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 Lovénbreen 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 overand 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, 1⁄4 1.375, is varied by –30% to +45% ( 1⁄4 [0.95, 2.00]) and the V-L scaling exponent, q 1⁄4 2.2, is varied by –30% to +45% (q 1⁄4 [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.