Calibrating error variance and scaling global covariance function of geoid gradients for optimal determinations of gravity anomaly and gravity gradient from altimetry

Abstract

With the advancements of satellite altimeter technology and data volume, the accuracy and spatial resolution of altimeter-derived marine gravity fields have been steadily improved. Ideally, a best marine gravity field from multi-altimeter missions is one that combines all data by optimally calibrating their relative weights. To this end, we use the minimum norm quadratic unbiased estimator theory to calibrate error variances of geoid gradients (GGs) from the Cryosat-2 mission and the Jason-1/2 geodetic missions and then use a scaling factor to modify the global covariance functions into local covariance functions. The calibrated error variances and the scaling factors are used in the least-squares collocation to estimate the gridded north and east components of GGs, which are used to compute gravity anomaly and vertical gravity gradient (VGG) by the methods of inverse Vening-Meinesz (IVM) and numerical differentiations. The assessment of the altimeter-derived gravity anomalies in the northern part of the South China Sea using the shipborne gravity data shows an average gravity accuracy improvement of 9.5% by calibrated and scaled covariances of GGs compared to the initial variances. The method for VGG computations is confirmed by examining the extinct ridges in the Gulf of Mexico.

Expected Precision of Gravity Gradient Recovered from Ka-Band Radar Interferometer Observations and Impact of Instrument Errors

“…Yu and Hwang [26] derived the VGG based on altimetry data from the Cryosat-2 and Jason-1/2. Zhou et al [27] developed a vertical gravity anomaly gradient model with a resolution of 1 × 1 for the Arabian Sea and its surrounding regions from the altimetry data of Cryosat-2.…”

“…Many studies have shown that the use of gravity gradients enhances the reliability of inversion of bathymetry and underwater gravity matching navigation [32][33][34][35]. However, most researchers primarily focus on computing VGG [26] using the derivation formula provided by Heiskanen and Moritz [36,37]. Wan et al [15] found that few methods have been proposed to invert full tensor of gravity gradients from altimetry data.…”