New Last Glacial Maximum Ice Thickness constraints for the Weddell Sea sector, Antarctica

. This paper describes new Last Glacial Maximum (LGM) ice thickness constraints for three locations spanning the Weddell Sea Embayment (WSE) of Antarctica. Samples collected from the Shackleton Range, Pensacola Mountains, and the Lassiter Coast constrain the LGM thickness of the Slessor Glacier, Foundation Ice Stream, and grounded ice proximal to the 15 modern Ronne Ice Shelf edge on the Antarctic Peninsula, respectively. Previous attempts to reconstruct LGM-to-present ice thickness changes around the WSE used measurements of long-lived cosmogenic nuclides, primarily 10 Be. An absence of post-LGM apparent exposure ages at many sites led to LGM thickness reconstructions that were spatially highly variable, and inconsistent with flowline modelling. Estimates for the contribution of the ice sheet occupying the WSE at the LGM to global sea level since deglaciation vary by an order of magnitude, from 1.4 to 14.1 m of sea level equivalent. Here we use a 20 short-lived cosmogenic nuclide, in situ produced 14 C, which is less susceptible to inheritance problems than 10 Be and other long-lived nuclides. We use in situ 14 C to evaluate the possibility that sites with no post-LGM exposure ages are biased by cosmogenic nuclide inheritance due to surface preservation by cold-based ice and nondeposition of LGM-aged drift. Our measurements show that the Slessor Glacier was between 310 and up to 655 m thicker than present at the LGM. The Foundation Ice Stream was at least 800 m thicker, and ice on the Lassiter Coast was at least 385 m thicker than present at the 25 LGM. With evidence for LGM thickening at all of our study sites, our in situ 14 C measurements indicate that the long-lived nuclide measurements of previous studies were influenced by cosmogenic nuclide inheritance. Our LGM thickness constraints point toward a modest contribution from the WSE to global sea-level since deglaciation, with an estimated minimum contribution of <4.6 m, and possibly <1.5 m, based on the evidence for the lower limit of LGM thickness change at our study sites. m and up to 655 m thicker than present at the LGM. Finally, LGM ice was at least 385 m thicker than present at the Lassiter Coast. Our thickness constraints resolve a significant disconnect between previous terrestrial evidence for minimal LGM thickening in some locations from long-lived nuclides, and marine evidence for a significantly laterally expanded ice sheet with the grounding line located at the offshore shelf edge. Our in situ 14 C measurements made from samples at the Schmidt Hills exhibit higher than expected scatter in replicate measurements. Identifying the source of excess scatter will take further 5 work. In terms of the contribution of the ice sheet sector to global sea-level rise since the LGM, we estimate that the WSE contributed modestly, with a rough minimum estimate of <4.6 m, and possibly as little as <1.5 m.


'covered and uncovered' in place or during transport, as long as it has been buried long enough and then deposited by the ice, with no subsequent movement? Also avoid moving back-and-forth between discussing bedrock and erratics.
We want to include the text in this section because we wanted to briefly discuss potential limitations of the method, as well as introduce some concepts that we discuss later on in the paper when we assess the in situ 14C data (Sect. 4.1). In particular we wanted to introduce the observation of Balco et al. (2019) of mass movement and supraglacial transport potentially resulting in saturated in situ 14C concentrations collected from lower elevations than finite ages, which goes against the assumption that erratics and bedrock will always yield the same information with respect to ice thinning when using in situ 14C.

P3, L46: specify which assumption.
We added "that bedrock and erratic samples provide the same information with respect to the timing of changes in ice thickness" to P4, line 6 to 7.

P4, L9-11: I don't think it is necessary to repeat this information here
We removed the text.

P6, L. 43-46: At present this section has a bit of an 'ad-hoc argument' feel to it, I think it would be better to first provide an objective discussion on what criteria can be used to assess the validity of this method before you go through each site.
We have added a few sentences to the start of this section to introduce the section. The following text is now on P7, lines 15 to 19: "To assess the validity of this method, we can, for example, identify where the in situ 14C data records ice thinning, with saturated samples or the oldest exposure ages at the highest elevations and a trend of decreasing in situ 14C age toward modern ice surfaces. Consistency between in situ 14C data and other nuclide concentrations (e.g. 10Be) could also help validate the in situ 14C measurements. We also look at factors beyond the in situ 14C concentrations, such as the glaciological link between study sites, which may add clarity where the in situ 14C measurements show a high degree of scatter."

P6, L. 44: I don't think the Lassiter coast dataset can be strictly described as having a 'linear ageelevation relation', as it requires at least two lines two fit the data. Perhaps rephrase to 'ages continuously decrease towards the present ice sheet surface'.
We have altered the text accordingly.

P7, L7: 008-NNS doesn't seem to be replicated here? I don't find a saturated (replica-) measurement in the table or figure.
This sample, 008-NNS, was measured once in this study, and also once in the study by Balco et al. (2016). We altered the text (P7, lines 31 to 33) to hopefully make this clearer.

P7, L12-13: You don't present replicate measurements from elsewhere than the Schmidt hills, so this sentence reads a bit strange.
To address this, we have changed the sentence to: "Why the replicate measurements from samples from the Schmidt Hills display a high degree of scatter remains to be determined." (P7, lines 36 to 37).

P7, L14: This transition was not obvious to me. This also goes for the next two paragraphs, I think you could link the various paragraphs discussing the poor replicability better. The 'Regardless,' makes it sounds like you are moving on to another subject. This paragraph is discussing whether there could be any geological reasons that the in-situ 14C profiles are 'inverted'?
To add clarity to this section we have altered the transitions between the paragraphs to help the section flow better and have also changed the order of the paragraphs to an order that is more logical. We also expanded on the sentence that started with "Regardless" so that it now reads: "Regardless of the cause of the high degree of scatter observed in the replicate measurements, we need to discuss possible explanations for apparently infinite ages at lower elevations than apparently finite ages to isolate which measurements (infinite vs finite replicates) are the most valid to base interpretations on." (P8, lines 3 to 5).

P7, L26-27: I couldn't follow this argument.
We agree that this was confusing, and have altered the text (P8, lines 16 to 18): "Whilst this could explain the low-elevation saturated sample at Mt. Skidmore, as well as infinite measurements situated beneath finite measurements at the Schmidt Hills, it does not explain the poor reproducibility of the Schmidt Hills measurements."

P7, L37: I think you need to discuss here whether or not you expect the same issue for the saturated, but non-replicated sample from Mount Provender. Given only two data points from this site, the fact that the 'profile' isn't inverted is not a very strong argument, or?
We agree that the fact that the profile of two data points at Mt. Provender is not a strong argument, which we think is adequately covered by the preceding phrase "Though limited by the number of samples". Regarding the saturated sample at Mt. Provender, we now explain our thoughts on the robustness of this measurement in the Discussion (see our response to the first main concern of reviewer 1). In the introduction and conclusion, we use the phrase "up to 655 m" in the Introduction and Conclusion (P1, line 24, and P11, line 1). We also highlight the limitation in the Results (P6, lines 21 to 25) and the Discussion. Despite the reasons to believe it is a robust measurement, we only use the minimum LGM ice thickness constraints for the sea-level contribution discussion.

