Glacier response to Holocene warmth inferred from in situ 10Be and 14C bedrock analyses in Steingletscher’s forefield (central Swiss Alps)

. Mid-latitude mountain glaciers are sensitive to local summer temperature changes. Chronologies of past glacier ﬂuctuations based on the investigation of glacial land-forms therefore allow for a better understanding of natu-ral climate variability at local scale, which is relevant for the assessment of the ongoing anthropogenic climate warming. In this study, we focus on the Holocene, the current in-terglacial of the last 11 700 years, which remains a matter of dispute regarding its temperature evolution and underlying driving mechanisms. In particular, the nature and sig-niﬁcance of the transition from the early to mid-Holocene and of the Holocene Thermal Maximum (HTM) are still de-bated. Here, we apply an emerging approach


Introduction
Mountain glaciers in most glacierized regions of the world, such as the European Alps, are currently rapidly retreating in 25 response to accelerating global warming, driven by human-induced greenhouse gas emissions into the atmosphere (IPCC, 2013). Small mountain glaciers are reliable indicators of regional climate variations on decadal to multi-millennial timescales, because their mass balance is sensitively controlled by variations of meteorological parameters, in particular summer temperature and precipitation (Oerlemans, 2005). Investigating past glacier behavior and the underlying regional climate variability provides the opportunity to better understand the natural driving mechanisms within Earth's climate system and to 30 help quantify the anthropogenic contribution to the ongoing climate evolution (e.g. Roe et al., 2021).
The current interglacial Holocene followed the end of the last glacial period ~11,700 years ago and is characterized by moderate climate variations, including both colder-than-today and warmer phases (Mayewski et al., 2004;Wanner et al., 2008).
In the northern mid-and high-latitudes, many studies provide evidence of several millennia of warm conditions during the early and mid-Holocene, generally referred to as the Holocene Thermal Maximum (HTM) (e.g. Renssen et al., 2009;Axford 35 et al., 2013;Heiri et al., 2015;Kobashi et al., 2017). However, the occurrence of extended periods that were significantly warmer than recent decades are still debated (e.g. Marcott et al. 2013;Marsicek et al., 2018;Affolter et al., 2019;Kaufman et al., 2020;Bova et al., 2021). The response of mountain glaciers to these Holocene warm periods remains unclear because records of when and how long mountain glaciers have receded to modern extents or beyond are still scarce and challenging, because much of the potential evidence is buried beneath ice. The European Alps are one of the regions that is best documented in terms of Holocene glacier behavior (Ivy-Ochs et al., 2009;Solomina et al., 2015), but existing Holocene glacial chronologies are dominated by studies of moraines and thus large glacier extents that occurred during cold episodes (e.g. Schimmelpfennig et al., 2012Schimmelpfennig et al., , 2014Moran et al., 2017;Le Roy et al., 2017;Protin et al., 2019Protin et al., , 2021Braumann et al., 2020Braumann et al., , 2021. Most of the existing constraints on the timing and amplitudes of glacier recessions come from discrete radiocarbon dates of sub-fossil wood and peat (e.g. Porter and Orombelli, 1985;Baroni 45 and Orombelli, 1996;Nicolussi and Patzelt, 2000;Hormes et al., 2001Hormes et al., , 2006Deline and Orombelli, 2005;Joerin et al., 2008;Nicolussi and Schlüchter, 2012;Le Roy et al., 2015), and only few studies provide records that characterize glacier extents during the majority of the Holocene, including periods of glacier retreat (Joerin et al., 2006;Luetscher et al., 2011;Badino et al., 2018).
A more recently developed and powerful approach to addressing the chronological reconstruction of millennial-scale Holocene 50 glacier retreat relies on the measurement of in situ cosmogenic 14 C exposure dating in deglaciated bedrock, combined with in situ cosmogenic 10 Be or other dating techniques, so far applied in only a few studies around the globe (Goehring et al., 2011 andWirsig et al., 2016 in the Alps; Schweinsberg et al., 2018;Pendleton et al., 2019, Young et al., 2021 in the Greenland/Baffin region; Rand and Goehring, 2019 in Norway;Johnson et al., 2019 in Antarctica). This method provides the possibility to quantitatively derive the total duration that deglaciated bedrock has been exposed, i.e. was ice-free, and how long it was buried 55 beneath ice throughout the Holocene. The pioneering studies applying in situ 14 C-10 Be exposure-burial dating showed that Rhône glacier, located in the central Swiss Alps, was smaller than its ~2005 CE extent for 6.4 ± 0.5 kyr, i.e. for the majority of the Holocene (Goehring et al., 2011(Goehring et al., , 2013. The challenge of this approach arises from the need of additional chronological constraints to determine the specific number and timing of recession periods, if they were interrupted by successive glacier advances.

