Centennial‐ and Orbital‐Scale Erosion Beneath the Greenland Ice Sheet Near Jakobshavn Isbræ

Erosion beneath glaciers and ice sheets is a fundamental Earth‐surface process dictating landscape development, which in turn influences ice‐flow dynamics and the climate sensitivity of ice masses. The rate at which subglacial erosion takes place, however, is notoriously difficult to observe because it occurs beneath modern glaciers in a largely inaccessible environment. Here, we present (a) cosmogenic‐nuclide measurements from bedrock surfaces with well constrained exposure and burial histories in front of Jakobshavn Isbræ in western Greenland to quantify centennial‐scale erosion rates since ∼1850 CE, and (b) a new method combining cosmogenic‐nuclide measurements in a shallow bedrock core with cosmogenic‐nuclide modeling to determine orbital‐scale erosion rates across the same landscape. Twenty‐seven 10Be measurements in surficial bedrock constrain the erosion rate during historical times to 0.4–0.8 mm yr−1. Seventeen 10Be measurements in a 4‐m‐long bedrock core yield a centennial‐scale erosion rate of 0.3–0.6 mm yr−1, corroborating the results from our surface samples, and reveal that 10Be concentrations below ∼2 m depth are greater than what is predicted by an idealized production‐rate depth profile. We utilize this excess 10Be at depth to constrain orbital‐scale erosion rates at Jakobshavn Isbræ to 0.1–0.3 mm yr−1. The broad similarity between centennial‐ and orbital‐scale erosion rates suggests that subglacial erosion rates have remained relatively uniform throughout the Pleistocene adjacent to Jakobshavn Isbræ.

Basal sliding, ice flux, effective pressure at the bed, and the erosivity of the bedrock (i.e., lithology) control subglacial abrasion and quarrying rates (Alley et al., 2019;Boulton, 1996;Hallet et al., 1996), yet empirical measurement of these processes is notoriously challenging, given that they take place beneath ice.Except for a few in situ measurements of contemporary subglacial erosion (Boulton, 1979;Cohen et al., 2005), most estimates of glacial erosion rely on sediment flux through proglacial rivers (modern timescales; e.g., Cowton et al., 2012), sediment volumes in proglacial depocenters (centennial-to-millennial timescales; e.g., Koppes & Montgomery, 2009), or denudation rates from thermochronometry (millions of years; e.g., Herman et al., 2013).These methods are crucial for constraining subglacial erosion rates, but they often cannot elucidate spatial patterns of erosional processes within a glacier catchment and, on longer timescales, are averages of times when erosion is rapid, slowed, or even absent (Ganti et al., 2016).Cosmogenic-nuclide measurements from bedrock-eroded subglacially offer an opportunity to capture spatial and temporal variability and provide empirical targets for glaciological models.
Production of cosmogenic nuclides in bedrock takes place only when the rock is ice-free and decreases exponentially with depth from the surface (e.g., Brown et al., 1992;Lal, 1991).Subglacial erosion removes bedrock to a depth determined by the erosion rate and the duration of ice cover, beginning with the upper surfaces of the rock with the highest cosmogenic-nuclide inventory.Therefore, cosmogenic nuclide concentrations in bedrock hold information about the exposure history and amount of subglacial erosion experienced at a given location (Balco et al., 2014;Bierman et al., 1999;Briner & Swanson, 1998;Fabel et al., 2004;Goehring et al., 2011;Harbor et al., 2006;Hippe, 2017;Knudsen et al., 2015;Young et al., 2016Young et al., , 2021)).For example, 10 Be and 26 Al concentrations from sub-ice bedrock at the GISP2 site in central Greenland constrain likely exposure, burial, and erosional histories at that site through the Pleistocene (Schaefer et al., 2016).While the accumulation of cosmogenic nuclides at the GISP2 ice-core site represents an extreme endmember, that is possible only when Greenland is nearly ice-free, the margins of the GrIS are retreating rapidly in response to modern warming (King et al., 2020).Deglaciation at the ice-sheet margins is revealing a bedrock landscape whose cosmogenic-nuclide inventory holds yet untapped information about exposure history and importantly, subglacial erosion rates during past periods of ice cover (Goehring et al., 2011;Pendleton et al., 2019;Rand & Goehring, 2019;Skov et al., 2020;Strunk et al., 2017;Young et al., 2021).For example, using the well constrained Holocene exposure history of bedrock in front of the GrIS in the Jakobshavn Isbrae (Sermeq Kujalleq) forefield, Young et al. (2016) quantified subglacial erosion rates at eight locations covered by ice during the late Holocene.
Here, we first build upon the data set of Young et al. (2016) by calculating centennial-scale subglacial erosion rates in the Jakobshavn Isbrae region from new bedrock locations uncovered by the retreating GrIS within the last few decades.With these data, we evaluate spatiotemporal patterns of subglacial erosion and sediment evacuation during the period of historical ice cover.In addition, we present a cosmogenic 10 Be depth profile in a 4-m-long bedrock core from the same landscape, which we use to corroborate the erosion rates obtained from our surficial bedrock samples.Using this 10 Be depth profile as a case study, we detail a novel approach to quantifying subglacial erosion rates on orbital timescales using muon-produced 10 Be inherited from previous Pleistocene interglacials.Combined, these methods allow us to quantify in situ centennial-and orbital-scale (glacial-interglacial timescales) subglacial erosion rates in the same location, opening new opportunities for estimating the rate of landscape development from bedrock in proglacial and subglacial environments.
The landscape in front of Jakobshavn Isbrae deglaciated during the early Holocene, after which ice reached a minimum extent during mid-Holocene warmth, and then readvanced to a position slightly larger than present during the late Holocene. 10Be ages near the mouth of Jakobshavn Isfjord reveal that ice retreated out of Disko Bugt and onto land just prior to ∼10 ka.This was followed by brief readvances of the ice margin near the fjord mouth at ca. 9.2 and 8.2 ka (Young, Briner, et al., 2013).Ice then retreated to within the historical limit, and likely behind the modern terminus, by 7,520 ± 170 ka (Young et al., 2011).Through the Holocene Thermal Maximum (HTM; ∼8-5 ka), when local summer temperatures were likely ∼2°C-3°C warmer than today in the Jakobshavn Isfjord region (Axford et al., 2013), Jakobshavn Isbrae continued to retreat inland, reaching a minimum extent after peak HTM warmth.Sedimentary sequences from proglacial-threshold lakes constrain the timing of the minimum GrIS position during the Holocene (Briner et al., 2010).When the glacier terminus is within the drainage catchment of a threshold lake, but not overriding the lake, the lake receives silt-laden meltwater from the GrIS; when ice retreats out of the lake's catchment, meltwater influx ceases and organic sedimentation dominates.Radiocarbon-dated material at the contact between organic matter and minerogenic layers provides limiting ages on the GrIS' withdrawal from, or advance into, a lake's basin.Minimum-limiting radiocarbon ages from South Oval Lake and Eqaluit Taserssaut (Figure 1), proglacial-threshold lakes whose catchments extend beneath GrIS today, show that this sector of the GrIS margin was behind its present position from at least ∼5.8 to 2.3 ka (Briner et al., 2010).Following this minimum, ice advanced during the late Holocene, culminating in the deposition of the historical moraine in ∼1850 CE (Weidick & Bennike, 2007).Since 1850 CE, ice-margin retreat has revealed a landscape that holds information about subglacial erosion during the most recent (historical) period of ice cover.Young et al. (2016) compared the 10 Be concentration in surficial bedrock samples immediately inboard (east) of the historical moraine to the 10 Be concentration of bedrock samples outboard of the moraine to derive a basin-wide average erosion rate of 0.75 ± 0.35 mm yr −1 for the period of historical ice cover.Here, we expand upon the data set of Young et al. (2016) to capture subglacial erosion rates near the modern terminus of Jakobshavn Isbrae.

Field Methods
In August 2018, we sampled bedrock surfaces located between the historical moraine and the modern ice margin north and south of Jakobshavn Isfjord (Figure 1).Sampling locations in Young et al. (2016) were inboard of, but close to, the historical moraine.Here, we aimed to provide a complementary sample set by focusing on bedrock surfaces directly adjacent to the 2018 CE ice margin; however, one pair of samples is located between the historical moraine and the ice margin, providing landscape coverage between previous sample locations and our ice-marginal sampling locations.We targeted bedrock surfaces atop whalebacks with visible evidence of glacial abrasion, such as glacial polish and striations, and avoided sediment-covered sites, locations shielded by erratic boulders and places where quarrying appeared to be the dominant form of subglacial erosion (Figure 2).At each site, we recorded the location and elevation using handheld GPS (±5 m accuracy), measured topographic shielding, and collected the upper 1-3 cm of the bedrock surface using Hilti brand AG500-A18 angle grinder-circular saw with diamond bit blades, and hammer and chisel.In addition to the surface samples, we extracted a 41-mm diameter bedrock core to 4.04-m depth using a Shaw Portable Backpack Drill.

Laboratory Methods
We processed samples at the Lamont-Doherty Earth Observatory cosmogenic dating laboratory following established quartz isolation and beryllium extraction procedures (e.g., Schaefer et al., 2009; https://www.ldeo.columbia.edu/cosmo/methods). 10 Be/ 9 Be ratios were measured at the Center for Accelerator Mass Spectrometry at Lawrence Livermore National Laboratory (LLNL-CAMS) relative to the 07KNSTD standard with a 10 Be/ 9 Be ratio of 2.85 × 10 −12 (Nishiizumi et al., 2007).Surface sample 10 Be concentrations ranged from (3.25 ± 0.23) × 10 3 to (4.71 ± 0.11) × 10 4 atoms g −1 , with analytical uncertainty from 1.8% to 4.9% (mean = 2.5% ± 0.8%; Table S1).Blank corrections for surface samples, calculated by subtracting the average number of 10 Be atoms from blanks processed with each sample batch, ranged from 0.5% to 20%, with the majority of corrections being <3.5% (Table S2).Reported uncertainties in 10 Be concentrations include analytical and blank errors propagated in quadrature, and uncertainties related to the 9 Be carrier concentration (1.5%), which are treated as systematic errors.

