Analysis of scaling methods in deriving future volume evolutions of valley glaciers

Volume-area scaling is a common tool for deriving future volume evolutions of valley glaciers and their contribution to sea-level rise. We analyze the performance of scaling relationships for deriving volume projections in comparison to projections from a one-dimensional ice-flow model. The model is calibrated for six glaciers (Nigardsbreen, Rhonegletscher, South Cascade Glacier, Sofiyskiy glacier, midre Lovenbreen and Abramov glacier). Volume evolutions forced by different hypothetical mass-balance perturbations are compared with those obtained from volume-area (V-A), volume-length (V-L) and volume-area-length (V-A-L) scaling. Results show that the scaling methods mostly underestimate the volume losses predicted by the ice-flow model, up to 47% for V-A scaling and up to 18% for V-L scaling by the end of the 100 year simulation period. In general, V-L scaling produces closer simulations of volume evolutions derived from the ice-flow model, suggesting that V-L scaling may be a better approach for deriving volume projections than V-A scaling. Sensitivity experiments show that the initial volumes and volume evolutions are highly sensitive to the choice of the scaling constants, yielding both over- and underestimates. However, when normalized by initial volume, volume evolutions are relatively insensitive to the choice of scaling constants, especially in the V-L scaling. The 100 year volume projections differ within 10% of initial volume when the V-A scaling exponent commonly assumed, gamma = 1.375, is varied by -30% to +45% (gamma = [0.95, 2.00]) and the V-L scaling exponent, q = 2.2, is varied by -30% to +45% (q = [1.52, 3.20]). This is encouraging for the use of scaling methods in glacier volume projections, particularly since scaling exponents may vary between glaciers and the scaling constants are generally unknown.