Geodetic degree-based Models for Robust Regional Geoid Refinement

Accurate geoid models are essential for converting GNSS-derived heights into physically meaningful elevations and for ensuring consistency in modern height reference systems. This study presents a unified geodetic framework for refining gravimetric geoids using GNSS/leveling residuals through physically interpretable fitting models. Five correction representations are evaluated, ranging from local Cartesian planar surfaces to geodetically consistent spherical formulations of increasing degree. The analysis demonstrates that low-order models effectively remove regional bias and tilt but show limited predictive stability. To enhance robustness, iteratively reweighted least squares is applied to mitigate the influence of outliers while preserving deterministic structure. Higher-order geodetic models are stabilized using ridge regularization, with the regularization strength selected objectively through leave-one-out cross-validation. This strategy ensures numerical conditioning while directly optimizing predictive performance. Results show that the full degree-2 geodetic model offers the best balance among accuracy, stability, and physical interpretability. It reduces long-wavelength distortions while maintaining consistent in-sample and cross-validated performance. The proposed approach supports reliable GNSS-based height determination in modern vertical datum realization and height modernization efforts.