Timescales of outlet-glacier flow with negligible basal friction: theory, observations and modeling

The timescales of the flow and retreat of Greenland's and Antarctica's outlet glaciers and their potential instabilities are arguably the largest uncertainty in future sea-level projections. Here we derive a scaling relation that allows the comparison of the timescales of observed complex ice flow fields with geometric similarity. The scaling relation is derived under the assumption of fast, laterally confined, geometrically similar outlet-glacier flow over a slippery bed, i.e., with negligible basal friction. According to the relation, the time scaling of the outlet flow is determined by the product of the inverse of (1) the fourth power of the width-to-length ratio of its confinement, (2) the third power of the confinement depth and (3) the temperature-dependent ice softness. For the outflow at the grounding line of streams with negligible basal friction, this means that the volume flux is proportional to the ice softness and the bed depth, but goes with the fourth power of the gradient of the bed and with the fifth power of the width of the stream. We show that the theoretically derived scaling relation is supported by the observed velocity scaling of outlet glaciers across Greenland as well as by idealized numerical simulations of marine ice-sheet instabilities (MISIs) as found in Antarctica. Assuming that changes in the ice-flow velocity due to ice-dynamic imbalance are proportional to the equilibrium velocity, we combine the scaling relation with a statistical analysis of the topography of 13 MISI-prone Antarctic outlets. Under these assumptions, the timescales in response to a potential destabilization are fastest for Thwaites Glacier in West Antarctica and Mellor, Ninnis and Cook Glaciers in East Antarctica; between 16 and 67 times faster than for Pine Island Glacier. While the applicability of our results is limited by several strong assumptions, the utilization and potential further development of the presented scaling approach may help to constrain timescale estimates of outlet-glacier flow, augmenting the commonly exploited and comparatively computationally expensive approach of numerical modeling.