Analytical computation of local gravitational effects of mountain glacier mass change from polyhedral and prismatic modeling - test case Vernagtferner, Austrian Alps

Abstract

Gravimetric measurements allow monitoring mass transport in the Earth system and one example is temporal variations in the global water cycle including the cryosphere. Coupling gravity observations to the underlying processes requires modeling of the relevant mass elements. When observing the gravity field from space (i.e., by satellites), point mass models or simple spherical surface layers (mascons) are a reasonable choice. However, for terrestrial observations taken right on the surface of the relevant masses, precise modeling of the geometry of those mass elements and the related gravitational effects becomes crucial for the quality of the modeling and the correct interpretation of the results. In this study, two different modeling techniques are investigated, the right rectangular prism and the general polyhedron. Both approximations provide the possibility to analytically calculate the corresponding gravitational signal. Although modeling in terms of polyhedrons is numerically more complex and less efficient, the representation of the actual surface is superior as the inclined polyhedral surface fits much better to the actual topographic surface than the step function implied by rectangular prisms with horizontal top plane. The case study presented here is related to the gravimetric mass balance of a mountain glacier (Vernagtferner in the Ötz valley, Austria) where on the one hand high resolution digital terrain models (DTM of resolution 1 m × 1 m) are available, while on the other hand, the accuracy requirements are very high (on the level of 10−7 m/s2, i.e., 10 μGal). We evaluate first and second order derivatives of the gravitational potential induced by the melting of ice masses between epochs 2009 and 2016 at gravity sites on and off the actual glacier body. Furthermore, the relation of ground surface slope to the differences between the modeling approaches is investigated for a small part of the DTM, containing a variety of different slope regimes. Besides the original grid spacing, denser and coarser grids are also evaluated in order to examine the relation of the considered DTM resolution to the modeling differences. The modeling choice, the location of the computation points and the morphology of the mass distribution are the main factors that determine the quality of the results. The comparison of the two methods for the original 1 m resolution, provides differences up to 2.9 μGal for the vertical component of the attraction Vz, 9.1 μGal/m for the gradient Vzx, 4.6 μGal/m for Vzy and 17.1 μGal/m for Vzz. Coarser grid resolutions increase these values significantly, up to 500 μGal at specific locations, while grids denser than the 1 m resolution decrease them for about 48%.