10 Be Apparent Exposure Age Calculations
10 Be apparent exposure ages are calculated in MATLAB® using code from Version 3 of the online exposure age calculator described by Balco et al. (2008), updated to include a computationally efficient approximation of muon production rates near the earth surface (Balco, 2017).For all exposure age calculations, we employ the regionally calibrated Baffin Bay 10 Be production rate (Young, Schaefer, et al., 2013) and the time-dependent "Lm" production rate scaling method of Lal (1991)/Stone (2000).All ages are presented without production rate uncertainty because we compare our 10 Be ages only with each other and not an independent dating archive.Here, "apparent" exposure ages refer to the calculated age of the bedrock sample given the measured cosmogenic 10 Be inventory, assuming that the bedrock has experienced only one period of exposure with no erosion or burial during that time.

Quantifying Subglacial Erosion Using Cosmogenic 10 Be
Cosmogenic 10 Be accumulates in quartz when rock is exposed to the secondary cosmic ray flux (i.e., during icefree conditions).The 10 Be concentration at the bedrock surface and the rate at which it decreases with depth holds information about exposure history and subglacial erosion, which we quantify using modeled and measured 10 Be depth profiles (e.g., Schaefer et al., 2016;Young et al., 2016).At Earth's surface, spallation reactions comprise the majority of production, but these high-energy neutron reactions decrease rapidly with depth (attenuation length (Λ) = 160 g cm −2 ).Muon interactions contribute only ∼1%-2% of the 10 Be production at the rock surface, but dominate production below ∼650 g cm −2 (∼2.5 m in rock), meaning that the percentage of muon production relative to spallation increases with depth.Muon interactions take place at all depths in rock and produce 10 Be via two pathways: negative muon capture and fast muon interactions.Fast muons with higher energies remain in motion at a farther depth in rock, thus the attenuation length (and proportion of production relative to negative muon capture) of fast muon 10 Be production increases with depth.As a result, the variation of 10 Be with depth is approximately exponential, taking the shape of the 10 Be production profile shown in Figure 3 (Balco, 2017).
Here, we leverage the near-exponential and predictable shape of 10 Be production with depth to quantify subglacial erosion.Assuming that bedrock started with a negligible amount of 10 Be, the change in 10 Be concentration with depth in rock mirrors that of the 10 Be production profile at the end of an exposure period.During subsequent ice Figure 2. Photographs of typical bedrock sampling locations in the Jakobshavn Isbrae forefield.We targeted sampling locations exhibiting evidence of abrasion (e.g., striations and glacial polish) and avoided those with evidence of plucking.Top row: sample locations north of Jakobshavn Isbrae.18-JAK-CR1 is the bedrock core location.Bottom row: sample locations south of Jakobshavn Isbrae, where the landscape is considerably more debris-laden than the north.cover, subglacial erosion removes bedrock to a depth determined by the erosion rate and the duration of ice cover beginning with the upper surfaces of the rock where the majority of 10 Be production takes place, truncating the 10 Be depth profile to the erosional depth.Using this concept, we compare measured 10 Be concentrations to modeled 10 Be depth profiles to recover erosional depth at our surface sample and bedrock core locations.
The 10 Be concentration in bedrock in front of Jakobshavn Isbrae holds information about the duration of Holocene exposure and any subglacial erosion that took place during historical cover.Because the ice-margin history at Jakobshavn Isbrae is well constrained by basal radiocarbon ages in proglacial-threshold lakes and 10 Be ages outboard of the historical moraine, we are able to use 10 Be concentrations inboard of the historical moraine to derive subglacial erosion rates for the most recent period of ice cover.Inboard of the historical moraine, the maximum exposure age a bedrock sample can have is the local deglaciation age minus the duration of historical cover (Figure 4).The local deglaciation age is determined from 10 Be concentrations outboard of the historical moraine.In Section 5, we describe threshold lake sediment records that approximate the onset of historical cover at our bedrock sample locations.To find when our new ice-marginal sites most recently became deglaciated, we use 1985-2018 Landsat/Copernicus satellite imagery, viewed in Google Earth using the historical imagery tool, to visually assess when the ice margin retreated inland of each site.At most locations, it is possible to ascertain exactly which year the site became ice-free from the satellite imagery.For locations where it is difficult to discern among several years of imagery exactly which year the site deglaciated, we include the range of years as uncertainty (Table 1).We compare the 10 Be exposure ages from bedrock samples inboard of the historical limit to the maximum allowable exposure age determined by the local deglaciation age and the duration of historical cover; a younger-than-expected 10 Be age indicates that a detectable amount of subglacial erosion took place during historical cover (Young et al., 2016, Figure 4).
We determine the depth of subglacial erosion during historical cover by locating the measured 10 Be concentration along modeled 10 Be depth profiles specific to each sample location.Depth profiles are derived by projecting the Figure 3. 10 Be production profile shown as percent of surface production at sea-level high latitude.Although the production rate varies with geomagnetic latitude and elevation, the relative proportion of production by muons and spallation is similar at Jakobshavn Isbrae, with ∼1% production by muons at the surface.Note that by ∼2.5 m depth, muon production exceeds spallation production.spallogenic component of the surface 10 Be concentration commensurate with the maximum possible exposure age to an arbitrary depth using an attenuation length of 160 g cm −2 .The muonic component of the 10 Be depth profile is quantified using MATLAB® code from Balco et al. (2008) [updated in Balco (2017)], which implements downward propagation of the muon energy spectrum after Heisinger, Lal, Jull, Kubik, Ivy-Ochs, Knie, et al. (2002) and Heisinger, Lal, Jull, Kubik, Ivy-Ochs, Neumaier, et al. (2002).To find the depth of subglacial erosion during historical cover, we locate the depth (in g cm −2 ) at which the measured 10 Be concentration matches that of the modeled profile.These are cast as erosional depths for different materials based on their density, such as depth in rock (2.65 g cm −3 ).Finally, we determine uncertainty in the erosional depth from the uncertainty in deglaciation age and duration of historical cover propagated in quadrature.
In addition to quantifying subglacial erosion from surficial bedrock samples, we compare measured 10 Be concentrations in a 4-m-long bedrock core to modeled depth profiles derived using the known exposure history at the core location.To simulate subglacial erosion during the most recent period of ice cover, we assume that the modern bedrock surface was covered by additional mass (in this case, rock) when the core site was first exposed during the Holocene (e.g., Schaefer et al., 2016).We then find the best-fitting 10 Be depth profile by adjusting how far below the modern surface the bedrock was when the measured 10 Be accumulated.The depth of this adjustment is equivalent to the erosional depth during historical cover at the core site.Ultimately, we show that modeling cosmogenic-nuclide accumulation and subglacial erosion throughout the Pleistocene yields a better fit to our data than the simple fitting adjustment described above.Because this modeling exercise provides further interpretation of the data set, we describe the rationale and model setup in Sections 6.2.1 and 6.2.2.2016)) of the moraine, shown in pink, has a complex exposure history, including the ∼90 years of ice cover at the end of the Holocene.During this most recent period of ice cover, any subglacial erosion would remove the upper portion of the 10 Be depth profile in the bedrock, accumulated from previous exposure, so the measured 10 Be concentration would be lower than the true exposure age.For the sake of illustration, a surface sample collected at the pink circle experienced 1-m of subglacial erosion during historical cover, and therefore its 10 Be concentration would be 20% of the expected concentration.

Number in
Figure 1 Sample ID   For the new sample locations in this study, the onset of historical cover is derived from lake sediment records, and the modern deglaciation year is constrained by satellite imagery (Section 5).
Uncertainty on these constraints are propagated in quadrature.b All information needed to calculate exposure ages, including latitude, longitude and elevation, is provided in Table S1.c Only calculated for samples interpreted to have possible sediment cover.Assume till density of 2.0 g cm −3 . d Sediment cover atop site during Holocene, assuming that bedrock was then abraded at the site-wide average rate of 0.31 mm yr −1 during historical cover.e Same assumptions as footnote d, but if the site were covered by a boulder or boulder-rich till prior to historical cover. 10.1029/2021JF006429 10 of 27

Apparent Exposure Ages in Surficial Bedrock Samples
Five new 10 Be measurements on bedrock just outboard of the historical moraine refine the timing of local deglaciation south of Jakobshavn Isfjord to 7,170 ± 80 years (mean ± SD).This age is slightly younger than the deglaciation age for the northern part of the study area of 7,510 ± 180 years (n = 7; statistically identical to deglaciation age of Young et al. (2016), but recalculated using v3 of the online calculator described in Section 3.3) (Figure 1, Table 1).Twenty-seven new 10 Be measurements from bedrock within the trimline are located throughout the study area and yield apparent exposure ages that range from 730 ± 50 to 7,600 ± 210 years (Figure 1, Table 1).Three distinct age groupings emerge from these data: 13 10 Be ages that are between 5,700 years and the local deglaciation age (∼7,500 years; Group 1), 8 of which overlap the local deglaciation age within uncertainty; 11 10 Be ages that date between ∼3,400 and ∼5,000 years (Group 2), and 3 10 Be ages that are <1,000 years (Group 3).Of the eight 10 Be ages from bedrock inboard of the historical limit published by Young et al. (2016), which are considered alongside our new data set, seven fall in Group 1 and one falls in Group 2.

