Glacier volume‐area relation for high‐order mechanics and transient glacier states

Abstract

[1] Glacier volume is known for less than 0.1% of the world's glaciers, but this information is needed to quantify the impacts of glacier changes on global sea level and regional water resources. Observations indicate a power-law relation between glacier area and volume, with an exponent g ≈ 1.36. Through numerical simulations of 3D, high-order glacier mechanics, we demonstrate how different topographic and climatic settings, glacier flow dynamics, and the degree of disequilibrium with climate systematically affect the volumearea relation. We recommend more accurate scaling relations through characterization of individual glacier shape, slope and size. An ensemble of 280 randomly-generated valley glaciers spanning a spectrum of plausible glaciological conditions yields a steady-state exponent g = 1.46. This declines to 1.38 for glaciers that are 100 years into a sustained retreat, which corresponds exceptionally well with the observed value for present-day glaciers.

An upper-bound estimate for the accuracy of glacier volume–area scaling

“…However, differences larger than 10 % (20 %) are assessed for subsample sizes smaller than 80 (40) glaciers. These numbers are consistent to first order with the findings by Adhikari and Marshall (2012), who analyzed a synthetic set of glaciers and found that "ca. 200 glaciers are required to produce stable solution[s] of scaling parameters".…”

“…This observation seems to contradict earlier findings that indicate time-varying parameters (e.g. Adhikari and Marshall, 2012), but can be explained by (a) the standard errors associated with the estimated parameters, which are mainly a function of the absolute number of (V, A)-pairs available for the estimate itself, and (b) the consistency of the estimated parameters for the two points in time, which is given when assuming constant parameters, but not when these are time-varying. For a population of 100 glaciers for instance, using 50 % of the sample for estimating the parameters would lead to (i) two subsamples of 50 (V, A)-pairs (one for t1 and one for t2), in the case of two different sets of parameters being estimated, or (ii) a subsample of 100 glaciers, if constant parameters were assumed.…”

“…This can be explained by the fact that the real data refer to transient geometries (e.g. Bahr et al, 1997;Adhikari and Marshall, 2012).…”

Ground-penetrating radar studies in Svalbard aimed to the calculation of the ice volume of its glaciers

“…According to Meier and others (2007), estimated volume errors for individual glaciers could exceed 50% but these uncertainties are reduced to 25% for an ensemble of glaciers. Consistent with these results, a recent study by Adhikari and Marshall (2012), using a V-A relationship based on a sample of 280 synthetic random mountain glaciers, has shown that, when estimating the volumes for all individual glaciers in their ensemble, the average glacier volume error is small (2.8%), with a mean absolute error of 18.3%.…”

Ice thickness measurements and volume estimates for glaciers in Norway

“…A minimum sample size of $100 glaciers is recommended (Bahr, 2012;Farinotti and Huss, 2013). Although more accurate scaling relations can be obtained through characterization of individual glacier shape, slope and size ( Adhikari and Marshall, 2012;Grinsted, 2013) and by local calibration, scaling approaches still have large uncertainties (Haeberli and Hoelzle, 1995;Cogley, 2012;Farinotti and Huss, 2013). Scaling does not, for instance, account for individual glacier characteristics such as surface geometry or local climate, and does not provide information on the spatial distribution of ice thickness.…”