  Ice sheet models are used to study the deglaciation of North America at the
end of the last ice age (past 21,000 years), so that we might understand
whether and how existing ice sheets may reduce or disappear under climate
change. Though ice sheet models have a few parameters controlling physical
behaviour of the ice mass, they also require boundary conditions for climate
(spatio-temporal fields of temperature and precipitation, typically on regular
grids and at monthly intervals). The behaviour of the ice sheet is highly
sensitive to these fields, and there is relatively little data from geological
records to constrain them as the land was covered with ice. We develop a
methodology for generating a range of plausible boundary conditions, using a
low-dimensional basis representation of the spatio-temporal input. We derive
this basis by combining key patterns, extracted from a small ensemble of
climate model simulations of the deglaciation, with sparse spatio-temporal
observations. By jointly varying the ice sheet parameters and basis vector
coefficients, we run ensembles of the Glimmer ice sheet model that
simultaneously explore both climate and ice sheet model uncertainties. We use
these to calibrate the ice sheet physics and boundary conditions for Glimmer,
by ruling out regions of the joint coefficient and parameter space via history
matching. We use binary ice/no ice observations from reconstructions of past
ice sheet margin position to constrain this space by introducing a novel metric
for history matching to binary data.
