The multiple processes which control motion at the bed of glaciers are
too heterogeneous to be modeled directly, but a simple stick-slip sli
der-block model of a glacier bed allows a statistical mechanical treat
ment of the physics beneath thin and shallow sloped glaciers. The tech
nique may reconcile apparently contradictory field observations of the
relationship between glacier sliding and basal water pressure. Simula
tions also predict hysteresis in the relationship between water pressu
re and basal velocities.