P8, L11: provide the in situ 14C ages with uncertainty here to make it easy for the reader to compare
We added the ages to the text. P9, L23: You first state that your data 'do not preclude a significant contribution earlier than (the early to mid-Holocene)', yet move directly on to suggest that MWP1A was not significant in this region, thus contra-arguing yourself. I don't think you can constrain MWP1A thinning on the basis of these data.
We agree and have removed any reference to MWP1a, see above responses.

Fig. 1: boxes should refer to Fig 4a-d, not 2a-d.
We have altered the labels of the boxes accordingly.

Fig. 3: specify that you used zero erosion (presumably) for these calculations. It looks strange to me that the saturated samples are labelled as 'true' exposure. The figure is a bit blurry compared to the others.
We have added "assuming no surface erosion" to the caption. By "true" we mean a concentration that is equivalent to the ice history in the left plot. We agree that using "age" is strange when it includes saturated samples, so we changed the caption to reflect this. Now reads: " "True exposure" refers to the resulting 14C concentration associated with the ice surface change history on the left plot." We updated the Figure so that it is the full resolution, thank you for highlighting this.

Fig. 4: green color of sample points in legend and on map does not appear to be the same
We have altered the figure so that the green colour is the same for the sample points in the map and the legend. We will make sure this is added in the final version.

Fig. 9+10: legend refers to maps on left, but they are on the right
Text changed accordingly.

P1, L32: Should Antarctic ice sheet(s) be in plural, west+east?
We think it would be fair to use the plural, but we stick to the singular when referring to both the east and west ice sheets at the same time. See Bentley and Anderson (1998) whom refer to the ice sheets individually as well as collectively as the "Antarctic ice sheet" in the first two paragraphs of their introduction. Also see the title of Hillenbrand et al. (2014) "Reconstruction of changes in the Weddell Sea sector of the Antarctic Ice Sheet since the Last Glacial Maximum".

P2, L18: specify 'non-erosive' burial
We have added this to the text.

P3, L22: 'measured today' seems unnecessary
Agreed, we removed this from the text.

P7, L17: fig 10 referred before fig. 9. Fontsize is odd
We have changed the text so that Fig. 10 is referred to after Fig. 9, and fixed the font size. (now Figs. 10 and 11 with the addition of a new figure).

Supplementary table S2: Spreadsheet tab is named '
We changed the name of the tab in Table S2. LGM-to-present ice thickness changes around the WSE used measurements of long-lived cosmogenic nuclides, primarily 10 Be. An absence of post-LGM apparent exposure ages at many sites led to LGM thickness reconstructions that were spatially highly variable, and inconsistent with flowline modelling. Estimates for the contribution of the ice sheet occupying the WSE at the LGM to global sea level since deglaciation vary by an order of magnitude, from 1.4 to 14.1 m of sea level equivalent. Here we use a 20 short-lived cosmogenic nuclide, in situ produced 14 C, which is less susceptible to inheritance problems than 10 Be and other long-lived nuclides. We use in situ 14 C to evaluate the possibility that sites with no post-LGM exposure ages are biased by cosmogenic nuclide inheritance due to surface preservation by cold-based ice and nondeposition of LGM-aged drift. Our measurements show that the Slessor Glacier was between 310 and up to 655 m thicker than present at the LGM. The Foundation Ice Stream was at least 800 m thicker, and ice on the Lassiter Coast was at least 385 m thicker than present at the

25
LGM. With evidence for LGM thickening at all of our study sites, our in situ 14 C measurements indicate that the long-lived nuclide measurements of previous studies were influenced by cosmogenic nuclide inheritance. Our LGM thickness constraints point toward a modest contribution from the WSE to global sea-level since deglaciation, with an estimated minimum contribution of <4.6 m, and possibly <1.5 m, based on the evidence for the lower limit of LGM thickness change at our study sites.

Introduction
This paper describes new in situ produced 14 C derived Last Glacial Maximum (LGM) ice thickness constraints from three locations within the Weddell Sea Embayment (WSE) of Antarctica (Fig. 1). We broadly define the LGM as the period between ~15 and 25 ka when the Antarctic ice sheet volume was near its maximum extent in the last glacial-interglacial cycle. The WSE drains approximately one fifth of the total area of the Antarctic ice sheet (AIS) (Joughin et al., 2006) and is 35 thus an important contributor to LGM-to-present and, potentially, future sea-level change. Previous attempts to reconstruct LGM-to-present ice thickness changes around the WSE used measurements of long-lived cosmogenic nuclides, primarily 10 Be (half-life 1.387 ± 0.012 Ma) and 26 Al (half-life 705 ± 17 ka). An absence of post-LGM apparent exposure ages at many sites led to LGM thickness reconstructions that were spatially highly variable, and inconsistent with flowline modelling. Consequently, estimates based on ice models constrained by field evidence (Le Brocq et al., 2011) and by relative sea-level 40 records and earth viscosity models (Bassett et al., 2007) for the contribution of the sector to global sea-level since deglaciation began vary by an order of magnitude, from 1.4 to 14.1 m, respectively. The lack of geological evidence for LGM thickening is also manifest in a misfit between present day geodetic uplift rate measurements in southern Palmer Land and predicted uplift rates from a glacial isostatic adjustment (GIA) model (Wolstencroft et al., 2015). Constraining the previous vertical extent of ice provides inputs to numerical models investigating both the response of the ice sheet to past and potential future changes in climate and sea-level (e.g. Briggs et al., 2014;Pollard et al., 2016;Whitehouse et al., 2017), as well as the response of the solid earth to past ice load changes to quantify present day ice-mass loss (e.g. 5 Wolstencroft et al., 2015). Furthermore, quantifying the LGM dimensions of the WSE sector of the AIS is required to further constrain the offset between estimates for post-LGM sea-level rise and estimates of the total amount of ice melted since the LGM. The former is sourced from sea-level index points, and the latter is sourced from our knowledge of the dimensions of ice masses at the LGM (Simms et al., 2019). Currently, the "missing ice" accounts for between 15.6 ± 9.6 m and 18.1 ± 9.6 m of global sea-level rise since the LGM (Simms et al., 2019).

