| Both low water and flood belong to the category of extreme hydrology,but low water is not got more attention due to the fact that it occurred less drastic than flood and the measured data are short.With the changes of the global climate,drought frequently happens.Therefore,the frequency calculations of low water runoff are more significant.However,most frequency analysis methods only have a good fitting effect on long sequence,and the frequency calculations of hydrological samples with zero values are not satisfactory.The impulse response of the kinematic diffusion(KD)is a new approach of solving the frequency calculation of hydrological samples with zero values.The researches show that KD model can be chosen as a distribution model to calculate hydrologic frequency.In this paper,derived the probability density function of KD model and analyzed the characteristic of it.The formula of parameter calculation of the moment method,the maximum likelihood method and the probability weight moment method are obtained respectively based on KD model.The confidence interval formula of KD model based on the moment method and the maximum likelihood method are deduced.First,Guanzhong area in Shaanxi Province was selected as the research object,and its monthly precipitation data for December was used to calculate the frequency.Then,by using intuitive graphical analysis method and a quantitative evaluation method,the fitting effects of three parameter estimation methods of KD model,the frequency proportional method and the type II multiplicative distribution method are evaluated.And the applicability of KD model in the frequency calculation of hydrological samples with zero values is studied.Finally,the confidence intervals of the design values under the 95% confidence level are calculated based on the moment method and the maximum likelihood parameter estimation method,and the uncertainty of the design values calculation based on the two parameter estimation methods are compared.The main conclusions of the study are as follows:(1)The graph shape and maximum value of the probability density function of KD model are influenced by the parameters ? and ?.When one parameter is fixed and another one parameter increases,the maximum value location of the probability density function graph is shifted to the right and the maximum value gradually decreases.(2)The parameter estimation formula of the moment method,the maximum likelihood method and the probability weight moment method of KD model are derived to estimate the KD model parameters of the research area.The results show that the value of parameter ? is obtained by the probability weight moment method is larger than those obtained by the moment method and the maximum likelihood method.On the contrary,the parameter ? deduced by the probability weight moment method is the smallest of the three parameter estimation results.The maximum value of parameter ? and the minimum value of parameter ? are obtained when the parameters are estimated based on the probability weight moment method.(3)The monthly precipitation series in the study area is fitted based on the KD model,and the fitting effect of KD model is evaluated by visual graphic analysis and quantitative evaluation.The results show that the KD model has a better fitting effect on the monthly precipitation sequence,but there are some differences in the fitting effect of the three parameter estimation methods.As a whole,the best fitting effect is obtained based on the probability weight moment method.The parameter estimations of the moment method and maximum likelihood method have different fitting effects on the upper and lower part of the frequency curve.The moment method is superior to the maximum likelihood method for the upper part of the frequency curve,while the KD model of the maximum likelihood parameter estimation is better than the moment method for the lower part.(4)The fitting effects of KD model,frequency proportion method and II multiplicative distribution method are evaluated respectively by visual graphic analysis and fitting effect quantitative evaluation method.The results show that KD model can be applied in the frequency calculation of precipitation series with zero values.Among the three frequency calculation methods,KD model has the best fitting effect on the monthly precipitation sequence in the study area,and the frequency proportion method has the worst fitting effect.(5)KD model is chosen as the frequency distribution model,and the confidence interval of 95% confidence level of the design value is estimated based on the moment method and the maximum likelihood method The results show that compared with the maximum likelihood method,the confidence interval estimated by the moment method is shorter in the upper part of the frequency curve,which indicates that the moment method has low uncertainty in the acquisition of the design value.However,the confidence interval of the moment method is longer in the lower part,which indicates that the moment method is more uncertain to calculate the design value. |
