基于Copula相依函数的安徽省气温与降雨量相关性研究

INTERACTION OF TEMPERATURE AND RAINFALL IN ANHUI PROVINCE BASED ON COPULA FUNCTION

当前全球气候变暖大背景下,气温和降雨量的交互作用引致农业气象灾害频发,给农业生产造成破坏性风险损失,因此探讨气温与降雨量之间的动态相依关系尤为重要。搜集安徽省24个气象观测站1980~2014年的气温与降雨量日数据,对原始数据进行矩平均处理,使两组数据列满足独立同分布的要求。采用非参数核估计的方法确定气温与降雨量的边缘分布。根据降雨量和气温的均匀分布散点图和频数分布直方图可知,安徽省气温和降雨量之间呈现一定程度的负相依关系,即图形中表现出气温与降雨量的上下尾之间的对称性。综上分析,选择可以刻画两个变量具有上下尾对称关系的Copula函数对气温与降雨量的相依关系进行拟合,最终在平方欧式距离最小的原则下选定二元t-Copula函数做出气温与降雨量之间的联合概率密度函数图。研究结果发现:1据安徽省气温与降雨量联合概率分布可知,当降雨量上升时,气温下降;或气温上升时,降雨量会下降,气温与降雨量之间呈现为中等负相关关系(–0.280)。2极值相关性方面,从t-Copula密度函数图和上下尾相关系数看,安徽省气温与降雨量在极值方面具有较为明显的相依关系,表现为当气温和降雨量超过正常范畴时,二者相依关系从负相关转变为正相关,此现象多出现在极端气候条件下,例如极端高温和大暴雨时气温与降雨量的正相依性。

Under the background of global warming, the interaction of temperature and rainfall makes the agricultural meteorological disasters occur frequently, causing destructive risk to agricultural production. In this paper, we collected daily data of rainfall and temperature observed at 24 meteorological stations in Anhui Province in the period of 1980-2014 and collected the monthly average rainfall data of each station. We calculated the moment average rainfall of each station by subtracting average monthly rainfall data from the monthly raw rainfall data divided by the average. Finally, we used the average of moment average rainfall of 24 stations as rainfall data of Anhui Province. According to the rainfall frequency histogram, the distribution of rainfall data was asymmetric, showing some level of right-skewness. According to the temperature frequency histogram, the distribution of temperature data was basically symmetric while presenting ＂peak thick tail＂ features. Therefore, we determined the marginal distributions of temperature and rainfall data through non parametric kernel estimation method. The frequency histograms of rainfall and temperature showed that there was a negative correlation between them, suggesting that the diagram presented the symmetric upper and lower tails of rainfall and temperature. Based on this symmetry, we selected three types of Copula functions, i.e., normal Copula, t-Copula and frankCopula. Finally, based on the principle of minimum squared Euclidean distance, bivariate t-copula function is chosen to draw the probability density function of rainfall and temperature. The results showed that from the perspective of joint probability distribution of temperature and precipitation in Anhui Province, when the rainfall was rising, the temperature dropped; or when the temperature was rising, the rainfall decreased. There was a medium negative correlation（–0.280）between rainfall and temperature. From the perspective of probability density function diagram of t-copula and upper and lower tail correlation coefficient, the temperature and rainfall in Anhui Province had a relatively obvious dependence relation in extreme, which means, when the temperature and rainfall were beyond normal range, their dependence changed from negative correlations to positive correlations. This phenomenon would occur more in extreme weather conditions,such as extreme high temperature or rainstorm.