Flood Characteristics Study Based On Multivariate Joint Distribution

With the global impact of climate change increasing,the extreme climate and hydrological events are increasingly frequent and the uncertainty of water supply has become one of the main factors which affecting the joint operation of cascade reservoirs and the risk control of flood control system.Since there are plenty of tributaries in upper and middle Yangtze River basin,occurrence of the extreme floods incident will greatly increase the risk of water conservancy project floods as well as bringing serious threats to the lives of people in the lower reaches of the region.Thus,a sound understanding and good knowledge of probability behaviors of meteor hydrological extremes are the first step into effective management of resources and enhancement of human mitigation to natural hazards.In the study,the flood peak,flood volume,flood time(flood peak time,flood time)And the time interval(between different tributaries)were selected as the flood characteristic variables.The upper reaches of the Yangtze River and its main tributaries were choosed as the research object.Based on the study of univariate flood characteristics analysis,the method of Normal Copula function is applied to construct the multivariate joint distribution model to study the temporal and spatial distribution characteristics of floods encounter.The results provide theoretical basis for realizing the safe utilization of flood resources in the region,and provide technical support for cascade reservoir joint dispatching and risk decision.The main contents and conclusions are as follows:(1)Select the P-? distribution,the generalized extreme value distribution(GEV),the generalized beta distribution of second kind(GB2)and the Von Mises distribution as the marginal distribution of the flood magnitude and flood time.The maximum likelihood method was employed to estimate parameters of distributions,the principle of maximum entropy method(POME)for parameter calibration was given at the same time.The RMSE,(Kolmogorov-Smir-nov,KS)and Akaike information criterion(AIC)were used as the criterial to evaluate and the fitting performance different distributions.The results show that: the distribution of GEV and GB2 distribution can describe the distribution of flood peak and magnitude in the upper reaches of the Yangtze River in addition to P-? distribution.The fitting effect is sometimes better than that of P-? distribution.The mixed Von Mises distribution is better to describe the periodic characteristics of flood time,especially for multi-peak random variables.The flood time of three stations should be described by mixed Von Mises distribution of second order and above.(2)The joint probability models of flood characteristic variables based on multivariate Normal Copula function were proposed and established.By calculating the RMSE and drawing P-P graphs,the applicability of the Normal Copula function and the correlation coefficient parameter estimation method in the study of regional application was verified.(3)Based on the analysis results of univariate study,the two-dimensional joint distribution of flood time with magnitude and flood peak with volume of single-station is estimated to calculate the probability of different floods in different periods of flood season and analysis the Relationship between flood peaks with volume.The results show that: the correlation between the occurrence time of flood peak and its magnitude is small.The annual maximum peak and the annual maximum flood time occurred with a strong positive correlation.The peak-volume correlation of Ping Shan station peak relationship is the best,while that of Gaochang station is the poorest.(4)In order to study the characteristics of temporal and spatial distribution of floods encounter,the paper introduced the characteristic variables of flood time interval.In the case of flood propagation time,the three-variable joint distribution model of flood peak and flood process is constructed based on multivariate Normal Copula function.The results show that: the floods in the Jinsha River(Ping Shan)and the Three Gorges(Yichang)are the most likely to encounter.The probility of Minjiang River and the Three Gorges(Yichang)floods encounter is higher than that of Jinsha River and the Minjiang River.The encounter risk of largest 15 d flood volume is greater than that of largest 15 d flood.