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In this study, we focus on Steingletscher, an often-visited, small mountain glacier in the central Swiss Alps (Fig. 1). Its evolution is well-monitored since the end of the 19 th century showing that it has been constantly retreating since 1985 CE. Its forefield has been subject to various scientific studies, including investigations of the glacier's responses to Holocene cold episodes (King, 1974;Schimmelpfennig et al., 2014). Schimmelpfennig et al. (2014) mapped and 10 Be-dated the Holocene moraines in the forefield of Steingletscher ( Fig. 1) providing evidence of several large glacier extents between the early

Study site, previous chronological work, and sampling strategy
Steingletscher is located in the eastern part of the Bernese Alps (~47°N, 8°E) at an altitude of 2220 m a.s.l. close to Susten Pass, and is part of a larger glacier catchment that hosts another glacier, Steinlimigletscher (Fig. 1b). It had a length of 3.35 km in 2019 CE and an area of 7.6 km 2 in 2013 (GLAMOS , 2019(GLAMOS , , 2020. Metagranitoids, gneisses and amphibolites constitute the geology of the glacier's surroundings. The climate at the nearest weather station (Meiringen 589 m a.s.l.) was characterized 90 during the reference period 1981-2010 CE by a monthly mean temperature range between -1.9° C and 17.7° C, an annual mean precipitation of 1375 mm, and 2.9 days of snow cover with a thickness of >50 cm (www.meteowiss.admin.ch; climsheet 2.1.6 / 05.01.2021).
Steingletscher's forefield, stretching almost linearly towards the north, features glacially smoothed hills, moraines, trimlines and the proglacial lake Steinsee in the center of the half-bowl-shaped distal part of the forefield. The catchment's outlet is 95 located in the north-western corner of this bowl and drains westward into Gadmen valley. On the left-lateral catchment flank, the up to 2090 m high "Plateau Hublen" and the lower "Plateau In Miseren" are characterized by glacially polished and lichencovered bedrock knobs (roches moutonnées; Fig. 2a, b), interspersed with vegetated depressions, and small peat bogs and lakes (Fig. 1c). This landscape is overprinted by relicts of several moraine belts, the outer and the inner Hublen moraines, which were 10 Be dated at ~11.0 ka, ~10.6 ka and ~10.0 ka, from outer to inner (Schimmelpfennig et al., 2014). King (1974) 100 obtained minimum radiocarbon ages for moraine formations from basal parts of peat bogs on Plateaus Hublen and In Miseren, which are in agreement with the 10 Be Holocene moraine data (Fig. 3a). They indicate that cold conditions still persisted during the deglaciation after the Younger Dryas (YD; 12.8-11.7 ka; Rasmussen et al., 2006). However, further evidence of YD related extents has not yet been identified. Here, we targeted two roches moutonnées located close to the highest point of Plateau Hublen, a few meters outboard of the outer Hublen moraine (Figs. 1,2a,b) with the objective to date the timing of initial 105 deglaciation of this plateau.
The absence of moraines after ~10ka and throughout the mid-Holocene indicates warmer climate at that time (Schimmelpfennig et al., 2014). This is supported by radiocarbon ages of ~9 ka cal BP and from the mid-Holocene obtained from peat bogs on Plateau In Miseren (King, 1974; Table 2 in Schimmelpfennig et al., 2014;Fig. 3a). In addition, evidence of a substantially retracted mid-Holocene extent of Steingletscher comes from two wood fragments melted out from the glacier 110 front between 1995 and 2000 CE and radiocarbon-dated at 5.3-4.8 ka cal BP and 4.8-4.6 ka cal BP (Hormes et al., 2006;Fig. 3a). In the same study, two organic silt samples from the forefield of the neighboring Steinlimigletscher, also collected between 1995 and 2000 CE, were radiocarbon-dated at 5.9-5.3 ka cal BP and 2.3-1.8 ka cal BP. Further information on the amplitude and duration of glacier recession during the early and mid-Holocene is missing, as geomorphic markers of glacier extents during that time were destroyed by the glacier re-advances during late Holocene cooling.

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Evidence of late Holocene moraine formation comes from glacial boulders in the vicinity of the catchment outlet dated at ~2.9 ka (Schimmelpfennig et al., 2014). This maximum glacier extent during the late Holocene is corroborated by radiocarbon dates of organic material from soil and peat on the right-lateral side of the catchment outlet, which provide bracketing ages for the glacier advance and retreat around 3 ka ago (King, 1974; Table 2 in Schimmelpfennig et al., 2014;Fig. 3a). One large moraine boulder located on a ridge inboard of the ~3 ka moraine was 10 Be dated at ~1.9 ka and might represent a glacier extent at that 120 time (Schimmelpfennig et al., 2014).
The most evident geomorphic markers of glacier expansion in Steingletscher's forefield are those from the Little Ice Age, including a sharp composite moraine on the eastern side of the forefield (Fig. 2d), multiple moraine ridges, and a clearly visible trimline (Figs. 2d,4). Boulders from the preserved moraines yield 10 Be ages between ~570 and 140 years, consistent with the period of the LIA (Schimmelpfennig et al., 2014).