Ice-Margin History for Calculating Erosion Rates
To calculate erosion depths and rates, we compare measured 10 Be concentrations to the maximum allowable 10 Be concentrations as defined by the local ice-margin history.Broadly, ice retreated across the study area ∼7,500 years ago to a position smaller than present, and then readvanced during the late Holocene, culminating in deposition of the historical moraine in 1850 CE (Figure 1).Following the deposition of the historical moraine, the ice-margin retreated toward its present position and continues to retreat today.Here, we estimate the local deglaciation age for each part of our study area and determine the likely total duration of historical cover at each sample location that can be used to constrain erosion rates.
Five new 10 Be ages from bedrock outboard of the historical limit in the southern part of our study area reveal that the deglaciation south of Jakobshavn Isbrae occured 7,170 ± 80 years ago, which is slightly later than deglaciation north of Jakobshavn Isbrae (7,510 ± 180 years; Young et al., 2016).Although the northern and southern deglaciation ages overlap within 2σ, several lines of evidence suggest that the younger age reflects later ice-margin retreat from the landscape in front of the GrIS south of Jakobshavn Isbrae.First, basal radiocarbon ages from proglacial-threshold lakes indicate that, compared to the GrIS margin north of Jakobshavn Isbrae, the GrIS margin south of Jakobshavn Isbrae likely retreated behind its 2018 CE position slightly later during deglaciation, and readvanced beyond the 2018 CE position earlier during the Late Holocene.A radiocarbon age near the base of the most recent organic unit in Loon Lake indicates that the GrIS margin did not retreat out of its catchment before ∼6,300 cal yr BP, suggesting delayed retreat across the southern landscape relative to north of the fjord (minimum age; Briner et al., 2010).Delayed retreat from this landscape is further corroborated by the earlier re-advance of the GrIS into the nearby Goose Lake catchment by ∼2,500 cal yr BP, indicating that the GrIS margin south of Jakobshavn Isbrae spent comparatively less of the Holocene behind its current position (Briner et al., 2010), which can in part be achieved by delayed initial deglaciation.Second, sample JAKS08-24 located ∼12 km outboard of the historical moraine south of Jakobshavn Isbrae, at a similar westward position as the historical moraine north of Jakobshavn Isfjord, has an age of 7,610 ± 340, which is commensurate with the deglaciation age of the north.Collectively, these chronological constraints suggest that (a) the younger deglaciation ages outboard of the historical moraine south of Jakobshavn Isbrae reflect the true deglaciation age of this landscape, and (b) the bedrock positioned between the historical moraine and the 2018 CE GrIS margin likely experienced slightly less total surface exposure than the equivalent bedrock landscape directly adjacent to and north of Jakobshavn Isford.
Assuming the quick and continuous retreat of the ice margin (Young et al., 2011(Young et al., , 2016)), the local deglaciation age marks the maximum amount of 10 Be that any bedrock surface can have, whether it is immediately inboard of the historical moraine or adjacent to the modern ice margin.For our new ice-marginal sites, eight 10 Be ages from Group 1 overlap with the local deglaciation age, confirming that the local deglaciation age calculated from 10 Be beyond the historical moraine indeed marks the start of the cosmogenic clock for these ice-marginal locations.Furthermore, the overlap of Group 1 ages with the deglaciation age further constrains the minimum extent of inland GrIS retreat during the mid-Holocene, as the ice margin must have retreated rapidly across the landscape just now emerging in front of Jakobshavn Isbrae, withdrawing to within the 2018 CE margin by ∼7,500 years ago in the north and ∼7,200 years ago in the south.Although we cannot determine with these data where the GrIS margin was positioned at its most retracted Holocene extent, the ice-marginal ages that overlap with the local deglaciation age confirm that this sector of the GrIS was inland of the 2018 CE margin during mid-Holocene warmth.
Lake sediment records and historical observations constrain when ice advanced across the landscape immediately inboard of the historical moraine during the late Holocene (Briner et al., 2011).Varved sediments indicate that Iceboom Lake, a proglacial-threshold lake whose catchment threshold is located east of the sample locations of Young et al. (2016), but west of our 2018 sample collection, became glacially fed in ∼1820 CE (Briner et al., 2011) and historical observations show the GrIS at its historical maximum before 1850 CE (Weidick, 1968).Historical observations place the GrIS margin at its historical maximum until at least 1900 CE (Weidick, 1968) and aerial imagery documents the subsequent glacial retreat, showing the GrIS margin just east of the sample locations inboard of the historical limit in 1944 CE (Csatho et al., 2008).Using these constraints, Young et al. (2016) 1).However, our new bedrock locations are farther east (adjacent to the 2018 CE ice margin) and thus would have become ice-covered earlier as ice advanced during the late Holocene, and became ice-free more recently, than the bedrock sites of Young et al. (2016).
To estimate the timing of ice advance across our sample locations, we rely on the sediment record of Glacial Lake Morten, situated just north of Jakobshavn Isfjord (Briner et al., 2011, Figure 1).Glacial Lake Morten is a drained, formerly ice-dammed proglacial lake.Satellite imagery documents ice retreat out of the lake's catchment, and thus draining of the lake, between 1986 and 1991 CE.Therefore, the 1991 CE ice terminus position is the approximate eastern limit of the lake catchment.Using that catchment boundary, we hypothesize that when Glacial Lake Morten became glacially fed as ice advanced toward the historical limit during the late Holocene, the GrIS ice margin position was similar to its 1991 CE configuration.In Landsat imagery from 1991 CE, all of our ice-marginal sample locations were ice covered, so we estimate that the latest ice could have advanced across our sample locations during the late Holocene is coincident with the advance of ice into the Glacial Lake Morten catchment.
Layer counting of varved sediments from Glacial Lake Morten reveal that ice advanced into the basin between 1795 and 1800 CE, and thus our ice-marginal bedrock sites must have become ice covered by 1795-1800 CE.
Considering the close proximity of our sample sites to Glacial Lake Morten, and the likely rapid advance of the GrIS margin in the region during historical advance (Briner et al., 2011), 1795-1800 CE is a likely close estimate for the onset of ice cover.As a conservative approach, we consider the onset of ice cover to be 1795 ± 5 years.Finally, our ice-marginal sites became ice-free most recently during the satellite era, so we use Landsat imagery viewed in Google Earth to determine when each site became exposed as Jakobshavn Isbrae and adjacent margins retreated in recent decades.Using the above, we estimate that the total late Holocene burial duration at our ice-marginal sites ranges from 185 to 222 years (Table 1).For the replicate pair 18JAK-37/18JAK-38, located about halfway between the historical moraine and the 2018 CE margin, we use 87 ± 27 years for the duration of historical cover as those sites were deglaciated before the first Landsat imagery in 1972 and likely have a similar burial history as the previously sampled locations adjacent to the historical moraine (Young et al., 2016).In sum, the maximum duration of Holocene exposure ranges between 6,950 and 7,420 years (Table 1).To derive erosion rates, we use this maximum duration of Holocene exposure to model 10 Be depth profiles at each sample location.

