Geophysical Research Letters
Supporting Information for
Deglaciation and glacial erosion: a joint control on the melting of the solid Earth
Pietro Sternai1, Luca Caricchi2, Sébastien Castelltort2, Jean-Daniel Champagnac3
1
Division of Geological and Planetary Science, California Institute of Technology,
Pasadena CA, USA. Now at: Department of Earth Sciences, University of Cambridge,
Cambridge, UK
2
Section of Earth and Environmental Science, University of Geneva, Switzerland
3
Geological Institute, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland
Contents of this file
Figures S1 to S6 and respective captions
Tables S1 and caption
Video caption
Software S1
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Figure S1: a-d) Selected time steps of a numerical experiment similar to the
experiment shown in Fig. 2, except that the reference point (i.e., the star) is located 10km
away from the watershed. In the upper panels, red and blue colours are used to represent
the glacier’s accumulation and ablation area respectively. The yellow line represents the
glacier’s Equilibrium Line Altitude (ELA). The mean glacial erosion rate above the
reference point throughout the glacial cycle is ~1.5mm a-1. We also show in d the initial
topography (dashed line), the mean ELA throughout the entire glacial cycle (purple line)
and the piedmont region.
2
Figure S2: Temporal evolution of (a) the contribution from ice-building/melting
and (b) glacial erosion to the surface load variations at the reference point (shown by the
yellow star in Fig. S1). In a and b, lines are coloured in red and blue when the reference
point is covered by the glacier’s accumulation and ablation area, respectively. Grey
shaded regions (in a and b) represent the time interval during which the surface load is
decreasing. Vertical dashed lines (in a and b) highlight the time interval during which the
reference point is directly below the ice. Note that panels c and d in Fig. 3 apply to this
figure as well.
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Figure S3: a-d) Selected time steps of a numerical simulation similar to the
experiment shown in Fig. 2, except that the ice mass balance slope constant, 𝛾, is equal to
1, implying reduced ice ablation (compare the ice thickness and extent with Fig. 2). In the
upper panels, red and blue colours are used to represent the glacier’s accumulation and
ablation area respectively. The yellow line represents the glacier’s Equilibrium Line
Altitude (ELA). The star shows the location of the reference point. The mean glacial
erosion rate above the star throughout the glacial cycle for this numerical experiment is
~1.8mm a-1. We also show in d the initial topography (dashed line), the mean ELA
throughout the entire glacial cycle (purple line) and the piedmont region.
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Figure S4: Temporal evolution of (a) the contribution from ice-building/melting
and (b) glacial erosion to the surface load variations at the reference point (shown by the
yellow star in Fig. S3). In a and b, lines are coloured in red and blue when the reference
point is covered by the glacier’s accumulation and ablation area, respectively. Grey
shaded regions (in a and b) represent the time interval during which the surface load is
decreasing. Vertical dashed lines (in a and b) highlight the time interval during which the
reference point is directly below the ice. The contributions from ice-building/melting and
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glacial erosion to the surface load variations are also shown in the space-time domain in
(c) and (d), respectively. To facilitate readability, values are sampled every 10ka and
10km. Time derivatives are computed through forward differences, so no value is
obtained between 0-10ka. The horizontal dashed lines (in c and d) highlight the evolution
of surface loading/unloading at the reference point. Note the different magnitudes of
surface unloading from ice building/melting and glacial erosion and see also Fig. 4b
where variations of peak surface unloading magnitudes by glacial erosion for different
imposed glacial erosion coefficients, 𝐾𝑔 , (i.e., mean glacial erosion rates) are shown.
Figure S5: a-d) Selected time steps of a numerical experiment similar to the
experiment shown in Fig. 2, except that the coefficient of glacial erosion, 𝐾𝑔 , is set to 102
, implying particularly high glacial erosion rates. In the upper panels, red and blue
colours are used to represent the glacier’s accumulation and ablation area respectively.
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The star shows the location of the reference point. The yellow line represents the
glacier’s Equilibrium Line Altitude (ELA). The mean glacial erosion rate above the
reference point throughout the glacial cycle is ~10mm a-1. We also show in d the initial
topography (dashed line), the mean ELA throughout the entire glacial cycle (purple line)
and the piedmont region.
Figure S6: Temporal evolution of (a) the contribution from ice-building/melting
and (b) glacial erosion to the surface load variations at the reference point (shown by the
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yellow star in Fig. S5). In a and b, lines are coloured in red and blue when the reference
point is covered by the glacier’s accumulation and ablation area, respectively. Grey
shaded regions (in a and b) represent the time interval during which the surface load is
decreasing. Vertical dashed lines (in a and b) highlight the time interval during which the
reference point is directly below the ice. The contributions from ice-building/melting and
glacial erosion to the surface load variations are also shown in the space-time domain in
(c) and (d), respectively. To facilitate readability, values are sampled every 10ka and
10km. Time derivatives are computed through forward differences, so no value is
obtained between 0-10ka. The horizontal dashed lines (in c and d) highlight the evolution
of surface loading/unloading at the reference point. Note the different magnitudes of
surface unloading from ice building/melting and glacial erosion and see also Fig. 4b
where variations of peak surface unloading magnitudes by glacial erosion for different
imposed glacial erosion coefficients, 𝐾𝑔 , (i.e., mean glacial erosion rates) are shown.
Parameter
Value
Definition
𝜌𝑟𝑜𝑐𝑘
2700kg m-3
Bedrock density
𝜌𝑖𝑐𝑒
990kg m-3
Ice density
𝐿𝑜𝑐𝑥
10km, 50km
Distance of the reference point from
(Figs. S1-S2)
the main divide along the x axis
𝑔
9.81m a2
Gravitational acceleration
𝐵𝑠
7x10-16
Ice sliding coefficient
𝛾
1, 2
Ice mass balance slope constant
(Figs. S3-S4)
𝜆
𝑇0 𝑚𝑖𝑛 , 𝑇0 𝑚𝑎𝑥
𝐾𝑔
0.0045°C m-1
Atmospheric lapse rate
7°C, 13°C
Min, Max sea surface temperature
1x10-5,
1x10-4,
1x10-3, Glacial erosion coefficient
1x10-2 (Fig. 4)
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𝑙
1
Exponent for glacial erosion
𝑞
2
Exponent for ice sliding
𝑀𝑚𝑎𝑥
1m a-1
Max ice accumulation
𝑀𝑚𝑖𝑛
-20m a-1
Min ice ablation
𝑛
1
Exponent for fluvial erosion
𝑚
0.5
Exponent for fluvial erosion
𝐾
4×10-4 a-1
Fluvial erosion coefficient
𝐷
200m2 a-1
Hillslope erosion coefficient
𝑈
2mm a-1
Rock uplift rate
𝑡
4.1Ma
Simulated time
3300kg m-3
Mantle density

0.2
Poisson’s ratio
𝑇𝑒
20km
Elastic thickness
𝜌𝑚𝑎𝑛𝑡 
Table S1: Parameter setting for all numerical experiments.
Video: Audio-visual abstract with divulgation purposes.
Software S1: Source code (Fortran90) used for the numerical experiments.
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