The Method Of Hydrology Frequency Calculation Based On Polynomial Normal Transformation

Hydrology frequency calculation aims to use existing hydrological data to analyze and calculate the quantitative relationship between hydrological design value and return period,and provide a scientific basis for water resources planning and utilization and water conservancy project design management.The polynomial normal transformation(PNT)method is a high-performance hydrological frequency calculation method.The method does not need to assume the distribution line type of the original hydrological variables during analysis and calculation.The transformation method is simple and effective,and has good versatility.Currently,the parameter estimation methods used in the PNT method mainly include the Product-moment(PM)method,the L-moments(LM)method,the Least-square(LS)method and the Fisher-Cornish(FC)asymptotic expansion method.Although scholars have compared and analyzed the overall performance difference between the PNT method and some hydrological frequency calculation methods,there is a lack of comparison of the application of the four parameter estimation methods in the actual flood frequency calculation research.Furthermore,these methods need to derive a great number of formulas when calculating and the steps need to be carried out gradually according to different variables which cause the calculation efficiency is not high.Based on the above problems,this article summarizes the calculation formulas of the four traditional parameter estimation methods of the PNT method for continuous samples and discontinuous samples containing historical floods.Besides,this article introduces particle swarm optimization(PSO)algorithm,differential evolution(DE)algorithm and genetic(GA)algorithm three kinds of intelligent optimization algorithms and establish intelligent optimization algorithm-polynomial coefficient solving model.The annual runoff sequence of 16 hydrological stations and the annual maximum peak discharge sequence of30 hydrological stations in the Yellow River Basin and the Yangtze River Basin are selected as the research objects.And the Root Mean Square Error criterion(RMSE),Absolute value and minimum deviation criterion(ABS),Akaike Information Quantity Criterion(AIC),Probability Point Distance Correlation Coefficient Criterion(PPCC)and Correlation Coefficient(R-square)5 kinds of error evaluation standards are selected to systematically analyze the normal transformation effect and fitting situation of PNT method under 7parameter estimation methods.Besides,by comparing with the P-? distribution and GEV distribution,we comprehensively evaluate the application of PNT method in hydrological frequency calculation and analysis in the study area.The main conclusions of the research are as follows.(1)Based on the principles of four traditional parameter estimation methods,we studied the parameter estimation formula and design value calculation formula of PNT method for continuous samples and discontinuous samples containing historical floods.Based on the detailed introduction of the principles of the three intelligent optimization algorithms of GA,DE and PSO,GA algorithm-polynomial coefficient solving model,DE algorithm-polynomial coefficient solving model,and PSO algorithm-polynomial coefficient solving model are established respectively.(2)Through the Monte Carlo test,the statistical performance and design value accuracy of four traditional parameter estimation methods are systematically analyzed.The results show that among the four traditional parameter estimation methods of the PNT method,the unbiasedness and effectiveness of the LS method are the best.The unbiasedness of the FC method is only slightly inferior to the LS method,but its effectiveness is lower than that of the LM method and the PM method is the least unbiased and effective.(3)Based on the frequency analysis of the annual runoff sequence based on the PNT method,the research results show that among the four traditional parameter estimation methods of the PNT method,the normality test result and the fitting effect of the LS method is the best.In the intelligent optimization algorithm,the results of GA method and PSO method are the best.In general,the annual runoff frequency curve obtained by the PNT method has a better fitting effect on each part of the empirical point data.But among the two types of parameter estimation methods,the stability and effectiveness of the intelligent optimization algorithm are better than the traditional estimation methods.(4)Based on the PNT method,the frequency analysis of the annual maximum peak discharge sequence considering historical floods is carried out.The research results show that among the four traditional parameter estimation methods of the PNT method,the normality test result and the fitting effect of the LS method is still the best.In the intelligent optimization algorithm,the normality test results of GA and PSO method are better,but the rare flood design value obtained by GA method is quite different from other methods,and the stability is not as good as PSO method.In summary,the PSO method has a better fitting effect.The annual maximum peak discharge frequency curve obtained by the PNT method has a better fitting effect on the middle part of the empirical point data,but the LS,GA and PSO methods are better for the upper part of the empirical point data.And the design value of the rare flood is more beneficial to the safety of water conservancy projects.In general,among the two types of parameter estimation methods of the PNT method,the stability and effectiveness of the intelligent optimization algorithm are better than those of traditional estimation methods.(4)Comprehensive analysis of the results of Monte Carlo test,normality test,fitting analysis and error analysis,the results shows that the PNT method has a higher estimation accuracy of hydrological design values and its fitting effect is better than that of P-?distribution and GEV distribution.When the composition is complex or the overall distribution is difficult to determine,the PNT method will be an excellent estimation method.