湖泊岸线分形特征及其生态学意义

The fractal character of lake shoreline and its ecological implica-(tion)

应用分形理论中的计盒维数、岸线长度与面积关系对保安湖及江汉平原一些湖泊的湖岸线长度和湖泊面积进行研究 ,借以对上述两个物理性质进行准确的特征化。此外还运用 Korcak法则对湖北省湖泊面积分布进行研究。结果可用于预测湖泊岸线长度如何随着湖泊面积而变化 ,以及预测不同大小的湖泊面积分布。探讨了湖岸形态和大型水生植物生物量间的关系 ,并讨论环境和人为因素对湖泊岸线的影响 ,以及湖泊岸线变化对湖泊生物的影响。

Based on the two physical properties lake perimeter and area, Baoan Lake and 30 other lakes in the Jianghan plain were studied, applying the shoreline development index (SDI), the box-dimension, the equation for shoreline length-area and it's transform. The shoreline box-dimension (SBD) was applied to each lake, while equation for shoreline perimeter-area (SPA_N) and its transform (SPA_T) treated 31 lakes altogether. We also used Korcak's Law to all the lakes in Hubei Province. The results showed that the average of SDI of the 31 selected lakes was 4.50, with a standard deviation of 2.088; the Shangjin Lake had the highest SDI of 11.33, and the Wangmu Lake had the smallest SDI of 1.68. The average of SBD of the 31 lakes was 1.219, with a standard deviation of 0.078; the Shangjin Lake had the highest SBD of 1.419, and the Dachang Lake had the smallest SBD of 1.096. By using the equation of perimeter-area (ln P=c+blnA,and SPA_N=2b) and its transform (lnA=c+blnP,and SPA_T=2/b), the 31 lakes had a SPA_N of 1.3998 and a SPA_T of 1.6956 with equations regression coefficients (R^2) higher than 0.80. This indicates that the shoreline of these lakes exhibited a self-similarity. The value of SPA_N was close to the mean of SBD of 31 lakes (1.219), and it can be used to forecast how the shoreline length varies according to the changes of lake area. Based on Korcak's Law and the area distribution of lakes in Hubei Province, the integrated fractal dimension of area distribution for lakes was 1.52, which showed that the lakes in Hubei Province had a higher self-similarity and more complex shorelines during the 1980s. By a stepwise regression analysis between macrophyte biomass in some lakes of Hubei Province and four morphological indexes (SDI, SBD, Area, Perimeter), we found that SDI and SBD are the influencing factors of the biomass. The result showed that the higher the shoreline complexity of a lake is, the higher the SBD of a lake gets. In order to protect the biodiversity of lake ecosystems, it is essential to keep the shoreline in a natural status.