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Historical and instrumental records provide constraints on glacial extents between 1850 and the beginning of the 21 th century, which are here mainly based on previous compilations by King (1974) and Wirz (2007). Fig. 3a shows the glacier outlines in https://doi.org/10.5194/cp-2021-110 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License. the years 1850, 1920, 1933, 1973, 1988, 1999, and 2007. The length measurements of Steingletscher between the years 1893 and 2019 (Fig. 3b) indicate that the glacier had never retreated as much as in 2007 during that time. The most pronounced retreat of the 20 th occurred between 1960 and 1970, leading very briefly to a minimum extent that was comparable to that of 130 the very beginning of the 21 th century, but still slightly bigger than that in 2007 (Fig. 3b).
To investigate how Steingletscher responded to Holocene warmth, specifically how long it was as small as or smaller than its modern configuration during the Holocene, we targeted two bedrock riegels for in situ 14 C-10 Be exposure-burial dating. One riegel is located east of Chüebergli ("Chüebergli riegel" thereafter) and ~400 m long. The other riegel is located north of Bockberg ("Bockberg riegel" thereafter) and ~200 long. Both riegels are characterized by glacially polished, recently 135 deglaciated roches moutonnées (Fig. 2c, d) that form steep cliffs towards the north. Chüebergli riegel was completely covered under at least ~140 m of ice during the LIA maximum, inferred from the altitude of the LIA composite moraine and trimline on the eastern catchment flank, and continued to be buried throughout most of the 20 th century. Eight samples were collected on a transect on Chüebergli riegel from the highest and outmost bedrock surface down to the lowest bedrock surface in the glacial trough, following the sampling approach in Goehring et al. (2011). Note that the three lowest sample surfaces were still 140 covered by ice in 2007 (Fig. 1c), but were ice-free by the sampling year 2010. From Bockberg riegel, two samples were analyzed (Fig. 1c).
After the glacier retreat in the 1960s, the outmost parts of the two riegels were temporarily ice-free, but ice-covered again in the 1970s-1980s by ~30 m of ice (Figs. 3a,4). Chüebergli riegel might have been completely ice-free briefly around 1970.
Both riegels were deglaciated in the early 21th century, and Steingletscher has continued to retreat since.

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The fourteen bedrock samples were collected during field campaigns in 2010 and 2016, targeting glacially polished and striated surfaces that were free of sediment cover. To minimize the risk of significant snow and sediment cover in the past, slightly sloping surfaces were preferred (Fig. 2d). Rock surface pieces with average thicknesses of ~2 cm to ~4 cm (Table 1) were sampled using either hammer and chisel alone or in combination with a cordless angle grinder and a diamond blade, preferring the quartz-rich parts of the gneissic lithologies. Latitude, longitude and elevation at the sample locations were recorded with a 170 Trimble GeoTX GPS, the data reduction was conducted using the WGS coordinate system relative to EGM896 Geoid (Table   1). Correction factors for the shielding by the surrounding topography and the strike and dip of the sampled surfaces were determined from measurements using a handheld inclinometer. These correction factors range from 0.87 to 1.0 (Table 1).

Analytical methods
We separated and decontaminated quartz from 14 samples, and extracted 10 Be from the clean quartz after spiking with pure 9 Be carrier (Table 1). Chemical processing was carried out at the Lamont-Doherty Earth Observatory (LDEO) Cosmogenic Nuclide Laboratory (New York, USA) according to the standard procedures described in Schaefer et al. (2009)  Géosciences de l'Environnement (CEREGE, Aix en Provence, France) following routine methods described e.g. in Protin et al. (2019). 10 Be/ 9 Be ratios were measured at the Lawrence Livermore National Laboratory -Center for Accelerator Mass Spectrometry (LLNL-CAMS) and at Accélérateur pour les Sciences de la Terre, Environnement, Risques (ASTER) at CEREGE. All data related to the 10 Be analyses are presented in Table 1.

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In situ 14 C was extracted from the quartz of the two bedrock samples from Chüebergli riegel with the highest 10 Be concentrations (STEI-16-10 and -12). These extractions were performed at LDEO following the procedure described in Goehring et al. (2014) and Lamp et al. (2019), with two updates: The purified CO2 sample and blank gas were diluted with only small amounts of 14 C-free gas corresponding to ~20 µg of C (Table 2); the sample and dilution gas mixtures were not converted into graphite, but sealed into pyrex break seals for 14 C/ 12 C ratio measurements at the AixMICADAS facility at 195 CEREGE using the ion source dedicated for gaseous samples (Bard et al., 2015, Tuna et al., 2018, thus avoiding the graphitization step. 14 C concentrations were calculated following the method of Hippe and Lifton (2014) ( Table 2).

