Parametric uncertainty assessment in hydrological modeling using the generalized polynomial chaos expansion

Abstract

An integrated framework is proposed for parametric uncertainty analysis in hydrological modeling using a generalized polynomial chaos expansion (PCE) approach. PCE represents model output as a polynomial expression in terms of critical random variables that are determined by parameter uncertainties, thus offers an efficient way of sampling without running the original model, which is appealing to computationally expensive models. To demonstrate the applicability of generalized PCE approach, both second- and third-order PCEs (PCE-2 and PCE-3) are constructed for Xinanjiang hydrological model using three selected uncertain parameters. Uncertainties in streamflow predictions are assessed by sampling the random inputs. Results show that: (1) both PCE-2 and PCE-3 are capable of capturing the uncertainty information in hydrological predictions, generating consistent mean, variance, skewness and kurtosis estimates with the standard Monte Carlo (MC) methodology; (2) Using more collocation points and more polynomial terms, PCE-3 approximation slightly improves the model simulation and provides more matched distribution with that of MC compared to PCE-2; (3) the computational cost using the PCE approach is greatly reduced by 71% (20%) with PCE-2 (PCE-3). In general, PCE-2 is recommended to serve as a good surrogate model for Xinanjiang hydrological modelling in future with much higher computation speed, more efficient sampling, and compatible approximation results.