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.