Uncertainty Analysis for Hydrological Models With Interdependent Parameters: An Improved Polynomial Chaos Expansion Approach

Abstract The use of polynomial chaos expansion (PCE) has gained a lot of attention due to its ability to efficiently estimate the effects of parameter uncertainty on model outputs. The traditional PCE technique requires the studied parameters to be independent. In hydrological modeling, although model parameters are often assumed to be independent for simplicity of computation, such an assumption is not always valid. Neglecting parameter correlations could significantly affect the analysis of uncertainty, leading to distorted modeling results. In this study, an improved PCE approach is proposed to address this issue and support the uncertainty analysis for hydrological models with correlated parameters. The proposed approach is based on the integration of principle component analysis (PCA) and PCE, where PCA is used to transform correlated parameters into orthogonal independent components. To demonstrate the applicability of this approach, the Soil & Water Assessment Tool (SWAT) model is applied to the Guadalupe River Watershed in Texas, US, and the integrated PCA‐PCE framework is used to assess the propagation of uncertainty of SWAT's interdependent parameters. A traditional Monte‐Carlo (MC) simulation is also used to address the uncertainty in the developed SWAT model. The results show that PCA‐PCE could generate similar probabilistic flow results compared to MC while maintaining a very high computational efficiency. The coefficients of determination ( R 2 ) for the mean and variance are 0.998 and 0.973, respectively, and the computational requirement is reduced by 99% using the developed PCA‐PCE approach. It is shown that the PCA‐PCE approach is reliable and efficient in assessing uncertainties in hydrological models with interdependent parameters. Key Points An improved polynomial chaos expansion approach was proposed to assess the propagation of uncertainties associated with interdependent parameters The proposed method reduces computational requirements for uncertainty analysis by 99% compared to traditional Monte Carlo simulation