Novel Techniques for Void Filling in Glacier Elevation Change Data Sets

Abstract

The increasing availability of digital elevation models (DEMs) facilitates the monitoring of glacier mass balances on local and regional scales. Geodetic glacier mass balances are obtained by differentiating DEMs. However, these computations are usually affected by voids in the derived elevation change data sets. Different approaches, using spatial statistics or interpolation techniques, were developed to account for these voids in glacier mass balance estimations. In this study, we apply novel void filling techniques, which are typically used for the reconstruction and retouche of images and photos, for the first time on elevation change maps. We selected 6210 km2 of glacier area in southeast Alaska, USA, covered by two void-free DEMs as the study site to test different inpainting methods. Different artificially voided setups were generated using manually defined voids and a correlation mask based on stereoscopic processing of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) acquisition. Three “novel” (Telea, Navier–Stokes and shearlet) as well as three “classical” (bilinear interpolation, local and global hypsometric methods) void filling approaches for glacier elevation data sets were implemented and evaluated. The hypsometric approaches showed, in general, the worst performance, leading to high average and local offsets. Telea and Navier–Stokes void filling showed an overall stable and reasonable quality. The best results are obtained for shearlet and bilinear void filling, if certain criteria are met. Considering also computational costs and feasibility, we recommend using the bilinear void filling method in glacier volume change analyses. Moreover, we propose and validate a formula to estimate the uncertainties caused by void filling in glacier volume change computations. The formula is transferable to other study sites, where no ground truth data on the void areas exist, and leads to higher accuracy of the error estimates on void-filled areas. In the spirit of reproducible research, we publish a software repository with the implementation of the novel void filling algorithms and the code reproducing the statistical analysis of the data, along with the data sets themselves.