On the errors involved in ice-thickness estimates III: error in volume

This paper is the third (Paper III) in a set of studies of the errors involved in the estimate of ice thickness and ice volume. Here we present a methodology to estimate the error in the calculation of the volume of an ice mass from an ice-thickness DEM.We consider the two main error sources: the ice-thickness error at each DEM grid point and the uncertainty in the boundary delineation. To accurately estimate the volume error due to the error in thickness of the DEM, it is crucial to determine the degree of correlation among the ice-thickness errors at the grid points. We find that the two-dimensional integral range, which represents the equivalent area of influence of each independent value, allows estimation of the equivalent number of independent values of error within the DEM. Hence, it provides an easy way to obtain the volume error resulting from the uncertainty in ice thickness of a DEM. We show that the volume error arising from the uncertainty in boundary delineation, often neglected in the literature, can be of the same order of magnitude as the volume error resulting from ice-thickness errors. We illustrate our methodology through the case study of Werenskioldbreen, Svalbard.