Validation of Space-Wise GOCE Gravitational Gradient Grids Using the Spectral Combination Method and GNSS/Levelling Data

Abstract

The launch of gravity-dedicated satellite missions at the beginning of the new millennium led to an accuracy improvement of global Earth gravity field models (GGMs). One of these missions was the Gravity field and steady-state Ocean Circulation Explorer (GOCE) launched in 2009. As the first European Space Agency’s Earth Explorer Mission, the satellite carried a novel instrument, a 3-D gradiometer, which allowed measurement of the second-order directional derivatives of the gravitational potential (gravitational gradients) with a uniform quality and a near-global coverage. The main mission goal was to determine the static Earth’s gravity field with the ambitious precision of 1-2 cm in terms of geoid heights and 1 mGal in terms of gravity anomalies for spatial resolution of 100 km (half wavelength at the equator). More than three years of the outstanding measurements resulted in three levels of data products (Level 0, Level 1b and Level 2), six releases of GGMs, and several global grids of gravitational gradients. The grids, which represent a step between gravitational gradients measured directly along the GOCE orbit and those represented by GGMs, found their usage mainly in geophysical applications. In this contribution, we validate the official Level 2 product GRD_SPW_2 using height anomalies over two test areas located in central and northern Europe (Czechia/Slovakia and Norway). A mathematical model based on the least-squares spectral weighting is employed with corresponding spectral weights estimated for validation of gravitational gradient grids. This model continues gravitational gradients from the mean orbital altitude of GOCE down to the irregular Earth’s surface (not to a sphere) and transforms them to height anomalies in one computational step. Analytical downward continuation errors of the model are estimated using a closed-loop test. Prior to the comparison of height anomalies estimated from gravitational gradients with their reference values derived from Global Navigation Satellite Systems (GNSS)/levelling over the two test areas, the gravitational gradients and reference data are corrected for all systematic effects such as the tide system conversion. Moreover, the high-frequency part of the gravitational signal is estimated and subtracted from reference data as it is attenuated in the gravitational gradients measured by GOCE. A relative improvement between the release 6 and release 2 gradient grids reaches 48\(\%\) in terms of height anomalies in Czechia/Slovakia. The relative improvement in Norway is even more significant and reaches 55\(\%\). The release 6 of the official Level 2 product GRD_SPW_2 gained the absolute accuracy with the standard deviation of 8.7 cm over Czechia/Slovakia and 9.3 cm over Norway.