Design and evaluation of SVR, MARS and M5Tree models for 1, 2 and 3-day lead time forecasting of river flow data in a semiarid mountainous catchment

Abstract

Accurate and reliable river flow forecasts attained with data-intelligent models can provide significant information about future water resources management. In this study we employed a 50-model ensemble of three data-driven predictive models, namely the support vector regression (SVR), multivariate adaptive regression spline (MARS) and M5 model tree (M5Tree) to forecast river flow data in a semiarid and ecologically significant mountainous region of Pailugou catchment in northwestern China. To attain stable and accurate forecast results, 50 different models were trained by randomly sampling the entire river flow data into 80% for training and 20% for testing subsets. To attain a complete evaluation of the ensemble-model based results, the global mean of six quantitative statistical performance evaluation measures: the coefficient of correlation (R), mean absolute relative error (MAE), root mean squared error (RMSE), Nash–Sutcliffe efficiency coefficient (NS), relative RMSE, and the Willmott’s Index (WI), and Taylor diagrams, including skill scores relative to a persistence model, were selected to assess the performances of the developed predictive models. The results indicated that all of the averaged R value attained was higher than 0.900 and all of the averaged NS values were higher than 0.800, representing good performance of the SVR, MARS and M5Tree models applied in the 1-, 2- and 3-day ahead modeling horizon, and this also accorded with the deductions made through an assessment of the Willmott’s Index. However, the M5Tree model outperformed both the SVR and MARS models (with NS = 0.917 vs. 0.904 and 0.901 for 1-day, 0.893 vs. 0.854 and 0.845 for 2-day, and 0.850 vs. 0.828 and 0.810 for 3-day forecasting horizons, respectively), which was in concurrence with the high value of WI. Therefore, based on the ensemble of 50 models, the performance of the M5Tree can be considered as superior to the SVR and MARS models when applied in a problem of river flow forecasting at multiple forecast horizon. A detailed comparison of the overall performance of all three models evaluated through Taylor diagrams and boxplots indicated that the 1-day ahead forecasting results were more accurate for all of the predictive models compared to the 2- and 3-day ahead forecasting horizons. Data-intelligent models designed in this study indicate that the M5Tree method could successfully be explored for short-term river flow forecasting in semiarid mountainous regions, which may have useful implications in water resources management, ecological sustainability and assessment of river systems.