Last glacial cycle glacier erosion potential in the Alps

The glacial landscape of the Alps has fascinated generations of explorers, artists, mountaineers and scientists with its diversity, including erosional features of all scales from high-mountain cirques, to steep glacial valleys and large over-deepened basins. Using previous glacier modelling results, and empirical inferences of bedrock erosion under modern glaciers, we compute a distribution of potential glacier erosion in the Alps over the last glacial cycle from 120 000 years ago to the present. 5 Despite large uncertainties pertaining to the climate history of the Alps and unconstrained glacier erosion processes, the resulting modelled patterns of glacier erosion include persistent features. The cumulative imprint of the last glacial cycle shows a very strong localization of glacier erosion with local maxima at the mouths of major Alpine valleys and some other upstream sections where glaciers are modelled to have flown with the highest velocity. The modelled erosion rates vary significantly through the glacial cycle, but show paradoxically little relation to the total glacier volume. Phases of glacier advance and max10 imum extension see a localization of rapid erosion rates at low elevation, while glacier erosion at higher elevation is modelled date from phases of less extensive glaciation. The modelled erosion rates peak during deglaciation phases, when frontal retreat results in steeper glacier surface slopes, implying that climatic conditions that result in rapid glacier erosion might be quite transient and specific. Our results depict the Alpine glacier erosion landscape as a time-transgressive patchwork, with different parts of the range corresponding to different glaciation stages and time periods. 15

Franz-Josef Glacier, mapped their chemical composition to geologic zones of distinctive glacier speed, and also concluded to a near-square relationship between basal sliding and glacier erosion. Cook et al. (2020) assembled a global compilation of erosion rates for 38 glaciers, showing a predominant role of glacier sliding velocity over climate variables, yet concluding at a sub-linear relationship to erosion.
Here, the non-linear erosion law by Koppes et al. (2015) is applied to previously published model results (Seguinot et al., 2018) and the patterns of modelled erosion rates ::::::: potential : and cumulative last glacial cycle erosion potential are analysed. We examine the glaciological conditions that cause erosion and discuss the implications of these conditions on understanding the :::: mark :: of ::::::: ancient ::::::: glaciers :: on :::::: Alpine :::::::::: topography ::: and ::: the : relationship between climate and glacier erosion. Despite aggregated uncertainties on paleoclimate, glacier flow and glacier erosion processes, out results provide insights into the diversity of the 70 Alpine glacial erosion landscape.

Ice sheet modelling
The ice-sheet model set-up was presented in an earlier publication (Seguinot et al., 2018) and is briefly summarized here.

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The modelled cumulative (time-integrated) glacial erosion potential (Fig. 1a) varies by several orders of magnitude from insignificant to hundred-metres-scale erosion potential. Its spatial patterns show a very strong localization along the Alpine valleys, with local maxima occurring both at the Alpine gates where ice flow transited from valley to piedmont glaciers, and further upstream where the valley slopes increase. While mountain cirques are poorly ::::: cirque :::::: glaciers :::: and ::::::: relevant ::::::: erosion :::::::: processes :::: may ::: not :: be captured by the model 's :::::: physics :::: and horizontal resolution, high cumulative erosion potential also occurs 115 near the valley heads. There is a general tendency for higher cumulative erosion in the north-western Alps where the input winter precipitation is higher (WorldClim, Fig. 1h in Seguinot et al., 2018) and the glacial relief more pronounced in the topography.
reached, there is a slight :::::: general tendency for slower erosion during periods of extensive glaciation (Fig. 2). However, the domain-integrated erosion volume is modelled to be consistently higher (by a factor 2 to 10) during periods of decreasing ice 125 volume, than during periods of increasing ice volume (Fig. 2).

