Analysis of Terrain Effects in cm-order Geoid Computations in Chinese Mainland

Based on conventional algorithm of terrain effect, three issues are discussed in this paper. Firstly, based on the most common method of dealing with terrain effects related to the planar reference surface, the traditional implementation of ellipsoidal terrain correction based on the GRS80 ellipsoid using tesseroid modeling is proposed for geoid determination in mountainous areas or far zones, and the formulae for the attraction components of potential derivatives is applied. Secondly, usually we only consider the Molodensky's first term for geoid computation. Earlier studies however have shown that the effects of Molodensky's high-degree terms may be essential in more mountainous areas. On the basis of the demand for a cm-order precision geoid, a suit of simple and applicable formulas to deal with the terrain effects using Molodensky's first to three order terms for height anomaly are derived based on the algorithm of first-order term. Furthermore, approximation error in cm-order hight anomalies using the terrain correction instead of the Molodensky solution for geoid computation is discussed.