A Comparative Study of Linear Stochastic with Nonlinear Daily River Discharge Forecast Models

Accurate forecast of the magnitude and timing of the flood peak river discharge and the extent of inundated areas during major storm events are a vital component of early warning systems around the world that are responsible for saving countless lives every year. This study assesses the forecast accuracy of two different linear and non-linear approaches to predict the daily river discharge. A new linear stochastic method is produced by evaluating a detailed comparison between three pre-processing approaches, differencing, standardization, spectral analysis, and trend removal. Daily river discharge values of the Bow River with strong seasonal and non-seasonal correlations located in Alberta, Canada were utilized in this study. The stochastic term for this daily flow time series is calculated with an auto-regressive integrated moving average. We found that seasonal differencing is the best stationarization method for periodic effect elimination. Moreover, the proposed non-linear Group Method of Data Handling (GMDH) model could overcome the known accuracy limitations of the classical GMDH models that use only two inputs in each neuron from the adjacent layer. The proposed new non-linear GMDH-based method (named GS-GMDH) can improve the structure of the classical linear GMDH. The GS-GMDH model produced the most accurate forecasts in the Bow River case study with statistical indices such as the coefficient of determination and Nash-Sutcliffe for the daily discharge time series higher than 97% and relative error less than 6%. Finally, an explicit equation for estimation of the daily discharge of the Bow River is developed using the proposed GS-GMDH model to showcase the practical application of the new method in flood forecasting and management.