The Use Of Copula Function And Entropy Theory In Flood Multivariate Analysis And Streamflow Stochastic Simulation

Hydrological multivariate analysis and streamflow simulation are two important issues in hydraulic engineering. These two kinds of work provide scientific reference for the design and implementation of hydraulic facilities. Copula functions can construct joint distributions between two or more different marginals, which makes it convenient to be used in frequency analysis of hydrological extreme values, i.e. flood, storm and drought. Information entropy can be used to evaluate the uncertainty of a system and maximum entropy theory provides a way to model random variables, especially when no pre-information is known about the distribution. This dissertation aims to analyze bivariate flood distributions and runoff distributions between adjacent stations using copula method. In the meanwhile, maximum entropy theory is implemented for monthly streamflow simulation. The results of this dissertation may provide information for hydrological multivariate analysis and stochastic simulation, and shade lights on future study.Three kinds of Archimedean copulas, i.e. Clayton copula, Frank copula and G-H copula are implemented to model the joint behavior of flood from Sanmenxia station and Huayuankou station on the Yellow River region. Five kinds of joint distributions are constructed, namely, the joint distribution between annual maximum flood magnitudes of the two stations, between annual maximum flood magnitude and occurrence date of Sanmenxia station, between annual maximum flood magnitude and occurrence date of Huayuankou station, between occurrence date of the two stations, between annual runoff of the two stations. The best fitted copula model were selected to model the joint behavior between those variables. The joint return period and concurrent return period are also deduced, providing reference for setting flood criterion and allocating water resources.In order to study how copula model is affected by data length, different length of data were intercepted from original data of annual maximum flood from Cuntan station and Yichang station on Yangtze river region. Clayton copula, Frank copula and G-H copula were used to model the bivariate distributions of each data series. Both marginal entropy and joint entropy were computed to show how they were impacted by the change of data length. Results show that when data length is reduced, the modeling result deteriorate on the whole, and the best fitting copula and parameter estimating method vary. Under different data length the marginal return periods, marginal return periods and conditional joint return periods which are derived from best fitted copula functinon were also deduced, while the joint return periods stay stable.Using maximum entropy theory, monthly streamflow from Huayuankou station of the Yellow River is modeled. The joint distribution is acquired through maximize joint entropy under constrains of first three non-central moments. The modeling results contains no negative value. Results show that the modeled series keep the statistics, i.e. mean, standard deviation, Cv, Cs from original streamflow quite well. The proposed model does not need pre-information for the distribution of streamflow, which makes it superior than traditional models.