青岛港日最大降水量及其出现日期的联合统计分析

Joint Statistical Analysis of Maximum Daily Rainfall and Its Occurrence Date at Qingdao Port

以青岛地区近30年历年日最大降水量(R_Y)与其在该年中的出现日期(L_Y),以及各月的日最大降水量(R_M)与其在该月中的出现日期(L_M)的13个样本序列为例,基于4种二维Copula函数(Clayton Copula、Frank Copula、Gumbel-Hougaard Copula和Gaussian Copula)建立二维联合分布模型;通过假设检验和拟合优度评价,选取拟合较优的二维Frank Copula函数所构建的日最大降水量及其出现日期的联合分布模型,对(R_Y,L_Y)和各月(R_M,L_M)进行了详细分析。通过历年各月日最大降水量及其出现日期的联合统计分析,在一定联合重现期时,当日最大降水量给定某一重现值时,可以估计该值在一年中(或某个月份中)最可能的出现日期,为合理港口装卸作业给建设意见。

Qingdao is situated on the west shore of the Pacific, located at the beautiful shore of HuangHai, lied on the southern coast of Shandong peninsula and the exit of Jiaozhou bay. It is an important port and naval station in China, and hundreds of ships are in and out of the Qingdao port every day.Because Qingdao lies in the transition between thehumid subtropical andhumid continentalregimes, the weather is humid with clear four seasons and abundant in rainfall, especially concentrating in the summer. However, rainfall has a significant influence on the harbor operation. Therefore, it is necessary to conduct the research on the correlation relationships between maximum daily rainfall and its occurrence date. In this paper, takethe maximum daily rainfall(over the years and the month: RY, RM) and its occurrence date(cumulative days from 1st Jan: LY, cumulative days from 1stof every month: LM) series observed at Qingdao port for 30 a as an example to analyze the correlation relationship of maximum daily rainfall and its occurrence date.At first, the probability distribution: Pearson type III distribution and maximum entropy(ME) distribution are utilized to fit the marginal distributions of maximum daily rainfall(RY, RM) and its occurrence date(LY, LM), respectively. Then, based on four kinds of common bivariate Copula functions(Clayton Copula, Frank Copula, Gumbel-Hougaard Copula and Gaussian Copula), the bivariate joint probability models of(RY, LY) and(RM, LM) in Qingdao are constructed to analyze the correlation between these two variables. In these copulas, the parameter estimation of maximum likelihood estimation is used, moreover the goodness-of-fit assess of Pearson’s χ2 test and Root Mean Square Error(RMSE) method are applied to select better copula to construct bivariate joint probability model. Through the statistical calculation and result comparison, the conclusions are given as follows:(1) The Pearson type III distribution and maximum entropy(ME) distribution are applied to fit the marginal distributions of maximum daily rainfall(RY, RM) and its occurrence date(LY, LM) very well, respectively(2) Through the goodness-of-fit evaluation, Frank Copula as the optimal bivariate function is used to construct the joint distribution models of maximum daily rainfall and the occurrence date:(RY, LY) and(RM, LM).(3) On the base of the joint statistical analysis of maximum daily rainfall and the occurrence date, the most likely date can be determined for a certain return period, when the maximum daily rainfall is the given univariate return value, which can keep away from the big rainfall and provide reasonable guiding opinions for harbor operation.