Subglacial drainage modelling and Bayesian calibration using Gaussian Process emulators

Subglacial drainage models sensitively depend on the values of numerous uncertain parameters. However, the computation time associated with running these models makes it difficult to quantify the associated uncertainty in model outputs and to use field data to calibrate parameter values. To overcome these computational limitations, we construct a Gaussian Process (GP) emulator that accelerates subglacial drainage modelling by ~1000x. The GP predicts spatiotemporally resolved water pressure as a function of eight model parameters and is trained using ensembles of up to 512 simulations with the Glacier Drainage System (GlaDS) model applied to the Kangerlussuaq sector of the western Greenland Ice Sheet. The GP reproduces the spatial patterns and daily temporal variations simulated by GlaDS within ~4%, with locally higher errors near moulins and during the early melt season. As an application of the GP, we compute the sensitivity of basal water pressure to each of the eight parameters and find that three parameters (ice-flow coefficient, bed bump aspect ratio and the subglacial cavity system conductivity) explain 90% of the variance in model outputs. Next, we explore using a borehole water-pressure timeseries to calibrate the eight uncertain parameters. We take a Bayesian perspective to quantify the uncertainty in parameter estimates and use the GP in place of the physics-based model to make Markov Chain Monte Carlo sampling computationally feasible. We find meaningful constraints relative to the prior assumptions on most parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.