Principles of the exposure-burial dating approach
Three types of glacial surfaces with different exposure histories are investigated in this study.
i) Moraine boulders: they can in most cases be assumed to have a simple exposure history, i.e. they were free from 200 cosmogenic nuclides at the moment of their stabilization after the glacier had retreated from its advance and have since been continuously exposed. In this case, the analysis of 10 Be alone usually provides the exposure age of the surface. Based on the consistency of the 10 Be moraine boulder ages of Schimmelpfennig et al. (2014), they seem to fulfill this condition.
ii) Bedrock surfaces that remained continuously ice-free during the Holocene: they are located outboard of the 205 maximum Holocene glacier extent. We assume that they were covered long and subglacially eroded deep enough during the ~100 ka lasting last glacial period that ended with the YD, that these surfaces were free from cosmogenic nuclides at the moment of their last deglaciation. Subsequently, they experienced a simple exposure history, if cover by sediment, soil or vegetation is negligible. The two dated bedrock samples from Hublen (STEI-16-1 and -2), located outboard of the outer Hublen moraine, are assumed to fulfill these conditions. 210 iii) Bedrock surfaces that were alternately ice-free and ice-covered during the Holocene: they are located inboard of any of the Holocene glacier advances. Like the bedrock type ii, their cosmogenic nuclide inventory is assumed to have been set to zero during the last glacial period. If during the Holocene phases of no-glacier-cover were followed by glacier-cover during 10 2 -10 3 years periods and with moderate subglacial erosion, cosmogenic nuclide concentrations cumulated from several exposure periods but were reduced through the glacial erosion 215 during ice-cover. Consequently, the analysis of 10 Be alone in this type of sample provides a minimum duration of the cumulative exposure period. The 10 samples from Chüebergli and Bockberg riegels correspond to this type of bedrock.
In the case of the bedrock type iii, the combined analysis of 10 Be and 14 C allows for solving for the unknown exposure duration and erosion depth, if the moment of initial deglaciation can be constrained (see Sect. 3.5 stops and only the decay of the 14 C concentration is notable on these relatively short time-scales leading to lower concentration ratios (Hippe, 2017). In addition, sub-glacial erosion reduces the concentrations of both nuclides. If this sub-glacial erosion 225 was negligible or largely dominated by abrasion, the 14 C/ 10 Be concentration ratio is less than 4-3, while higher ratios indicate surface quarrying by the glacier (Rand and Goehring, 2019). The latter is because production at depth of 14 C is higher relative to that of 10 Be due to a higher 14 C contribution from muons, which penetrate deeper under the subsurface than neutrons (Hippe, 2017). Thus, in the case of moderate erosion rates dominated by abrasion, the apparent (i.e. non-burial-and erosion-corrected) 10 Be and 14 C ages provide both minimum exposure durations, with apparent 14 C ages being younger than their 10 Be counter 230 parts, and 14 C/ 10 Be concentration ratio is less than ~3. Also note that we make the assumption that during the periods of burial, the ice cover was always thick enough at our sample locations to hinder significant 14 C accumulation via muogenic production (>70 m; Hippe, 2017

Calculations of simple exposure ages
The 10 Be moraine and apparent bedrock ages discussed below were calculated with CREp (http://crep.crpg.cnrs-nancy.fr/#/; Martin et al., 2017) choosing the local "Alpine" 10 Be spallation production rate (Claude et al., 2014) (4.11 ± 0.10 atoms g -1 yr -250 1 as calculated in CREp via the link to the ICE-D calibration database), the ERA40 atmosphere model (Uppala et al., 2005), Lal-Stone time-corrected scaling (Lal, 1991;Stone, 2000;Balco et al., 2008) with atmospheric 10 Be-based VDM (Muscheler et al., 2005;Valet et al., 2005). The apparent 14 C bedrock ages were calculated accounting for spallogenic and muogenic production and radioactive decay, using the global 14 C spallation production rate of 12.22 ± 0.89 atoms g -1 yr -1 , the muon parameters from Balco (2017) and the half-life of 5730 years. The same atmosphere model and scaling methods as for 10 Be 255 were applied. A density of 2.7 g cm -3 is assumed for all samples.
As most of the recent studies in the Alps used the former CRONUS-Earth calculator by Balco et al. (2008) to calculate cosmogenic nuclide ages, we also show the 10 Be moraine and apparent 10 Be and 14 C exposure durations of bedrock calculated with version 3 of this tool, choosing the same parameters as above regarding the 10 Be production rate (calculated as 4.04 ± 0.38 atoms g -1 yr -1 in the former CRONUS-Earth calculator using the calibration data from the ICE-D calibration database), 260 atmosphere model and scaling scheme. Note that the calculator applies default parameters for the geomagnetic field model and the 14 C production rate.
All 10 Be and 14 C exposure ages and durations are shown in Tables 2 and 3. 10 Be exposure ages and durations calculated with both calculators differ by 1-2 % for early Holocene ages, and by at most 8 % for younger ages and exposure durations. 14 C exposure durations differ by 3-5 %. Higher differences in the results are due to high late Holocene inter-and intra-variability

