Abstract

Glacier surface elevation responds to a variety of localized processes occurring beneath the ice. Subglacial-lake volume change in particular is inherently time-dependent, producing time-varying perturbations in ice-surface elevation. Here, we introduce inverse methods for quantifying time-varying subglacial perturbations from altimetry data and, when available, horizontal surface velocity data. The forward model is based on a small-perturbation approximation of the Stokes equations that is solved efficiently with Fourier transform methods. The inverse methods are derived from variational least-squares optimization problems and the associated normal equations are solved with the conjugate gradient method. We conduct synthetic tests for reconstructing time-varying basal vertical velocity and drag perturbations that are motivated by subglacial-lake activity and slippery spots beneath Antarctic ice streams. We show that incorporation of horizontal surface velocity data as additional constraints can refine altimetry-based inversions or facilitate reconstruction of multiple fields, depending on whether the data are spatially discrete or continuous. We further validate the method by showing that it can reconstruct basal perturbations from synthetic elevation data that are produced by a nonlinear subglacial lake model. With the advent of high spatial and temporal resolution altimetry data from NASA's ICESat-2 mission, these inverse methods will facilitate further assessment of the relation between ice-sheet flow and subglacial processes.