一种自适应定权地形复杂度模型

摘要

Terrain Complexity Index(TCI)is an important parameter in digital terrain analysis.Proper determina-tion of TCI would well serve terrain feature sampling theory,uncertainty analysis of digital terrain and hydrological analysis,etc.Most available topographic feature indexes scarcely arrive at an appreciable approximation for terrain due to poor inclusion of necessary physical factors into TCI. In this study,an integrated terrain complexity index(ITCI)was introduced to define terrain using multiple topo-graphic factors.The procedure of ITCI construction is described consecutively as below:Principle component analy-sis was conducted to develop an adaptive weighting terrain complexity model,in which four single topographic fea-ture indexes,including slope,total curvature,terrain roughness and relief,were collected to build ITCI; Based on training data from experiments,ITCI was examined and an empirical formula of ITCI was shaped accordingly; Ac-cording to the empirical formula,ITCI values at experimental areas were computed for formulating connections be-tween ITCI and landform classification; In order to verify our suggested formulation of ITCI with landform types, three experimental regions with characteristic feature attributes,were selected and then calculated.Results showed that ITCI could effectively describe topographic features and the formulation of ITCI with landform types was agreea -bly matched.The study has great value for terrain sampling and uncertainty analysis in digital terrain analysis.%地形复杂度指标是数字地形分析中重要的参数.地形复杂度的定量表达能够为地形特征采样理论、数字地形分析(Digital terrain analysis,DTA)的不确定性分析、水文分析等方面提供重要依据.本文基于多因素地形因子指标,采用主成分分析方法构建一个自适应定权地形复杂度模型,以实现地形特征的综合描述:选取坡度(Slope, S)、全曲率(Total Curvature,Cur)、地形起伏度(Relief,Rel)和地形粗糙度(Rough,Rou)四个单一地形因子指标构建综合地形复杂度指标(Integrated terrain complexity index,ITCI,后文简称C);通过实验训练数据实现地形复杂度指标的解算,得到C与S、Cur、Rel、Rou之间的经验公式;根据经验公式计算实验区域的地形复杂度指标值,并结合实验区域的地形类型,得到地形复杂度指标值与地形类型之间的对应关系;选取了平原、丘陵和山区三个实验区域,计算C值对其对应关系进行验证.实验结果表明,本文构建的地形复杂度指标与地形特征之间的对应关系是合理的,能够有效描述地形特征.本文研究对于地形特征采样理论和DTA的不确定性分析等方面具有重要的参考价值和应用价值.