Improving probabilistic streamflow predictions through a nonparametric residual error model

Abstract

Reliable probabilistic hydrological prediction requires appropriate handling of residual errors, which can pose considerable complexity. This paper proposes a nonparametric residual error (NRE) model that effectively captures the statistical characteristics of raw residuals. The NRE model employs a local linear estimator with a robust bandwidth selector to estimate the regression and conditional volatility functions of raw residuals. Additionally, the AR(1) model and location-mixture Gaussian distribution are used to estimate the temporal correlation structure and innovation distribution. Through two case studies in South-East China, this research demonstrates the superiority of the NRE model over the benchmark Box-Cox transformation approach in terms of prediction reliability, precision, and bias correction capabilities. Simulation experiments further reveal that the NRE model can effectively fit the residual regression function, conditional volatility function, and innovation distribution under varying scenarios. The proposed residual error model is anticipated to promote the adoption of probabilistic predictions in hydrological modeling applications.