Robust and efficient uncertainty quantification for extreme events that deviate significantly from the training dataset using polynomial chaos-kriging

Abstract

This study presents the strengths of polynomial chaos-kriging (PCK), a new surrogate model that merges polynomial chaos extension (PCE) and Gaussian process with kriging variance. This combination enabled streamflow prediction for extreme events that deviated significantly from the trained data space, and allowed for quantifying predictive uncertainty robustly and efficiently. The uncertainty quantification results to eight testing flood events through a modeling framework that applies generalized likelihood uncertainty estimation (GLUE) to surrogate models are as follows. (1) PCK outperformed PCE and ordinary kriging (OK) in mimicking predictive and sensitive behaviors of the original model with a smaller-sized training dataset. (2) Three surrogate models trained on the identical dataset exhibited equivalent predictability with the original model for six smaller events similar to their training data space. However, for two extreme events, which differed significantly from the training set, only PCK was found to accurately predict the hydrograph and flood peaks. (3) Since two types of acceptance thresholds, defined here as “accuracy-aimed” or “efficiency-aimed” threshold, have their own pros and cons, the type and size of the threshold should be determined depending on the availability of computational resources and the degree of accuracy needed. (4) A new “performance score” is proposed here to assess the overall performance of the surrogate models. This compensates for situations in which the performance of a surrogate model can be misjudged through individual indices of efficiency or accuracy in the process of uncertainty quantification.