10
Although the use of cosmogenic nuclide geochronology to study the AIS is clearly proven (e.g. Stone et al., 2003;Ackert et al., 2007), applications in the WSE are challenging. Many studies, despite making multiple cosmogenic nuclide measurements from relatively large numbers of samples, observed no or few post-LGM exposure ages (Hein et al., 2011Balco et al., 2016;Bentley et al., 2017). With no evidence for LGM ice cover, it was not clear whether sites were covered by ice at the LGM, or whether sites were covered but the ice left no fresh deposits on top of those yielding pre-LGM 15 ages. It is therefore currently unknown whether ice was thicker than present during the LGM at the Schmidt Hills in the Pensacola Mountains, and in the Shackleton Range (Figs. 1 and 2). Results from the Schmidt Hills ( Fig. 2) indicating no LGM thickening of the Foundation Ice Stream (FIS) are particularly problematic, as thickening of 500 m from the Williams Hills, 50 km upstream of the Schmidt Hills, produces a LGM surface slope that exceeds glaciological models and presentday ice surfaces (Huybers, 2014;Balco et al., 2016). Cold-based ice and an associated lack of subglacial erosion is the likely 20 cause of the complex 10 Be data sets, evidenced by numerous studies in the WSE that report 10 Be and 26 Al ratios significantly below those predicted for continuous exposure which is indicative of significant periods of non-erosive burial (e.g. Bentley et al., 2006;Sugden et al., 2017). Cold-based ice preserves surfaces (Sugden et al., 2005), allowing nuclide concentrations to persist within surfaces from previous periods of exposure to the present, a phenomenon known as inheritance. Long-lived nuclides are particularly susceptible to inheritance due to their long half-lives which, when protected from erosion beneath 25 cold-based ice, require long periods of burial to reduce concentrations to below measurable levels. When covered by coldbased ice during glaciations, concentrations of long-lived nuclides record exposure during multiple separate ice free periods rather than just the most recent one. Inheritance thus hinders interpretations of cosmogenic nuclide measurements.
We resolve conflicting LGM thickening estimates based on 10 Be measurements by using measurements of in situ produced 14 C, a cosmogenic nuclide that is, owing to a short half-life of 5730 yr, largely insensitive to inheritance. We 30 present the in situ 14 C analysis of transects of erratic and bedrock samples from the Shackleton Range, Lassiter Coast and Pensacola Mountains (Fig. 1). Our results constrain the LGM thickness of the Slessor Glacier to between 310 and up to 655 m. We show that ice was at least 385 m thicker than present during the LGM at the Lassiter Coast, proximal to the modern Ronne Ice Shelf edge. Our data also constrain the LGM thickness of the FIS to at least 800 m at the Schmidt Hills. Replicate measurements made from four samples revealed higher than expected variability of in situ 14 C measurements, which is 35 discussed in Sect. 4.1. Our thickness estimates are comparable to those of Hein et al. (2016) in the Ellsworth Mountains, as well as those of Balco et al. (2016) and Bentley et al. (2017) in the Williams and Thomas Hills. Although our results show that locations around the WSE were buried by hundreds of metres of ice, this is less than called for by some reconstructions, and our inferred LGM configuration indicates a relatively modest contribution to sea-level since the LGM, with a minimum estimate of <4.6 m, and possibly <1.5 m.

The Last Glacial Maximum in the Weddell Sea Embayment
Although it is clear that grounded ice in the WSE has been thicker in the past (Bentley and Anderson, 1998), there is little evidence as to the thickness and grounding line position of the ice sheet at the LGM, with contrasting evidence from marine sources, and those inferred from terrestrial studies (Hillenbrand et al., 2014). Terrestrial evidence for the extent of ice 45 in the WSE during the LGM takes the form of numerous cosmogenic nuclide studies. Bentley et al. (2006) Fogwill et al, 2014;Hein et al., 2016;, the Pensacola Mountains (Hodgson et al, 2012;Balco et al, 2016;Bentley et al, 2017), and the Shackleton Range (Fogwill et al., 2004;Hein et al, 2011;2014). Figure 2 summarises the ice thickness estimates from these studies. The majority of estimates are sourced from 10 Be measurements, with some accompanying 26 Al measurements. Two exceptions are Fogwill et al. (2014) and Balco et al. (2016), whom combined some in situ 14 C measurements with 10 Be measurements to constrain the thickness of the Rutford and Institute ice streams and the 5 Foundation Ice Stream, respectively. The highest elevation post-LGM exposure ages at each site delineate the minimum vertical extent of ice at the LGM. Ice thickness estimates vary spatially around the embayment, ranging from zero to hundreds of metres of LGM thickening.
Marine geological and geophysical evidence in the southern Weddell Sea indicates a significantly expanded WSE LGM configuration, with subglacial till, subglacial bedforms and a grounding zone wedge found towards the offshore shelf 10 edge 2014;Larter et al., 2012;Arndt et al., 2017). As a result, there is currently a disconnect between marine evidence for a greatly expanded WSE sector and terrestrial evidence indicating little to no vertical change at the LGM in some areas. Hillenbrand et al. (2014) propose two potential LGM configurations of the WSE sector of the AIS. The first scenario, based on terrestrial evidence for vertical LGM ice thicknesses, involves a complex configuration with the grounding line of the ice sheet situated towards the offshore shelf edge and a largely ice-free Filchner Trough and western 15 margin of the WSE. The second scenario, based on marine evidence, places the grounding line of the ice sheet at the offshore shelf edge across the width of the WSE. Flowline modelling of the response of the FIS, which occupied the Filchner Trough at the LGM, to the onset of glacial conditions shows that there are two plausible LGM grounding line positions for the ice stream: one situated at the offshore shelf edge, and another at the northern margin of Berkner Island (Whitehouse et al., 2017). 20

In situ 14 C exposure dating
Cosmogenic nuclides 10 Be and 26 Al have half-lives that are much longer than glacial-interglacial cycles, so 10 Be and 26 Al concentrations produced in previous interglacials persist to the present if buried by non-erosive, cold-based ice. The short half-life of in situ 14 C means that only short periods of burial are required to significantly reduce concentrations from 25 previous periods of exposure, making in situ 14 C less sensitive to inheritance than longer lived nuclides. For example, a burial duration beneath non-erosive, cold-based ice of 11 kyr results in ca. 74% of the original in situ 14 C decaying away. Furthermore, continuously-exposed, slowly-eroding surfaces reach an equilibrium between production and decay of in situ 14 C ("saturation") after approximately 30 to 35 kyr. A sample that has reached saturation thus requires low erosion and continuous exposure from before the LGM, whilst a sample that yields a concentration below saturation requires ice cover 30 during the last ca. 35 kyr. Surfaces yielding saturation concentrations therefore provide an upper limit on LGM thickening. Figure 3 shows a hypothetical ice surface elevation change history at a nunatak partially buried by cold-based, non-erosive ice during the LGM, with associated in situ 14 C measurements from samples collected along an elevation transect on the surface of the nunatak. There is a transition from undersaturated to saturated samples, a discontinuity in the 14 C concentrations which constrains the LGM ice thickness. The "true exposure" data points represent in situ 14 C concentrations 35 with resulting exposure ages matching the post-LGM ice-surface lowering history. The "apparent exposure" data points were saturated at the onset of ice cover and include in situ 14 C that persists to the present due to an insufficient amount of time passing for it to decay away. For the five undersaturated samples, which were buried by ice for differing durations, a range of ~2 to ~4 % of the 14 C accumulated prior to burial will persist to the present. In terms of the effect on resulting exposure ages, the sample exposed at 10 ka yields an apparent exposure age of 11.41 ka (~13 % increase), and the sample exposed at 2 40 ka yields an apparent exposure age of 2.17 ka (~8 % increase). Without knowing the burial duration of the samples or whether or not the samples were indeed saturated upon burial by LGM ice, we do not know the exact quantity of in situ 14 C inherited in the samples. The in situ 14 C exposure ages are therefore maximum deglaciation ages. In the same hypothetical scenario with the same samples, ca. 98 % and 97 % of the 10 Be and 26 Al accumulated prior to burial will persist to the present, respectively.

