The effect of the spatial pattern of mass balance on the steady-state
geometry of a glacier is examined using a Vialov -Nye glacier-flow model
based on non-linear internal deformation of the ice with no basal motion.
Surface profiles are predicted using a range of spatial variations of mass
balance that include uniform shifts that cause a change in the mean and
spatial patterns with zero mean representing changes in balance gradient and
curvature. The corresponding effect on geometry induced by the different
mass-balance patterns are described in terms of the volume and measures of
surface slope and convexity. The change in glacier volume, slope and
convexity induced by uniform changes in mass balance with non-zero mean are
more than one order of magnitude larger than corresponding changes caused by
spatial patterns of similar amplitude, but with zero mean. These results
show that the mean mass balance contains most of the mass-balance
information relevant to the dynamic changes of a glacier. An important
consequence is that the memory of a change in climate, which is controlled
by the consequent volume change, should be insensitive to the spatial
pattern other than how that affects the mean. The spatial pattern of mass
balance does induce small changes in the shape of the steady-state profile,
which indicates the spatial pattern could affect the short time-scale
response characteristics.