Flood Risk Measurement Based On Copula Function And Its Error Analysis

At present,the flood disaster is particularly serious in China,so it is imperative to analyze and manage flood risk effectively.In this paper,based on three common Archimedean Copula Functions,the two-dimensional and three-dimensional joint distribution functions of maximum flood peak,3-day flood volume and 7-day flood volume are constructed respectively in Weihe River Basin,and the multivariate return period and its corresponding risk rate are discussed to quantify flood risk,The error of Copula function is analyzed from the structure and parameters of Copula function.The main conclusions are as follows:(1)The multivariate co-occurrence return period is greater than the joint return period,and the corresponding joint risk rate is greater than the corresponding co-occurrence risk rate;The joint risk and co-occurrence risk of Huaxian station are higher than those of the other three stations,which indicates that preventive measures should be taken for the higher risk of Huaxian station.(2)According to the conditional return period and conditional risk rate of two variables and three variables,when a certain flood peak occurs,the probability of3-day flood volume and 7-day flood volume decreases with the increase of its magnitude;With the increase of flood peak magnitude,the risk rate of 3-day flood volume and 7-day flood volume increases gradually,especially when the flood peak increases from 5-year return period to 20-year return period;In addition,the conditional risk rate of two variables is greater than that of single variable.(3)Different copula function structure will bring some uncertainty to the flood risk analysis results,but the performance of different copula is different;With the increase of flood peak and flood volume,the relative error of Clayton copula’s estimation of joint return period and joint risk rate decreases,while the relative error of co-occurrence return period,co-occurrence risk rate,conditional return period and conditional risk rate increases,while the uncertainty of Gumbel copula’s estimation of all risk measures increases;In addition,compared with joint return period,joint risk rate,conditional return period and conditional risk rate,the relative error of two copula structures for co-occurrence return period and co-occurrence risk rate estimates is larger.(4)Different parameter estimation methods will also bring some relative errors to flood risk analysis results.For the estimation of joint return period and joint risk rate,the relative error caused by MPL and mom did not change significantly with the increase of return period;For the estimation of co-occurrence return period,co-occurrence risk rate,conditional return period and conditional risk rate,the relative error caused by the two methods increases with the increase of return period;The relative error of mom method is larger than that of MPL method;In addition,the uncertainty of flood risk analysis results caused by parameter estimation method is far less than the influence of Copula function structure.