Quantifying snow water equivalent (SWE) with ground-penetrating radar (GPR) in a warming climate is complicated by the incidence and variability of liquid water in snow. Snow surveys conducted during the melt season serve as a valuable analog to conditions under future warming. Here, we determine the variability of wet snowpack properties (relative permittivity and density) to quantify their impact on SWE estimates using GPR. We collected spatially continuous snowpack measurements with 400 MHz GPR in 2012 and 2021 across repeat transects (∼150 km each year) along with spring and summer snow depth and density measurements from snow pits and snow cores. Snow relative permittivity values ranged from 2.06 to 2.62 in 2012 and 2.11 to 5.11 in 2021, resulting in calculated volumetric liquid water content (LWC) between 1.7% and 5.7% in 2012 and 2.1% and 16% in 2021. This variability in snow relative permittivity results in SWE uncertainties of 8% —33%, with more extreme cases reaching 13%—45%. We attribute this uncertainty to spatial and temporal variability in LWC when using GPR to estimate SWE. As snowpacks become wetter with rising atmospheric temperatures, GPR surveys should include in situ relative permittivity measurements to reduce depth and SWE interpretation uncertainties.

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. 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.

This study introduces a custom implementation of the Ensemble Kalman Filter (EnKF) for calibrating a three-dimensional glacier evolution model. The EnKF can assimilate observations as they become available and provides uncertainty measures for the initial state after calibration. We calibrate an elevation-dependent surface mass balance (SMB) model using elevation change observations and test the EnKF’s performance in a Twin Experiment by varying internal and external hyperparameters. The best-performing configuration is applied to the Rhône Glacier in a Real-World Experiment. Using satellite-based elevation change fields for calibration, the EnKF estimates an average equilibrium line altitude of $2920 \pm 37$ m for the period 2000–19. A comparison of the results with glaciological measurements demonstrates the capabilities of the EnKF to simultaneously calibrate multiple SMB parameters. With this proof of concept, we expect that our methodology is readily extendable to other map or point observations and their combination, as well as to other calibration parameters.