杏子河流域地貌多重分形特征与传统地貌量化参数关系研究

Research on the Relationship Between Multi-fractal Parameter and Traditional Quantization Parameters of Geomorphology in Xingzi River Watershed

利用杏子河流域数字高程DEM,采用流域地貌多重分形模型及其实现方法,对杏子河流域中的12个子流域地貌多重分形参数——奇异指数分布范围Δα及其与传统地貌量化参数关系进行了研究。结果表明:杏子河流域地貌奇异指数分布范围Δα从上游至下游呈明显递减趋势,反应地貌形态变化自上游向下游复杂性逐步减弱;地貌奇异指数分布范围Δα与地表粗糙度、平均坡度、平均地形起伏度呈正相关,其关系可用线形函数描述,与流域主沟比降表现出负相关,与相对高差和沟谷密度之间没表现出明显的相关关系。将传统地貌量化参数逐步引入多元回归方程,回归方程的决定系数呈现递增趋势,结果表明:与揭示地貌形态某方面特征的传统地貌量化参数相比,地貌奇异指数变化范围Δα对揭示流域地貌整体特征的量化更具有全面性、概括性和综合性。本研究对于有效地解决地貌学中的复杂性问题,掌握各种地貌现象的特征及规律具有非常重要的意义。

Based on the digital elevation model （DEM） of twelve sub-watershed of the Xizi River watershed, the geo-morphological multi- fractal parameter, i.e., the range of singular index （△α） , is caleulated by using watershed geo-morphological multi-fractal model. Meantime, the relationship between the range of singular index （△α） and traditional quantization parameters which include surface roughness, average gradient, average relief amplitude, gradient of watershed, relative relief and gully density are analyzed. Range of singular index （ △α） obviously decreases from upstream to downstream in Xizi Rriver watershed, which suggests that the complexity of geo-morphological feature weakened gradually. There are positive linear relationship between range of singular index （△α） and surface roughness, average gradient and average relief amplitude. A negative linear relationship exists between the range of singular index （△α） and gradient of watershed. There is no obvious relationship between the range of singular index （△α） and the relative relief and gully density. The determination coefficients increase when gradually entering traditional quantization parameters into the multiple linear regressions between the range of singular index （△α） and traditional quantization parameters. Compared with the traditional quantization parameters of geomorphology, these results indicate that the range of singular index can fully quantify the variations of geomorphic feature in the watershed. The results in this paper are of great seientific significance to resolving the complex issues effectively and master the characteristics of various landforms in geomnrphology.