<p>In geostatistical modeling, traditional covariance models based on Euclidean distance often fail in complex geographic environments, especially when natural barriers or irregular terrains distort spatial relationships. This study explores the use of non-Euclidean distance metrics, including Manhattan, Minkowski, and Chebyshev distances, to improve the accuracy of spatial estimation in such environments. We apply several covariance models—exponential, Gaussian, spherical, Matérn, Spartan (SSRF), and the recently developed Hybrid Spectral Ornstein-Uhlenbeck (HSOU) model—to estimate soil aluminum concentration data from a region with complex physical barriers. Gaussian anamorphosis implemented by means of the non-parametric kernel cumulative density estimator (KCDE) is used to normalize the data. The model parameters for all covariance models and all distance measures are determined via maximum likelihood estimation (MLE). The models were tested for admissibility with respect to non-Euclidean distances by calculating the eigenvalues of the resulting covariance matrices to ensure positive definiteness. In this case study, the Gaussian and spherical models led to non-positive-definite matrices for non-Euclidean distances. On the other hand, the SSRF, exponential, Matérn (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\nu =3/2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ν</mi> <mo>=</mo> <mn>3</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>), and HSOU models consistently provided valid covariance matrices. In particular, the HSOU and Matérn models outperformed the other models with respect to all distance metrics. These results demonstrate the robustness and usefulness of HSOU for geostatistical applications involving non-Euclidean distances in the context of the dataset and sampling configuration considered in this study.</p>