Modeling diurnal Temperature-Rainfall relationships under multicollinearity using PLS-SEM: A case study of Ghana

Rainfall variability in tropical climates is influenced by interacting thermal processes, yet maximum (TMAX) and minimum (TMIN) temperatures are often highly collinear, complicating the estimation of their distinct relationships with precipitation. This study applies Partial Least Squares Structural Equation Modeling (PLS-SEM) to long-term station-based climate data from Ghana (1981-2020; N = 252 station × calendar month observations) to examine structural associations among TMAX, TMIN, and rainfall (RAIN), including differences between coastal and inland regimes. The model represents a simplified component of the broader hydroclimatic system. The results indicate a statistically significant negative association between TMAX and rainfall (β = -0.454, p < 0.001) and a positive association between TMIN and rainfall (β = 0.166, p < 0.001). The relationship between TMAX and TMIN is positive but not statistically significant (β = 0.152, p = 0.053). Mediation analysis does not support a significant indirect pathway from TMAX to rainfall via TMIN (β = 0.025, p = 0.076). The model explains 21.1% of rainfall variance. Multi-group analysis reveals spatial heterogeneity, with a stronger negative TMAX-rainfall association inland (β = -0.721) than along the coast (β = -0.427), and a stronger TMAX-TMIN association in coastal regions (β = 0.753 vs. 0.337). The findings suggest that TMAX and TMIN exhibit distinct statistical relationships with rainfall that vary across climatic regimes. However, given the limited variables and observational design, the results should be interpreted as structural associations rather than definitive physical mechanisms. The study demonstrates the utility of PLS-SEM for handling multicollinearity and interdependent relationships in climate data while highlighting the need to incorporate additional atmospheric variables to improve explanatory depth.