Assessing uncertainty propagation in hybrid models for daily streamflow simulation based on arbitrary polynomial chaos expansion

•A hybrid model framework is proposed to improve streamflow predictions.•The hybrid model provided more reliable streamflow predictions for the case study.•An arbitrary polynomial chaos expansion (aPCE) method is introduced to assess parameter uncertainty of the hybrid model.•The aPCE method is over 90% more effective than Monte Carlo simulation (MCS). Accurate streamflow prediction is of significant importance in watershed management and has been attracting a lot of research interest. Hybrid hydrological models that employ advantages of physically-based models (PBMs) and data-driven models (DDMs) emerge recently as reliable tools for analyzing hydrological processes. Both PBMs and DDMs have uncertain parameters that could affect the hybrid modeling results. Conventional computational algorithms that rely on repeated sampling, such as Monte Carlo Simulation (MCS), have been recognized as robust tools for assessing the propagation of parameter uncertainties. However, the efficiency of these computational algorithms can decrease exponentially as the number of parameters increases. Meanwhile, although parameter uncertainty of PBMs has been widely studied, that of DDMs in a hybrid modeling framework has not been well investigated. In this study, a hybrid model framework is proposed for streamflow prediction, and an effective arbitrary polynomial chaos expansion (aPCE) method is implemented to assess the propagation of DDM parameter uncertainty within the hybrid modeling framework. The hybrid hydrological model integrating fully-distributed MIKE SHE and four machine-learning techniques increases the coefficient of determination (R2) from 0.70 to 0.82 for two validation periods. The aPCE method generates highly similar probabilistic results as MCS and achieves a 90% efficiency enhancement in uncertainty assessment. The results prove that aPCE is an efficient alternative to MCS for assessing uncertainties of hyperparameters in hybrid models. This study helps improve the performance of the streamflow prediction and also provide an insight into the uncertainty propagation involved in the hybrid models.