Research Of Joint Distribution And Return Period On The Combination Of Flood And Tide For Tide Affected River Based On Maximum Entropy-Copula

In hydrological calculation,hydrological frequency calculation is an important area of research.The researchers concluded the change of hydrological event in the future based on the measured hydrologic data.There is a variety of methods to estimate the linear parameter of hydrological variables,but the traditional parameter estimation methods have some deficiencies.Entropy is to describe the characteristics of material system,Copula is a joint distribution function.It has extremely strong compatibility and extensive applicability.This paper based on the hydrological variable frequency calculation,using the maximum entropy principle and Archimedean-Copula function in Shenzhen Baoan distriction as the research object,calculated the appropriate marginal distribution functions and suitable copula function,established the rainfall-tide joint probability distribution model,risk probability model,return period distribution model in the study area,designed the value of different rainfall-tide combination probability and th return period value has also be carried on the analysis.The results of the analysis for the study area could provide a scientific basis for engineering construction,water conservancy project management,flood control planning,etc.This paper's main conclusions are as follow:(1)The paper summarized the research progress of the entropy in the field of hydrology,pointed out that the application of the maximum entropy principle in hydrological variable frequency parameter estimation could make the results more reasonable and objective.It could also effectively reduce the man-made calculation error.At present our country for hydrological variable frequency distribution fitting adopt P-? distribution curve.This paper applied the maximum entropy principle to the P-? distribution curve parameters,drew the theoretical frequency curve,and this way would accurately understand the changes in hydrological events.(2)Based on the four kinds of Archimedean Copulas function fitting test,Frank Copula was better than other three kinds of Copulas in expressing the relationship of the annual maximum tidal level and the corresponding 24-hour rainfall,annual maxima of 24-hour rainfall and tidal level.(3)The model about the correlation of the annual maximum tidal level and the corresponding 24-hour rainfall,annual maxima of 24-hour rainfall and tidal level was established.Maximum Entropy-Frank Copula was used to build conditional waterlog prevention risk model,simultaneous risk model,joint risk model and encounterd risk model.The results showed that the simultaneous risk probability of two kinds of combinations was less than the single variable frequency;Compared to the correlation between the annual maximum tidal level and the corresponding 24-hour rainfall,a similar correlation was between the annual maxima of 24-hour rainfall and tidal level.In the actual engineering design,Improving the tide level(rainfall)standard could reduce the risk probability of the two variables.(4)The definition and calculation of return periods and design values are difficult.In this paper,by constructing the joint distribution of annual maximum one-hour rainfall and the corresponding tidal level,we introduced the definition of Kendall return period and calculation methods,pointed out the differences in the identification of dangerous regions between Kendall return period and traditional return period.The data analysis showed that the definition of Kendall return period is more precise.The design value based on Kendall return period was reasonable.It could provide useful imformation for risk analysis of waterlogging.