Modelling of complex bedrock exposure history and erosion depth
Regarding the complex exposure history of bedrock type iii, three variables are unknown: the cumulative exposure duration texp, the cumulative burial duration tb and the erosion depth E, while the two-nuclide system allows for two of these unknowns 280 to be solved (Goehring et al., 2011). In our study, the age of the youngest early Holocene moraine (In Miseren moraine, ~10 ka), provides the timing of initial deglaciation of Steingletscher's forefield, and therefore the cumulative burial duration can be constrained by tb = 10 ka -texp (Goehring et al., 2011). In the pioneer Rhône Glacier study by Goehring et al. (2011) the remaining two unknowns, texp and E, were determined for each sample through analytical calculations using the two equations for 10 Be and 14 C production and loss at the rock surface. In a follow-up study, Goehring et al. (2013) proposed an isochron 285 Bayesian approach that allows considering several samples simultaneously with the purpose to reduce the uncertainties for the whole data set.
Here, we use a Monte Carlo-Markov Chain inversion (MCMC) to constrain the values of texp and E. We define a forward model to predict 10 Be and 14 C concentrations as a function of texp and E in each of the two 10 Be-and 14 C-analyzed rock samples (STEI-16-10 and -12) during their exhumation toward the surface, using the same production parameters and scaling method 290 as for the simple exposure ages calculations. We assume that the 10 Be and 14 C concentrations were set to zero due to deep and sustained glacial erosion during the previous glacial phase. The onset of the exposure history is set at 10 ka, as constrained by In Miseren moraine,. The subsequent history is divided into two steps. First, the surface is exposed for a duration texp, leading to steady accumulation of 10 Be and 14 C. Second, the surface is covered by ice until present, leading to zero nuclide production and bedrock erosion of a thickness E. We then use a standard MCMC approach to sample the parameter plane defined by texp 295 and E with the Metropolis-Hasting algorithm, and obtain the posterior distributions of these parameters for both samples. For each sample, we run 6 MCMC chains of length 10 5 , including a 10 3 burn-in phase. For each parameter we report the average and standard deviation of the chain. The average erosion rate e is subsequently determined by e = E/tb.
The advantage of using this forward model is the simulation of the concentration evolution in the analyzed sample during its exhumation toward the eroding surface, i.e. considering the depth-dependent production and decay of 14 C as a function of time, 300 instead of summing up nuclide production and loss in a virtual surface sample, independent of time, as applied in Goehring et al. (2011). The portion of decayed 14 C at each time step is thus quantified more precisely.
In addition, Fig. 6l depicts the evolution of the concentrations at the surface through time for the above-described single exposure-burial scenario and a more complex scenario with several exposure-burial alternations.

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The previously published radiocarbon ages discussed in this study were calibrated with the online program OxCal 4.4 (Bronk Ramsey, 2009), using its standard options and the IntCal20 calibration curve (Reimer et al., 2020) and are reported relative to the year 1950 CE.

Results
Tables 2, 3 and Figs. 1c, 5a show the exposure ages and apparent exposure durations directly calculated from the measured 310 10 Be and 14 C concentrations. Also listed in Table 3 are all 10 Be moraine boulder ages and moraine mean ages previously published in Schimmelpfennig et al. (2014) and recalculated with the methods presented in Sect. 3.4. In the Tables, ages are shown with their full uncertainties (i.e. including analytical and production rate uncertainties) and analytical uncertainties only.
The two oldest apparent 10 Be bedrock exposure durations from the Chüebergli riegel profile are 5.90 ± 0.10 kyr  and 4.10 ± 0.07 kyr . The other samples on this profile range between 2.67 ± 0.07 kyr (STEI-5) and 0.05 ± 0.01 320 kyr (STEI-2). All eight apparent 10 Be ages from the profile present a general trend from high values at the outer margin towards low values at the inner, lowest sample locations (Fig. 5a). This trend is consistent with the higher ice flow velocity in the center of a glacial trough that leads to deeper sub-glacial bedrock erosion during periods of ice-cover, thus reducing the 10 Be surface concentrations at a higher rate (Goehring et al., 2011).
Only the two samples with the oldest apparent 10 Be exposure durations (STEI-16-12 and STEI-16-10) were chosen for 14 C 325 analyses to ensure 14 C measurements precise enough for a meaningful interpretation. The apparent 14 C exposure durations of the two analyzed samples are 3.74 ± 0.10 kyr and 2.20 ± 0.05 kyr, respectively, i.e. both are apparently younger than their 10 Be counterparts. This trend and the low 14 C/ 10 Be concentration ratios of 1.67 ± 0.05 and 1.62 ± 0.04, respectively, are consistent with temporary burial of the surfaces and indicate that subglacial erosion was moderate and dominated by abrasion (see Sect. 3.3; Table 2).

