Comparative analysis of correlation and causality inference in water quality problems with emphasis on TDS Karkheh River in Iran

Water quality management is a critical aspect of environmental sustainability, particularly in arid and semi-arid regions such as Iran where water scarcity is compounded by quality degradation. This study delves into the causal relationships influencing water quality, focusing on Total Dissolved Solids (TDS) as a primary indicator in the Karkheh River, southwest Iran. Utilizing a comprehensive dataset spanning 50 years (1968-2018), this research integrates Machine Learning (ML) techniques to examine correlations and infer causality among multiple parameters, including flow rate (Q), Sodium (Na⁺), Magnesium (Mg²⁺), Calcium (Ca²⁺), Chloride (Cl^-), Sulfate (SO₄^2-), Bicarbonates (HCO₃^-), and pH. For modeling the causation, the "Back door linear regression" approach has been considered which establishes a stable and interpretable framework in causal inference by focusing on clear assumptions. Predictive modeling was used to show the difference between correlation and causation along with interpretability modeling to make the predictive model transparent. Predictive modeling does not report the causality among the variables as it showed Mg is not contributing to the target (TDS) while the findings reveal that TDS is predominantly positive influenced by Mg, Na, Cl, Ca and SO₄, with HCO₃ and pH exerting negative (inverse) effects. Unlike correlations, causal relationships demonstrate directional and often unequal influences, highlighting Mg as a critical driver of TDS levels. This novel application of ML-based causal inference in water quality research provides a cost-effective and time-efficient alternative to traditional experimental methods. The results underscore the potential of ML-driven causal analysis to guide water resource management and policy-making. By identifying the key drivers of TDS, this study proposes targeted interventions to mitigate water quality deterioration. Moreover, the insights gained lay the foundation for developing early warning systems, ensuring proactive and sustainable water quality management in similar hydrological contexts.