Gamaliel Moreno Chávez

Knowledge of the spatial distribution of hydraulic conductivity within an aquifer is required for groundwater flow modeling. The number of hydraulic conductivity measurements is usually scarce, making it necessary to interpolate available data. Commonly, a larger number of hydraulic head values measured in wells are available; therefore, they have been used as a secondary variable to improve hydraulic conductivity estimates. However, this relationship is clearly non-linear, leading to poor performance of models based on linear correlations, such as co-kriging. To address this limitation, we model the joint distribution of these variables using nonparametric Bernstein copulas within a bivariate cosimulation framework, where hydraulic head is incorporated as a supporting variable to improve the estimation of hydraulic conductivity. However, copula-based approaches often produce non-unique solutions, requiring selection criteria. Common strategies based on the mean or median produce overly smooth realizations that fail to preserve the aquifer's natural variability. To overcome these limitations, we propose a tri-objective function that integrates spatial structure, interpolation accuracy, and distributional consistency. The first term minimizes the discrepancy between reference and simulated experimental variograms, the second minimizes the interpolation error at known locations, and the third incorporates the Wasserstein distance to enforce distributional similarity. To further capture spatial dependence, the copula is estimated locally within defined neighborhoods. The tri-objective function is optimized using a two-stage genetic algorithm. To evaluate our proposal, we compared our approach against the mean and median reference values derived from Bernstein copula‐based spatial stochastic cosimulation. Our method achieved substantially better performance across all metrics: Wasserstein distance of 0.031 compared to 0.417 (mean) and 0.344 (median); interpolation NRMSE of 0.131 compared to 0.529 (mean) and 0.484 (median); and Pearson correlation of 0.991 compared to 0.856 (mean) and 0.882 (median). These results suggest that the proposed framework yields a more faithful representation of aquifer heterogeneity by optimizing spatial structure, point accuracy, and distributional fidelity.

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.

Rainfall is one of the most important meteorological phenomena since it provides water to the Earth's surface, which has a significant impact on the daily life of human beings. Gaining the knowledge of its behavior in a semi-arid basin is an important and challenging task to take advantage of this natural resource, given that water is usually scarce in such regions. Artificial intelligence and machine learning algorithms help to identify rainfall patterns and trends within a region. Multiple linear regression, random forest (RF), support vector machine, and artificial neural network (ANN) algorithms were implemented using daily rainfall data from climatological stations located within the basin using one station as a predictor variable and the remaining ones as input variables. The metrics to evaluate the model were the coefficient of determination (R2), mean absolute error, root mean square error, and the Kling–Gupta efficiency coefficient. The results showed that the daily rainfall prediction is better individually than overall, finding that the models obtained by RF and ANN simulate better daily rainfall in the basin.