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The two apparent 10 Be bedrock exposure durations from the Bockberg riegel are 0.05 ± 0.02 kyr (STEI-16-7) and 0.62 ± 0.03 kyr . We decided to not use them for 14 C analyses due to the low cosmogenic nuclide inventory. These samples are therefore only briefly discussed in the following text.
Modelling of the 10 Be and 14 C data yields cumulative exposure durations texp for STEI-16-12 and STEI-16-10 of 8.0 ± 0.3 kyr and 6.8 ± 0.3 kyr (1σ analytical uncertainties), burial durations tb of 2.1 ± 0.1 kyr and 3.2 ± 0.1 kyr, and subglacial erosion 335 depths E (rates e) of 21 ± 3 cm (0.10 ± 0.02 mm yr -1 ) and 36 ± 3 cm (0.11 ± 0.01 mm yr -1 ), respectively. If we assume that STEI-16-12 and STEI-16-10 experienced the same exposure history on millennial time scales, an average ice-free duration and standard deviation of 7.4 ± 0.8 kyr can be deduced. the results from the two innermost samples due to their low 10 Be concentrations). This approach allows evaluation of the range of possible erosion depths and rates, illustrated by the yellow lines, even without combination with 14 C analyses. Assuming 345 that these four samples experienced a similar exposure-burial history as samples STEI-16-12 and STEI-16-10, their 10 Be concentrations indicate subglacial erosion rates of >0.2 mm yr -1 (Fig. 5b). This erosion rate estimate and the values inferred from the combined 10 Be and 14 C data (~0.10-0.11 mm yr -1 ) agree with those from Rhône Glacier (~0.02-0.33 mm yr -1 ) and the steep Trift riegel (0->2 mm yr -1 ) obtained with the same analytical method (Goehring et al., 2011;Steinemann et al., 2021). Yellow lines indicate selected theoretical bedrock erosion rates.

Holocene timing and duration of Steingletscher retreat
Given the similarity in ages of the Hublen bedrock (highest and stratigraphically outmost position; 11.5 ± 0.3 ka) and the outer 360 Hublen moraine (11.0 ± 0.3 ka), we infer that these bedrock surfaces experienced a simple exposure history and that their age represents the timing of the first general deglaciation of the summit of Plateau Hublen at ~11.5 ka, during the transition from the YD to Holocene. This supports our assumption that the Hublen bedrock was free from significant 10 Be inheritance from

