Research On New Theory And Application Of Hydrologic Frequency Analysis

Hydrologic frequency analysis is an important content in hydrology research. Aims atstudy and analysis the hydrological random phenomena, reveal the statistic laws that beingcontained in hydrological phenomena, in order to forecast the possible hydrological regime inthe future, and satisfy the requirements of hydraulic engineering planning, designing,management and water resources utilization.Aiming at several problems existing in current hydrologic frequency analysis research,this dissertation reviewed the present researches around these issues both at home and abroad,summarized some disadvantages existing in the present study. The hydrometeorological dataof typical region in Shaanxi province were used for case studies. Univariate and multivariatehydrologic frequency analysis were studied respectively, several new theoretical method wereemployed and proposed, and were used for case studies.The main contents of this dissertation are as follows.1. Research on the application of tail-index estimation theory in hydrological events.Whether the monthly precipitation series obey the heavy-tailed distribution was judged. Threekinds of estimators were selected to estimate the extreme index and tail index of the data.2. Research on the principle of nonidentically distributed hydrologic data and itsapplication in annual runoff series. By dividing the nonidentically distributed annual runoffseries into several sub-series according to the change points, the formulas of the theoreticalprobability, the empirical probability, the moments and the quantile were deduced. P-IIIdistribution was chosen for application and assessment.3. Research on the method of partial probability weighted moments, the method ofhigher-order probability weighted moments and their application in annual runoff series andannual maximum flows. Giving different censoring levels, the parameters of GEV distributionwere estimated using partial probability weighted moments. The effects of fitting the largervalue of data were evaluated. Monte Carlo simulation was carried to analyze the statisticalproperties of partial probability weighted moments. The expressions of higher-orderprobability weighted moments for P-III distribution were derived. The parameters of GEVdistribution and P-III distribution were estimated separately. The effects of fitting the largervalue of data were evaluated. Monte Carlo simulation was carried to analyze the statistical properties of higher-order probability weighted moments.4. Research on the application of Bayesian theory in parameter estimation for P-IIIdistribution. The estimators of parameters for P-III distribution based on Bayesian theorywere presented. Three kinds of MCMC sampling methods were used to obtain the parametersamples of annual maximum flows, and their properties were evaluated in application.5. Research on the application of hierarchical Archimedean copulas in multivariatedraught analysis. Commonly-used Archimedean copulas are distribution functions of severalexchangeable uniform random variates, and take no account of dependence differencebetween variates. For this reason, these copulas suffer from a very limited dependencestructure. Contrapose this disadvantages of ordinary multivariate Archimedean copulas, weconstructed trivariate hierarchical Archimedean copulas (HAC) that combines Claytoncopulas with Frank copulas to model multivariate joint distributions according to thedependence of draught duration, draught severity and severity peak. The expressions ofdensity, cumulative distribution functions and conditional copulas of the trivariate HAC werederived. A goodness-of-fit test for trivariate copulas was conducted. This kind of trivariateHAC was used for draught analysis.The main conclusions are shown as follows.1. The distribution of monthly precipitation series belongs to heavy-tailed distribution,and the tail-index estimation theory is suitable to measure its tail behavior. All of thecommonly-used Hill estimator, Pickands estimator and moment estimator can estimate theextreme index and the tail index conveniently. Sum-plot was used for selecting the best k, andwas justified its good effect and high accuracy.2. The formulas of nonidentically distributed hydrologic data have definite physicalsignificance and strict mathematical foundation. Case studies show that this method can befitted by arbitrary common distributions and is convenient to use.3. Both method of partial probability weighted moments and method of higher-orderprobability weighted moments can improve the fitting effect of larger value of flood dataeffectively, and can significantly reduce the error of design values. The errors of design valuesthat calculated using PPWM for GEV distribution and higher-order PWMs for P-IIIdistribution are relatively smaller. The errors of design values that calculated usinghigher-order PWMs for GEV distribution are relatively larger. However, the calculation ofhigher-order PWMs for GEV distribution is extremely simple.4. Regarding annual runoff series, neither method of partial probability weightedmoments nor method of higher-order probability weighted moments can improve the fittingeffect of larger value of runoff data. Method of PWMs for P-III distribution can fit the annual runoff data quite well.5. In estimating the parameters of P-III distribution based on Bayesian method, differentsampling method has some influence on the performance of the MCMC method. Fast inconvergence rate, high in computational efficiency and good effects in parameter estimation,AM algorithm was much better than MH and DR algorithm.6. Trivariate hierarchical Archimedean copulas that combine Clayton copulas with Frankcopulas can describe the joint distribution of drought duration, drought severity and severitypeak. Comparing with the symmetrical trivariate Archimedean copulas, trivariate HACreflected the different dependence structures among draught variates more reasonably, andhad more flexible structure. This kind of copulas describes the joint distributioncharacteristics of drought variates comprehensively.