Centennial-Scale Erosion
To calculate subglacial erosion rates, we compare the measured 10 Be concentrations in our surficial bedrock samples to the expected 10 Be concentrations obtained from the maximum Holocene exposure duration under zero subaerial erosion (Sections 3.4 and 5).A measured 10 Be concentration less than expected (after considering the burial durations described above) likely reflects erosion through the upper portion of the 10 Be production profile.Below, we also discuss the possibility that a lower 10 Be concentration could result from more ice cover during the Holocene, although that is not our preferred interpretation for most sites.A 10 Be concentration more than expected indicates isotopic inheritance from pre-Holocene (and likely pre-Last-Glacial-Maximum) exposure.All of our measured 10 Be ages at the ice-marginal sites are equal to or less than the maximum Holocene exposure duration (i.e., do not contain detectable inherited 10 Be), and the corresponding 10 Be concentrations equate to ∼0-150 cm of rock removed during historical ice cover.Erosional depths for the three apparent age groupings equate to ∼0-11 cm (Group 1), ∼23-43 cm (Group 2), and ∼125-150 cm (Group 3) (Table 1; Figure 5).
The distinct groupings of erosional depths (vs. a random distribution of samples) in our data set suggest that multiple and distinct subglacial processes are represented.Because we targeted bedrock locations that exhibited evidence of subglacial abrasion (i.e., striations and polish) rather than quarrying (Figure 2), we consider our erosional depths to represent abrasion depths.While it is likely that samples in erosional Group 1 represent abrasion, no sample plots between Groups 1 and 2 on Figure 1, and the apparent abrasion rates (erosion depths corrected for the duration of historical cover) implied by the erosional depths of Groups 2 (1.63 ± 0.56 mm yr −1 ) and 3 (6.24± 0.56 mm yr −1 ) exceed most estimates of subglacial erosion (which include both abrasion and quarrying) in Greenland (Hogan et al., 2020 and references therein) as well as many estimates from the midlatitudes and polar regions (Cook et al., 2020, Figure 5).Thus, we find it unlikely that the 10 Be concentrations of Groups 2 and 3 were solely achieved by rock abrasion.There are two alternative explanations for the lower 10 Be concentrations (higher apparent erosional depths) of Groups 2 and 3. First, it is possible that these sites were ice-covered for more of the Holocene.Alternatively, following deglaciation ca.7,500 years ago, these sites may have been covered by sediment that was removed during historical cover.If these sites were covered in sediment prior to historical cover, the 10 Be that accumulated during the Holocene would have done so at a significantly lower production rate.
The spatial distribution of these erosion groupings helps to elucidate which of the above explanations are most plausible.The agreement between neighboring sample pairs indicates that abrasion rates are generally consistent across several meters (Figure 1).However, there are two exceptions: pair 18JAK-CR1-SURFACE (Group 1; 0.06 ± 0.11 mm yr −1 )/18JAK-25 (Group 2; 1.91 ± 0.16 mm yr −1 ) north of the fjord and pair 18JAK-15 (Group 2; 1.40 ± 0.11 mm yr −1 )/18JAK-16 (Group 3; 5.70 ± 0.167 mm yr −1 ) south of the fjord (Figure 1, Table 1).The difference in abrasion rate within these pairs is surprising because (a) replicate samples were only a few meters apart, and therefore would have experienced the same ice-margin history; (b) each sample in these pairs was Note that this line is not fit for the calculated erosion depths, rather this production profile is used to determine erosional depths so all data will fall on this line.Symbols are colored according to apparent exposure age as in Figure 1, circles represent data from this study and triangles show results from Young et al. (2016).The mean erosional depth for each group is plotted as a horizontal dashed black line, and the average erosional depth and abrasion rate (mean ± SD) are plotted above and below the line, respectively.Abrasion rates were determined using site-specific durations of historical cover, ranging from 87 to 222 years.
collected from sculpted bedrock atop whalebacks that looked like abraded, rather than quarried surfaces; and (c) all samples were of the same lithology and were not covered by sediment at the time of sample collection.In addition, sample regions did not appear to display any noticeable difference in fracture patterns.The factors thought to control subglacial erosion (basal sliding velocity, climate, and the amount of meltwater at the bed) vary on greater-than-meter scale (Alley et al., 2019;Koppes et al., 2015), so it is unlikely that abrasion rates would vary significantly across sample replicates.In addition, the distribution of samples from Group 2 throughout the study area (Figure 1), and in several cases, their position near samples that overlap with the deglaciation age, suggests that shorter Holocene exposure does not explain the relatively low 10 Be concentrations in Group 2. Rather, we observe that most (although not all) Group 2 samples are located south of Jakobshavn Isfjord (Figure 1; Table 1), where the landscape is substantially more debris-laden than the north side (Figure 2).Therefore, we suggest that during initial deglaciation, the retreating GrIS left the Group 2 sample locations covered in glacial sediments (likely till, which covers the landscape south of Jakobshavn Isfjord today).This sediment cover would have resulted in lower 10 Be production at the bedrock surface during the middle Holocene, before the overlying sediment was subsequently stripped from the landscape during the period of historical ice cover.
Sediment cover prior to historical ice cover may also explain the substantially higher apparent erosion depths (low 10 Be concentrations) of Group 3, but it is also possible that these sample locations experienced more ice cover during the Holocene.Two of the three Group 3 samples (8JAK-23 and 18JAK-24) are located in the easternmost part of the study area on a nunatak that was just emerging from the ice at the time of collection (2018 CE); Landsat imagery from 2012, viewed in Google Earth, shows the nunatak completely ice covered.It is possible that the retreating ice margin may just now be revealing a landscape that was ice-covered for most of the Holocene, which could explain the extremely low 10 Be concentrations in samples 18JAK-23 and 18JAK-24.If so, the GrIS margin likely stabilized near its current position during mid-Holocene warmth and the magnitude of ongoing retreat is nearly unprecedented during the Holocene.Yet, similar work in the Kangiata Nunaata Sermia region in southwest Greenland suggests that the ice margin has yet to retreat behind its minimum Holocene extent (Young et al., 2021).In sum, the low 10 Be concentrations of 18JAK-23 and 18JAK-24 could tentatively represent the ice margin revealing unprecedented terrain, or could indicate significant sediment cover, but we cannot distinguish between the two scenarios with our current data set.
By recasting the erosional depths as sediment depths using a material density appropriate for till (2.0 g cm −3 ), sites from Groups 2 and 3 could have been covered by 30-58 and 168-195 cm, respectively, of sediment that shielded bedrock between the timing of deglaciation and late Holocene readvance (note that this calculation could be made for any material density).While rock cover and sediment cover are two endmember scenarios, we also present a mixed model whereby sediment was removed and then bedrock abraded at the site-wide average rate of 0.31 mm yr −1 (see below).Using this model, 20-50 and 160-190 cm of sediment covered these sites for Groups 2 and 3, respectively (Table 1).Although we cannot distinguish between rock cover, sediment cover, and ice-margin history with our current 10 Be data set, the spatial distribution of samples from Groups 2 and 3 point to a role for sediment cover in yielding such high erosional depths.
We suspect that the Group 2 samples experienced sediment cover, and the Group 3 samples experienced either sediment cover or longer Holocene ice cover, or both, and thus we exclude these samples when calculating an average abrasion rate for the study area.To derive abrasion rates from the Group 1 erosional depths, we correct for the duration of historical cover, which yields abrasion rates of 0-1.05 mm yr −1 (Table 1).Because we sampled only bedrock with evidence of recent subglacial abrasion (striations, polish, and within trimline), we know that some amount of non-zero subglacial erosion (even if small) occurred during historical cover at these sites.Since eight of the erosional depths in Group 1 overlap with 0 cm, these samples are at the detection limit for our method of determining erosional depths.Therefore, we use the upper limit of the abrasion rate range for the samples overlapping 0 cm erosion when determining a site-wide average, but note that using a value of zero for all of these samples only lowers the average abrasion rate by 0.03 mm yr −1 .Combined, the average historical abrasion rate derived from bedrock in the Jakobshavn Isbrae forefield is 0.31 ± 0.34 mm yr −1 (Table 1).Integrated basin-wide erosion rates are often derived using sediment volume measurements from proglacial rivers or marine basins (e.g., Bierman & Steig, 1996;Cowton et al., 2012;Koppes et al., 2015).Unlike our point measurements, these records smooth variability throughout the glacier catchment and crucially include the effects of quarrying, which could account for ∼30%-60% of total subglacial erosion (Hallet, 1996;Riihimaki, 2005).To best compare our results to these studies, we calculate the total subglacial erosion implied by our calculated abrasion rates, assuming they account for only 40%-70% of total erosion.Using this relationship, we find that subglacial erosion occurred beneath Jakobshavn Isbrae at a rate of 0.4-0.8mm yr −1 during the period of historical ice cover.

Orbital-Scale Erosion
We assess the potential for using bedrock cores in proglacial settings to constrain the magnitude of subglacial erosion over multiple timescales.Here, we explore the effects of both short-and long-term subglacial erosion on 10 Be depth profiles in bedrock.We demonstrate that modeling erosion rates during the Pleistocene yields realistic estimates of recent erosion, as well as constraints on subglacial erosion rates on orbital timescales at the same location.

