Development of Functional Quantile Autoregressive Model for River Flow Curve Forecasting

Abstract

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. This paper proposes a functional quantile autoregressive model of order one, which is used to predict the entire distribution of the realizations of river flow time series curve. The proposed model allows modeling the conditional quantiles of the response variable as a function of its past values of it. The proposed method for historical river flow curves is an excellent alternative to existing mean regression methods at the 0.5 quantile level (median regression). Also, as an advantage over existing methods, it offers a more thorough explanation of the connection among previous and future realizations of river flow curves at various quantile levels, providing a more extensive understanding of the relationship. Moreover, this feature of the proposed method allows for the effortless generation of pointwise prediction intervals for future realizations of river flow curves. The numerical results obtained by Monte Carlo experiments and empirical data analyses exhibit that, compared with existing methods, the proposed method produces competitive or even better forecasting results. The results also indicate that the future realizations of the river flow measurements are well covered by the prediction intervals constructed by the proposed method. Predicting the mean and extreme values of the river flow curve is important for various applications in water resources management The FQAR(1) allows predicting the entire distribution of future realizations of the river flow curve as a function of its past values of it Numerical results based on river flow measurements collected from the Australia Continent confirmed the potential of the FQAR(1)