Hybrid Geoid Modeling with AI Enhancements: A Case Study for Almaty, Kazakhstan

Developing a high–precision regional geoid model is a key element in moderniz-ing Kazakhstan’s vertical reference framework and ensuring consistent GNSS-based height determination. However, the mountainous terrain of southeastern Kazakhstan, characterized by strong topographic gradients and sparse terrestrial gravity coverage, poses significant modelling challenges. This study presents the first AI–enhanced hy-brid geoid model developed for the Almaty region, integrating classical gravimetric modelling with modern machine-learning simulation. The baseline solution was com-puted using the Least-Squares Modification of Stokes’ Formula with Additive correc-tions, combining digitized Soviet-era terrestrial gravity data, the global geopotential model XGM2019e_2159, and the FABDEM 30 m digital elevation model. Validation using GNSS/leveling benchmarks revealed a systematic bias of −0.08 m and an RMS of 0.10 m. To improve the fit between modelled and observed undulations, three ma-chine-learning regressors – Gaussian Process Regression (GPR), Support Vector Re-gression (SVR), and LSBoost—were applied to model the residual correction surface. Among them, the SVR model achieved the optimal balance between accuracy and generalization, reducing the test RMS to 0.032 m without overfitting. The resulting hybrid model, designated NALM2025, achieved centimeter-level consistency with GNSS/leveling data. The results demonstrate that integrating classical geoid computa-tion with AI–based residual modelling provides an efficient computational framework for high-precision geoid determination in complex mountainous environments.