Possibly the most interesting dynamical phenomenon is the glacier
surge, a relaxation oscillation typified by the behaviour of the
Variegated glacier (see the description in Paterson's book, The
Physics of Glaciers). Normally, people say surging is unexplained, but
this is not quite right. You can explain surging behaviour via a
multi-valued sliding law, and it is possible to obtain such laws from
realistic theories of hard bed sliding (see my 1987 JGR paper, cited
below). The outstanding problem here is to describe how the drainage
transition is effected in a three-dimensional geometry. I think this
is a major control on the size of the surge. For the other `type' of
surging glacier, the sub-polar (or polythermal) Trapridge, thermally
controlled and sliding over till, the overall mechanism may be
similar, though the details would be very different. The situation
looks a bit like the ice sheet surge theory developed by Doug MacAyeal
(see also Fowler and Johnson 1995, etc.).
Ice sheet dynamics
At the large scale, ice sheet modelling is probably in quite good
shape. At the small to medium scale, however, this is less obviously
true. The apparent occurrence of massive surges of the Hudson Strait
ice stream of the Laurentide ice sheet in the last ice age (causing
Heinrich events) must depend on the interplay between basal sliding
and basal drainage, and modelling this is still at a rudimentary
stage. Nor is it clear how such drainage theories will be included in
the next generation of large ice sheet models.
At a smaller scale, the formation of ice streams may well be caused by
the same positive feedback between sliding and drainage. Clare
Johnson's thesis showed this to be feasible, though further work
remains to be done.
Basal sliding
Sliding theory itself is rather dead, though it is certainly true that
it is starved of data. For deformable tills, rheology is the main
issue, but there are also interesting problems to do with erosion, for
example the formation of drumlins. The main interest of sliding in
terms of dynamics is through its dependence on the basal water
pressure. Another weakly perceived point is that under cold ice, there
should usually be a region between the frozen parts of the bed, and
those where excess water is produced. In this `subtemperate' region,
one has two thermal conditions and the sliding rate is
indeterminate. I've been preaching this particular point for nearly 20
years.
Subglacial hydrology
This is full of interesting problems. The theory of jökulhlaups
is simply stated, but still needs development in terms of describing
sediment transport and erosion. Indeed, time dependent drainage and
sediment transport theories (and their interaction) hardly exist, and
in view of the (relative) ease with which data can be gathered, there
is a lot of scope for developing theories which can use such data as a
diagnostic tool for describing basal conditions.
Relevant publications
Fowler, A.C. and D.A. Larson 1978 On the flow of
polythermal glaciers, part I: Model and
preliminary analysis. Proc. R. Soc. Lond. A363, 217-242.