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

Developing a high-precision regional geoid model is a key element in modernizing 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 hybrid geoid model developed for the Almaty region, integrating classical gravimetric modelling with modern machine-learning simulation. The baseline solution was computed using the Least-Squares Modification of Stokes’ Formula with Additive Corrections, combining digitized Soviet-era terrestrial gravity data, the global geopotential model XGM2019e_2159, and the FABDEM 30 m digital elevation model. Validation using GNSS/levelling benchmarks revealed a systematic bias of −0.06 m and an RMS of 0.08 m. To improve the fit between modelled and observed undulations, three machine-learning regressors—Gaussian Process Regression (GPR), Support Vector Regression (SVR), and LSBoost—were applied to model the residual correction surface. Among them, SVR provided the best held-out performance (RMSE = 0.04 m), while LOOCV, 10-fold and spatial CV confirmed stable generalization across terrain regimes. The resulting hybrid model, designated NALM2025, achieved centimetre-level consistency with GNSS/levelling data. The results demonstrate that integrating classical geoid computation with AI-based residual modelling provides an efficient computational framework for high-precision geoid determination in complex mountainous environments.