Monthly water quality forecasting and uncertainty assessment via bootstrapped wavelet neural networks under missing data for Harbin, China

In this paper, bootstrapped wavelet neural network (BWNN) was developed for predicting monthly ammonia nitrogen (NH⁴⁺–N) and dissolved oxygen (DO) in Harbin region, northeast of China. The Morlet wavelet basis function (WBF) was employed as a nonlinear activation function of traditional three-layer artificial neural network (ANN) structure. Prediction intervals (PI) were constructed according to the calculated uncertainties from the model structure and data noise. Performance of BWNN model was also compared with four different models: traditional ANN, WNN, bootstrapped ANN, and autoregressive integrated moving average model. The results showed that BWNN could handle the severely fluctuating and non-seasonal time series data of water quality, and it produced better performance than the other four models. The uncertainty from data noise was smaller than that from the model structure for NH⁴⁺–N; conversely, the uncertainty from data noise was larger for DO series. Besides, total uncertainties in the low-flow period were the biggest due to complicated processes during the freeze-up period of the Songhua River. Further, a data missing–refilling scheme was designed, and better performances of BWNNs for structural data missing (SD) were observed than incidental data missing (ID). For both ID and SD, temporal method was satisfactory for filling NH⁴⁺–N series, whereas spatial imputation was fit for DO series. This filling BWNN forecasting method was applied to other areas suffering “real” data missing, and the results demonstrated its efficiency. Thus, the methods introduced here will help managers to obtain informed decisions.