Modeling total dissolved gas (TDG) concentration at Columbia river basin dams: high-order response surface method (H-RSM) vs. M5Tree, LSSVM, and MARS

The accuracy of ordinary response surface method (RSM) is improved using the high-nonlinear polynomial basis functions for modeling total dissolved gas (TDG). The third-order (3O), fourth-order (4O), and fifth-order (5O) polynomial functions are applied as the mathematical relations of TDG. The accuracy of third-, fourth-, and fifth-order polynomial basis function based on high-order RSM (H-RSM) is compared with least squares support vector machine (LSSVM), M5 model tree (M5Tree), and multivariate adaptive regression spline (MARS) models. The H-RSM, LSSVM, MARS, and M5Tree models were developed and compared using four input combinations and evaluated using several statistical indices namely coefficient of correlation (R), Willmott index of agreement (d), Nash-Sutcliffe coefficient of efficiency (NSE), RMSE, and MAE. The models were developed using data collected from four USGS stations at Columbia River, USA. According to the obtained results, it was demonstrated that the models worked with high level of satisfactory accuracy with respect to the five statistical indices. Overall, the 5H-RSM1 with four input variables provided the best accuracy at the four stations with R, NSE, d, RMSE, and MAE ranging from 0.911 to 0.965, 0.829 to 0.931, 0.952 to 0.982, 1.456 to 2.263, and 1.022 to 1.751, respectively.