A Study Of Short-duration Rainstorm Formula Based On Different Sample Selection Methods

With the acceleration of climate change and urbanization,problems such as urban waterlogging and mountain torrents in small river basins caused by short-duration rainstorms need to be solved urgently,which pose a serious threat to people's life and property security and economic and social development.Scientific,reasonable and accurate formulation of rainstorm formula is the basis of solving flood and waterlogging disaster,which can objectively reflect the law of urban rainfall change,provide basis for urban drainage system planning and design,and is of great significance to the prevention and control of rainstorm disaster and urban sustainable development.This paper is based on the data of minuter-by-minute rainstorm of 39 meteorological stations in the weihe river basin,shaanxi province,from 1981 to 2017,covering a total of 37 years.11 short duration statistical periods(5min,10 min,15min,20 min,30min,45 min,60min,90 min,120min,150 min and 180min)were selected using the minute-by-minute sliding statistical method.Three sample selection methods(annual maximum method,annual several samples method and annual super-large value method)were adopted.13 kinds of frequencydistribution linestyle commonly used at home and abroad are selected.On the basis of the theoretical frequency analysis of short-duration rainstorm in the research area,the formula of rainstorm was deduced based on the measured rain intensity and frequency distribution,and the rationality of the formula and parameters was analyzed.The main research contents and results are as follows:(1)Study on frequency distribution of short-duration rainstorm.The L-moment method was used to estimate the parameters of 13 frequency distributions(normal distribution(NOR),two parameters of the lognormal distribution(LN2),three parameters of lognormal distribution(LN3),Pearson type ? distribution(P-?),logarithmic Pearson type ? distribution(LP-?),two parameters ?(G2)and exponential(EXP),generalized extreme value distribution(GEV),the gumbel distribution(GUM),the Weibull distribution(WEL),generalized pareto distribution(GEP),Logistic distribution(LGS)and generalized Logistic distribution(GLO)).The optimal frequency distribution of short-duration rainstorm under three different sample selection methods were studied using three evaluation criteria: probability distance correlation coefficient(PPCC),quasi-optimal sum of squares(RMSE)and quasi-optimal absolute value criterion(MAE).The results show that: Sampling by annual maximum method,the number of rainstorm sequences in each station and the number of rainstorm sequences in each statistical period with LP-? as the first dominant distribution was much higher than that of other distributions.Sampling by annual several samples method and annual super-large value method,the number of rainstorm sequences in each station and the number of rainstorm sequences in each statistical period with GEP as the first dominant distribution was much higher than that of other distributions.Under different sample selection methods,GEP distribution showed obvious advantages in two aspects: the most suitable quantity of rainstorm sequence and the most suitable quantity of station,with stronger adaptability.The quasi-optimal sum of squares(RMSE)method is more consistent and the optimal distribution is more concentrated when selecting the frequency distribution of shortduration rainstorm.(2)Rainstorm formula based on different paths.Based on the actual rainstorm intensity and the calculated rainstorm intensity by the optimal frequency distribution,the rainstorm formula under different sample selection methods were solved by utilizing LevenbergMarquart algorithm and genetic algorithm.By comparing the two rainstorm formula derived paths,it is found that the formula based on actual rain intensity has less error and higher accuracy in fitting the actual rain intensity samples than the formula based on the optimal frequency distribution.(3)Comparison and analysis of rainstorm formula with different sample selection methods.From the aspects of the fitting error of rainstorm formula,the safety and economy of engineering practice,the independence,randomness and universality of sample selection method,the rainstorm formula derived by different sample selection methods was compared and analyzed.The annual maximum method has obvious advantages over the annual several samples method and the annual super-large value method.Therefore,the annual maximum method is selected as the best sample selection method to deduce the rainstorm formula.(4)Rationality analysis of rainstorm formula and parameters.Compared with the current formula,the new formula can better reflect the characteristics of current rainstorm.Isoline maps were drawn for 39 stations in the study area by using the annual maximum method based on the parameters of rainstorm formula derived from the actual rain intensity.It can be seen from the figure that each parameter has a certain regional distribution regularity.