45
We report in situ 14 C concentrations measured from both erratic and bedrock samples, with primarily erratic samples from the Shackleton Range and the Pensacola Mountains, and solely bedrock from the Lassiter Coast. We assume both materials provide the same information regarding the timing of ice retreat and constraining LGM ice thicknesses. For example, we assume that both erratics and bedrock samples saturated with in situ 14 C indicate that their respective sampling locations were ice free for the last 30 to 35 kyr. With the exception of two samples, all of our erratic samples have previously been measured for their 10 Be content (Hein et al., 2011;2014, Balco et al., 2016, with the vast majority yielding ages far in excess of the LGM. It is highly likely that these erratic samples have been repeatedly covered and exposed by cold-based ice. Having been covered and uncovered in situ, the erratic samples can thus effectively be considered bedrock. There are, however, 5 potential situations where our assumption that bedrock and erratic samples provide the same information with respect to the timing of changes in ice thickness is not met and resulting 14 C concentrations misrepresent the age of deglaciation, creating scatter in the measured in situ 14 C data. Erratic samples may, for example, be sourced from mass movement onto glacier surfaces, producing spuriously high 14 C concentrations (See Balco et al., 2019). Spuriously high, in excess of saturation, in situ 14 C concentrations sourced from bedrock samples, however, can only result from analytical errors and thus provides an important test for the premise of the technique. Additionally, erratic cobbles may have undergone downslope movement postdeposition and may have flipped over, or may have been subjected to high erosion rates, which could produce in situ 14 C concentrations with resulting exposure ages lower than the true age of deglaciation. Snow shielding of sample locations is another mechanism leading to exposure ages which underestimate the age of deglaciation and can influence both bedrock and erratic samples. Whilst not without challenges, our in situ 14 C measurements provide an opportunity to unambiguously show 15 whether sites around the WSE were covered by ice at the LGM.

Shackleton Range
The Shackleton Range is located in Coats Land in the northeast WSE, adjacent to the Slessor Glacier (Figs. 1 and 4a). The Slessor Glacier drains ice from the East Antarctic Ice Sheet (EAIS) into the Filchner Ice Shelf. Mt. Skidmore is 20 located approximately 25 km upstream of the modern Slessor Glacier grounding zone, with the Köppen and Stratton glaciers respectively joining the Slessor Glacier to the north and south of Mt. Skidmore (Fig. 4a). Proximal to sampling locations are Ice Tongue A and Ice Tongue B of the Stratton Glacier, and the Snow Drift Glacier (Fig. S1). We assume that samples collected from Mt. Skidmore record changes in the thickness of the Slessor Glacier. However, it is possible that samples collected proximal to the smaller ice masses may have been buried by them, rather than by the Slessor Glacier, potentially 25 complicating the interpretation of results. The modern Slessor Glacier surface is situated at ~200 m asl proximal to Mt. Skidmore, with exposed surfaces of Mt. Skidmore located up to over ~820 m asl. Mt. Provender is located adjacent to the Slessor Glacier grounding zone and is bounded by the Stratton and Blaiklock glaciers to the north and south, respectively. Exposed rock of Mt. Provender rises from the modern ice surface up to over ~900 m asl. We analysed 11 samples from the Shackleton Range (Table S1), with two from Mt. Provender and nine from Mt. Skidmore (Fig. 4a). At Mt. Provender we 30 analysed one erratic cobble from near the modern ice surface and one bedrock sample from ~650 m above it (Fig. S2). Samples from Mt. Skidmore include one bedrock sample and eight cobbles that form an elevation transect from near the modern ice surface to ~300 m above it (Fig. S1). The two highest elevation samples collected from Mt. Skidmore are proximal to the main trunk of the Stratton Glacier more so than the Slessor Glacier, and were collected from ca. 115 and 130 m above the modern Stratton Glacier surface. The two highest elevation samples on Mt. Skidmore therefore may represent a 35 Stratton Glacier ice surface lowering more so than the Slessor Glacier, and thus are presented as a separate sample group to those collected proximal to the Slessor Glacier.

Lassiter Coast
The Lassiter Coast is located on the east coast of southern Palmer Land, adjacent to the present position of the Ronne Ice Shelf edge (Fig. 1). The modern ice surface is situated at 490 m asl. Johnson et al. (2019) collected samples from 40 several sites in this area (Fig. 4) and carried out 10 Be measurements; we subsequently carried out 14 C measurements on these samples as part of the present study, and the 14 C results are reported both here and in Johnson et al. (2019). Here we discuss results for a total of eight bedrock samples from Mt. Lampert and the Bowman Peninsula collected from 20 to 385 m above the modern ice surface (Figs. 4 and S3); see Table S1 for sample data and Johnson et al. (2019) for 10 Be measurements. The adjacent Johnston Glacier drains ice from central Palmer Land into the WSE. We interpret the samples together as 5 effectively a single elevation transect that records changes in the thickness of grounded ice in the WSE immediately east of these sites after the LGM.

Pensacola Mountains
The Schmidt Hills are a series of nunataks adjacent to the FIS in the southeast WSE (Figs. 1 and 4c) downstream and proximal to the modern grounding zone. The FIS is a major ice stream that drains ice from both the EAIS and West 5 Antarctic Ice Sheet (WAIS) into the WSE. The surface of the FIS adjacent to the Schmidt Hills is situated ca. 200 m asl., with exposed surfaces of the Schmidt Hills reaching up to 1100 m asl. The Thomas Hills are another series of nunataks adjacent to the FIS, located ~130 km upstream of the Schmidt Hills (Fig. 4d). The main trunk of the FIS adjacent to the Thomas Hills is near 550 m asl, with the Thomas Hills rising up to 1050 m asl. The local ice margin of the FIS at the Thomas Hills is situated ~75 m below the centre of the FIS. We analysed 17 samples from the Pensacola Mountains (Table   10 S1); 15 from the Schmidt Hills and two from the Thomas Hills. We made a further seven repeat measurements from four samples collected from the Schmidt Hills. Samples from the Schmidt Hills were collected from Mount Coulter and No Name Spur (Figs. 4c and S4) from close to the modern ice surface to approximately 800 m above it. We also analysed two samples from the Thomas Hills which were collected from Mount Warnke ca. 320 m above the FIS ice margin (Figs. 4d and S5). The highest elevation sample from the Schmidt Hills, collected from ca. 1035 m asl, is the only bedrock sample analysed from 15 the Pensacola Mountains, with the rest being erratic cobbles.

Methods
We used between 0.5 and 10 g of quartz from each sample for in situ 14 C analysis. The methodology used for the isolation of quartz varies for samples from different sample sites because quartz was previously isolated for prior cosmogenic nuclide studies (see Hein et al., 2011;Balco et al., 2016). For samples processed at the Tulane University 20 Cosmogenic Nuclide Laboratory (primarily those from the Lassiter Coast), quartz was isolated through crushing, sieving, magnetic separation and froth flotation (modified from Herber, 1969) of sample material. Samples were then etched for at least two periods of 24 hours on both a shaker table in 5 % HF/HNO3 and then in an ultrasonic bath in 1 % HF/HNO3. This leaching procedure removes the organic compound laurylamine used in the froth flotation procedure (Nichols and Goehring, in review.) that could otherwise potentially contaminate our samples with modern carbon.