Excess Muon-Produced 10 Be at Depth
To evaluate subglacial erosion at the bedrock core site, we first compare our measured 10 Be concentrations with depth to the theoretical 10 Be production curve with depth (i.e., Schaefer et al., 2016).In the upper ∼2 m of the rock column, the measured 10 Be concentrations are congruent with the predicted concentrations (Figure 6).However, below ∼2 m, our measured 10 Be concentrations consistently exceed the predicted 10 Be concentrations, yielding a poor fit to the data overall (χ 2 = 11.6; Figure 6).In other words, below ∼2 m depth the e-folding length (depth over which the 10 Be concentrations decrease by a factor of e) of our measured 10 Be concentrations is greater than the attenuation length of 10 Be production at those depths (i.e., 10 Be decreases more slowly with depth than expected).
To simulate subglacial erosion during the most recent period of ice cover, we assume that the modern bedrock surface was covered by some additional mass (presumably rock) when the core site was first exposed during the Holocene and determine the erosional depth by adjusting how far the bedrock was below the modern surface when the measured 10 Be accumulated (Schaefer et al., 2016).Using this method, we find a good model-data fit (χ 2 = 1.4; Figure 6); however, the best-fitting curve implies an exposure duration of ∼15 kyr and an erosional depth of ∼50 cm (Figure 6).These results are seemingly realistic for postglacial landscapes that lack independent constraints on the exposure history and subglacial erosion rate, yet they are inconsistent with the known exposure duration of the core location (∼7,300 years during the Holocene) and the erosional depth derived from the surface sample 18JAK-CR1-SURFACE (1.30 ± 2.31 cm), which was taken from bedrock immediately surrounding the borehole.Indeed, with this fitting method it is possible to simulate 10 Be concentrations that match the measured concentrations at our sample depths only when using exposure durations and erosional depths that far exceed those known for our field site.While this fitting method for determining subglacial erosional depths may recover realistic results for landscapes where little is known about the glacial history, using bedrock cores to reconstruct subglacial erosion is more useful in landscapes where the exposure history has prior constraints.
Next, we derive 10 Be concentrations with depth using the known exposure history for this site (deglaciation 7,510 years ago, 222 years of late Holocene cover, and 10 years recent exposure) and varying amounts of subglacial erosion during historical cover (Figure 7).The 10 Be concentrations in the top ∼2 m of the core fit best with ∼0-10 cm of erosion during historical cover, which is statistically identical to the erosion depth derived solely from our surface measurement (erosional depth from 18JAK-CR1-SURFACE is 1.30 ± 2.31 cm).However, the 10 Be measurements below ∼2 m depth, again, exceed those predicted by all erosion scenarios.This finding points to surplus 10 Be measured below ∼2 m depth, even when considering uncertainty in the muon production rate of 10%-25% (Balco, 2017) (at the core location, the muon production rate uncertainty is likely closer to 10% as the muon production rate was calibrated in Antarctica, another high-latitude location [Balco, pers comm]).We also cast the measured 10 Be concentrations in the bedrock core as apparent exposure ages using the 10 Be production rate at the sample depth.When compared to the known Holocene exposure duration for the site (∼7,300 years), the apparent exposure ages in the upper ∼1.5 m of the core are slightly less than 7,300 years, implying that we measured less 10 Be than we expected and that some amount of recent subglacial erosion has taken place (Figure 7).In other words, recent subglacial erosion has removed 10 Be in the spallation-dominated part of the 10 Be depth profile.In contrast, the apparent 10 Be ages below ∼1.5 m are, within error, increasingly older than 7,300 years.For example, in order to get the measured concentration of ∼620 atoms g −1 in the lowermost sample, the surface would have to have been exposed for 12,600 years, which is 5,300 years, or 70%, longer than expected.If some of this 10 Be accumulated when the sample was deeper in the rock column (i.e., deeper than the modern sample depth), the integrated production rate experienced by the sample would be lower, so these excess 10 Be ages are minima.
Excess 10 Be at depth represents a buildup of muon-produced 10 Be over many glacial cycles, which erosion (surface lowering) during glacial periods gradually brings toward the surface (Ploskey & Stone, 2014, Figure 8).This is possible because muon production (albeit low) continues to all depths in rock, so even high subglacial erosion rates are often insufficient to remove the muon signature of previous exposure periods (e.g., Briner et al., 2016).Therefore, all rock surfaces that have undergone at least one episode of burial since initial exposure Be depth profiles modeled using the known Holocene history at the bedrock core site, with subglacial erosion of 0-50 cm during historical cover (plotted every 5 cm).Note that a higher degree of subglacial erosion effectively "truncates" the 10 Be depth profile from the top.Measured 10 Be concentrations in the bedrock core are plotted in red, and are most consistent with ∼0-10 cm of erosion during historical cover.However, measured 10 Be below ∼2 m depth exceeds modeled 10 Be in all scenarios.Dark gray envelope is 10% uncertainty in the muon production rate and light gray envelope is 25% muon uncertainty.(b) Measured 10 Be concentrations plotted as apparent exposure ages in excess of the known exposure age for the core site (∼7,300 years).Ages that plot to the left of zero require erosion (i.e., exposure ages are less than expected), and those that plot to the right of zero contain muon inheritance (i.e., exposure ages are greater than expected), which can be used to determine orbital-scale erosion rates.In both panels, widths of red boxes show 1σ measurement uncertainty.
likely contain some muon-produced 10 Be inherited from prior exposure periods.Yet, in many settings inherited 10 Be from muon production is well below the measurement detection limit, meaning that a sample at the surface yields a 10 Be concentration commensurate with its exposure age.No newly exposed bedrock surface would have a 10 Be concentration of zero, but the inherited muon-produced 10 Be concentration in a surface sample is often within measurement error.Given the abundance of inherited muon-produced 10 Be at depth, recent and long-term subglacial erosion are differentially recorded in 10 Be depth profiles.The spallation-dominated upper ∼2-3 m of the depth profile is sensitive to recent subglacial erosion, as 10 Be concentrations near the surface decrease rapidly with depth.In contrast, the 10 Be concentration below ∼2-3 m, where muon interactions comprise the majority of production, is increasingly less sensitive to recent erosion because the 10 Be concentrations (albeit generally low) decrease slowly with depth.Therefore, muon-produced 10 Be inherited from prior periods of exposure becomes increasingly important with depth in rock below the modern surface (Figure 8).This combination results in the spallation-dominated portion of the depth profile recording recent subglacial erosion, while the build-up of muon-produced 10 Be records the long-term average erosion rate (i.e., orbital timescales).Not only does this inherited muon-produced 10 Be allow for the evaluation of long-term erosion rates (Ploskey & Stone, 2014), but failing to incorporate it into our analysis of the bedrock core data at Jakobshavn Isbrae leads to erroneous results for the historical erosion rate (Figure 6).

Quantifying Orbital-and Centennial-Scale Erosion Rates From a Bedrock Core
To simulate the excess muon-produced 10 Be observed in our downcore 10 Be measurements, we model 10 Be concentrations with depth in bedrock through the Pleistocene for a range of exposure histories and subglacial erosion rates using the model framework described below.We test several pre-Holocene exposure histories using different threshold values on the benthic δ 18 O stack of Lisiecki and Raymo (2005) and for the Holocene implement the known exposure history at the bedrock core site.We then invert the 17 measured 10 Be concentrations in our (2) During the following burial (glacial) period, subglacial erosion takes place, removing 10 Be from the top down.At the end of the glacial period, the 10 Be depth profile will appear truncated according to how much erosion took place.
(3) During a subsequent exposure (interglacial) period, 10 Be will again accumulate with the shape of the 10 Be production profile (black).At the surface, where production is spallation-dominated, this new production would overpower any 10 Be leftover from the last glacial cycle.At depth, however, where 10 Be production is low and muon-dominated, the leftover 10 Be from the previous glacial period becomes important.(4) Over many glacial cycles, this muon-produced 10 Be from previous exposure periods builds up and, while generally overpowered by the most recent spallation signal at the surface, causes there to be measurable excess 10 Be at depth.Therefore, excess 10 Be only occurs after at least one period of erosion from the surface.For the sake of illustration, the glacial periods used to create this cartoon are 90 kyr, the interglacial periods are 10 kyr, and 4 m of erosion takes place during each glacial period.In reality, the amount of excess 10 Be at depth is dependent on the erosional depth (rate) during glacial periods.
4-m-long bedrock core for the best estimate of centennial-and orbital-scale erosion rates at the coring location.
To determine the best-fitting erosion rates for each combination of exposure history, historical subglacial erosion rates and Pleistocene subglacial erosion rates, we used the reduced chi-squared statistic, which is weighted using the measurement uncertainty in the 10 Be concentrations.
In our 10 Be model, cosmogenic 10 Be accumulates when the bedrock core site is ice free and subglacial erosion occurs when the site is ice covered.The two free parameters in our model are the historical subglacial erosion rate and the Pleistocene (pre-Holocene) subglacial erosion rate.The Pleistocene erosion rate is kept constant for all Pleistocene burial periods.The exposure history (nuclide accumulation) and the subglacial erosion rate (nuclide removal) ultimately determine the 10 Be concentration at the end of the model run, and infinite combinations of these parameters can yield the same 10 Be concentration (i.e., more exposure during the Pleistocene would require higher erosion rates to arrive at the same 10 Be concentration).Therefore, the exposure history that we select to drive the model determines what erosion rates will yield 10 Be concentrations that best fit our measurements.An advantage of using the bedrock in front of Jakobshavn Isbrae is that the Holocene ice-margin history is well constrained, meaning that unique erosion rate results are possible for historical ice cover.The pre-Holocene glacial history of our study area, however, is unconstrained, so we use the benthic δ 18 O stack as a proxy for the exposure history at our bedrock core location.To determine plausible exposure histories at our core site prior to the Holocene, we explore exposure/burial histories by employing threshold values on the marine benthic δ 18 O LR04 stack (Lisiecki & Raymo, 2005;Knudsen et al., 2015;30 kyr smoothing).We run our model for exposure histories derived from δ 18 O thresholds of 3.3-4.0‰.Doing so allows us to test exposure histories that span a range of plausible Pleistocene exposure/burial scenarios at our core site, from having almost zero pre-Holocene exposure (3.3‰ threshold) to having ice-free conditions for ∼60% of the Pleistocene (4.0‰ threshold).From 7,510 ka (known timing of local deglaciation at the core site) to the present, we use the known ice-margin history described in Section 5 to drive the model (deglaciation age = 7,510 ka, historical ice cover = 213 years, and 10 years of recent exposure prior to sampling).Unlike the pre-Holocene exposure history, for which we test a range of scenarios, the exposure history from 7,510 ka to the present is the same in all model runs because it is well known.
We compute the 10 Be production rate with depth as described in Sections 3.3 and 3.4, but here use "St" scaling of Lal (1991)/Stone (2000).Although we do not implement time-variant scaling methods, the use of such a method would yield nearly identical 10 Be concentrations for the Holocene, the only time period for which we expect to have remaining spallation-produced 10 Be at the core site, because the production rate we employ was calibrated locally (Young, Schaefer, et al., 2013).Finally, while the elevation of the Earth's surface at the core site cannot be known through the Pleistocene, muon interactions, which account for the production of 10 Be preserved on glacial-interglacial timescales, are less sensitive to changes in the surface elevation than spallation reactions because of the longer attenuation length of muons traveling through the atmosphere.
We assume that the core location was ice free prior to the model start and that the bedrock began with a 10 Be inventory in steady state (i.e., nuclide production is balanced by nuclide loss from decay and erosion).We initialize the model with steady-state 10 Be concentrations using subaerial erosion rates of 5, 10, and 50 m Myr −1 .Note that the starting depths of our samples are >100 m for our best-fitting model runs (Table 3), meaning that starting 10 Be concentrations are extremely low even with the initial steady state conditions.To assess the importance of the steady state starting conditions, we also run the model with a starting 10 Be concentration of zero, although this assumption is unrealistic given that the site would have been exposed prior to the first period of ice cover.Model time begins either at 2.7 Ma (beginning of the Pleistocene) or with the first burial period after 2.7 Ma if the δ 18 O is below the threshold (i.e., site is ice free) at the beginning of the Pleistocene.
Model time runs toward the present with the length of each exposure/burial period determined by the δ 18 O threshold.Nuclide accumulation is quantified during exposure using the equation, where N new is the 10 Be concentration at the end of the time step (in this case, exposure period), N old is the 10 Be concentration at the start of the time step, λ is the 10 Be decay constant (4.99 × 10 −17 yr −1 ; Chmeleff et al., 2010;Korschinek et al., 2010), t exp is the exposure duration for that time step, and P(z) is the total 10 Be production rate (spallation + muon) at the depth z in rock.Subaerial erosion during interglacial periods is not included in this version of our model, but is thought to be extremely low in this region.During the current interglacial, well preserved striations and glacial polish between the mouth of Jakobshavn Isfjord (deglaciated ∼10.2 ka) and the historical moraine are evidence for extremely low subaerial erosion rates (Young et al., 2011).Furthermore, subaerial erosion rates derived using cosmogenic-nuclide analysis on tors on Baffin Island at a similar latitude to our fieldsite suggest subaerial erosion rates are <2 mm ka −1 (Margreth et al., 2016).
When the site is ice covered, nuclide decay continues following, where t bur is the burial duration for that time step.During each burial period, we also simulate subglacial erosion by advecting the depth profile toward the surface (i.e., moving the depth profile up in the rock column) according to the prescribed erosion rate and burial duration.The modeled depth profile then begins the next exposure period at an updated 10 Be production rate commensurate with its new depth below the earth's surface.
In sum, we model cosmogenic 10 Be concentrations through the Pleistocene with two free parameters: the pre-Holocene subglacial erosion rate and the historical subglacial erosion rate.For the Holocene, we use the known exposure history at the bedrock core location, and we test a range of Pleistocene exposure histories calculated using threshold values on the benthic δ 18 O stack of Lisiecki and Raymo (2005).Ultimately, we invert for the best-fitting erosion rates using the reduced chi-squared statistic to recover centennial-and orbital-scale subglacial erosion rates at our bedrock core location.

