Turning-based precision machining produces non-Gaussian spatial surface topographies, inherently defined by skewness (\(R_{sk}\)) and kurtosis (\(R_{ku}\)), which govern surface quality, tribology, and functional performance of the machined workpiece. However, surface roughness modeling remains challenging due to process uncertainty, measurement variability, and the limited integration of \(R_{sk}\) and \(R_{ku}\) into spatial surface roughness analyses, despite their fundamental role in defining non-Gaussian topographies produced by turning operations. This paper presents a novel data-driven metamodeling framework–Spatial Non-Gaussian Roughness Metamodeling (SNGRM)–that integrates geospatial analysis and kriging interpolation to achieve spatial mapping of arithmetic mean roughness (\(R_a\)) under explicitly non-Gaussian surface conditions defined by \(R_{sk}\) and \(R_{ku}\), thereby advancing multivariate characterization of non-Gaussian machined surfaces. For the interpolation of \(R_{a}\), ordinary kriging captures spatial variability inferred from the \(R_{sk}\)-\(R_{ku}\) domain, while universal kriging advances this metamodeling framework by incorporating machining parameters as external drift to explain systematic variations in surface roughness. Consequently, group-wise cross-validation demonstrates that universal kriging achieves superior predictive performance by more effectively capturing both non-Gaussian spatial variability and deterministic trends associated with machining parameters. The proposed framework directly exploits empirical machining data while retaining measurement variability arising from repeated observations, which is frequently averaged out or neglected in conventional roughness models. By jointly incorporating non-Gaussian spatial characteristics and machining parameters, SNGRM enables robust spatial interpolation of the roughness quality index, \(R_a\), with explicit quantification of associated uncertainty via kriging variance. This framework provides a rigorous data-driven metamodel for a reliable digital roughness mapping in precision machining.
