Hybrid denoising-jittering data pre-processing approach to enhance multi-step-ahead rainfall–runoff modeling

Successful modeling of stochastic hydro-environmental processes widely relies on quantity and quality of accessible data and noisy data might effect on the functioning of the modeling. On the other hand in training phase of any Artificial Intelligence based model, each training data set is usually a limited sample of possible patterns of the process and hence, might not show the behavior of whole population. Accordingly in the present article first, wavelet-based denoising method was used in order to smooth hydrological time series and then small normally distributed noises with the mean of zero and various standard deviations were generated and added to the smoothed time series to form different denoised-jittered training data sets, for Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) modeling of daily and multi-step-ahead rainfall–runoff process of the Milledgeville station of the Oconee River and the Pole Saheb station of the Jighatu River watersheds, respectively located in USA and Iran. The proposed hybrid data pre-processing approach in the present study is used for the first time in modeling of time series and especially in modeling of hydrological processes. Furthermore, the impacts of denoising (smoothing) and noise injection (jittering) have been simultaneously investigated neither in hydrology nor in any other engineering fields. To evaluate the modeling performance, the outcomes were compared with the results of multi linear regression and Auto Regressive Integrated Moving Average models. Comparing the achieved results via the trained ANN and ANFIS models using denoised-jittered data showed that the proposed data pre-processing approach which serves both denoising and jittering techniques could improve performance of the ANN and ANFIS based single-step-ahead rainfall–runoff modeling of the Milledgeville station up to 14 and 12% and of the Pole Saheb station up to 22 and 16% in the verification phase. Also the results of multi-step-ahead modeling using the proposed data pre-processing approach showed improvement of modeling for both watersheds.