A polynomial chaos ensemble hydrologic prediction system for efficient parameter inference and robust uncertainty assessment

Abstract

Summary This paper presents a polynomial chaos ensemble hydrologic prediction system (PCEHPS) for an efficient and robust uncertainty assessment of model parameters and predictions, in which possibilistic reasoning is infused into probabilistic parameter inference with simultaneous consideration of randomness and fuzziness. The PCEHPS is developed through a two-stage factorial polynomial chaos expansion (PCE) framework, which consists of an ensemble of PCEs to approximate the behavior of the hydrologic model, significantly speeding up the exhaustive sampling of the parameter space. Multiple hypothesis testing is then conducted to construct an ensemble of reduced-dimensionality PCEs with only the most influential terms, which is meaningful for achieving uncertainty reduction and further acceleration of parameter inference. The PCEHPS is applied to the Xiangxi River watershed in China to demonstrate its validity and applicability. A detailed comparison between the HYMOD hydrologic model, the ensemble of PCEs, and the ensemble of reduced PCEs is performed in terms of accuracy and efficiency. Results reveal temporal and spatial variations in parameter sensitivities due to the dynamic behavior of hydrologic systems, and the effects (magnitude and direction) of parametric interactions depending on different hydrological metrics. The case study demonstrates that the PCEHPS is capable not only of capturing both expert knowledge and probabilistic information in the calibration process, but also of implementing an acceleration of more than 10 times faster than the hydrologic model without compromising the predictive accuracy.