胶东半岛丘陵区冲沟沟长曲折度分形研究  

Study of the Fractal Curvature of Gully Length in the Jiaodong Peninsula

作　　者：王涛 何福红[1] 顾丽娟[2] 张振华[1] 吴孟泉[1] 

机构地区：[1]鲁东大学资源与环境工程学院,山东烟台264025 [2]海军航空工程学院基础部,山东烟台264001

出　　处：《水土保持研究》2017年第4期27-31,共5页Research of Soil and Water Conservation

基　　金：国家自然科学基金(41471223);山东省自然科学资助项目(ZR2014JL026);烟台市科技计划项目(2015ZH091)

摘　　要：冲沟沟长的分维数和分形曲折度是表征沟道形态复杂程度的重要指标。以栖霞市庵里水库西缘流域为研究区,基于SA地形指标模型阈值法提取冲沟系统,测算冲沟沟长盒维数,研究地形参数同冲沟沟长分维和沟长分形曲折度间的相关性,并建立模型模拟沟长分维数及分形曲折度,并对模型进行检验。结果表明:(1)流域内沟长分维数和曲折度同平均坡度、地表粗糙度、剖面曲率和沟壑密度具有极显著的线性关系,沟长分维数和沟长分形曲折度可以作为评价区域地形形态特征的综合指标。(2)建立了沟长分维数和曲折度单因子模拟模型,其中沟壑密度单因子模型,模拟沟长分维数和分形曲折度的相对误差分别为0.007 8%和0.025 2%,精度高,可用于冲沟沟长分维数和曲折度的快速估算;坡度、剖面曲率、地表粗糙度构建的单因子模型模拟精度相对较低。The fractal dimension （FD） and fractal curvature （FC） of gully length are the indicators of the shape complexity of a gully. The west watershed of the Anli Reservoir in the Jiaodong Peninsula was selected as the study area, the gully heads were located, and the gully lengths were derived using the slope area index （SA） model. The FDs of the study area were calculated by the box counting method. The relationship between the FDs and the topographic parameters was analyzed, and the single-factor models were constructed to estimate the FD and FC of gully length, which were tested in an examined watershed. The results showed that. （1） the ravine density, surface roughness, profile curvature, and terrain average gradient were found to have significant positive correlation with the FDs of gully length in the study watersheds, and the FD and FC of gully length were two comprehensive indicators of topographic morphology; （2） among the single- factor models for estimating FD and FC, the models with the ravine density single factor can be used to quickly estimate the fractal dimension and fractal curvature of gully length with higher accuracy, and the relative errors of gully length fractal dimension and fractal curvature are 0. 007 8% and 0. 025 2%, respectively. The models with other single factors, such as slope, plan curvature and surface roughness, are not suitable for estimating the fractal dimension and fractal curvature of ~ully length, and they have low accuracy.

关 键 词：沟谷 SA模型 盒维数 分形曲折度 回归分析 

分 类 号：K909[历史地理—人文地理学]