Design Flood Estimation Based On Copulas

Flood events (or processes) usually have multivariate characteristics, which need multivariate analysis methods to describe their internal rules. In this thesis, the application and research progress of traditional univariate flood frequency analysis with historical infirmation, flood risk analysis and design flood estimation for cascade reservoir were briefly reviewed and discussed. The developments of multivariate analysis and applications of Copula function in flood frequency analysis were also reviewed. The research mainly focuses on flood frequency analysis with historical information, bivariate design flood estimation and flood risk analysis for cascade reservoirs. The main conclusions and innovations were summarized as follows:(1) Copula theories, mainly including the most frequently-used and newly-emerged copulas in hydrological field, constructions of multivariate copulas, estimation of parameters, goodness of fit methods and tail dependence, were introduced.(2) A bivariate flood frequency analysis model which considers historical information was established by Copula function. The modefied inference function for margins (MIFM), i.e. bivariate maximum likelihood method was proposed to estimate model parameters with histotical information. The Three Gorges reservoir (TGR) was selected as case study and the application results show that the marginal design values derived by MIFM method are no different than the orginal design values of TGR. Meanwhile, the joint design values derived by MIFM method are larger than that of IFM method which is much safer in practice.(3) A boundary identification method was proposed for selecting bivariate combinations of flood peak and volume. Two statistically-based combinations of flood peak and volume, i.e. bivariate equivalent frequency combination and bivariate conditional expectation combination were derived with a given return period. The application results of Geheyan reservoir located at the Qingjiang River show that the bivariate flood combinations are safer design to reservoirs compared with univariate design floods. The proposed boundary identification and combination selection methods can narrow the design flood selection boundary and expand the application range of multivariate flood frequency analysis technique in hydrological engineering.(4) A bivariate flood risk analysis method was proposed based on joint return period. The Monte Carlo (MC) and Copula function were coupled to jointly simulate flood peak and volume. The typical flood hydrographs were chosen by the similarity between simulated and observed flood values, which can sufficiently consider the randomness and uncertainty of flood hydrographs. The Geheyan reservoir was selected as case study and the flood risk of different flood limited water levels was estimated to provide reference information for reservoir operation.(5) A modified discrete summation method was proposed to estimate the design flood of cascade reservoirs system. The Copula function was used to establish the joint distribution of flood volumes between dam-site section and interval basin and derive the explicit formulation of conditional probability function. The proposed method, which considers the spatial correlation of each section and discretizes the conditional distribution curve directly without independence transformation, can overcome the shortcomings of traditional discrete summation method and avoid error accumulation.