25
Carbon was extracted using the Tulane University Carbon Extraction and Graphitization System (TU-CEGS), following the method of . Quartz is step-heated in a lithium metaborate (LiBO2) flux and a high-purity O2 atmosphere, first at 500 °C for 30 minutes, then at 1100 °C for three hours. Released carbon species are oxidised to form CO2 via secondary hot-quartz-bed oxidation, followed by cryogenic collection and purification. Sample yields are measured manometrically, and samples are diluted with 14 C-free CO2. A small aliquot of CO2 is collected for δ 13 C analysis, and the 30 remaining CO2 is graphitised using H2 reduction over an Fe catalyst. We measured 14 C/ 13 C isotope ratios at either Lawrence Livermore National Laboratory Center for Accelerator Mass Spectrometry (LLNL-CAMS) or Woods Hole National Ocean Sciences Accelerator Mass Spectrometry (NOSAMS) ( Table S2). Stable carbon isotope ratios were measured at the UC-Davis Stable Isotope Facility.
Apparent exposure ages were calculated using v. 3 of the online calculators formerly known as the CRONUS-Earth 35 online calculators (Balco et al., 2008). The online calculators use the production rate scaling method for neutrons, protons and muons of Lifton et al. (2014) (also known as LSDn). We use repeat measurements of the in situ 14 C concentration of the CRONUS-A interlaboratory comparison standard (Jull et al., 2015; to calibrate the 14 C production rate. We assume CRONUS-A is saturated with respect to in situ 14 C, given that, based on geological mapping and an ash chronology, the sampling location has remained ice-free since >11.3 Ma (Marchant et al., 1993). All reported in situ 14 C 40 measurements from CRONUS-A, made at multiple laboratories, yield concentrations equivalent to saturation based on other calibration data from elsewhere in the world (e.g. Jull et al., 2015;Fülöp et al., 2018;Lamp et al., 2019). We use the CRONUS-A measurements to calibrate the 14 C production rate to reduce scaling extrapolations. Repeat measurements of both CRONUS-A and other samples using the TU-CEGS show that the reproducibility of in situ 14 C measurements is approximately 6 %. We therefore use a 6 % uncertainty for our measured in situ 14 C concentrations when 45 Deleted: analysed Deleted: et al.

Deleted: preparation
Deleted: was not covered by ice during the LGM. 6 calculating exposure ages, as this exceeds the reported analytical uncertainty for all of our in situ 14 C measurements. Ages are included in Table S2 for completeness but are primarily discussed in the text as either finite or infinite ages. Infinite ages are those for which the measured concentration is above the uncertainty of the saturation concentration for the elevation of a given sample.
As stated in Sect. 1., we made seven replicate measurements from four samples from the Schmidt Hills that initially 5 yielded saturation or near-saturation in situ 14 C concentrations. We made the first four replicate measurements using the same samples to test the validity of the saturation or near-saturation initial measurements. The second set of measurements produced in situ 14 C concentrations below saturation. Given the difference between the initial measurements and the replicates, we made a further three measurements from three of the same four samples. The results of the replicate measurements are discussed in Sect. 3. and 4.1.

Results
The vast majority of the 10 Be ages reported by Hein et al. (2011;2014) in the Shackleton Range exceed 100 ka, whilst we find finite 14 C ages at both Mt. Skidmore and Mt. Provender (Figs. 5 and S6). At Mt. Skidmore, finite ages are evident across the entire Mt. Skidmore transect, including those sampled proximal to the Stratton Glacier (Fig. 5). Samples were collected from multiple ridges of Mt. Skidmore and thus would not necessarily be expected to form a single age-15 elevation line. The uppermost sample proximal to the Slessor Glacier, collected ~310 m above the modern ice surface, provides a lower limit for the LGM ice thickness of the ice mass. The two samples proximal to the Stratton Glacier, an erratic and bedrock sample with ~17 m asl between them, are indistinguishable from one another within uncertainties and constrain the LGM thickness to at least 130 m thicker than present. At Mt. Provender, one sample collected proximal to the local Slessor Glacier margin yields a finite age. A second sample from ~890 m asl (~655 m above the modern ice surface) 20 yields an infinite age, placing an upper limit on the LGM thickness at ~655 m greater than present. We note that the upper limit of 655 m is based on a single in situ 14 C measurement and discuss this limitation further in Sect. 4.2. If quartz was available for additional samples previously collected from Mt. Provender (Hein et al, 2011;2014), then further measurements could have been made to validate this measurement. The quartz was, however, exhausted in the process of measuring long-lived nuclides. One sample from Mt. Skidmore, collected from ~284 m asl, yields an infinite age. Above the 25 saturated sample we observe seven finite-aged samples which require significant periods of burial beneath ice to account for their in situ 14 C concentrations. It is glaciologically impossible to have the sample at ~284 m asl exposed for ca. 35 kyr whilst those above it were covered presumably by the Slessor and Stratton glaciers. The infinite age of the sample could be due to scatter within the 14 C measurements, and the fact that the sample is an erratic does allow the possibility of an unlikely geomorphic scenario. As described in Sect. 1.2, erratic samples may be sourced from mass movement onto glacier surfaces, 30 producing spuriously high 14 C concentrations (Balco et al., 2019).
On the Lassiter Coast, Johnson et al. (2019) report 10 Be ages which, with the exception of three measurements, all exceed ~100 ka, whilst all of the in situ 14 C ages are finite and fall within the Holocene (Figs. 6 and S7). The associated in situ 14 C concentrations are similar over the range of sample elevations (Fig. 6). The uppermost sample, collected ~385 m above the modern ice surface, provides a lower limit on the thickness of LGM ice at the Lassiter Coast. The small range of ages 35 across ca. 300 m elevation transect indicate that ice thinning occurred rapidly at this study site (Johnson et al., 2019).
At the Schmidt Hills, 10 Be ages from Balco et al. (2016) and Bentley et al. (2017) range from ~140 ka to 3 Ma (Fig.  7). We observe finite ages at low elevations and finite, close to infinite, and infinite ages at higher elevations (Figs. 7 and S8). Given that higher elevations cannot be covered by ice unless lower elevations were also covered, we remeasured the apparently infinite and near-infinite aged samples (~500 to ~920 m asl, or ~270 to ~690 m above the modern ice surface).

40
The replicate results (Fig. 7) show high variability, greater than that observed in previous repeat measurements of CRONUS-A and other samples . There is no apparent analytical reason for the initial measurements yielding infinite or near-infinite ages and then yielding differing concentrations with repeat measurements. Samples yielding only finite ages (those that were not measured multiple times) are observed up to ~420 m asl, or ~190 m above the modern ice surface. In addition, the bedrock sample collected from ca. 1035 m asl yields a finite age, indicative of an LGM thickness at 45 least ~800 m greater than present for the FIS at the Schmidt Hills. The agreement between the bedrock age and the finite The two samples collected from the Thomas Hills yield finite ages within ~0.2 ka of one another (Figs. 8 and S9). Results thus indicate that the FIS was at least ~320 m thicker than present at the LGM at the Thomas Hills. The apparent in situ 14 C ages, at ~10 ka, are consistent with a cluster of 10 Be ages between 7 and 9 ka in the Thomas Hills reported by Balco 5 et al. (2016) from 225 m above the modern FIS surface, as well as a 10 Be age of 4.2 ka reported by Bentley et al. (2017) collected 125 m above the modern ice surface. Considering the evidence for significant LGM thickening of the FIS from our in situ 14 C results from the Thomas Hills, as well as 10 Be ages of Balco et al. (2016) and Bentley et al. (2017) from both the Williams and Thomas Hills, we conclude that it is likely that the FIS reached up to 800 m above its present thickness at the LGM at the Schmidt Hills. We discuss this conclusion further in the following section.

