On the Omission Errors Due to Limited Grid Size in Geoid Computations

Abstract

Based on the assumption that the ultra-high frequencies of thes gravity field are produced by the topography variations, we compute the omission errors by using 3 arc-second elevation data from the Shuttle Radar Topography Mission (SRTM). It is shown that the maximum omission errors to the geoid are in the range of dm, cm and sub-cm level for grid sizes of 5^′′, 2^′′ and 1^′′ over the contiguous United States (CONUS), respectively. The results suggest that a 1 arc-minute grid size is sufficient for the 1-cm geoid, even for areas with very rough topography. The results also show that the omission errors to gravity are significant even for 1^′′ grid size, at which the smoothed-out gravity still reaches tens of mGals. The omission errors to gravity at a 5^′′ grid size peaks above 100 mGals, demonstrating the importance of correction of residual terrain to gravity observations in data gridding or block mean value computations.The results are also compared with those based on Kaula s rule. While the omission errors based on Kaula’s rule are ± 0. 5 and ± 3. 0 cm for 1^′′ and 5^′′ grid size, respectively, the RMS values of the omission error in this paper are ± 0. 1 and ± 1. 1 cm. The differences suggest Kaula s rule may overestimate the power of the gravity field at the ultra-high frequency band, which renders the convergence studies of the spherical harmonic series based on Kaula’s rule questionable.