Modeled Orbital-and Centennial-Scale Erosion Rates
Some combination of historical and long-term erosion rates yields a good model-data fit for each exposure history we modeled (determined using threshold values on the δ 18 O curve of 3.3‰-4.0‰;Figures 9 and 10).With the exception of the histories derived using δ 18 O thresholds of 3.3‰ and 3.4‰, historical abrasion rates are consistent across exposure histories (∼0.2 mm yr −1 ), and long-term erosion rates increase with increasing cumulative exposure duration during the Pleistocene (Figure 10).As with the surface samples, we consider the historical erosion rate to be an abrasion rate because we selected a coring site with evidence of abrasion only; however, we consider the Pleistocene erosion rate to be a total erosion rate as both abrasion and quarrying likely took place at this site over the course of the Pleistocene.

Influence of Muon-Produced 10 Be on Recent Erosion Rates and Apparent Exposure Ages
Comparing results from model runs with δ 18 O thresholds of 3.3-3.4‰to those with longer cumulative exposure during the Pleistocene elucidates the role of excess muon-produced 10 Be in influencing recent subglacial erosion rate results.In the exposure histories determined using 3.3‰ and 3.4‰ δ 18 O thresholds, there is little pre-Holocene exposure, and therefore less 10 Be produced throughout the rock column during the Pleistocene.Similar to the curve-fitting exercises described in Section 6.2.1 (Figure 6), a good fit to the data is only achieved when a higher amount of recent erosion is invoked because there is not enough build-up of muon-produced 10 Be at depth.In other words, the inherited muon-produced 10 Be we know to be present at the site increases the e-folding length of the measured 10 Be depth profile, so the modeled depth profiles that fit the data imply that our samples were deeper in the rock column when the measured 10 Be accumulated.Ultimately, the 3.3‰ and 3.4‰ thresholds do not provide enough Pleistocene exposure to account for the excess muon-produced 10 Be observed in the measured concentrations unless we invoke a near-zero Pleistocene erosion rate and a likely too-high historical abrasion rate of ∼0.5 mm yr −1 .
In contrast, the exposure histories from δ 18 O thresholds between 3.5‰ and 4.0‰ have enough cumulative exposure during the Pleistocene to simulate inherited muon-produced 10 Be below ∼2 m depth without relying on an unrealistically high historical erosion rate to replicate that excess 10 Be.The historical erosion rate therefore is constrained by the known Holocene ice-margin history, where too-low (too-high) erosion rates yield too-high (too-low) modeled 10 Be concentrations in the upper ∼2 m when compared with our measurements.Thus, these histories yield a remarkably consistent historical abrasion rate (∼0.2 mm yr −1 ) and a long-term erosion rate that increases with greater cumulative exposure (increasing threshold value) during the Pleistocene (Figure 10).Within uncertainty, this historical abrasion rate of ∼0.2 mm yr −1 is in closer agreement with the abrasion rate determined using surface sample 18JAK-CR1-SURFACE (0.06 ± 0.11 mm yr −1 ).Indeed, the slightly higher historical abrasion rate recovered from the bedrock core may be more realistic than that from the surface sample, as our inverse modeling exercise accounts for the small amount of inherited muon-produced 10 Be present even at the bedrock surface.The presence of inherited muon-produced 10 Be at the bedrock surface also has implications for the generating apparent exposure ages at and beyond Jakobshavn Isbrae.For example, in southwestern Norway, a setting with long ice-free periods during glacial cycles, apparent exposure ages from erratic boulders are, on average, ∼10% older than a basal radiocarbon age on a downflow marine sediment core, which can be perhaps explained by the presence of inherited muon-produced 10 Be in the boulders (Briner et al., 2016).Surprisingly, even at Jakobshavn Isbrae, a setting thought to have negligible inheritance (i.e., exposure ages from surficial bedrock samples are statistically identical to local radiocarbon chronologies from proglacial-threshold lakes), we observed inherited muon-produced 10 Be at depth.The inherited component of the lowest bedrock core sample is <1% of the 10 Be concentration at the surface, a value less than measurement error in our surface sample and therefore undetectable.Even in places where the inherited muon-produced 10 Be comprises a larger fraction of the surface concentration, use of a locally calibrated 10 Be production rate likely counteracts the overall effect of inheritance on the chronology.Here, the production rate we use for calculating apparent exposure ages was calibrated using samples just down-fjord from our field site (Young, Schaefer, et al., 2013), which likely contain a similar amount of inherited muon-produced 10 Be as these calibration samples were likely sourced from the same bedrock terrain (i.e., same long-term exposure and burial history).When calculating exposure ages, the inherited muon-produced 10 Be in the calibration data offsets the inherited component of our surface samples of unknown age, so the deglaciation chronology presented here is likely unaffected by inheritance.Nevertheless, identifying an inherited muon component at depth highlights the potential for using bedrock cores to identify inherited nuclides that lead to spurious glacial chronologies.

Best-Fitting Orbital-Scale Erosion Rates
The long-term erosion rate that best fits the measured 10 Be concentrations in our bedrock core is directly related to the duration of exposure during the Pleistocene, as more (less) exposure requires higher (lower) subglacial erosion rates to produce modeled 10 Be concentrations that match the measured data.Although the Holocene exposure history at our core location is precisely known, little is known about pre-Holocene configurations of Jakobshavn Isbrae and, more broadly, the GrIS margin.Nevertheless, we can determine which of our employed δ 18 O thresholds yield the most plausible glacial histories for our site given broad constraints on GrIS configurations throughout the Pleistocene and ultimately narrow down the range of possible orbital-scale subglacial erosion rates at Jakobshavn Isbrae.
We first compared the amount of modeled exposure during the last interglacial period (Marine Isotope Stage [MIS] 5e) in each of our model runs to what is known about the likely duration of MIS 5e exposure along the western GrIS.Triple cosmogenic-nuclide measurements ( 14 C-26 Al-10 Be) from the Nuuk region indicate that ∼10-15 kyr of inheritance is present in the surficial bedrock at several ice-marginal locations that also deglaciated during historical times; based on the 26 Al/ 10 Be concentrations at these locations, this excess exposure most likely comes from MIS 5e (Young et al., 2021).The exposure histories for our core site derived using δ 18 O thresholds of 3.3‰ (zero exposure during the Last Interglacial) and 3.4‰ (3 kyr exposure during the Last Interglacial from 131-129 ka), likely have too little exposure during the Last Interglacial, while the history associated with the δ 18 O threshold of 4.0‰ (53 kyr exposure during the Last Interglacial and into the last glacial period), likely has too much, although not impossible, exposure during the last glacial cycle (Table 3).In contrast, δ 18 O thresholds between 3.5‰ and 3.9‰ yield plausible exposure durations at our field site during MIS 5e (7-19 kyr; Table 3).
That the Pleistocene exposure histories derived using δ 18 O thresholds of 3.3‰ and 3.4‰ have too little cumulative exposure is corroborated by other cosmogenic nuclide studies that have implications for the general Pleistocene exposure history in Greenland.Strunk et al. (2017) used multiple cosmogenic isotopes to suggest that sample locations in western Greenland positioned similarly to our site (i.e., low elevation, adjacent to fast flowing ice streams) were perhaps exposed for ∼60% of the last million years.Although our model considers the entire Pleistocene, the histories associated with δ 18 O thresholds of 3.3‰ and 3.4‰ indicate ice-free conditions at the core site only 2% and 6% of the Pleistocene, respectively, which is probably too little exposure (Table 3; i.e., Strunk et al., 2017).Finally, 10 Be concentrations from a bedrock core from beneath the GISP2 ice-core site, at the center of the GrIS (Figure 1), likely equate to ∼200-280 kyr of cumulative exposure during the Pleistocene (Schaefer et al., 2016).Our bedrock core location at the margin of the GrIS must have experienced more cumulative surface exposure than an interior site such as GISP2, yet histories derived using δ 18 O thresholds of 3.3‰ and 3.4‰ have only 44 and 166 kyr exposure, respectively (Table 3).Given this sparse knowledge of pre-Holocene configurations of the GrIS, we suggest that the histories associated with δ 18 O thresholds of 3.5‰-3.9‰are most plausible for our core location at Jakobshavn Isbrae.The best-fitting orbital-scale erosion rates for these exposure histories are between 0.1 and 0.3 mm yr −1 (denudation rate of 70-140 m Myr −1 ; Figure 10; Table 3).The historical abrasion rates recovered from this modeling effort (0.2 mm yr −1 ) scales to a total erosion (abrasion + quarrying) rate of 0.3-0.6 mm yr −1 , which is in agreement with the erosion rate derived from the surface samples of 0.4-0.8mm yr −1 .
Down-core 10 Be measurements in proglacial bedrock cores are a novel tool for directly quantifying subglacial erosion rates.Using simulations of 10 Be accumulation/decay and subglacial erosion through the Pleistocene, we are able to replicate centennial-scale subglacial erosion rates determined from surficial bedrock samples.Furthermore, concentrations of inherited 10 Be below ∼2 m depth provide plausible orbital-scale subglacial erosion rates at Jakobshavn Isbrae.When using this method in proglacial settings, known constraints on the glacial history are useful for recovering the most accurate erosion rates.Failing to account for the build-up of muon-produced 10 Be at depth by including a Pleistocene history with sufficient cumulative exposure leads to spuriously high recent (historical) erosion rates (Sections 6.2.3.1).Moreover, our findings indicate that collecting bedrock cores that are ≥4 m depth is required to sufficiently capture the inherited muon-produced component needed for orbital-scale simulations; in cores <4 m, the inherited muon component could be obscured by 10 Be that more recently accumulated.
To further explore the constraints and applications of this method, future model iterations could include multiple cosmogenic nuclides (e.g., 26 Al, 36 Cl, and 14 C), subaerial erosion during intervals of surface exposure in regions where subaerial erosion might be significant, and variable subglacial erosion rates through intervals of ice cover.Nevertheless, with our current model, we demonstrate that the use of bedrock cores in proglacial settings unlocks new applications for using muon-produced cosmogenic nuclides as a means for quantifying both short-and long-term subglacial erosion rates.In sum, we find erosion (abrasion + quarrying) rates at Jakobshavn Isbrae of 0.3-0.8mm yr −1 on centennial timescales (from surface samples and depth profile modeling) and 0.1-0.3mm yr −1 on orbital timescales (from depth profile modeling) provide the best explanation for our measured 10 Be concentrations.

