Brief communication: On area- and slope-related thickness estimates and volume calculations for unmeasured glaciers

Abstract. Area- and slope-related techniques have been used to estimate thicknesses and to calculate volumes of unmeasured glaciers on the basis of glacier outlines and corresponding glacier surface areas in glacier inventories. The present communication critically reflects key aspects involved with the application of these approaches to field data. Area-related empirical statistics are known to only provide order-of-magnitude estimates if applied to individual glaciers or glacier ensembles spanning less than several orders of magnitude. Even at this scale, however, problems exist with respect to calibration/validation, error propagation, artefacts (immediate mass loss in case of coalescing/disintegrating composite glaciers) and shortcomings (no detection of ice below sea level or below lake levels on land in view of glacier contributions to sea-level rise). 3-D-flux/stress/slope-related approaches and numerical models are better constrained by calibration/validation with field measurements. They help with overcoming the problems of 2-D-area-related statistics in that they allow for calculating detailed glacier bed topographies at all scales, from individual glaciers to global ensembles. Corresponding results are available today and can be further improved.