Development of clustered polynomial chaos expansion model for stochastic hydrological prediction

Abstract

This study introduced a clustered polynomial chaos expansion (CPCE) model to reveal random propagation and dynamic sensitivity of uncertainty parameters in hydrologic prediction. In the CPCE model, the random characteristics of the streamflow simulations resulting from parameter uncertainties are characterized through the polynomial chaos expansion (PCE) model based on the probabilistic collocation method. At the same time, a multivariate discrete non-functional relationship between PCE coefficients and hydrological model inputs is established based on stepwise cluster analysis. Therefore, compared with traditional PCE method, the developed CPCE model cannot only reflect uncertainty propagation in stochastic hydrological simulation, but also have the capability of random forecasting. Moreover, the dynamic sensitivities of model parameters are investigated through the multilevel factorial analyses. The developed approach was applied for streamflow forecasting for the Ruihe watershed, China. Results showed that with effective quantification for the random characteristics of hydrological processes, the CPCE model can directly predict runoff series and generate the associated probability distributions at different time periods. The dynamic sensitivity analysis indicates that the maximum soil moisture capacity within the catchment plays a key role in the accuracy of the low-flow forecasting, while the degree of spatial variability in soil moisture capacities has a remarkable impact on the accuracy of the high-flow forecasting in the studied watershed.