基于GIS的Horton水系分维值估算——以韩江流域为例

GIS-based Estimation of Horton Fractal Dimension of Water System in the Case of Hanjiang River Basin

利用Arcgis平台及其Model Builder基于DEM(Digital Elevation Model,数字高程模型)提取系列阈值下的韩江流域及9个子流域水系,从低级到高级逐次移除低级河道,再统计各级河道信息,计算基于Horton定律的水系分维值。结果表明:韩江流域系列阈值下的分枝比稳定,长度比上下波动,分维值变化幅度大,平均分维值为2.21。当不统计最高级河道信息时,分枝比均值与整个河网的分枝比均值相同,长度比均值则变大,平均分维值为1.53。结合韩江9个子流域的河网结构、河道特征,观音桥、溪口、上杭、杨家坊、潮安子流域采用完整河网的统计方法,宝坑、河口、水口、横山子流域采用不统计最高级河道的方法,计算的分枝比平均值4.51,长度比平均值2.66,平均分维值1.54,与韩江整个流域不统计最高级河道时的河道特征和分维值较为一致。

Based on DEM, the Arcgis platform and its Model Builder are used to extract the water system in the Hanjiang River Basin and its nine sub-basins under a series of thresholds. The river channels of the lower levels were removed successively from the lower to the higher level, and then the data of each level were statistically analyzed for the fraetal dimension of the water system based on Horton＇s Laws. The results show that： under a series of thresholds, the branching ratios of the Hanjiang River basin are stable ; its length ratios fluctuated ; and its fractal dimensions varies in a large range, which averages 2.21. When the data of the highest level are not included, the average branching ratio is the same as that of the whole river network, while the average length ratio is larger and the average fractal dimension is 1.53. According to the structures of the river networks and the features of the channels in the nine sub-basins of the Hanjiang River, the data of the whole networks are statistically analyzed for Guanyinqiao, Xikou, Shanghang, Yangjiafang and Chaoan, while the data of the highest-level channels are not counted for Baokeng, Hekou, Shuikou and Hengshan. The results show that an average branching ratio of 4.51, an average length ratio of 2.66 and an average fractal dimension of 1.54, which are relatively consistent with the channel features and fractal dimension of the whole Hanjiang River Basin when its channel of the highest level is not counted.