Truncated Distributions And Their Applications In Hydrological Frequency Analysis

Hydrological frequency analysis is a major part of hydrology contents.Its precision is directly related to the investment and security of hydraulic engineering.In practice,hydrological frequency analysis is usually used to predict the value of exceedance-probability event in large return period.In this dissertation,much attention was paid to study truncated distributions and their applications in hydrological frequency analysis,in addition,comparison with higher-order linear moment(LH moments).This dissertation aimed to improve the design values' accuracy of large return period,and provide some reasonable reference and data support for design and operation of water conservancy projects.This dissertation summarized the present researches progress about hydrological frequency analysis and the application of truncated and censoring distribution both at home and abroad,and explored the application of truncated distribution and LH moments in hydrological frequency analysis.The main conclusions of this dissertation are as follows:(1)Comparative study of truncated and censoring distribution.In practice,the distinction between the mechanism of the truncated distribution and the censoring distribution is not strict.There is a certain difference between the probability density function,the accumulation function and the sample moment calculation.When calculating the sample moment,the truncated part should be assigned as truncated threshold,while censoring is zero.(2)For Pearson type three distribution and GEV type distribution,the derivations of formulas to truncated linear moments and LH moments by means of transformation of variables and mathematical integration were given,respectively.Monte Carlo experiment was conducted to illustrate the statistical properties.Monte Carlo experiment was employed to analyze the statistical properties of parameter estimation methods.Under different truncated levels and orders,the statistical properties truncated moments,linear moments and LH moments performed well.With truncated level and order increasing,design values have lower bias,in some case,when return period increased,the improvement is more apparent.And the increase in sample size is useful for improving the accuracy of the design value.(3)These methods above were applied to annual precipitation series from 37 meteorological stations in Guanzhong area of Shaanxi,and the fitting results were evaluated qualitatively and quantitatively by the sequence fitting curve and five evaluation criterion,which including probability point correlation coefficient test method(PPCC),quasi-optimal square sum criterion(MSE),quasi-definite qualitative coefficient test method(QD),quasi-optimal value criterion(MAE)and fitting error.Compared with the commonly used linear moment method,both truncated linear moments and LH moments can improve the fitting effect of larger value of the precipitation series,so they can be expected to improve the design precipitation's precision of large return period.Remarkably,not the biggest level or order liner moment has the most optimal fitting result.And taking into account the integral error,computer running time,measured sequence quality and other issues,the choice of the truncated level,linear moments should not be too big.In practice,the truncated level or order should be selected based on the actual sequence length and sequence quality.(4)Given GEV type distribution,research on comparative study of truncated method and LH moments based on fitting curve and the five evaluation criteria.Most of the optimal parameters estimation methods are truncated method,which showed that the truncated estimation method has some advantages in the application of some stations in the study area.Especially for the sequences which have suspicious extremes,the truncated method has a significant advantage.However,the formula derivation of LH method is simpler,and it needs a concrete analysis of specific situations.(5)Research on the dominant distribution type of study areas by comparative study of LH moments of GEV type distribution and P-? type distribution,and the results were evaluated by the sequence fitting curve and the five evaluation criteria.Different evaluation criteria had different optimal distribution type.In the study area,the most sequences preferred the P-? type distribution,which showed that P-? distribution and GEV distribution can be used to describe the annual precipitation sequence of each station in the study area,and P-? distribution has certain advantages.However,it needs a concrete analysis of specific situations.