Comparison to Other Erosion Rate Estimates
Our historical (centennial-scale) erosion rate of ∼0.3-0.8 mm yr −1 (abrasion + quarrying; full range encompassed by surface sample and bedrock core results) is consistent with most other modern to millennial-scale estimates from Greenland.Empirical evidence constrains subglacial erosion rates in polar climates to ∼0.01-0.1 mm yr −1 (Hallet et al., 1996;Koppes et al., 2015).In east Greenland, sediment flux data yield a canonical Greenland erosion rate of 0.01-0.04mm yr −1 (Andrews et al., 1994), which Cowton et al. (2012) revised to 0.3 mm yr −1 after accounting for sediment entrained in iceberg mélange after Syvitski et al. (1996).Suspended sediment and solute data from the Watson proglacial river near Kangerlussuaq in central-west Greenland constrain average subglacial erosion to 0.5 mm yr −1 for the years 2006-2016 (Hasholt et al., 2018), although individual years were perhaps as high as 4.5 mm yr −1 (Hogan et al., 2020).Furthermore, suspended sediment load from an individual glacier within the Watson River catchment yielded a higher erosion rate of 4.8 ± 2.6 mm yr −1 from 2009 to 2010 (Cowton et al., 2012).At the Petermann Glacier in northwest Greenland, the thickness of glaciomarine deposits emplaced during the last deglaciation correspond with a deglacial erosion rate of 0.29-0.34mm yr −1 (Hogan et al., 2020).Finally, glaciomarine facies deposited at the mouth of Jakobshavn Isfjord during an 800-year stillstand amid deglaciation in the early Holocene translate to a deglacial erosion rate at Jakobshavn Isbrae of 0.52 mm yr −1 (Hogan et al., 2012(Hogan et al., , 2020)).Notably, these erosion rate estimates in western Greenland are from periods when temperatures were either warm (interglacial) or warming, a factor associated with higher erosion rates owing to increased basal sliding and meltwater flux to the bed (Alley et al., 2019).
Our orbital-scale erosion rate of 0.1-0.3mm yr −1 (denudation rate of 70-140 m Myr −1 ; Table 3) also agrees with previous estimates, although even fewer erosion rate estimates exist for Greenland prior to the last deglaciation.Goehring et al. (2010) estimate 2-34 m of erosion during the last glacial period using 10 Be depth profiles in raised marine and lacustrine deposits in the Scoresby Sund region, eastern Greenland, which scales to tens to hundreds of meters of subglacial erosion at this location since the start of the Pleistocene.In western Greenland, Strunk et al. (2017) use the lack of inherited 10 Be in some surficial bedrock samples to suggest that >50 m Myr −1 of denudation must have taken place during the Pleistocene.Finally, Corbett et al. (2021) posit that cobbles emerging directly from the GrIS in western Greenland were sourced from deeply eroded interior landscapes that, at minimum, experienced ∼20-50 m Myr −1 erosion over the Pleistocene.Our long-term erosion rate is consistent with these previous estimates, but provides more specificity in that it does not rely on a lack of inheritance (which gives a minimum estimate) but rather on the presence of inherited muon-produced 10 Be that holds direct information about erosion rates on orbital timescales.

Are Centennial-and Orbital-Scale Erosion Rates the Same Near Jakobshavn Isbrae?
In comparing erosion rates across millions-of-years to modern timescales, several studies have observed the so-called "Sadler Effect" (Sadler, 1981;Schumer & Jerolmack, 2009) or an apparent decrease in glacial erosion rate with increasing averaging timescale (Ganti et al., 2016;Herman et al., 2013;Koppes & Montgomery, 2009;Willenbring & Jerolmack, 2016).That is, it appears that erosion rates have increased through the late Cenozoic toward the present, with the highest erosion rates occurring today.For example, apparent erosion rates increased two-to three-fold in Alaska, the Pacific Northwest, and Patagonia on timescales from 10 7 to 10 1 years (Koppes & Montgomery, 2009).While some authors interpret this to mean that the magnitude of erosion has increased as a result of late Cenozoic cooling and concomitant glacial expansion (Herman & Champagnac, 2016), others posit that the intermittency of glacial erosional processes can explain the apparent increase as the methods used necessarily integrate erosion rates from some time in the past to the present, including times when erosion is fast, slow, and even absent (Ganti et al., 2016;Willenbring & Jerolmack, 2016).
The similarity between our centennial-scale erosion rate (0.3-0.8 mm yr −1 ) and orbital-scale erosion rate (0.1-0.3 mm yr −1 ) suggests that, broadly, average erosion rates in the Jakobshavn forefield have remained relatively constant throughout the Pleistocene.Because our model simulates erosion only during glacial periods, our results are not biased by averaging timescale, as are methods that integrate over erosional pulses and hiatuses on long timescales (Ganti et al., 2016;Sadler, 1981;Willenbring & Jerolmack, 2016).We recognize that our model does not simulate variable erosion rates throughout the Pleistocene; rather, our orbital-scale erosion rate represents a Pleistocene average.Nevertheless, had a pattern of increasing erosion rates through the Pleistocene been present at Jakobshavn Isbrae, we might expect historical erosion rates to be an order of magnitude or two higher than the long-term rate.Yet, our findings do not preclude times with higher-than-average and lower-than-average erosion rates during the last ∼2.7 Myr, as such variability might be expected given the degree of climate variability on these timescales (e.g., Ganti et al., 2016).
Although in apparent disagreement, the relatively uniform erosion rates across the Pleistocene derived from our bedrock core and the increasing erosion rates implied by sediment flux records might actually be compatible when considering the evolution of glaciated landscapes.Our measurements are from a low-relief, interfjord plateau, whereas sediment-flux-derived erosion rates likely bias toward erosion within fjords.Interfjord plateaus like the one we sampled are thought to result from either selective linear erosion (Jamieson et al., 2014;Sugden, 1978) or feedbacks between erosion, ice dynamics, topography, and glacial-isostatic adjustment (Egholm et al., 2017).In these respective frameworks, subglacial erosion rates over interfjord plateaus are either expected to remain uniformly low or even decrease through the Pleistocene (Egholm et al., 2017).In contrast, landscape evolution modeling shows that fjord development over the Pleistocene initiated positive feedbacks between topographic steering, ice thickening, and faster ice flow that enhanced erosion within valleys, resulting in increased erosion with successive glaciations (e.g., Kessler et al., 2008), which is consistent with empirical measurements biased toward erosion in fjords.On first order, this comparison provides empirical evidence for the theoretical feedbacks that create fjords and otherwise preserve topography in glaciated landscapes.

Conclusions
New 10 Be measurements in bedrock in front of Jakobshavn Isbrae afford direct constraints on centennial-and orbital-scale erosion rates.Erosion rates calculated from thirty-five 10 Be measurements in surficial bedrock represent an overall abrasion rate of 0.31 ± 0.34 mm yr −1 , which scales to a total erosion rate (abrasion + quarrying) of 0.4-0.8mm yr −1 for historical times.Fourteen surficial bedrock samples with significantly younger apparent 10 Be ages were likely covered by sediment during the middle Holocene that was later removed during the interval of historical ice cover, experienced more Holocene ice cover, or both.
Below ∼2 m depth, samples from a 4-m-long bedrock core contain excess 10 Be compared to an idealized cosmogenic 10 Be depth profile, affording quantification of subglacial erosion on Pleistocene timescales.Modeling of 10 Be accumulation and subglacial erosion through the Pleistocene indicate that the measured 10 Be concentrations in our bedrock core are most consistent with a historical erosion rate of 0.3-0.6 mm yr −1 , in agreement with our results from the surficial bedrock samples, and an orbital-scale erosion rate of 0.1-0.3mm yr −1 .Here, we demonstrate the efficacy of using 10 Be measurements in proglacial bedrock cores to directly quantify past subglacial erosion rates.When applying this method, we recommend using bedrock cores that are ≥4-m-long to sufficiently capture any excess muon-produced nuclides at depth.Our results reveal that subglacial erosion rates have likely remained relatively constant through the Pleistocene on the interfjord plateau near Jakobshavn Isbrae.

