Dynamics of the low- and high-degree components of a vertical datum: towards the effect of omission error

This paper studies the effect of omission error on height system unification by analysing the contributions of the low and high spherical harmonic degree components of a local vertical datum (LVD). Previous studies have combined the satellite-only GOCE (Gravity field and steady-state Ocean Circulation Explorer) global geopotential models (GGMs) with a high-resolution GGM (and in some cases topography-implied gravity field signals) in order to account for (or minimize) the omission error of GOCE. This study attempts to answer the question of whether the omission error should be accounted for and to what extent by decomposing the Brazilian Vertical Datum (BVD) referenced to a tide gauge station at Imbituba (BVD-I) into low- and high-degree components using the Gaussian averaging function. A combined EIGEN–GOCE GGM is used to compute the high-degree datum offset. Overall, the results confirm that (1) the low-degree component accounts for the majority of the discrepancy between the BVD-I and the global datum but is insufficient to accurately determine the BVD-I offset parameter, (2) the high-degree component contributes little to the overall discrepancy between the datums, but significantly improves the errors in the low-degree component and (3) the signals beyond the resolution of the high-resolution GGM do not significantly impact the datum offset parameters, so that it is not necessary to account for the omission error of the high-resolution GGM using topography-implied gravity field signals. The approach used in this work adds little computational cost, especially over large spatial extents and dense GPS/levelling data, compared to the computation of topography-generated gravity field quantities and has the added advantage of being able to determine the low-degree systematic errors in the GPS/levelling data (LVD) using the unbiased satellite-only GOCE models as reference.