A Direct Approach for Local Quasi-Geoid Modeling Based on Spherical Radial Basis Functions Using a Noisy Satellite-Only Global Gravity Field Model

Abstract

The remove–compute–restore (RCR) approach is widely used in local quasi-geoid modeling. However, the classical RCR approach usually does not take into account the noise of the satellite-only global gravity field model (GGM), which may lead to a suboptimal result. This paper presents an approach for local quasi-geoid modeling based on spherical radial basis functions that combines local noisy datasets and a noisy satellite-only GGM. This approach includes an RCR procedure using a satellite-only GGM. This is a direct approach that takes the spherical harmonic coefficients of satellite-only GGM as a noisy dataset and includes the corresponding full-noise covariance matrix in the least-squares estimation, aiming to obtain a statistically optimal local quasi-geoid model. The direct approach goes beyond the indirect approach, which treats the height anomalies generated from the satellite-only GGM as a noisy dataset. However, the generated GGM height anomaly dataset is not an equivalent representation of the satellite-only GGM, which may result in the loss of information from the satellite-only GGM. Through mathematical deduction, we demonstrate the theoretical consistency between the direct approach and the indirect approach. The direct approach also has an advantage over the indirect approach in terms of computational complexity due to the simpler algorithm. We conducted a synthetic closed-loop test with a real data distribution in Colorado, and numerical results demonstrated the advantage of the direct approach in local quasi-geoid modeling. In terms of the root mean square of the differences between the predicted values and the true reference values, the direct approach provided an improvement of approximately 14% compared to the indirect approach.