Multi-step-ahead predictor design for effective long-term forecast of hydrological signals using a novel wavelet neural network hybrid model

Abstract. In order to increase the accuracy of serial-propagated long-range multi-step-ahead (MSA) prediction, which has high practical value but also great implementary difficulty because of huge error accumulation, a novel wavelet neural network hybrid model – CDW-NN – combining continuous and discrete wavelet transforms (CWT and DWT) and neural networks (NNs), is designed as the MSA predictor for the effective long-term forecast of hydrological signals. By the application of 12 types of hybrid and pure models in estuarine 1096-day river stages forecasting, the different forecast performances and the superiorities of CDW-NN model with corresponding driving mechanisms are discussed. One type of CDW-NN model, CDW-NF, which uses neuro-fuzzy as the forecast submodel, has been proven to be the most effective MSA predictor for the prominent accuracy enhancement during the overall 1096-day long-term forecasts. The special superiority of CDW-NF model lies in the CWT-based methodology, which determines the 15-day and 28-day prior data series as model inputs by revealing the significant short-time periodicities involved in estuarine river stage signals. Comparing the conventional single-step-ahead-based long-term forecast models, the CWT-based hybrid models broaden the prediction range in each forecast step from 1 day to 15 days, and thus reduce the overall forecasting iteration steps from 1096 steps to 74 steps and finally create significant decrease of error accumulations. In addition, combination of the advantages of DWT method and neuro-fuzzy system also benefits filtering the noisy dynamics in model inputs and enhancing the simulation and forecast ability for the complex hydro-system.