基于矩阵理论的全球气温的时空关联性研究

Temporal and spatial correlation analysis of global temperature data based on the correlation matrix theory

采用1948—2005年NCEP/NCAR全球气温和随机序列分别构建气温关联矩阵和随机关联矩阵并进行比较,发现气温关联矩阵既存在关联"噪声",又存在真实关联;格点气温序列之间既存在临近格点间的短程关联,又存在如厄尔尼诺、三大洋暖池等区域格点间的远程关联。不同时间尺度,这两种关联的表现各有差异,1—10天等小尺度情况下,格点间的关联以短程关联为主;15天及以上尺度短程关联比例显著下降,长程关联有所上升。对关联矩阵和随机关联矩阵求解本征值和本征矢量发现,格点气温序列之间的关联信息主要包含在几个较大本征值所对应的本征矢量中,且格点气温序列在这些本征矢量上的投影能够在一定程度上体现全球气温变化的整体特征。此外,格点气温序列的关联性在时间和空间上均存在显著的变异性,主要表现为1950—1956年、1972—1977年和1996—2000年3个时段相对较高,而1978—1982年和1991—1996年则均值相对较低,存在显著的准10—20年周期振荡;关联系数的空间分布在上述两类尺度下均表现为沿纬向呈准带状分布,但1天尺度的纬向平均具有较好的对称性,由于海陆差异的原因,15天尺度的纬向对称性相对较差,而15天尺度的经向平均具有一定的准对称性。

The temperature correlation matrix C and random correlation matrix R are constructed based on the NCEP/NCAR temperature reanalysis data and random series with the characteristics of these two matrixes analyzed in this paper.The results show that there are genuine correlations as well as the correlation‘noise＇ existing in the temperature correlation matrixes. These genuine correlations can be divided to two parts,one is the correlation between the nearest and next-nearest points, called the short distance correlation（SC）;the other is the long distance correlation（LC）,i.e.the correlation between the El Nio area and other remote areas such as the warm pools.For the different scales,these two kinds of correlations show different features.On the 1-10 d scale,the SC is more important than the LC,while on the 15 d and larger scales,the SC and LC both play an important role in the temperature correlation matrixes.Most correlation information is contained in several eigenvectors with larger eigenvalues,and the projection of the global temperature series on these eigenvectors will show,in some cases, the whole characteristics of global temperature changes.Besides,the temperature correlations have significant temporal and spatial variabilities：for example,the correlation is better during 1950-1956,1972-1977 and 1996-2000 than during 1978-1982 and 1991-1996.On the 1d scale,the correlation shows however a good latitudinally symmetric spatial distribution, but it is relatively worse on the 15 d scale owing to the ocean-land difference between the Northern and Southern Hemisphere. In contrast,on the 15 d scale,the correlation shows a longitudinally symmetric distribution.