Uncertainty Quantification of Hydrologic Predictions and Risk Analysis

Fan, Yurui
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Faculty of Graduate Studies and Research, University of Regina

Hydrologic models are designed to simulate the rainfall-runoff processes through conceptualizing and aggregating the complex, spatially distributed and highly interrelated water, energy, and vegetation processes in a watershed into relatively simple mathematical equations. A significant consequence of process conceptualization is that the model parameters exhibit extensive uncertainties, leading to significant uncertainty in hydrologic forecasts. Consequently, to facilitate more reliable probabilistic hydrologic predictions and multivariate hydrologic risk analysis, innovative uncertainty quantification approaches are desired in order to reveal the inherent uncertainty in hydrologic models. Water is the life-giving resource required by all species on our planet and is the integral link within ecosystems. Severe surplus or deficit of water, has been more devastating in terms of deaths, suffering and economic damage, than other natural hazards such as earthquakes and volcanoes. Consequently, hydrologic risk analysis is an essential tool to analyze and predict flood events and provide decision support for actual flood control. However, a flood is usually characterized by multidimensional characteristics, including flood peak, flood volume and flood duration. Therefore, innovative multivariate hydrologic risk analysis methods are required to reveal the interactive impact among flood variables on hydrologic risk values. In this dissertation research, a series of innovative methodologies have been developed for uncertainty quantification of hydrologic models, and multivariate hydrologic risk analysis. These methods include: (i) a PCM-based stochastic hydrological model for uncertainty quantification in watershed systems; (ii) a coupled ensemble filtering and probabilistic collocation (EFPC) approach for uncertainty quantification of hydrologic models; (iii) a hybrid sequential data assimilation and probabilistic collocation (SDAPC) method for uncertainty quantification of hydrologic models; (iv) a copula-based bivariate hydrologic risk for the Xiangxi River in the Three Gorges Reservoir (TGR) area, China; (v) a hybrid entropy-copula method for bivariate hydrologic risk analysis for the Xiangxi River in TGR area; and (vi) a coupled GMM-copula method for hydrologic risk analysis for the Yichang Station of the Yangtze River. The major accomplishments of this research are summarized as follows: (a) the probabilistic collocation method is firstly integrated into the hydrologic model to reveal the impacts of uncertainty in model parameters on the hydrologic predictions; (b) the backward uncertainty quantification methods (EnKF and PF) and the forward uncertainty prediction method (PCM) are integrated together through Gaussian anamorphosis to provide a better treatment of the input, output, parameters and model structural uncertainties in hydrologic models; (iii) an integrated risk indicator based on interactive analysis of multiple flood variables and bivariate copulas is developed for exploring the risk of concurrence of flood extremes such as flood peak and volume; and (iv) copulabased hydrologic risk analysis methods are developed through integrating advanced nonparametric distribution estimation (entropy and Gaussian mixture model) methods into the copulas to improve the performance of copulas in quantifying the dependence among flood variables. Reasonable results have been generated from the case studies. They provide valuable bases for not only revealing the inherent probabilistic characteristics of hydrologic predictions stemming from uncertain model parameters, but also exploring the significance of effects from persisting high risk levels due to impacts from multiple interactive flood variables.

A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy in Environmental Systems Engineering, University of Regina. xiv, 328 p.