An imbalancing act: the dynamic response of the Kaskawulsh

The Kaskawulsh Glacier is an iconic outlet draining the icefields of the St. Elias Mountains in Yukon, Canada. We determine and attempt to interpret its catchment-wide mass budget since 2007. Using SPOT5/6/7 data we estimate a 2007--2018 geodetic balance of -0.46 ± 0.17 m w. e.a-1. By comparing computed balance fluxes with observed ice fluxes at nine flux gates we examine the discrepancy between the climatic mass balance and internal mass redistribution by glacier flow. Balance fluxes are computed using a fully distributed mass-balance model driven by downscaled and bias-corrected climate-reanalysis data. Observed fluxes are calculated using NASA ITS_LIVE surface velocities and glacier crosssectional areas derived from ice-penetrating radar data. We find the glacier is still in the early stages of dynamic adjustment to its mass imbalance. We estimate a committed terminus retreat of ∼23 km under the 2007-2018 climate and a lower bound of 46 km3 of committed ice loss, equivalent to ∼15% of the total glacier volume. By combining our observations and model output using the continuity equation, we highlight challenges and opportunities in exploring the mass budget of Cambridge University Press Journal of Glaciology

The global population of glaciers has been identied as a key contributor to recent (Gardner and others, 2013; 24 Vaughan and others, 2013; Zemp and others, 2019) and near-future projected sea-level rise (s.l.r.) (Meier 25 and others, 2007; Radi¢ and others, 2014; Hock and others,

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The processing of the DEMs follows the workow presented in Berthier and Brun (2019). A horizontal 95 pixel size of 20 m is chosen here for the analysis. All DEMs are coregistered to TanDEM-X ( Rizzoli and 96 others, 2017) on stable terrain following Berthier and others (2007), masking out glacierized areas using the 97 Randolph Glacier Inventory (RGI) v6.0 (Pfeer and others, 2014; Kienholz and others, 2015 To extract elevation change with altitude and compute the mass balances of individual glaciers, we exclude 102 data outside ±3 standard deviations from the mean elevation dierence in each 50 m altitude interval for 103 each glacier ( Berthier and others, 2004). We also exclude pixels where the surface slope, calculated from 104 the TanDEM-X DEM, is larger than 45 • . The total volume change is calculated as the integral of the mean 105 elevation dierence in each 50 m band over the total areaaltitude distribution. The mass balances are 106 then derived using a volume-to-mass conversion factor of 850 kg m −3 (Huss, 2013) where T is the three-hourly temperature obtained from downscaled temperature and geopotential data 142 (described below) across the Kaskawulsh Glacier catchment, I is the potential direct clear-sky radiation,

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MF is the melt factor and a snow/ice are the radiation factors for snow and ice, respectively. MF and a snow/ice 144 must be empirically determined.

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Accumulation 146 A statistical downscaling approach adapted from Guan and others (2009) is applied to the regional reanalysis surface precipitation input, with a prescribed rain-to-snow temperature threshold (e.g. Saelthun, 1996;Kienzle, 2008; Clarke and others, 2015) of 1 • C ( Johannesson and others, 1995). This threshold value is selected to reduce the dierence between modelled and measured accumulation at multiple snow depth and density measurement locations throughout the study time period (considering threshold values of 02 • C).
Refreezing of melt water within the seasonal snow pack is accounted for by implementing a distributed thermodynamic parameterization adapted from Janssens and Huybrechts (2000) in the study time period, total energy consumed by refreezing is approximated as a proportion (P r ) of the seasonal snow pack: transmissivity of 0.75 (Hock, 1998(Hock, , 1999 where T c (x, y, t) is the bias-corrected temperature at position x, y and time t, T ds (x, y, t) is the temperature where ∆T i (t) is the mean monthly value computed using one of the eight AWS records, and the weights α i 209 are proportional to the AWS record lengths. We did not consider using spatially variable values of ∆T (t) where C c (x, y, t) is the bias-corrected accumulation at position x, y and time t, C ds (x, y, t) is the 241 accumulation at the same position and time downscaled from the NARR precipitation data and ∆C(z)          In (b) u = u s . In (c), we estimate the contribution of deformation to surface velocity using the shallow ice approximation, up to a maximum of the observed surface velocity:

Comparison of modelled and inferred mass-balance distribution 453
Using the surface elevation change of the Kaskawulsh Glacier (Figure 2), the ice uxes at each of nine ux gates ( Figure 8) and the modelled surface mass balance (Figure 7), we are able to independently estimate each term in the continuity equation: where ∂h/∂t is the local rate of change of ice thickness, ∇·q is the divergence of the ux andḃ sfc is the surface    ) for each section of the glacier (labelled with downstream ux gate as in Figure   9): ∂h ∂t cal = −∇ · q obs +Ḃ mod ,Ḃ cal = ∂h ∂t obs + ∇ · q obs , ∇ · q cal =Ḃ mod − ∂h ∂t obs . Values of ∇ · q are converted to m w.e. a −1 using an ice density of 900 kg m −3 .

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Visual inspection of Figure 9 reveals changes in the sign of the mismatch betweenḂ mod andḂ cal in some 522 adjacent sections of the glacier, suggesting that mismatch could be reduced by combining these sections.

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The modelled mass-balance gradient is therefore steeper than that inferred from ∂h/∂t + ∇ · q.

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Missing physical processes can also explain some of the mismatch betweenḂ mod andḂ cal . For example, 529 the section above KW5 is inuenced by the presence of an ice-marginal lake with a calving front (Bigelow

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Entertaining the possibility that Q ref (Table 3) Table 3), we reduce metrics of overall mismatch between ∇ · q obs and ∇ · q cal (Table   555 4) by ∼2040% and section-wise mismatch of ∇ · q obs and ∇ · q cal downstream of the tributary ux gates 556 from >75% to <25% (not shown). The resulting mismatch betweenḂ cal andḂ mod is more systematic and 557 spatially coherent than that using Q ref in Figure 9, particularly below the tributary ux gates (not shown

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It also corroborates our nding that the modelled mass-balance gradient is steeper than that inferred from 563 ∂h/∂t + ∇ · q.  With the exception of the SW and SA ux gates, where the balance uxes are impacted by the suspected 573 overestimation of modelled accumulation, the spatial structure of Q obs resembles that of Q bal0 (Figure 10).

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The magnitudes of Q obs are lower than those of Q bal0 , but signicantly higher than those of Q bal   Program. The data presented in this manuscript will be made available upon acceptance.