Urban water demand forecasting and uncertainty assessment using ensemble wavelet-bootstrap-neural network models


  • Mukesh K. Tiwari,

    1. Department of Soil and Water Engineering, College of Agricultural and Technology, Anand Agricultural University, Godhra, Gujarat, India
    Search for more papers by this author
  • Jan Adamowski

    Corresponding author
    1. Department of Bioresource Engineering, McGill University, Ste Anne de Bellevue, Quebec, Canada
    • Corresponding author: J. Adamowski, Department of Bioresource Engineering, McGill University, Ste Anne de Bellevue, 21 111 Lakeshore Road, Quebec H9X 3V9, Canada. (jan.adamowski@mcgill.ca)

    Search for more papers by this author


[1] A new hybrid wavelet-bootstrap-neural network (WBNN) model is proposed in this study for short term (1, 3, and 5 day; 1 and 2 week; and 1 and 2 month) urban water demand forecasting. The new method was tested using data from the city of Montreal in Canada. The performance of the WBNN method was compared with the autoregressive integrated moving average (ARIMA) and autoregressive integrated moving average model with exogenous input variables (ARIMAX), traditional NNs, wavelet analysis-based NNs (WNN), bootstrap-based NNs (BNN), and a simple naïve persistence index model. The WBNN model was developed as an ensemble of several NNs built using bootstrap resamples of wavelet subtime series instead of raw data sets. The results demonstrated that the hybrid WBNN and WNN models produced significantly more accurate forecasting results than the traditional NN, BNN, ARIMA, and ARIMAX models. It was also found that the WBNN model reduces the uncertainty associated with the forecasts, and the performance of WBNN forecasted confidence bands was found to be more accurate and reliable than BNN forecasted confidence bands. It was found in this study that maximum temperature and total precipitation improved the accuracy of water demand forecasts using wavelet analysis. The performance of WBNN models was also compared for different numbers of bootstrap resamples (i.e., 25, 50, 100, 200, and 500) and it was found that WBNN models produced optimum results with different numbers of bootstrap resamples for different lead time forecasts with considerable variability.