Development of Functional Quantile Autoregressive Model for River Flow Curve Forecasting

Among several hydrological processes, river flow is an essential parameter that is vital for different water resources engineering activities. Although several methodologies have been adopted over the literature for modeling river flow, the limitation still exists in modeling the river flow time series curve. In this research, a functional quantile autoregressive of order one model was developed to characterize the entire conditional distribution of the river flow time series curve. Based on the functional principal component analysis, the regression parameter function was estimated using a multivariate quantile regression framework. For this purpose, hourly scale river flow collected from three rivers in Australia (Mary River, Lockyer Valley, and Albert River) were used to evaluate the finite-sample performance of the proposed methodology. A series of Monte-Carlo experiments and historical data sets were examined at three stations. Further, uncertainty analysis was adopted for the methodology evaluation. Compared with the existing methods, the proposed model provides more robust forecasts for outlying observations, non-Gaussian and heavy-tailed error distribution, and heteroskedasticity. Also, the proposed model has the merit of predicting the intervals of future realizations of river flow time series at the central and non-central locations. The results confirmed the potential for predicting the river flow time series curve with a high level of accuracy in comparison with the benchmark existing functional time series methods.