基于联合熵的旱涝空间场关联性研究

利用一种信息熵空间场相关性测算方法，给出一个具有统计学中相关系数性质的离散空间场相关指数，探讨中国旱涝事件发生的内在规律及其空间分布情况.利用联合熵的概念研究了1470—2000年各年份旱涝分布之间的关联性，通过计算实际和随机旱涝分布场的联合熵的概率密度分布和联合熵矩阵的本征值，发现实际旱涝分布场各年份之间的关联性同随机旱涝分布场相比有明显差别，是非随机的，具有一定的内在相关联系.各年份旱涝分布情况同其余年份之间的平均联合熵，表征了该年份的旱涝分布情况同其他年份旱涝分布之间的关联程度，其值越大，相关越强，反之亦然，气候状态相似程度以1820年为界有明显的准周期特征，周期尺度维持在113年左右，周期强度也较稳定；其后从1820—2000年，准周期的尺度从113年增大至约130年，强度也比前一时期有所下降；对于68年尺度的准周期，在1595—1820年期间比较明显，并且周期尺度从开始的61年上升至81年，周期强度保持稳定，而在其余时期，该尺度均没有明显的准周期特征.关键词：旱涝指数联合熵空间场相关

Research on the correlation of drought/flood spatial fields by using joint entropy

Using a method of calculating the entropy based on the relativity of spatial fields to give a correlative index having the statistic characteristic of discrete spatial fields, we discuss the inherent rule of drought/flood and their spatial distributions in China. The result gives the associations of drought/flood distributions from 1470 to 2000, and shows that the actual relativity of drought/flood distributed fields is relative and not stochastic, being different from the random distributed fields, by calculating their entropy and matrix latent values. The every year's entropy shows the degree of the year's association with other ones. The greater the entropy is, the bigger the degree is, and vice versa. The similitude of climate state has a steady and obvious quasi-periodicity before 1820, whose size is about 113 years. After 1820, the size adds up to 130 years and the intensity is weakened. Another steady quasi-periodicity is 68 years, which is obvious from 1595 to 1820, and its size is changed from 61 years to 81 years. In other periods, the 68-year periodicity is not found obviously.