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This date of deglaciation of the plateau summit also implies that the glacier had a greater extent prior to ~11.5 ka. However, chronological constraints on positions of Steingletscher prior to or during the YD do currently not exist.
Subsequent to the ~11.5 ka deglaciation of the Hublen Plateau summit, Steingletscher experienced a slow oscillatory retreat for about 1.5 kyr, similar to other glaciers in the Alps (Protin et al., 2021), and deposited the three preserved early Holocene moraines on Plateaus Hublen and In Miseren. Steingletscher's forefield was thus most likely completely covered by ice until 370 the deposition of the In Miseren moraine (10.0 ± 0.9 ka). Chüebergli riegel was covered by at least 140 m of ice until then.
Subsequently, the glacier considerably retreated, most probably for the first time in the Holocene. Although the amplitude of Steingletscher's recession at that time is unknown, we assume that Chüebergli and Bockberg riegels already became ice-free at ~10 ka. This is supported by radiocarbon-dated subfossil wood relicts that melted out of several glaciers across the Swiss Alps between 1990 and 2006 CE, indicating that these glaciers were as small as or smaller between ~10 and ~8.2 cal BP than 375 in modern times (Hormes et al., 2001(Hormes et al., , 2006Joerin et al., 2006Joerin et al., , 2008Nicolussi and Schluechter, 2012).
Apart from two wood fragments collected in Steingletscher's forefield and radiocarbon-dated at 5.3-4.8 cal ka and 4.8-4.6 cal ka testifying to a glacier recession upstream of its ~2000 CE extent, no further direct constraints exist for the timing and amplitudes of Steingletscher's fluctuations during the mid-Holocene (Hormes et al., 2006;Fig. 6k). Evidence of recession of the neighboring Steinlimigletscher at 5.9-5.3 cal ka suggests that Steingletscher was in a retreated position, too, at that time 380 (Hormes et al., 2006). During the late Holocene, the glacier considerably readvanced at ~3 ka ago and covered Chüebergli riegel again with ~140 m of ice or more. This happened again from at the latest 0.6 ka onward during the period of the LIA until the general retreat trend from 1850 CE on, which eventually uncovered Chüebergli riegel completely around 2000 CE.
Between ~3 ka and the LIA, the exact timing of further Steingletscher fluctuations is unknown, but the bracketing radiocarbon age of a wood fragment in peat near the LIA glacier limit suggests warm climate at ~2.5-1.9 cal ka (King, 1974), that might 385 have led to glacier retreat. Significant glacier recession to modern extents during that time has also been documented at other Alpine glaciers, in particular in the detailed late Holocene records at Great Aletsch (Holzhauser et al., 2005) and Mer de Glace (Le Roy et al., 2015) (Fig. 6g, h). At Steinlimigletscher, one organic silt sample radiocarbon-dated at ~2.3-1.8 cal ka, attesting to glacier retreat beyond the ~2000 CE extent, supports a local impact of this probably regional-scale warming event (Hormes et al., 2006;Fig. 6k). A subsequent readvance of Steingletscher is tentatively suggested by one 10 Be boulder age of ~1.9 ka 390 (Schimmelpfennig et al., 2014). Another period of considerable retreat can be assumed for the Medieval Warm Period (~1.3-0.7 ka), when several glaciers in the Alps are known to have retreated again to modern extents (Holzhauser et al., 2005;Le Roy et al., 2015;Fig. 6g, h).
Based on the 10 Be and 14 C data from Chüebergli riegel, we now explore the duration that the glacier had uncovered this area during the Holocene and put it into the context of the above described glacier fluctuations. The apparent 10 Be exposure 395 durations from Chüebergli riegel alone already indicate that at least the outmost part of the profile has been exposed for a cumulative period of more than ~5.9 kyr during the Holocene, i.e. that the glacier was smaller for that duration than its extent in 2000 CE. The general trend of decreasing apparent 10 Be durations on the profile (by 2 orders of magnitude) indicates that the glacier temporarily covered and subglacially eroded the riegel again, otherwise similar apparent exposure durations would be expected for all samples on the profile. The erosion-corrected exposure durations modelled from the 10 Be-14 C data of the 400 two samples, indicate that the glacier was smaller than its 2000 CE extent for a total of ~7.4 kyr during the Holocene. Based on the assumptions and knowledge of relatively rare and short periods of glacier retreat after 3 ka ago, it is most likely that almost all of this glacial retreat occurred between ~10 ka and ~3 ka. In Fig. 6l  12 and -10 were collected. The simplest scenario, consistent with the measured concentrations of STEI-16-10, consists of a single ice-free period between 10 ka and 3 ka, and a continuously ice-covered period between ~3 ka and modern times (orange curves). In the more complex scenario, which yields final theoretical concentrations similar to the measured concentrations of STEI-16-12, the glacier retreat beyond the 2000 CE glacier extent occurred not only between 10 ka and 3 ka, but also during the late Holocene warm periods at 2.5-2 ka and 1.3-0.7 ka (green curves). The sum of the exposure durations in this scenario 410 amounts to 8.1 kyr and is thus indistinguishable from the exposure duration of 8.0 ± 0.3 kyr analytically inferred from the 10 Be and 14 C measurements in sample STEI-16-12. For comparison, the scenario with a single exposure period between 10 ka and 2 ka is also shown for sample STEI-16-12 (also leading to consistent 10 Be and 14 C concentrations), which however is not consistent with the recorded glacier advance at ~3 ka and therefore appears less realistic.
Taken together, it is most likely that frequent glacier oscillations led to temporary burial of Chüebergli riegel, and that during 415 the ~10 ka -3 ka period, burial beneath ice occurred very rarely or not at all, while the ~3 ka to 2000 CE period was dominated by Steingletscher advances and ice cover of Chüebergli riegel.

Comparison with Holocene glacier reconstructions in the European Alps
At a growing number of glacier sites, millennia-spanning records support the observed trend by providing evidence of 445 significant and long-lasting glacier retreat during the early and mid-Holocene and progressive glacier re-advance during the late Holocene. Rutor Glacier in the western Italian Alps was smaller than its LIA maximum extent between 8.8 ka and 0.85 ka, and it was at least as contracted as in the 1960s CE between 8.8 ka and 3.7 ka (Badino et al., 2018;Porter and Orombelli, 1985; Fig. 6d). Upper Grindelwald Glacier experienced high-frequency elevation changes that were dominated by ice-loss between 9.2 ka and 3.8 ka, followed by predominant advances close to the glacier's Holocene maximum (Luetscher et al., 450 2011; Fig. 6e). Radiocarbon-dated subfossil wood and peat fragments that had melted out of several retreating glaciers across Switzerland since 1990 CE, revealed frequent and prolonged periods of recession between ~10 ka and 3.5 ka followed by rare and short recessions during the late Holocene (Hormes et al., 2001;Joerin et al., 2006Joerin et al., , 2008Fig. 6f). Detailed reconstructions of late Holocene glacier fluctuations of Great Aletsch (central Swiss Alps) and Mer de Glace (northern French Alps), based on radiocarbon-dating founds, historical data and dendrochronology, reveal frequent large advances from ~4 ka onward 455 (Holzhauser et al., 2005;Le Roy et al., 2015) (Fig. 6g, h). Finally, Fig. 6i shows the Holocene retreat-advance scenario for Rhône Glacier (central Swiss Alps) inferred from combining the retreat duration of 6.4 ± 0.5 kyr with chronological data on glacier advances from the Alps (Goehring et al., 2011(Goehring et al., , 2013. The general consistency of the findings from Steingletscher with the Rhône Glacier scenario and with the findings from the other locations in the Alps validate the here applied approach and confirms that the millennial retreat behavior of Steingletscher and Rhône Glacier represent regional glacial responses to 460 Holocene climate warming. Quantitative differences in the cumulative retreat durations inferred from the different methods seem to be consistent with the amplitude of glacier recession that is associated with the investigated sample material or location. While the in situ 14 C-10 Be dating approach suggests that glaciers were as retracted as the ~2000 CE glacier extents for ~7 kyr during the Holocene (Goehring et al., 2011; this study), the recession periods inferred from the radiocarbon record by Joerin et al. (2006) add up to 465 less, ~5 ka. The reason could be that the subfossil organic material implies glacier retreat significantly upstream of the sampling locations and the ~2000 CE glacier extents, as tree growth and peat development can only occur in deglaciated basins. This would roughly imply that since the final deglaciation (~10 ka), glaciers in the Alps were similar in size as in ~2000 CE during https://doi.org/10.5194/cp-2021-110 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License. a total of ~2 kyr, while they were smaller than this extent for ~5 kyr. However, this interpretation is tentative and will need to be verified, as the observed differences in the cumulative retreat durations might also be inherent to uncertainties in the dating 470 approaches (e.g. unaccounted-for production through thin ice at Steingletscher or lacking organic material from unknown retreat periods at the radiocarbon-dated sites).

