以数字高程模型（Digital Elevation Model, DEM）为基础的数字地形分析（Digital
Terrain Analysis, DTA）已经逐渐发展成为一门独立的学科。基于数字化地形图上的
等高线通过插值建立规则格网 DEM，是最常见的 DEM 建立方法，其中栅格尺寸的
确定是建立 DEM 的最基本问题之一，等高线曲率的计算则是合理设置栅格尺寸的
基础。
本文对矢量等高线曲率的科学概念和计算方法进行了研究，以期为 DEM 建立
过程中定量表征等高线的复杂程度和信息含量、合理设置栅格尺寸参数等提供理论
依据。本文主要研究结果如下：
（1）分析并界定了等高线曲率的概念，总结了常见地形曲率（如剖面曲率、
平面曲率和正切曲率）与等高线曲率的区别和联系。
（2）以曲率的数学概念为基础，提出了计算矢量等高线曲率的圆拟合算法，
利用编程方法实现了基于矢量等高线和规则格网 DEM 的等高线曲率计算。
（3）在县南沟流域典型实验样区，通过对比基于矢量的和多种栅格尺寸 DEM
的等高线曲率，发现黄土丘陵 II 副区 2.5m 栅格尺寸 DEM 上的等高线曲率与 1:1 万
地形图的曲率最接近。
（4）在多种复杂程度地貌类型区，等高线曲率与相关地形属性指标的比较表
明，等高线曲率与沟壑密度、平面曲率和坡向的关系比较密切，而与研究区平均坡
度的关系不明确。
关键词：数字地形分析；等高线曲率；最佳栅格尺寸；地形复杂度
其他摘要
Digital Terrain Analysis (DTA) has developed into a subject which is based on
Digital Elevation Model (DEM). Constructing DEMs from contours is the most popular
way of getting DEMs. One of the basic problems is to define the resolution of DEM.
Contour curvature calculation is the foundation of defining a proper resolution.
Systematic research on contour curvature's concept and method of calculation has
been done in this article. The propose of this article is to provide a scientific basis for
quantitative analysis of complexity and quantity of information of contours, and defining
of the best resolution. Main conclusions are as follows:
(1) Analysed concept and definition of contour curvature, and summarized the
relationships between contour curvatrue and other curvatures (profile curvature, plan
curvature and tangent curvature).
(2) Propoed the circle fitting method of calculate contour curvature on contours
based on mathematical definition of curvature. Programmed the circle fitting method and
algorithm of contour curvature based on grid DEM.
(3) Compared vector contour curvtaure to series resolutions grid contour curvature
in Xinannangou sample terrain data. Found that 2.5m DEM has contained more terrain
information of contours in the second sub-region of Loess Plateau, which meets former
research.
(4) Analysed contour curvature on different complex terrain area, found that contour
curvature has a close relationship with gully density, but not with mean slope of research
area.
Key Words ：Digital Terrain Analysis; contour curvature; the best resolution; terrain
complexity.
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