Evaluation of precise terrain effects using high‐resolution digital elevation models

Abstract

Currently available high‐resolution digital elevation models (DEMs) permit computations of terrain‐related gravitational parameters, such as the terrain effect, with an unprecedented accuracy. In addition, given the increasing availability of new high‐resolution global DEMs specifically over continental regions, such as the Shuttle Radar Topography Mission (SRTM) model, which offers a 3‐arc sec resolution for selected parts of the Earth, the investigation and assessment of the short‐wavelength part of the Earth's gravitational spectrum becomes an issue of high demand. The article deals with the numerical evaluation of the first‐order radial derivative of the gravitational potential (terrain effect) by two modeling methods based on a prismatic and tesseroidal description of the terrain masses. The prismatic method, which offers exact analytical formulations, is connected to the planar or spherical approximation. The tesseroidal method related to the spherical or ellipsoidal approximation provides results at the same accuracy level, however, in significantly shorter computational times. Numerical investigations have been performed to assess the two modeling methods by elaborating on them through various computational strategies for evaluating the terrain effect from the view of computational precision and complexity. Additionally, the effect of the accuracy of the two modeling methods on the accuracy of the corresponding geoidal height is presented. The test area chosen for the numerical investigations is an alpine region in central Europe with a very complex topography. Two DEMs, with respective resolutions of 3 and 30 arc sec, represent the input elevation data. The obtained results indicate that for the current high‐resolution DEMs, the choice of a particular modeling method becomes less critical when an appropriate computational strategy is used. The results of the two modeling methods converge to the same values, even at complex mountainous terrain.