Quantification of predictive uncertainty with a metamodel: toward more efficient hydrologic simulations

Hydrologic flood prediction has been a quite complex and difficult task because of various sources of inherent uncertainty. Accurately quantifying these uncertainties plays a significant role in providing flood warnings and mitigating risk, but it is time-consuming. To offset the cost of quantifying the uncertainty, we adopted a highly efficient metamodel based on polynomial chaos expansion (PCE) theory and applied it to a lumped, deterministic rainfall-runoff model (NedbOr-AfstrOmnings model, NAM) combined with generalized likelihood uncertainty estimation (GLUE). The central conclusions are: (1) the subjective aspects of GLUE (e.g., the cutoff threshold values of likelihood function) are investigated for 8 flood events that occurred in the Thu bon river watershed in Vietnam, resulting that the values of 0.82 for Nash-Sutcliffe efficiency, 4.05% for peak error, and 4.35% for volume error are determined as the acceptance thresholds. Moreover, the number of ensemble behavioral sets required to maintain the sufficient range of uncertainty but to avoid any unnecessary computation was set to 500. (2) The number of experiment designs (N) and degree of polynomial (p) are key factors in estimating PCE coefficients, and values of N=50 and p=4 are preferred. (3) The results computed using a PCE model consisting of polynomial bases are as good as those given by the NAM, while the total times required for making an ensemble in the PCE model are approximately seventeen times faster. (4) Two parameters (CQOF and CK12) turned out to be most dominant based on a visual inspection of the posterior distribution and the mathematical computations of the Sobol' and Morris sensitivity analysis. Identification of the posterior parameter distributions from the calibration process helps to find the behavioral sets even faster. The unified framework that presents the most efficient ways of predicting flow regime and quantifying the uncertainty without deteriorating accuracy will ultimately be helpful for providing warnings and mitigating flood risk in a timely manner.