A reliable hybrid outlier robust non-tuned rapid machine learning model for multi-step ahead flood forecasting in Quebec, Canada

Reliable and accurate flood forecasting is a complex and challenging problem that is essential for the creation of disaster preparedness plans to protect life and reduce economic losses. This study suggests a novel hybrid model for real-time multi-steps-ahead flood forecasting within the Saint-Lawrence River in Quebec by integrating the discrete wavelet transform (DWT) and improved outlier-robust extreme learning machine (IORELM) models. The DWTIORELM model was constructed with three main novelties: (i) Consider the sparsity characteristics of the outliers to enhance the performance of the ELM-based model in the presence of outliers, (ii) Introduce an iter-ative process to overcome the random definition of the two main matrices in the ELM-based approaches, (iii) Integrate IORELM with DWT as a preprocessing technique to decompose the main input signals to high-scale and low-frequency signals. The performance of the individual IORELM is compared with the original version of ELM, Regularized ELM (RELM), and Weighted RELM (WRELM) in terms of global accuracy and accuracy in peak flow forecasting. The results indicated that the IORELM outperformed other models. However, there was a need for a model that could perform better for peak flow detection. IORELM, as the best individual model, was integrated with DWT, and the DWTIORELM model was developed to overcome this limitation. In addition, the comparison results of the hybrid DWTIORELM and individual IORELM models in terms of accuracy and simplicity as well as peak flow forecasting indicate that the introduced hybrid model (R = 0.99, NSE = 0.99; RMSE = 0.234; NRMSE = 0.021; MARE = 0.02) in the current study not only overcomes all limitations of the existing ELM-based methods but also could be applied in multi-steps-ahead flood forecasting. The optimum values of the number of hidden neurons, decomposition level, and iteration number were found to be 200, 1, and 500, respectively. Furthermore, the Sigmoid function and Discrete Meyer (DM) were selected as the best activation function and mother wavelet, respectively. The developed hybrid model was applied to check its performance in multi-steps -ahead flood forecasting for one to nine hours ahead. The results showed that it could forecast peak flows with an average relative error of less than 5 %.