Combining Outlier Robust Extreme Learning Machine (ORELM) with seasonal autoregressive moving average linear model (SARIMA) to improve the accuracy of runoff modeling

Accurate and reliable runoff forecasting has an important role in water resources management, but the complex nature of this parameter can create major challenges for the development of appropriate forecasting models. Two hybrid models based on the combination of two simple linear and non-linear models have been proposed for runoff modeling at hydrological station 02PL005 in the St. Lawrence River basin in Canada. Seasonal autoregressive moving average (SARIMA) linear model is proposed to address the linear and seasonal characteristics of runoff. While the artificial neural network (ANN) and Outlier Robust Extreme Learning Machine (ORELM) models have been used to deal with the nonlinear characteristics of the data through machine learning and pattern recognition. In order to increase the accuracy of the modeling, in the first stage of modeling, the normality and stationary of the data was examined, and by performing appropriate pre-processing, the data were prepared for modeling in the linear part. Then by defining different sub-scenarios and performing modeling through linear model, the best linear model was selected through different mathematical statistics including MAE, RMSE, R and AIC. In the final stage, the residuals of the linear model were modeled by two non-linear models including ANN and ORELM models. Comparing the results of the proposed hybrid models showed that the SARIMA-ORELM hybrid model with AIC=249.29, R=0.71, MAE=11.2 and RMSE=14.33 performs better than the SARIMA-MLP model in all mathematical criteria. Also, the results of the hybrid models were compared with the common MLP, ORELM and SARIMA models.