Calculation Method Of Confidence Interval For Hydrologic Quantile

Hydrological phenomena are affected by multiple factors, include certainty factor and random factors, so it is a very complicated natural phenomenon. Coupled with the impact of human activities, these reasons will lead to uncertainty in the hydrological sequence. Uncertainty is an undeniable objective existence of hydrology and water resources system. Using hydrologic frequency analysis to calculate the hydrologic quantile, its reliability will decrease gradually with the increase of uncertainty, and the results may bring risks for project if they are used to planning and design of water conservancy project. Therefore, it is very necessary to analyze the uncertainty of the hydrologic quantile.This paper summarized the research progress of hydrological uncertainty at domestic and abroad,and the calculation method of confidence interval of hydrologic quantile is studied.The main research contents of this paper are as follows:(1) Derivation of the approximate variance formula and confidence interval formula of hydrological quantile based on the moment method and the maximum likelihood parameter estimation for GEV distribution and P-III distribution. Based on the MATLAB 2010 b platform, developing the program of the approximate variance and confidence interval of hydrological quantile for GEV distribution and P-III distribution.(2) Comparison and analysis fitting effect of GEV distribution frequency curve and PIII distribution by using the cumulative relative deviation square sum criterion.(3) The research object is the annual precipitation series of 35 weather stations in Guanzhong Area. Selected GEV distribution and P-III distribution as distribution model, calculating annual precipitation sequence hydrologic quantle and its 95% confidence interval for the research Area. Comparing the hydrologic quantile confidence interval length based on the moment method and the maximum likelihood method parameter estimation.(4)Selected the optimal estimation method of and the distribution model for annual precipitation series of each station in the research Area according to the length of hydrologic quantile confidence interval.Through the above research, we can obtain several conclusions are as follows:(1)The fitting effect of GEV distribution and P-III distribution is comparised by the cumulative relative deviation square sum criterion, the results show that selecting the GEV distribution as the distribution function is feasible for some weather station.(2)Using two model distribution, the empirical point of annual precipitation series are almost included within the scope of the two curves which are the upper and lower limit of hydrologic quantle confidence interval based on the moment method and the maximum likelihood method. The results shows that the confidence interval can be used to quantitatively analyze the uncertainty of hydrologic quantile.(3) Selected GEV distribution and P-III distribution as the distribution model, most stations using the maximum likelihood method to estimate the confidence interval length is less than the moment method to estimate the onfidence interval length under the same design frequency, only a handful weather stations are exceptions. It indicates that the confidence interval calculation based on the maximum likelihood method parameter estimation can reduce the uncertainty of hydrologic quantle more effectively.(4) According to the confidence interval length, Select optimal theoretical distribution of annual precipitation series for all stations in Guanzhong Region. There are 23 stations with a minimum interval length based on maximum likelihood method parameter estimation for P-III distribution, and the 12 other stations with a minimum interval length based on maximum likelihood method parameter estimation for GEV distribution.