A PCM-based stochastic hydrological model for uncertainty quantification in watershed systems

In this study, an uncertainty quantification framework is proposed for hydrologic models based on probabilistic collocation method (PCM). The PCM method first uses polynomial chaos expansion (PCE) to approximate the hydrological outputs in terms of a set of standard Gaussian random variables, and then estimates the unknown coefficients in the PCE through collocation method. The conceptual hydrologic model, Hymod, is used to demonstrate the applicability of PCM in quantifying uncertainties of the hydrologic predictions. Two parameters in Hymod are considered as uniformly distributed in certain intervals. Two-dimensional 2-order and two-dimensional 3-order PCEs are applied to quantify the uncertainty of Hymod’s predictions. The results indicate that, both 2- and 3-order PCEs can well reflect the uncertainty of the streamflow predictions. The means and variances of 2- and 3-order PCEs are consistent with those obtained by Monte Carlo (MC) simulation method. However, for detailed distributions at selected periods, the histograms obtained by 3-order PCE are more accurate than those generated by 2-order PCE, when compared with the histograms obtained by MC simulation method.