vice versa. The appropriate assumptions are site specific, and different assumptions may be valid for different problems. For the problem near the WDC site considered here, we focus on inferring centennial-scale variations in accumulation through the Holocene. We are able to make reasonable assumptions about the flow field over this time period, and we evaluate the sensitivity of our solution to these assumptions. We can learn from ice-sheet configurations and climate histories that match available internal layers, and also from those that do not match, and we are able to draw robust conclusions.

While the Holocene is relatively well constrained, at this site we cannot validate the ice core-derived accumulation rate history further back in time than 9.2 kyr B.P. because we do not have radar-detected stratigraphy along a transect following the likely flowline, which is necessary to model paths of ice particles that originated farther upstream. Even if such radar data were available, further back in time it becomes more likely that the ice-sheet geometry and/or the accumulation pattern, in addition to the accumulation rate, have changed significantly.

6 Conclusions

We present a detailed Holocene climate accumulation-rate history inferred from the WAIS Divide ice core that we evaluate against ice-sheet internal layers in the vicinity of the core site. We demonstrate that a robust strategy to infer a climate accumulation rate history for the ice sheet interior from a high-resolution ice core record is to (1) estimate the climate accumulation history using an ice core record and a 1-D flow model, and an advection correction (if necessary), and (2) validate this history by using the climate accumulation history as boundary forcing in an appropriate flowband model to generate internal layers. A good match between modeled layers and observed internal layers is an independent check that the climate history from the temporally resolved ice-core record is consistent with the spatially resolved radar-detected internal layers; this consistency brings confidence that the inferred accumulation history is realistic. In addition, we show that internal layers contain distinct spatial information that helps constrain the ice-flow history. This work further demonstrates to the ice-core community that interpreting climate histories from ice cores drilled on the flanks of an ice divide may require corrections for the advection of ice from different climate conditions upstream; our study provides a robust strategy for the joint interpretation of ice-core data and radar data.

Results from the WDC record indicate that the accumulation rate was ~20% lower than at present 9.2 kyr B.P. and increased to a maximum ~20% higher than modern between 4 and 2 kyr ago; there was an ~40% increase in accumulation between 9 and 4 kyr B.P.. The accumulation rate has been greater than at present for the past 6 kyr. Even though we cannot extrapolate our results more broadly across West Antarctica, we note that the Holocene accumulation history presented here from the WDC record is significantly different from histories derived from East Antarctic records, which are often used to reconstruct the evolution of West Antarctica. Caution is needed when using climate histories from a single site or from distant sites to reconstruct paleoclimate forcing across Antarctica.

Our finding that the accumulation rate has changed significantly while the ice divide position in Central West Antarctica has remained relatively stable through the Holocene also needs to be considered when evaluating continent-scale model reconstructions of Antarctic ice volume from the last glacial to present. Separate studies could investigate the magnitude of accumulation-rate change near the coast implied by our inferred changes in the interior and the drivers of WAIS accumulation change. We show that accumulation changes in the interior have a direct impact on the interior ice-surface elevation there, but the surface elevation of interior West Antarctica also responds to dynamically driven changes that are primarily initiated near the ice-sheet margins. Accurate accounting of the effects of changing dynamics of fast-flowing outlet glaciers and ice streams is needed to develop realistic continent-scale ice-sheet models and global climate models that are required to address dynamic and climatic drivers of ice-sheet evolution.

This work is part of a growing effort to interpret the increasing wealth of radar-detected internal layers across Antarctica, and also in Greenland [e.g., MacGregor et al., 2015]. The problem that we address here takes advantage of what we know from the ice-core record and from the radar data and examines the sensitivity of the solution to what we do not know about ice flow. Due to the inherent nonuniqueness of inferring multiple spatiotemporally variable parameters from dated internal layers this is a robust strategy that can be applied to infer accumulation and flow histories at other locations.

Acknowledgments

This work would not have been possible without the collective effort of the WAIS Divide ice core community. National Science Foundation grants OPP-0440666 and ANT-0944197 and NASA IceBridge grant NNX12AB74G supported this work at the University of Washington, as well as an NSF International Research Fellowship Program award to M.R.K. C.B. was supported by NSF grant 1043518. K.M.C. was supported by NSF grants 0539232 and 0537661. This work was also supported by a NASA Earth and Space Science Fellowship to T.J.F. We acknowledge the WAIS Divide Science Coordination Office at the Desert Research Institute of Reno, Nevada, and University of New Hampshire for the collection and distribution of the WAIS Divide ice core and related tasks (NSF grants 0230396, 0440817, 0944348, and 0944266). The National Science Foundation Office of Polar Programs also funded the Ice Drilling Program Office and Ice Drilling Design and Operations group for coring activities, the National Ice Core Laboratory for curation of the core, Raytheon Polar Services for logistics support in Antarctica, and the 109th New York Air National Guard for airlift in Antarctica. We also thank UNAVCO, Raytheon Polar Services, Antarctic Support Contractor, and Kenn Borek Air for their logistical and field support. We thank K. Matsuoka for providing the layer-picking interface “RadarGUI.” All data for this paper are properly cited and referred to in the reference list. We thank Neil Ross and two anonymous reviewers for comments that improved the manuscript and helped us to refine the implications of this work. We thank Scientific Editor Bryn Hubbard for additional comments.