A Computational Investigation of Physicochemical Water Quality Parameters through Condensed Matter Physics and Statistical Modelling: A Case Study of Groundwater and Surface Water Sources in a Basement Complex Terrain, North-Central Nigeria

Abstract

Water quality assessment in basement complex terrains in sub-Saharan Africa has traditionally relied on descriptive, standards-compliance reporting, with limited investigation of underlying geochemical mechanisms. This study reanalyses physicochemical data — pH, temperature, total dissolved solids (TDS), total hardness, total alkalinity, and lead — from two boreholes and three surface-water streams at the Federal University Lokoja campus, Kogi State, Nigeria, within a condensed matter and statistical physics framework. Data were analysed using descriptive statistics, Pearson correlation, principal component analysis (PCA), hierarchical cluster analysis (HCA), and a weighted arithmetic water quality index (WQI). The first PCA component accounted for 69.1% of total variance and separated groundwater from surface water, a partition corroborated by Ward-linkage HCA. Groundwater exhibited markedly higher TDS (392.5 mg/L) and total hardness (185.0 mg/L) than surface water, consistent with prolonged water–rock interaction and mineral accumulation through transport-limited weathering of crystalline basement aquifers. The only significant correlation was between hardness and alkalinity (r = −0.95, p = 0.014), suggesting that elevated hardness at one borehole (200 mg/L, above the NSDWQ limit of 150 mg/L) is predominantly non-carbonate. The WQI was highly sensitive to lead, which carries a unit weight exceeding 99% owing to its very low permissible limit (0.01 mg/L); absent lead, all sites would be rated excellent-to-good. The measured parameters are interpreted through hydrogen-bond network reorganisation, Debye–Hückel screening, ion hydration thermodynamics, and diffusion-limited mineral dissolution, providing a framework through which condensed matter physics can offer mechanistic interpretations unavailable within descriptive hydrogeochemistry. The principal limitation is the small dataset (n = 5); multivariate outputs are therefore exploratory.