Stochastic residual-error analysis for estimating hydrologic model predictive uncertainty

A hybrid time series-nonparametric sampling approach, referred to herein as semiparametric, is presented for the estimation of model predictive uncertainty. The methodology is a two-step procedure whereby a distributed hydrologic model is first calibrated, then followed by brute force application of time series analysis with nonparametric random generation to synthesize serially correlated model residual errors. The methodology is applied to estimate uncertainties in simulated streamflows and related flow attributes upstream from the mouth of a rapidly urbanizing watershed. Two procedures for the estimation of model output uncertainty are compared: the Gaussian-based l-step forecast and the semiparametric ensemble forecast. Results show that although both methods yielded comparable uncertainty bands, the Gaussian l-step forecast underestimated the width of the uncertainty band when compared to the semiparametric method. An ensemble of streamflows generated through Latin-hypercube Monte Carlo simulations showed relatively larger values of the coefficient of variation for long-term average annual maximum daily flows than for long-term daily, monthly maximum daily, and monthly median of daily flows. Ensemble of flow duration curves is generated from the error-adjusted simulated flows. The computed low flows displayed greater values of the coefficient of variation than flows in the medium and high range. The ensemble flow durations allow for the estimation of daily flow range upstream from the outlet with 95% confidence for a specified design recurrence period. The computed uncertainties of the predicted watershed response and associated flow attributes provide the basis for communicating the risk to stakeholders and decision makers who are involved in the future development of the watershed.