Auxiliary material for Paper 2008GL036765
Constraints on the lake volume required for hydro-fracture through ice sheets
M. J. Krawczynski
MIT/WHOI Joint Program, Cambridge, Massachusetts, USA
M. D. Behn and S. B. Das
Department of Geology and Geophysics, Woods Hole Oceanographic Institution,
Woods Hole, Massachusetts, USA
I. Joughin
Applied Physics Lab, University of Washington, Seattle, Washington, USA
Krawczynski, M. J., M. D. Behn, S. B. Das, and I. Joughin (2009), Constraints on
the lake volume required for hydro-fracture through ice sheets, Geophys. Res.
Lett., 36, L10501, doi:10.1029/2008GL036765.
Introduction
This auxiliary material contains a detailed outline of the numerical modeling
approach we undertook for our study of supraglacial lake drainage in thick ice
sheets. The equations and sample calculations are outlined in Text S1. In
addition we provide several figures to aid in understanding our thought process
and calculations, as well as some the field evidence in support of our model.
The data used to obtain total lake volume for West Greenland is from MODIS
satellite imagery, and the data reduction for that is also included in Text S1.
All references can be found in the main article.
1. 2008gl036765-txts01.tex, 2008gl036765-txts01.pdf
Text and equations outlining our model and field observations.
2. 2008gl036765-fs01.eps
Critical crack length for complete ice sheet fracture. Crack length needed to
support critical propagation as a function of the differential stress in the ice
sheet. Cracks will propagate even in areas with overall compression as long as a
long enough initial crack is provided, such as a dry crevasse.
3. 2008gl036765-fs02.eps
Crack penetration depth, as a function of water content. Maximum propagation
depth versus water content. The lines represent longitudinal differential stress
contours. For a given amount of water, a greater tensile stress will create a
deeper crevasse. Note also that any crevasse that stays filled with water to at
least ~95% will not have a maximum depth and will penetrate to the base of an
ice sheet, as long as the far field stress is tensile or neutral.
4. 2008gl036765-fs03.eps
Comparison of opening geometries for 2 model calculations, dry versus water-
filled. Calculation of opening geometries for 15 m crevasses, one dry and one
water-filled. The overall tension is 0.1 MPa and the shear modulus is 1.5 GPa.
The water-filled crevasse is much wider and keeps a more constant opening shape.
Note the extreme horizontal exaggeration.
5. 2008gl036765-fs04.eps
Mean flux of water through moulins and cracks. Mean flux of water through a
channel or pipe versus the depth of the crevasse. As depth increases so does the
width of the channel, and thus the flux as well. Flux through the channel is
always greater than for a pipe, leading to faster drainage times. Curve labels
are for longitudinal differential stress.
6. 2008gl036765-fs05.eps
A healed crevasse in the field with dimensions typical for a deep water-filled
crack. A healed crack in an area of ice that was once underneath a lake. This
crack maintains an average width of ~10 cm for over 100 m. In the middle of the
healed crevasse is a line of bubbles, indicative of that the crevasse froze from
the sides in. This crevasse is typical of many found in the field area.
7. 2008gl036765-fs06.eps
An ice canyon which yields a 3-D view of crack geometry, again with opening
geometry consistent with a deep water-filled crack. An ice canyon allowing for a
3-D view of one of the healed crevasses. The canyon is ~50 m deep, and the
crevasse shown by the arrows has a similar opening width at the top and bottom
of the canyon. This "U-shaped" geometry is consistent with the Weertman model
for water filled cracks. Note the ~1.5m scientists for scale.