Learning the Mechanics of Slip Along Glacier Beds From Time-Dependent Surface Velocity and Elevation Data

Abstract:

Reliable projections of sea-level rise largely depend on accurately describing how fast-flowing glaciers and ice streams slip over their beds. Specifically, ice-flow models require a quantitative sliding law that relates basal drag to sliding velocity and/or glacier geometry. While multiple forms of the sliding law have been proposed, it remains unclear which best represents the mechanics of basal slip. Here, we present a novel deep learning-based framework for learning the time evolution of basal drag from time-dependent ice surface velocity and elevation observations. We formulate a multi-task learning objective for training a pair of artificial neural networks to reconstruct velocity and elevation observations and assimilate these observations through well-known governing equations of ice flow in order to predict time-varying basal drag. Comparing inferred, time-dependent basal drag with time-dependent observations of surface velocity and elevation provides constraints on the form of the sliding law that relates the observed and inferred values. The learning objective represents a form of physics-guided deep learning where various physical constraints can be encoded into the loss function to regularize the learning process. We test the framework on 1D and 2D ice flow simulation outputs, as well as time-dependent surface velocity data over Rutford Ice Stream (RIS), Antarctica, and demonstrate the recovery of the underlying sliding law. For RIS, we infer drag variations driven by changes in effective pressure, which is a potential signature of hydrological effects with tidal periodicity. Our approach requires no prior assumption about the form of the sliding law and is particularly suitable for blending large volumes of time-dependent remote sensing data with established physical relationships.