Determination of the optimal parameters in regression models for the prediction of chlorophyll-a: A case study of the Yeongsan Reservoir, Korea

Statistical regression models involve linear equations, which often lead to significant prediction errors due to poor statistical stability and accuracy. This concern arises from multicollinearity in the models, which may drastically affect model performance in terms of a trade-off scenario for effective water resource management logistics. In this paper, we propose a new methodology for improving the statistical stability and accuracy of regression models, and then show how to cope with pitfalls in the models and determine optimal parameters with a decreased number of predictive variables. Here, a comparison of the predictive performance was made using four types of multiple linear regression (MLR) and principal component regression (PCR) models in the prediction of chlorophyll-a (chl-a) concentration in the Yeongsan (YS) Reservoir, Korea, an estuarine reservoir that historically suffers from high levels of nutrient input. During a 3-year water quality monitoring period, results showed that PCRs could be a compact solution for improving the accuracy of the models, as in each case MLR could not accurately produce reliable predictions due to a persistent collinearity problem. Furthermore, based on R² (goodness of fit) and F-overall number (confidence of regression), and the number of explanatory variables (R-F-N) curve, it was revealed that PCR-F(7) was the best model among the four regression models in predicting chl-a, having the fewest explanatory variables (seven) and the lowest uncertainty. Seven PCs were identified as significant variables, related to eight water quality parameters: pH, 5-day biochemical oxygen demand, total coliform, fecal indicator bacteria, chemical oxygen demand, ammonia-nitrogen, total nitrogen, and dissolved oxygen. Overall, the results not only demonstrated that the models employed successfully simulated chl-a in a reservoir in both the test and validation periods, but also suggested that the optimal parameters should cautiously be considered in the design of regression models.