Least square support vector machine-based variational mode decomposition: a new hybrid model for daily river water temperature modeling

Abstract

Machines learning models have recently been proposed for predicting rivers water temperature (T_w) using only air temperature (T_a). The proposed models relied on a nonlinear relationship between the T_w and T_a and they have proven to be robust modelling tools. The main motivation for this study was to evaluate how the variational mode decomposition (VMD) contributed to the improvement of machines learning performances for river T_w modelling. Measured data collected at five stations located in Poland from 1987 to 2014 were acquired and used for the analysis. Six machines learning models were used and compared namely, K-nearest neighbor's regression (KNNR), least square support vector machine (LSSVM), generalized regression neural network (GRNN), cascade correlation artificial neural networks (CCNN), relevance vector machine (RVM), and locally weighted polynomials regression (LWPR). The six models were developed according to three scenarios. First, the models were calibrated using only the T_a as input and obtained results show that the models were able to predict consistently water temperature, showing a high determination coefficient (R²) and Nash-Sutcliffe efficiency (NSE) with values near or above 0.910 and 0.915, respectively, and in overall the six models worked equally without clear superiority of one above another. Second, the air temperature was combined with the periodicity (i.e., day, month and year number) as input variable and a significant improvement was achieved. Both models show their ability to accurately predict river T_w with an overall accuracy of 0.956 for R² and 0.955 for NSE values, but the LSSVM2 have some advantages such as a small errors metrics, and high fitting capabilities and it slightly surpasses the others models. Thirdly, air temperature was decomposed into several intrinsic mode functions (IMF) using the VMD method and the performances of the models were evaluated. The VMD parameters appeared to cause much influence on the prediction accuracy, exhibiting an improvement of about 40.50% and 39.12% in terms of RMSE and MAE between the first and the third scenarios, however, some models, i.e., GRNN and KNNR have not benefited from the VMD. This research has demonstrated the high capability of the VMD algorithm as a preprocessing approach in improving the accuracies of the machine learning models for river water temperature prediction.

Keywords: CCNN; GRNN; KNNR; LSSVM; LWPR; Modelling; RVM; VMD; Water temperature.