Assessment of 14 C elevation transects
The premise of our study is that one can clearly infer if a site was ice-covered at the LGM by determining whether the in situ 14 C concentration of samples from that site are at or below saturation. In this section we assess the success of the approach. To assess the validity of this method, we can, for example, identify where the in situ 14 C data records ice thinning, 15 with saturated samples or the oldest exposure ages at the highest elevations and a trend of decreasing in situ 14 C age toward modern ice surfaces. Consistency between in situ 14 C data and other nuclide concentrations (e.g. 10 Be) could also help validate the in situ 14 C measurements. We also look at factors beyond the in situ 14 C concentrations, such as the glaciological link between study sites, which may add clarity where the in situ 14 C measurements show a high degree of scatter.
At some sites our results are consistent with the premise, as well as internally consistent. At the Lassiter Coast, ages 20 decrease toward the present ice sheet surface. Though limited by the number of samples, two measurements from Mt. Provender align with the premise of our study, in that we find a finite age located at a low elevation with an infinite age above it. In the Thomas Hills we see consistency between the finite 14 C ages and previously-published 10 Be ages (Balco et al., 2016;Bentley et al., 2017). Fogwill et al. (2014) also observe consistency between 14 C and 10 Be ages, which constrain the LGM thickness and dynamics of the Rutford Ice Stream. However, we observe apparently finite ages above apparently 25 infinite ages at the Schmidt Hills, a scenario that is glaciologically impossible if our assumptions are correct that samples are indeed glacial erratics that have either been deposited previously and repeatedly covered by cold-based ice or delivered to their sampling location during the last glaciation and were sourced subglacially. The scatter observed in the repeat measurements ( Fig. 7) is greater than that of repeat measurements made of CRONUS-A and other samples made in our laboratory (Goehring et al., 2019). Three samples from the Schmidt Hills (006-COU, 008-NNS and 046-NNS, collected 30 from ~920, ~710 and ~500 m asl, respectively) were previously measured for their in situ 14 C content and were published by Balco et al. (2016). All three of the samples previously measured by Balco et al. (2016) yielded higher concentrations (two of which were above saturation with the third at saturation) than their new measurements presented in this study. Furthermore, two of the three samples (006-COU and 046-NNS) were measured multiple times (in this study) and display the high scatter under discussion. Balco et al. (2016) proposed unrecognised measurement error as the cause of the 35 spuriously high in situ 14 C concentrations. Why the replicate measurements from samples from the Schmidt Hills display a high degree of scatter remains to be determined. The most likely reason for 14 C measurement error is contamination by modern 14 C, which would result in a spuriously high concentration. In contrast, a spuriously low concentration is less likely, and we are not aware of any documented instances of this. In our laboratory we have found that it is relatively easy to contaminate a sample with modern 40 carbon through the use of organic compounds in the froth flotation mineral separation procedure (Nichols and Goehring, in review). However, froth flotation was not used to isolate the quartz of any of the samples for which replicate measurements were made. On multiple occasions we have observed spuriously high 14 C concentrations, far in excess of saturation concentrations, from quartz separates of fine grain sizes (ca. 60 μm) that were not isolated using froth flotation. We do not yet know the reason for the fine grain sizes yielding elevated 14 C concentrations, but one hypothesis is that the finite-aged 45 replicate measurements were unintentionally made using quartz separates with a higher average grain size than the initial infinite measurements. We believe the above observations indicate that the increased scatter may be the result of measurement difficulties, perhaps lithology-or grain size-specific.
Regardless of the cause of the high degree of scatter observed in the replicate measurements, we need to discuss possible explanations for apparently infinite ages at lower elevations than apparently finite ages to isolate which measurements (infinite vs finite replicates) are the most valid to base interpretations on. At the Schmidt Hills, the hypothesis 5 that infinite ages situated below finite ages are spurious and due to measurement errors is consistent with the glaciological relationship amongst the Schmidt, Thomas and Williams Hills (see Sect. 4.2) and is also consistent with the finite bedrock age sourced from a higher elevation. The bedrock age is a robust constraint because the sample cannot have been subjected to geomorphic scenarios that could cause the resulting age to misrepresent the timing of deglaciation. The hypothesis that the infinite ages are correct produces a steep LGM surface slope and is not consistent with thickness estimates from the 10 Williams and Thomas Hills. We elaborate on this point in Sect. 4.2.
As described in Sect. 1.2, it is theoretically possible for in situ 14 C saturated erratic samples to occur at lower elevations than finite ages in rare situations if the former were transported by LGM ice. Balco et al. (2019) observed an apparently saturated sample beneath finite aged samples. Supported by field observations, Balco et al. (2019) propose that the saturated sample was sourced from a rockfall upstream and transported to the study site as supraglacial debris, explaining the elevated in situ 14 C concentration. Whilst this could explain the low-elevation saturated sample at Mt. Skidmore, as well as infinite measurements situated beneath finite measurements at the Schmidt Hills, it does not explain the poor reproducibility of the Schmidt Hills measurements.
We conclude that the basic concept works, as shown at the Lassiter Coast and the Shackleton Range, as well as in other aforementioned studies. In the following section we discuss the implications for LGM ice sheet reconstructions.

20
However, it is clear that more investigation into laboratory issues, geological and geomorphic factors is required to identify the cause or causes of apparently site-or lithology-specific excess scatter in in situ 14 C measurements.

LGM ice thicknesses in the Weddell Sea Embayment
Our LGM thickness estimates are summarized in Fig. 9. The new in situ 14 C concentrations indicate that the vast 25 majority, if not the entirety, of Mt. Skidmore, and presumably much of Mt. Provender, was covered by ice at the LGM (Figs. 5 and 10). The highest elevation samples on Mt. Skidmore proximal to the Slessor Glacier yield infinite ages and suggest that the ice stream was at least 300 m thicker at the LGM than at present. This assumes the samples were not influenced by expansion of local ice masses from the southeast (Fig. S1). If so, and assuming the surface gradient of Slessor Glacier during the LGM was similar to today, this would suggest the Slessor Glacier was ~300 m thicker at Mt. Provender at the LGM.

30
With no high-elevation infinite ages found on Mt. Skidmore, our thickness estimates for the Slessor Glacier are likely conservative estimates. Finite ages are observed across the entire Mt. Skidmore transect and there is only a single exposed peak (between Ice Tongue A and Ice Tongue B of the Stratton Glacier, Fig. S1) that is at a higher elevation than our sampling locations (ca. 25 m higher). Presumably, given the evidence for the expansion of the Slessor and Stratton glaciers, this small peak was covered by these or local ice masses at the LGM. Our data therefore indicate that, regardless of the 35 source, the Mt. Skidmore site was covered by ice during the LGM, whilst the top of Mt. Provender remained exposed. Whilst the upper limit of LGM ice at Mt. Provender is based on a single sample, we believe this sample is a reliable indicator of LGM ice thickness for the following reasons. The sample is sourced from bedrock and therefore cannot have been subjected to geomorphic scenarios causing the exposure age to misrepresent the timing of ice retreat. Furthermore, froth flotation, which introduces modern carbon to sample material (Nichols and Goehring, in review), was not used to isolate 40 quartz for this sample. Our thickness constraints (~300-655m) supersede those of previous exposure dating studies that found no evidence from long-lived isotopes for a thicker Slessor Glacier at the LGM (Hein et al, 2011;2014). Our LGM thickness constraints for the Slessor Glacier are consistent with our other sites as well as those of previous authors for a significantly thicker FIS at the LGM (Balco et al., 2016;Bentley et al., 2017).  (Balco et al., 2016).

