Snapshot and time-dependent inversions of basal sliding using automatic generation of adjoint code on graphics processing units

Basal sliding and other processes affecting ice flow are challenging to constrain due to limited direct observations. Inversion methods, which typically fit an ice flow model to observed surface velocities, enable the reconstruction of basal properties from readily available data. We present a numerical inversion framework for reconstructing the glacier basal sliding coefficient, applied to both synthetic and real-world alpine glacier scenarios. The framework employs automatic differentiation to generate adjoint code and runs in parallel on graphics processing units (GPUs).

We explore two inversion workflows using the shallow ice approximation (SIA) as the forward model: a time-independent approach fitting to a single snapshot of annual ice velocity and a time-dependent inversion accounting for both ice velocity and changes in geometry. We find that the time-dependent inversion yields more robust and accurate velocity fields than the snapshot inversion. However, it does not significantly improve the problematic initial transients often encountered in forward model runs that employ sliding fields from snapshot inversions. This is likely due to the limitations of the forward model. This methodology is transferable to more complex forward models and can be readily implemented in languages supporting automatic differentiation.