Multivariate adaptive regression splines for estimating riverine constituent concentrations

Regression-based methods are commonly used for riverine constituent concentration/flux estimation, which is essential for guiding water quality protection practices and environmental decision making. This paper developed a multivariate adaptive regression splines model for estimating riverine constituent concentrations (MARS-EC). The process, interpretability and flexibility of the MARS-EC modelling approach, was demonstrated for total nitrogen in the Patuxent River, a major river input to Chesapeake Bay. Model accuracy and uncertainty of the MARS-EC approach was further analysed using nitrate plus nitrite datasets from eight tributary rivers to Chesapeake Bay. Results showed that the MARS-EC approach integrated the advantages of both parametric and nonparametric regression methods, and model accuracy was demonstrated to be superior to the traditionally used ESTIMATOR model. MARS-EC is flexible and allows consideration of auxiliary variables; the variables and interactions can be selected automatically. MARS-EC does not constrain concentration-predictor curves to be constant but rather is able to identify shifts in these curves from mathematical expressions and visual graphics. The MARS-EC approach provides an effective and complementary tool along with existing approaches for estimating riverine constituent concentrations.