Spatial migration
A closer look at the Rhine Glacier, one of the paleo-ice sheet's largest outlets, reveals a spatial migration of the modelled rapid erosion areas. During stages of glacier advance and maximum extension, erosion is modelled to be under 1 mm a −1 and restricted the lower parts of the catchment, while much :: of the intra-montane Alps (modelled to be largely cold-based, Fig The results found on the Rhine Glacier catchment can be generalized to the entire model domain by using (present-day) bedrock altitude as a proxy for along-flow distance (Fig. 4). Thus more generally, periods of modelled increasing and maximum ice volume correspond to lower values for elevation-aggregated ::::::: potential erosion rates, with significant erosion ::::::: potential 135 restricted to lower elevations. On the opposite, periods of modelled decreased ice volume correspond to higher local modelled erosion rates and more extensive rapid erosion ::::::: potential into higher-elevation areas (Fig. 4). advance ::: and ::::: retreat : ages, ::: and ::: the :::: final ::::: model ::: state ::: for ::::::::: topographic ::::::: reference. (d) :: (e) Interpolated instantaneous :::::: potential : erosion rate along a Rhine Glacier transect for the entire last glacial cycle (upper panels dashed line) :: for ::: the ::::: entire ::: last ::::: glacial :::: cycle.

Choice of erosion law
The choice of erosion law significantly impacts the results (Fig. 6). Our default, based on quantified sediment yields from Patagonian and Antarctic Peninsula tidewater glaciers (ė = 5.2 × 10 −8 u 2.34 b , Koppes et al., 2015) yields a moderate and strongly localized cumulative erosion potential (Figs 1 and 6a). The erosion law based on measured suspended sediment load from Franz-Joseph Glacier (ė = 2.7 × 10 −7 u 2.02 b , Herman et al., 2015) also yields a strongly localized, and yet much higher, mod-155 elled erosion potential (Fig. 6b). The erosion law based on measured suspended sediment load during a surge of Variegated Humphrey and Raymond, 1994) results in similarly high values, but a less localized pattern of cumulative erosion potential (Fig. 6c). Finally, The erosion law based on a global compilation of glacier velocities and erosion rates (ė = 1.665 × 10 −1 u 0.6459 b , Cook et al., 2020) yields an even flatter pattern of cumulative erosion potential (Fig. 6d).
low elevations results in a steepened topographic profile (Figs. 7a), as observed and further expected on currently retreating glaciers (Huss et al., 2010;Zekollari and Huybrechts, 2015). The buttress formed by the glacier foot against gravitational forces This result is corroborated by a recent denudation record from the Mediterranean Alps, which includes an increase in glacier erosion in the Var Valley, roughly at 25 ka following an extended period of low denudation rates (Mariotti et al., 2021).

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Finally, the time-transgressive nature of the modelled glacial erosion rates hint at a new explanation for the Alpine glacier trim-line and lack of cold-based glaciation evidence. Due to their geographic location in the mid-latitudes, and their steep topographic gradient, the Alps appear as a mountain range that hosted glaciers of various sizes throughout the varying climate of the Quaternary, resulting in a transgressive localization of glacier erosion throughout their elevational range, from the piedmont during glacial maxima, to the highest cirques during interglacial periods. The Alpine trim-line, in this case, would 250 neither correspond to the upper reach of the Last Glacial Maximum glaciers (e.g., Kelly et al., 2004), nor to an englacial temperate-ice boundary (Coutterand, 2010;Seguinot et al., 2018), but to a time-transgressive upper limit of erosion from :::::::: advancing :::: and retreating glaciers on steep terrain.
Due to compounded uncertainties regarding paleoclimate, glacier sliding and erosion processes, our quantitative results are 255 very likely inaccurate. Yet ::::::: However, we draw the following qualitative conclusions: -The non-linear physics of glacier deformation and sliding, combined with non-linear empirical erosion laws, results in a very strong localization of rapid glacier erosion in regions of fast flow.
-This high spatio-temporal variability hints at a complex relationship between climate and glacier erosion, so that a highly variable response of glacier erosion to climate should be expected.

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-Increased gravitational drag due to surface profile steepening provide ::::::: provides : a mechanism for accelerated erosion during deglaciation periods, irrespective of surface meltwater penetration to the glacier bed.
-If a non-linear glacier erosion law is used, the climate-induced slowdown of erosion counterbalances glacier expansion, so that Alpine-wide glacier erosion volumes do not correlate with the ice volume.
-Rapid glacier erosion is restricted to low elevation during stages of glacier advance and maximum glaciation, but propa-265 gates up-valley to higher elevations during periods of glacier retreat.