Holocene glacier evolution in the Alps in the context of regional and global temperatures
Alpine summer temperature reconstructions based on Chironomid and pollen assemblages are consistent with the Holocene glacier behavior in the Alps (e.g. Heiri et al., 2015;Badino et al., 2018;Fig. 6c, d). These summer temperature records indicate 475 that the HTM might have been ~1-3°C warmer than modern times. Also, the proxy-based global mean temperature reconstructions by Marcott et al. (2013) and Kaufman et al. (2020) reveal a very similar trend suggesting an early to mid HTM followed by long-term cooling until the LIA (Fig. 6b). By contrast, model simulations of mean annual temperatures indicate that steady warming prevailed throughout the Holocene and that the recent decades are the warmest of the whole Holocene (Liu et al., 2014;Marsicek et al., 2018). Amongst the possible causes that have been proposed to explain these discrepancies, 480 recent studies pay particular attention to the effect of seasonal biases (Marsicek et al., 2018;Affolter et al., 2019;Bova et al., 2021). According to this hypothesis, proxy-based global temperature reconstructions reflect warm-season, rather than annual temperatures, because the growth of biogenic proxies is controlled by summer temperatures.
As mid-latitude glacier records at regional scale are mainly driven by summer temperature evolutions (Oerlemans, 2005;Solomina et al., 2015), our results corroborate the existence of an extended warm-season HTM and thus seem to support the 485 hypothesis of seasonality during the early and mid-Holocene. However, the amplitude of this seasonality cannot be determined from glacier chronologies. Further investigations are therefore necessary to resolve the controversial annual temperature evolution of the Holocene. A recent reconstruction of seasonally unbiased temperatures in Greenland, based on argon and nitrogen isotopes, provides evidence of several early and mid-Holocene episodes (amounting to 27 % of the Holocene) with temperatures above the average of the recent decades (Kobashi et al., 2017;Fig. 6a). This reconstruction is incompatible with 490 the model-based steady warming and rather points to a hemispheric teleconnection with the trend of glacier fluctuations in the Alps.
In addition, we note that none of the continuous proxy records reveals a significant cooling event at ~3 ka that could explain the deposition of late Holocene moraines outboard of the LIA extent of Steingletscher. This inconsistency will also need to be further investigated, because several other moraines of similar age are preserved across the Alps (Schimmelpfennig et al., 495 2012;Le Roy et al., 2017;Moran et al., 2017), indicating a regional glacier and climate signal.

Conclusions
The Steingletscher record is consistent with the regional Holocene glacier evolution in the Alps suggesting that glaciers across the Alps were smaller than their modern extents for most of the Holocene. The correlation between reconstructed summer 500 temperature variability and the established glacier pattern demonstrates that at least the warm season was warmer than in recent decades for several millennia of the HTM. However, additional investigations are needed to fully understand whether or not the early and mid-Holocene was characterized by significant seasonality.
Uncertainty also remains with regard to the amplitude of glacier recessions and thus the magnitude of warming. The exact amplitude of glacier retreat can indeed not be inferred from the here applied paired-nuclide approach, because the dated 505 bedrock does not delineate a past glacier extent. As a perspective, applying this approach at various distances from the current glacier front could be a valuable strategy to add further spatial constraints on the amplitudes of glacier recessions, provided subglacial bedrock erosion is low enough. In addition, the combination with complementary dating methods and glacier https://doi.org/10.5194/cp-2021-110 Preprint. Discussion started: 2 September 2021 c Author(s) 2021. CC BY 4.0 License. reconstruction approaches will help refine the long-term records both in terms of chronological and spatial constraints and thus add important knowledge to the Holocene glacier and climate picture in the region.

Data availability
All data will be availability in the ICE-D Alpine database (http://alpine.ice-d.org)