Moved up [1]:
The most likely reason for 14 C measurement error is contamination by modern 14 C, which would result in a spuriously high concentration. In contrast, a spuriously low concentration is less likely, and we are not aware of any documented instances of 60 this. In our laboratory we have found that it is relatively easy to contaminate a sample with 14 C, for example through the use of organic compounds in the froth flotation mineral separation procedure (Nichols et al., in preparation). However, froth flotation was not used to isolate the quartz of any of the samples for which 65 replicate measurements were made. On multiple occasions we have observed spuriously high 14 C concentrations, far in excess of saturation concentrations, from quartz separates of fine grain sizes (ca. 60 μm). Perhaps the finite-aged replicate measurements were unintentionally made using quartz separates with a higher average 70 grain size than the initial infinite measurements. We believe the above observations indicate that the increased scatter may be the result of measurement difficulties, perhaps lithology-or grain sizespecific. ¶ 10 Be measurements that were likely influenced by cold-based ice cover, resulting in nuclide inheritance (Johnson et al., 2019). The finite in situ 14 C ages of samples collected from 628 to 875 m asl, with ages between 6.0 ± 0.7 ka and 7.5 ± 0.9 ka, are consistent with a minimum age of grounded ice retreat from a marine sediment core close to the modern ice shelf edge of 5.3 ± 0.3 kcal yr BP (Hedges et al., 1995;Crawford et al., 1996; Fig. 1). The fact that significant thinning occurred in the Holocene may help explain the misfit between GIA models and GPS measurements in Palmer Land (Wolstencroft et al., 5 2015). A thicker ice load at the LGM than that used by current ice models, or present ice load estimates that persist into the Holocene, are two potential solutions postulated by Wolstencroft et al. (2015) to explain the misfit. Further work is needed to take our new ice history into account and to investigate if a minimum of 385 m of ice at the LGM and subsequent rapid thinning at ~7 ka at the Lassiter Coast can help account for the offset.
Our in situ 14 C data indicate that the FIS was at least 800 m thicker than present at the LGM at the Schmidt Hills, 10 which contrasts with previous studies which found no evidence for the LGM thickness of the FIS at the Schmidt Hills (Balco et al., 2016;Bentley et al., 2017). We base our LGM thickness estimate on the aforementioned finite-aged repeat measurements and the finite aged bedrock sample, rather than on the poorly reproduced infinite aged-measurements. There is robust evidence for a FIS that was at least 500 m thicker than present at the LGM at the Williams Hills, located only 50 km upstream of the Schmidt Hills (Figs. 1 and 11; Balco et al., 2016;Bentley et al., 2017). Given the evidence for a significantly 15 thicker FIS proximal to the Schmidt Hills, we argue that the repeat measurements and the bedrock measurement indicative of the FIS being 800 m thicker are glaciologically most-likely, and thus base our LGM ice thickness estimates on them. Using the infinite measurements and accompanying constraint for the LGM thickness of 320 m thicker than present at the Schmidt Hills produces a steep surface slope from the nearby Williams Hills (Fig. 11), though less so than the surface slope produced when no LGM thickening is inferred at the Schmidt Hills based on 10 Be measurements (Balco et al., 2016). The two 20 measurements from the Thomas Hills provide a lower limit for the LGM thickness, but the possibility remains that there was more thickening than the ca. 320 m in situ 14 C constraint. Fig. 11 tentatively suggests that the FIS may have been ~900 m thicker when using the modern surface profile of the FIS increased in elevation up to the height of the finite ages from the Schmidt Hills and post-12 ka 10 Be ages from Balco et al. (2016) and Bentley et al. (2017) from the Williams Hills. This is a tentative interpretation because, if thickening is sea level controlled, there would be progressively less thinning expected 25 upstream.
Our LGM ice thickness constraints are consistent with evidence for significantly thicker ice at the LGM in the Ellsworth Mountains (Hein et al., 2016, Fig. 2), and also likely consistent with measurements in Bentley et al. (2006). The post-LGM exposure ages of Hein et al. (2016) constrain LGM thicknesses to between 475, 373 and 247 m greater than present at three study sites in the Ellsworth Mountains. A pulse of up to 410 m of thinning appears similar both in scale and 30 timing to the rapid ice surface lowering of 385 m recorded at the Lassiter Coast. Furthermore, measurements of long-lived nuclides by Bentley et al. (2006) show that there has been at least 300 m of thinning since the LGM in the Behrendt Mountains. Whitehouse et al. (2017) use their flowline model to reproduce the modern FIS ice surface profile and investigate 35 the response of the ice stream to the onset of glacial and interglacial conditions. The following results from Whitehouse et al. (2017) are from their experiments in which the FIS is routed to the east of Berkner Island, which it is believed to have done during the LGM based on modelling studies (Le Brocq et al., 2011;Whitehouse et al., 2012) and aforementioned marine geological evidence for the former presence of grounded ice (Sect. 1.1). Under glacial conditions the FIS thickens by ~300 to ~500 m adjacent to the Thomas Hills, ~200 to ~400 m adjacent to the Williams Hills, ~150 to ~350 m adjacent to the 40 Schmidt Hills, and ~100 to ~300 m proximal to the Shackleton Range. The lower value for each location is sourced from flowline experiments during which the grounding line of the FIS reaches a stable position at the northern margin of Berkner Island, with the higher value sourced from a scenario during which the grounded ice stream stabilises at the offshore shelf edge. Our in situ 14 C LGM thickness constraints at each study location in the Pensacola Mountains and Shackleton Range exceed the upper estimates of the FIS flowline model of Whitehouse et al. (2017) under glacial conditions. The flowline 45 model shows that the FIS, a major contributor to the total WSE ice flux, is able to reach a stable position at the offshore shelf 10 edge when tuned using LGM thickness constraints lower than those presented here. Therefore, our thickness estimates add strength to the hypothesis that grounded ice occupying the WSE during the LGM reached a stable position located at the offshore shelf edge (Bentley and Anderson, 1998;Hillenbrand et al., 2014).