Figure 4 .
Figure 4. Schematic of the Jakobshavn Isbrae forefield describing how erosion rates are derived from the measured 10 Be concentrations.The bedrock outboard (left) of the historical moraine experienced only one continuous period of exposure during the Holocene, as shown in the timeline, so a surface sample collected at the light green circle would have an apparent exposure age that reflects the true deglaciation age of the site.The bedrock inboard (right; sample location similar to that of Young et al. (2016)) of the moraine, shown in pink, has a complex exposure history, including the ∼90 years of ice cover at the end of the Holocene.During this most recent period of ice cover, any subglacial erosion would remove the upper portion of the 10 Be depth profile in the bedrock, accumulated from previous exposure, so the measured 10 Be concentration would be lower than the true exposure age.For the sake of illustration, a surface sample collected at the pink circle experienced 1-m of subglacial erosion during historical cover, and therefore its 10 Be concentration would be 20% of the expected concentration.

Figure 5 .
Figure5.Calculated erosional depths and abrasion rates from 10 Be measurements in surficial bedrock samples inboard of the historical moraine near Jakobshavn Isbrae.The dashed line is the 10 Be production profile, normalized to surface production.Note that this line is not fit for the calculated erosion depths, rather this production profile is used to determine erosional depths so all data will fall on this line.Symbols are colored according to apparent exposure age as in Figure1, circles represent data from this study and triangles show results fromYoung et al. (2016).The mean erosional depth for each group is plotted as a horizontal dashed black line, and the average erosional depth and abrasion rate (mean ± SD) are plotted above and below the line, respectively.Abrasion rates were determined using site-specific durations of historical cover, ranging from 87 to 222 years.

Figure 6 .
Figure6.10 Be production rate curves fit to measured 10 Be concentrations in 4-m-long bedrock core 18JAK-CR1.(a) Best-fitting 10 Be production profile with depth.Here, the curve is fit by multiplying the 10 Be production rate curve by a scalar that is roughly equivalent to the exposure age.Widths of red boxes show 1σ measurements uncertainty.Measured 10 Be concentrations below ∼2 m depth are consistently higher than those predicted from the 10 Be production with depth, giving a poor fit to the data overall.(b) Best-fitting 10 Be depth profile adjusted for mass cover prior to the historical period (i.e., adjusted for subglacial erosion during historical ice cover).Predicted 10 Be concentrations are consistent with measured concentrations throughout the core.(c) Historical erosion rate and exposure age used to find the bestfitting curve in panel b.Best-fitting scenario shown as a black square.Red circle denotes the erosion rate and exposure age calculated from the 10 Be concentration of the surface sample 18JAK-CR1-SURFACE, taken from the bedrock surface immediately surrounding the top of the borehole.The simple adjustment for mass in the middle panel yields results with an exposure duration and erosion rate that are inconsistent (considerably higher) with those derived from the surface sample.

Figure 7 .
Figure 7. Measured 10 Be concentrations represent subglacial erosion on a range of timescales.(a)10 Be depth profiles modeled using the known Holocene history at the bedrock core site, with subglacial erosion of 0-50 cm during historical cover (plotted every 5 cm).Note that a higher degree of subglacial erosion effectively "truncates" the 10 Be depth profile from the top.Measured 10 Be concentrations in the bedrock core are plotted in red, and are most consistent with ∼0-10 cm of erosion during historical cover.However, measured 10 Be below ∼2 m depth exceeds modeled 10 Be in all scenarios.Dark gray envelope is 10% uncertainty in the muon production rate and light gray envelope is 25% muon uncertainty.(b) Measured 10 Be concentrations plotted as apparent exposure ages in excess of the known exposure age for the core site (∼7,300 years).Ages that plot to the left of zero require erosion (i.e., exposure ages are less than expected), and those that plot to the right of zero contain muon inheritance (i.e., exposure ages are greater than expected), which can be used to determine orbital-scale erosion rates.In both panels, widths of red boxes show 1σ measurement uncertainty.

Figure 8 .
Figure 8. Cartoon showing how excess10 Be builds up at depth over many glacial cycles (concept adapted fromPloskey and Stone (2014)).Each panel shows the same bedrock coring location (red arrow) and associated 10 Be depth profiles at different points throughout several glacial cycles.The black depth profiles show the expected 10 Be concentration based on the 10 Be production curve, and red depth profiles show the 10 Be concentration that would be measured at the end of each period represented by that panel.(1) At the end of the first exposure (interglacial) period, the measured 10 Be depth profile will look like the 10 Be production profile.(2) During the following burial (glacial) period, subglacial erosion takes place, removing 10 Be from the top down.At the end of the glacial period, the 10 Be depth profile will appear truncated according to how much erosion took place.(3) During a subsequent exposure (interglacial) period, 10 Be will again accumulate with the shape of the 10 Be production profile (black).At the surface, where production is spallation-dominated, this new production would overpower any 10 Be leftover from the last glacial cycle.At depth, however, where 10 Be production is low and muon-dominated, the leftover 10 Be from the previous glacial period becomes important.(4) Over many glacial cycles, this muon-produced 10 Be from previous exposure periods builds up and, while generally overpowered by the most recent spallation signal at the surface, causes there to be measurable excess 10 Be at depth.Therefore, excess 10 Be only occurs after at least one period of erosion from the surface.For the sake of illustration, the glacial periods used to create this cartoon are 90 kyr, the interglacial periods are 10 kyr, and 4 m of erosion takes place during each glacial period.In reality, the amount of excess 10 Be at depth is dependent on the erosional depth (rate) during glacial periods.

Figure 9 .
Figure 9. Best-fitting centennial-and orbital-scale erosion rates for the glacial history determined using a δ 18 O threshold of 3.7‰, the known glacial history for the Holocene (Section 5) and an initial steady-state erosion rate of 5 m Myr −1 .This is one example of a model result, illustrating how 10 Be accumulation/removal during the Pleistocene explains the measured excess 10 Be at depth.Model results for all exposure histories are shown in Figure 10.(a) Benthic δ 18 O stack (Lisiecki & Raymo, 2005) with horizontal red line showing threshold value for this model run.Glacial history at the core site shown in the bar at the top of the figure, where blue is times the core site is ice covered (erosion) and red is times the site is exposed (nuclide accumulation).(b) Misfit of modeled 10 Be depth profiles to measured 10 Be concentrations using different combinations of historical and orbital-scale subglacial erosion rates.The best-fitting combination of Pleistocene and historical erosion rates is shown at the red circle.(c) Modeled best-fitting 10 Be concentrations at the core sample depths (black) and the measured 10 Be concentrations of the core samples (red).Widths of red boxes show 1σ measurement uncertainty.The reduced χ 2 statistic, historical abrasion rate, and orbital-scale erosion rate of the best-fitting scenario are shown in text within the figure.In the best-fitting scenario, modeled 10 Be concentrations are consistent with the measured 10 Be concentrations at all depths and the historical abrasion rate is comparable to that determined from the surface sample 18JAK-CR1-SURFACE.

Figure 10 .
Figure 10.Best-fitting erosion rates for glacial histories determined using δ 18 O thresholds of 3.3-4.0‰,the known glacial history for the Holocene (Section 5), and an initial steady-state erosion rate of 5 m Myr −1 .Model runs with initial steady-state erosion rates of 10 and 50 m Myr −1 are nearly identical and shown in Figure S1 in Supporting Information S1.(a) Glacial history at the core site shown in the bar at the top of each figure, where blue is times the core site is ice covered and red is times the site is exposed.The color maps show the misfit of modeled 10 Be depth profiles to measured 10 Be concentrations using different combinations of historical abrasion and orbital-scale subglacial erosion rates for each of the glacial histories.The reduced χ 2 statistic of each best-fitting scenario is shown in text within each figure.(b) Scatter plot of the best-fitting Pleistocene erosion and historical abrasion rates for each δ 18 O threshold, with the δ 18 O thresholds yielding the most plausible glacial histories shown within the gray box.

Table 2
10Be Concentrations in Bedrock Core18JAK-CR1  et al., 2016, Table Model start time is no earlier than the beginning of the Pleistocene (2.7 Ma), but begins at the first burial.bFor the exposure history derived using a δ 18 O threshold of 3.9‰, there is also 6 kyr of exposure during MIS 5c.The exposure history determined using a δ 18 O threshold of 4.0‰ has 53 kyr total exposure across MIS 5.Best-fitting Pleistocene erosion rate from model described in Section 6.2.2.d Best-fitting Pleistocene erosion rate from model scaled up to m/Myr.e Total erosion since model start divided by model start time.In comparison to other studies that report a total denudation rate.f Best-fitting historical abrasion rate from model described in Section 6.2.2.g Best-fitting historical erosion rate, scaled up from abrasion rate to include the effects of quarrying.
a c

Table 3
Information About Glacial History Inputs to Cosmogenic-Nuclide Model for Bedrock Core 18JAK-CR1 and Erosion Outputs