INTEGRATED STATISTICAL MODELLING OF IRON EXCEEDANCE RISK: A MONTE CARLO, LOGISTIC REGRESSION, RANDOM FOREST, AND SOBOL ANALYSIS APPROACH

The quality of water resources in the Inaouen watershed, northern Morocco, is increasingly threatened by metal contamination, particularly iron (Fe). This study implements an integrated statistical framework to assess the risk of exceeding regulatory iron concentration thresholds. After preprocessing local physico-chemical data, a binary indicator variable was constructed to flag exceedances of the critical 30 µg/L threshold. Iron concentrations were modeled using log-normal and Weibull distributions, with a Monte Carlo simulation (n = 10,000) based on the log-normal law estimating exceedance probabilities across multiple thresholds (30, 50, 100 µg/L), revealing an 18% risk at 30 µg/L. Predictive modeling via logistic regression and random forest analysis identified calcium (Ca) as the dominant driver of iron exceedances, a finding corroborated by Sobol sensitivity analysis (S1 index = 0.74), with bicarbonate (HCO₃⁻) emerging as a secondary factor (S1 = 0.10). These results demonstrate the power of combining distribution fitting, machine learning, and global sensitivity analysis to effectively quantify and interpret iron contamination risks in vulnerable watersheds such as Inaouen. The proposed methodology offers a robust decision-support tool for sustainable water resource management and public health protection.