  Basal motion is the primary mechanism for ice flux outside Antarctica, yet a
widely applicable model for predicting it in the absence of retrospective
observations remains elusive. This is due to the difficulty in both observing
small-scale bed properties and predicting a time-varying water pressure on
which basal motion putatively depends. We take a Bayesian approach to these
problems by coupling models of ice dynamics and subglacial hydrology and
conditioning on observations of surface velocity in southwestern Greenland to
infer the posterior probability distributions for eight spatially and
temporally constant parameters governing the behavior of both the sliding law
and hydrologic model. Because the model is computationally expensive, classical
MCMC sampling is intractable. We skirt this issue by training a neural network
as a surrogate that approximates the model at a sliver of the computational
cost. We find that surface velocity observations establish strong constraints
on model parameters relative to a prior distribution and also elucidate
correlations, while the model explains 60% of observed variance. However, we
also find that several distinct configurations of the hydrologic system and
stress regime are consistent with observations, underscoring the need for
continued data collection and model development.
