Propagation of parameter uncertainty in SWAT: A probabilistic forecasting method based on polynomial chaos expansion and machine learning

Soil and Water Assessment Tool (SWAT) is one of the most widely used semi-distributed hydrological models. Assessment of the uncertainties in SWAT outputs is a popular but challenging topic due to the significant number of parameters. The purpose of this study is to investigate the use of Polynomial Chaos Expansion (PCE) in assessing uncertainty propagation in SWAT under the impact of significant parameter sensitivity. Furthermore, for the first time, a machine learning technique (i.e., artificial neural network, ANN) is integrated with PCE to expand its capability in generating probabilistic forecasts of daily flow. The traditional PCE and the proposed PCE-ANN methods are applied to a case study in the Guadalupe watershed in Texas, USA to assess the uncertainty propagation in SWAT for flow prediction during the historical and forecasting periods. The results show that PCE provides similar results as the traditional Monte-Carlo (MC) method, with a coefficient of determination (R-2) value of 0.99 for the mean flow, during the historical period; while the proposed PCE-ANN method reproduces MC output with a R-2 value of 0.84 for mean flow during the forecasting period. It is also indicated that PCE and PCE-ANN are as reliable as but much more efficient than MC. PCE takes about 1% of the computational time required by MC; PCE-ANN only takes a few minutes to produce probabilistic forecasting, while MC requires running the model for dozens or hundreds, even thousands, of times. Notably, the development of the PCE-ANN framework is the first attempt to explore PCE's probabilistic forecasting capability using machine learning. PCE-ANN is a promising uncertainty assessment and probabilistic forecasting technique, as it is more efficient in terms of computation time, and it does not cause loss of essential uncertainty information.