329
drainage system. There then follows another quiescent phase where the maximum value
of H increases from H _ to H + before the next. surge is initiated.
3.3 Sliding and ice streams
It is not. known why t.he ice flow on the Siple Coast of Antarctica, which flows out to
the float.ing Ross ice shelf, segregat.es it.self int.o t.he five distinct. ice streams A to E. The
pict.ure which one has of t.his region is of a gent.ly sloping (slope ex ~ 10- 3 ) kilometer
t.hick ice sheet. which flows in t.he ice st.reams at. typical rates of 500 my-I. Such rapid
velocity can only be due to basal sliding, and the seismic evidence indicat.es that the ice
is underlain by several met.res of wet. t.ill. One can expect that a sliding law of the form
advocated previously is appropriate, that. is
(3.17)
with T and s positive. The issue t.hen arises as to how to prescribe N. Recall from section
2 that for drainage through Rothlisberger channels, an appropriate law is N = f3Q;,;4n,
where Qw is water flux. vVhen ice flows over t.ilL an alternative flow route is possible,
that is, t.hat. water excavates 'canals' in the subglacial till. A t.heoretical description of
this drainage system suggests that it is more likely for gently sloping ice flow, and also
that the relation bet.ween Nand Qw is of the opposite sense, that. is, that aN / aQw < O.
In t.his case an interest.ing feedback exists. In Antarctic ice streams. there is little, if
any, surface melt reaching the bed, and the basal water flow is due t.o melt.ing there. The
quantity of meltwater produced per unit area per unit time is given by the melt velocit.y
G + Tb'llb - 9
'Urn, ==
Pw L
(3.18)
where Pw is water densit.y, L is lat.ent. heat., G is geot.hermal heat flux, and 9 is the basal
heat flux int.o t.he ice. This assumes the base is at. the melting point.. Thus we expect the
basal water flux Qw ~ G + Tb'llb - g. and so Qw increases wit.h "Ilb (t.he dependence of 9
on l1b is likely to be weaker -- boundary layer theory would suggest 9 ~ 1J~/2). If also N
decreases with Qw, then N decreases as "/ib increases. But t.his causes further increase of
"Ilb via the sliding law. This posit.ive feedback can lead to a runaway phenomenon which
we may call hydraulic runaway.
To get. a crude idea of how this works, we denote the ice thickness as II and slope sin a.
If the velocity is "Il, then the ice fl ux is
Q = hll.
(3.19)
the basal shear stress is
drainage system. There then follows another quiescent phase where the maximum value
of H increases from H _ to H + before the next. surge is initiated.
3.3 Sliding and ice streams
It is not. known why t.he ice flow on the Siple Coast of Antarctica, which flows out to
the float.ing Ross ice shelf, segregat.es it.self int.o t.he five distinct. ice streams A to E. The
pict.ure which one has of t.his region is of a gent.ly sloping (slope ex ~ 10- 3 ) kilometer
t.hick ice sheet. which flows in t.he ice st.reams at. typical rates of 500 my-I. Such rapid
velocity can only be due to basal sliding, and the seismic evidence indicat.es that the ice
is underlain by several met.res of wet. t.ill. One can expect that a sliding law of the form
advocated previously is appropriate, that. is
(3.17)
with T and s positive. The issue t.hen arises as to how to prescribe N. Recall from section
2 that for drainage through Rothlisberger channels, an appropriate law is N = f3Q;,;4n,
where Qw is water flux. vVhen ice flows over t.ilL an alternative flow route is possible,
that is, t.hat. water excavates 'canals' in the subglacial till. A t.heoretical description of
this drainage system suggests that it is more likely for gently sloping ice flow, and also
that the relation bet.ween Nand Qw is of the opposite sense, that. is, that aN / aQw < O.
In t.his case an interest.ing feedback exists. In Antarctic ice streams. there is little, if
any, surface melt reaching the bed, and the basal water flow is due t.o melt.ing there. The
quantity of meltwater produced per unit area per unit time is given by the melt velocit.y
G + Tb'llb - 9
'Urn, ==
Pw L
(3.18)
where Pw is water densit.y, L is lat.ent. heat., G is geot.hermal heat flux, and 9 is the basal
heat flux int.o t.he ice. This assumes the base is at. the melting point.. Thus we expect the
basal water flux Qw ~ G + Tb'llb - g. and so Qw increases wit.h "Ilb (t.he dependence of 9
on l1b is likely to be weaker -- boundary layer theory would suggest 9 ~ 1J~/2). If also N
decreases with Qw, then N decreases as "/ib increases. But t.his causes further increase of
"Ilb via the sliding law. This posit.ive feedback can lead to a runaway phenomenon which
we may call hydraulic runaway.
To get. a crude idea of how this works, we denote the ice thickness as II and slope sin a.
If the velocity is "Il, then the ice fl ux is
Q = hll.
(3.19)
the basal shear stress is