Tuesday, March 10, 2015

Marine Ice Sheet Retreat Rates and the Coulomb Friction Model

                                                        The Coulomb Friction Model Triumphs Again!

In a brilliant new scientific paper, Prof. Victor Tsai of the California Institute of Technology has shown that ice sheets change the way they flow when they enter the sea, making them more susceptible to collapse due to Greenhouse Warming.  

Its long been known that ice sheets are much thicker and steeper on land then they are in coastal areas where the margins off the ice sheet are grounded in the sea.  Nonetheless, glaciologists have tended to assume that the flow mechanisms were similar through the glacier, i.e. the glacier was everywhere sliding across bedrock.  

About 25 years ago a few scientists suggested that in some places  ice sheets were resting on a layers of sediment and glacial till rather than on bedrock,  the rheology of the basal sediments, which can be described using the Coulomb Friction Model, was playing an important role in the flow of the glacier.*   More recently drilling and seismic studies in Antarctica and Greenland have proved that a weak layer of till underlies fast-flowing ice streams and outlet glaciers at the coast.  

Victor Tsai in his paper shows that a transition in the flow mechanism of the Antarctic Ice Sheet occurs near the coast where ice sheets flow into the sea.  Flow of the main part of the ice sheet obeys a power law, but  the  flow of the grounded marine portion of the ice sheets around the margin of the Ice Sheet reflects the presence of sediment under the glacier and is governed by the Coulomb Friction Model rather then by a power law tied solely to ice thickness.    The Coulomb Friction model was developed by Charles-Augustin de Coulomb and first published in 1785.

  Coulomb's model takes the form
F_\mathrm{f} \leq \mu F_\mathrm{n}
  • F_\mathrm{f}\, is the force of friction exerted by each surface on the other. It is parallel to the surface, in a direction opposite to the net applied force.
  • \mu\, is the coefficient of friction, which is an empirical property of the contacting materials,
  • F_\mathrm{n}\, is the normal force exerted by each surface on the other, directed perpendicular (normal) to the surface.

The margin of much of the the Antarctic Ice Sheet consists of grounded marine ice sheets that rest on slopes that dip inward toward the center of Antarctica. The implication of Tsai's model is that as calving progresses inward around the margins of the ice sheet, the velocity of calving will increase. This will occur because while is a function of the basal sediment and so is essentially constant, ecomes larger and larger as the calving line moves into the glacier, and the product of becomes greater and greater then , resulting in progressively higher ice velocities and higher calving rates.

Higher calving rates from the Antarctic and Greenland Ice Sheets mean more rapid global sea level rise. More rapid sea level rise means the dislocation of millions of people living on deltas in India, China and Pakistan will occur sooner then previously thought, and the abandonment of the low lying portions of many great coastal cities of the world---New York, Washington DC, London, Barcelona, San Francisco, and Nome....will come sooner then previously projected.

*I wrote two of the early papers using the Coulomb Friction model derived from the characteristics of basalt till---one paper showed that the southern Laurentide Ice Sheet was very thin in marginal areas because it was flowing across deforming till, and a second showed that the same conditions existed at the northwest margin of the Laurentide Ice Sheet as it flowed across the McKenzie Delta area of Arctic Canada, and I linked the rapid retreat of the NW Laurentide Ice Sheet at the end of the last Ice Age to its low profile. I must confess I am delighted to see these ideas expanded to Antarctica.

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