Sea-Level contribution
To estimate the contribution to post-LGM sea-level rise of the WSE we use a highly simplified scenario in which a 5 range of minimum LGM thickness change estimates are distributed evenly across the WSE using an area for the sector defined by Hillenbrand et al (2014). Distributing the lowest of our minimum LGM thickness constraints, 310 m for the Slessor Glacier, over the entire WSE produces a minimum sea-level equivalent (SLE) of 2.2 m. When using the highest of our minimum thickness estimates, 800 m for the FIS, the minimum SLE increases to 5.8 m. Using the average minimum LGM thickness constraint for our three study sites (580 m) produces a minimum SLE for the sector of 4.2 m. This scenario 10 lacks any glaciological basis and is unrealistic, with no variation in ice thickness with location and no consideration of ice dynamics, isostasy, or bathymetry, thus further work is required to produce a realistic SLE for the WSE using our in situ 14 C thickness constraints.
We compare our in situ 14 C LGM thickness estimates with the predicted LGM thickness change of three published ice sheet models at each of our study sites to evaluate our minimum SLE estimates. We also quantify the WSE-sourced sea-15 level equivalent (SLE) for each model output. By comparing our data with the predicted LGM thickness from the model outputs, we can see which models predict LGM thickness changes in excess of and below our in situ 14 C thickness constraints. We compare our data with the predicted LGM thickness change at each of our sites from the ice sheet modelling of Le Brocq et al. (2011), Whitehouse et al. (2012, and Golledge et al. (2014), which predict a SLE for the WSE of ca. 3.0 m, 1.5 m, and 4.6 m, respectively. 20 From Fig. 12 it is apparent that the model output of Golledge et al. (2014) exceeds the thickness constraints at each of our sites. With a SLE of ca. 4.6 m for the WSE, this places a more robust upper limit on the minimum SLE contribution of the WSE using our data, showing that our upper minimum SLE estimate of 5.8 m is likely an overestimation due to the limitations outlined above. The only site where our minimum LGM ice thickness constraint exceeds any of the predicted LGM thickness changes from the model outputs is at the Lassiter Coast, where a LGM thickness of 385 m greater than 25 present exceeds the model output-based thickness estimate of both Le Brocq et al. (2011) and Whitehouse et al. (2012). The Lassiter Coast data suggest that the lower limit for the SLE for the WSE is between 3.0 m and 4.6 m, whilst evidence from all other sites suggests it was <1.5 m.
Based on the above, we conclude that our minimum LGM thickness constraints indicate that the WSE contributed <4.6 m, and possibly as little as <1.5 m, toward postglacial sea-level rise. This is a range of minimum contributions to sea-30 level rise and not a minimum-maximum range, as the values are informed using only minimum thickness constraints. Because this is an estimate for the lower limit of the SLE for the WSE, we cannot rule out a greater contribution.
A SLE value of <4.6 m places our estimate between those modelled by Bentley et al. (2010) (1.4 m to 2 m) and Bassett et al. (2007) (13.1 to 14.1 m). Using the estimate based on all sites with the exception of the Lassiter Coast data, the minimum SLE estimate of <1.5 m is consistent with the lower end of published SLEs for the sector. Our exposure ages 35 indicate the Weddell Sea sector contributed to sea-level during the early to mid-Holocene, though they do not preclude a significant contribution earlier than this. Our estimates imply that the sector provided a modest contribution to global sealevel. Whitehouse et al. (2017) estimate the sea-level contribution of the FIS to between ~0.05 and ~0.13 m. Given that our 14 C thickness constraints for the FIS, including those in the Shackleton Range, exceed all of those used by Whitehouse et al. (2017) to tune their flowline model, we propose that the sea-level contribution for the FIS was greater than their upper 40 estimate of ~0.13 m.

Conclusions
This study presents LGM ice thickness constraints for three locations within the WSE of Antarctica. In situ 14 C measurements constrain the LGM thickness of the FIS to at least ca. 800 m thicker than present in the Schmidt Hills and at least 320 m thicker than present in the Thomas Hills, both in the Pensacola Mountains. The Slessor Glacier was at least 310 11 m and up to 655 m thicker than present at the LGM. Finally, LGM ice was at least 385 m thicker than present at the Lassiter Coast. Our thickness constraints resolve a significant disconnect between previous terrestrial evidence for minimal LGM thickening in some locations from long-lived nuclides, and marine evidence for a significantly laterally expanded ice sheet with the grounding line located at the offshore shelf edge. Our in situ 14 C measurements made from samples at the Schmidt Hills exhibit higher than expected scatter in replicate measurements. Identifying the source of excess scatter will take further 5 work. In terms of the contribution of the ice sheet sector to global sea-level rise since the LGM, we estimate that the WSE contributed modestly, with a rough minimum estimate of <4.6 m, and possibly as little as <1.5 m.

Data availability
All sample data, including photographs when available, are available in the Informal Cosmogenic-Nuclide Exposure-Age Database (ICE-D) (http://antarctica.ice-d.org). Williams and Thomas Hills, respectively. FH, P/M and MH are the Flower Hills, Patriot and Marble Hills, and the Meyer Hills, respectively. Black is exposed rock. Red boxes show extent of satellite images in Fig. 4. Exposed rock and coastline sourced from the SCAR Antarctic Digital Database. Bathymetry sourced from the International Bathymetric Chart of the Southern Ocean V1.0 (IBSCO; Arndt et al., 2013). Surface topography (shading) is sourced from the Reference Elevation Model of Antarctica (REMA; Howat et al., 2019). PS1423-2 is a marine sediment core from Crawford et al. (1996).

Figure 2:
Current terrestrial ice thickness constraints inferred from measurements of long-lived nuclides around the WSE. Acronyms are as in Fig. 1. Constraints for the SH, WH, and TH are sourced from Balco et al. (2016) and Bentley et al. (2017). MB is Mount Bragg (Bentley et al., 2017). Thickness estimate for the Dufek Massif (DM) is sourced from Hodgson et al. (2012). Constraints for the P/M are sourced from Hein et al. (2016). For the MH and FH, the LGM thickness 35 constraints are sourced from Fogwill et al. (2014). The thickness constraints sourced from Fogwill et al. (2014) were interpreted using modern ice surface elevations for the Rutford Ice Stream and Union Glacier measured using the Reference Elevation Model of Antarctica (REMA; Howat et al., 2019). Thickness constraints for the Shackleton Range are sourced from Hein et al. (2011;2014). The range of LGM thicknesses for the Behrendt Mountains are sourced from multiple locations (Bentley et al., 2006).   (Rignot et al., 2011;2014;.    is shown in the map (right). Infinite 14 C measurements are offset in regard to their distance along flowline to improve readability. The 10 Be data included are those from Hein et al. (2011;2014) which yield exposure ages below 12 ka (LSDn scaling, antarctica.ice-d.org). Elevation data for ice surfaces and map shading is sourced from the Reference Elevation Model of Antarctica (REMA; Howat et al., 2018). Grounding zone positions sourced from the MEaSUREs program V2 (Rignot et al., 2011;2014;. Minimum LGM surface is the modern day surface profile with the elevation increased 40 above present using our minimum LGM thickness estimates.  (Rignot et al., 2011;2014;). Minimum LGM surface is the modern day surface profile with the elevation increased above present using our minimum LGM thickness estimates. LGM thickness change at each site based on our in situ 14 C data. For A. and B., the two vertical blue lines show 5 the range of thickness estimates for the two sites, with the upper limit constrained by the highest elevation saturated sample at Mt. Provender. "G2014" refers to Golledge et al. (2014), "LB2011" refers to Le Brocq et al. (2011), and "W2012" refers to Whitehouse et al. (2012). Errors are not provided for the model outputs. The average error of published SLEs associated with model outputs for the entire ice sheet is 1.45 m (see Simms et al., 2019). We therefore use an error of 0.3 m for the three model SLEs, which is 22% of the average error (22% is the proportion of the AIS that the WSE drains, see Joughin et