Volume-area scaling vs flowline modelling in glacier volume projections

Volume-area scaling provides a practical alternative to ice-flow modelling to account for glacier size changes when modelling the future evolution of glaciers; however, uncertainties remain as to the validity of this approach under non-steady conditions. We address these uncertainties by deriving scaling exponents in the volume-area relationship from one-dimensional ice-flow modelling. We generate a set of 37 synthetic steady-state glaciers of different sizes, and then model their volume evolution due to climate warming and cooling as prescribed by negative and positive mass-balance perturbations, respectively, on a century timescale. The scaling exponent derived for the steady-state glaciers (gamma = 1.56) differs from the exponents derived for the glaciers in transient (non-steady) state by up to 86%. Nevertheless, volume projections employing volume-area scaling are relatively insensitive to these differences in scaling exponents. Volume-area scaling agrees well with the results from ice-flow modelling. in addition, the scaling method is able to simulate the approach of a glacier to a new steady state, if mass-balance elevation feedback is approximated by removing or adding elevation bands at the lowest part of the glacier as the glacier retreats or advances. If area changes are approximated in the mass-balance computations in this way, our results indicate that volume-area scaling is a powerful tool for glacier volume projections on multi-century timescales.