On the limit to resolution and information on basal properties obtainable from surface data on ice streams

Abstract

Abstract. An optimal estimation method for simultaneously determining both basal slipperiness and basal topography from variations in surface flow velocity and topography along a flow line on ice streams and ice sheets is presented. We use Bayesian inference to update prior statistical estimates for basal topography and slipperiness using surface measurements along a flow line. Our main focus here is on how errors and spacing of surface data affect estimates of basal quantities and on possibly aliasing/mixing between basal slipperiness and basal topography. We find that the effects of spatial variations in basal topography and basal slipperiness on surface data can be accurately separated from each other, and mixing in retrieval does not pose a serious problem. For realistic surface data errors and density, smallamplitude perturbations in basal slipperiness can only be resolved for wavelengths larger than about 50 times the mean ice thickness. Bedrock topography is well resolved down to horizontal scale equal to about one ice thickness. Estimates of basal slipperiness are not significantly improved by accurate prior estimates of basal topography. However, retrieval of basal slipperiness is found to be highly sensitive to unmodelled errors in basal topography.

Parameter and state estimation with a time-dependent adjoint marine ice sheet model

“…Rather, it is to examine the degree of compensation between the two parameters in their inverted fields: since both lubrication and topography control velocity, it is possible that the inversion is nonunique. This type of compensation is similar to the "mixing" referred to by Gudmundsson and Raymond (2008).…”

“…In this section we explore the potential of using this approach both to minimize drift in model initializations and to provide improved estimates of basal topography. We note that methods for such inversions have been previously developed (Thorsteinsson et al, 2003;Gudmundsson and Raymond, 2008). However, these methods assume Newtonian rheology and rely on linear transfer functions of small perturbations, so it is not clear that their results carry over to large deviations and nonlinear rheologies.…”

Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming

“…Instead, many models of modern ice sheets use an empirical drag factor or slip coefficient, derived from observed ice velocity and estimated shear stresses (e.g. MacAyeal et al, 1995;Gudmundsson and Raymond, 2008;Ryser et al, 2014). Using an empirical drag factor is reasonable to describe and understand present-day, near-instantaneous ice-sheet behaviour but cannot reliably predict or reconstruct ice velocities if parameters such as ice thickness, driving forces and meltwater production change significantly.…”

Glacier volume estimation as an ill-posed inversion

“…For many ill-posed geophysical problems, approximate rather than exact solutions are possible, though 'inverse source problems' of the type discussed here will have an infinite number of possible approximations (Zhdanov, 2002, p. 4 and 18). Within glaciology, the theoretical and practical implications of illposed inversions have been evaluated by a number of authors, including Hantz and Lliboutry (1981), Balise and Raymond (1985), Lliboutry (1987, p. 177), MacAyeal (1993, Bahr and others (1994), Joughin and others (2004), Truffer (2004), Chandler and others (2006), Gudmundsson and Raymond (2008), Maxwell and others (2008) and Raymond and Gudmundsson (2009), among many others. The theoretical implications are that information is lost exponentially as a calculation progresses deeper into a glacier and becomes increasingly unstable (Bahr and others, 1994;Zhdanov, 2002, p. 26).…”

“…Until there are additional data specified at points other than at the surface of the glacier, the volume solution will remain ill-posed (e.g. Courant and Hilbert, 1966;Zhdanov, 2002).…”