1368-1948年陇中地区干旱灾害时间序列分形特征研究

采用标度变换法对陇中地区1368—1948年(明代至新中国建立前)各等级干旱灾害及旱季序列的时间分维值进行测算。并深入讨论了各旱灾序列时间分维与其线性特征之间的关系,以及分维随时间演进的变化趋势。对4个干旱等级、4个旱季序列的分维值进行研究,发现:①干旱灾害具有客观的分形结构,其时间序列是具有自组织性质的,干旱灾害是自组织系统;②各等级干旱灾害有自己的时间重演律,干旱灾害越轻,无标度区越宽,分维值越高,短周期更明显;③各旱季分维值与其发生频次成正比;④整个时期的动态总体上表现为:各旱灾序列(旱灾、大旱灾、中度干旱、春旱及伏旱)分维值逐渐增大,旱灾发生趋向混沌无序,旱灾系统趋向平衡态,稳定性减小;⑤分形分析法与常规统计方法之间有着内在联系。

Characteristics of Fractal Dimension of Drought Disaster Sequences from 1368 to 1948 in Longzhong Area

Based on the fractal viewpoint, the characteristics of different ranks and seasonal drought disasters sequences which is from 1368 to 1948 in middle Gansu province are studied by using box counting algorithm. Then discuss the relation between temporal fractal dimensions and linear features in depth. Finally, the dynamic variation of the temporal fractal dimension is analyzed. It is found that: ①Drought disaster is an objective fractal structure, the time series have self-organizing nature, drought disaster is self-organizing system;②The drought disaster lighter, the time fractal dimension bigger, the scaling range broader and the time span oscillations shorter. ③The seasonal drought disaster′ temporal fractal dimension increases with the increasing of it is frequency; ④Mainly temporal fractal dimension of these sequences increases during the 581 years, and drought disasters tend to turbulence, the drought disaster system tends to balance and the stability drops. ⑤There is internal relationship between fractal analysis and conventional statistical methods.