| With the impact of global climate change and human activities intensified,floods have posed a serious challenge to the human's living environment.Therefore,to improve the accuracy of hydrological frequency calculation is of great scientific significance and application prospect for water conservancy project planning,design and management.In the case of selecting the distribution function,the estimation accuracy of the hydrological design value is determined on the selection of the method of calculating the plotting position.This paper reviewed the progress of hydrological frequency analysis at home and abroad in recent years,and systematically studies the unbiased plotting position calculation method of new hydrological sequence.Main research contents are given in the following:(1)Based on the principle of expected values of order statistics and unbiased plotting position,the statistical formula of the mathematical expected values of order statistics of P-? type distribution and generalized extreme value(GEV)type distribution is derived respectively.The expected values of P-? distribution order statistics is calculated by using the Gauss Laguerre numerical integration method and the double exponential transformation numerical integration method.The numerical integration of the double exponential transformation has the characteristics of fast and high precision compared with the Harter checklist.Basis on it,the fast and high precision method of calculation of P-? type distribution and GEV type distribution is recommended.(2)The mathematical of formula ofexpected values of order statistics of the GEV type distribution order statistics is derived by binomial expansion method,the mathematical expectation value of GEV type distribution order is calculated by using the cumulative form.(3)For the convenience of practical use,The plot position is generalized to approximate the unbiased plotting position formula by the linear regression method.the P-? type distribution approximation unbiased plotting position formula and existing formula such as the formula of Weibull formula,Blom formula,Gringorten formula,Cunnane formula and Nguyen formula Perform a goodness test by statistical test.The results show that the approximate of the partial plotting formula is better in statistical test and can be used for the calculation and calculation of hydrological frequency of P-? distribution.Similarly,In this paper,the new GEV type distribution approximation unbiased plotting position formula is used to test the goodness of fit,the GEV4 formula can be applied to the extreme ? and ? distributions.The GEV1 formula can be applied to the extreme type ? distribution.(4)A high-precision calculation method of drawing point position was used to establish the moving line optimization model and the model is applied to the precipitation sequence of 36 stations in Guanzhong area of Shaanxi Province.Distribution parameters of the P-? distribution and GEV-type distribution were obtained by optimizing fitting curve estimation.The best approximation of the unbiased plotting position formula was used to optimize fitting curve again and the optimal results of the approximate unbiased plot position formula were compared with the high precision numerical solution.The results show that it for the precipitation data of the study area,the optimal formula can be optimized by using the formula and the Nguyen formula to replace the high-precision numerical solution if the P-? type is used.The optimal results of GEV3 and GEV4 are smaller than those of high-precision numerical solution If GEV-type distribution line type is used.Finally,the statistical parameters of P-? distribution and the statistical parameters of GEV type distribution were used to the high-precision calculation formula of the position of the drawing points in each station which can calculate the numerical solution of the P-? distribution and the GEV-type distribution of the precipitation data in the study area. |
PDF Full Text Request