Multi-objective variogram model optimization via genetic algorithms for reliable kriging estimations and associated uncertainties: application to hydrological data

ABSTRACT Interpolation methods such as kriging depend on variogram parameters that must be appropriately optimized to ensure accurate estimates. While kriging has the advantage of providing estimation uncertainty (error variances), variogram fitting typically prioritizes estimation accuracy, often neglecting the trustworthiness of those variances. This study presents a novel multi-objective optimization framework based on genetic algorithms that simultaneously addresses three key objectives: (1) achieving a robust match between experimental and theoretical variograms, (2) minimizing the root mean squared error between measured and predicted values, and (3) ensuring reliable error variance estimates. The methodology was first applied to hydraulic head data from the ‘El Palmar’ aquifer in Zacatecas, Mexico, and then validated using the Walker Lake vanadium concentration dataset to test robustness and broader applicability. In both cases, the framework effectively balanced the three objectives, resulting in standardized mean squared error (SMSE) values between 0.8408 and 1.1031. Incorporating SMSE into variogram model selection enhances the potential of kriging by improving both estimation accuracy and uncertainty reliability.