等高线曲率计算方法研究

Study on the Algorithm of Contour Curvature in Topographic Map

等高线曲率是数字地形分析中重要的地形属性指标之一,基于矢量等高线直接计算等高线曲率,对于量化分析等高线复杂程度,确定合理的DEM分辨率均具有重要意义。根据曲率的数学意义,提出了用圆拟合方法计算单条等高线曲率的算法,并在黄土丘陵区、黄土塬区和东北漫岗丘陵区进行了计算分析。结果表明:在等高线比较弯曲或地形比较复杂的地方等高线曲率值较大,而在等高线比较平直或地形比较简单的地方等高线曲率值较小,三个样区取值范围在0.000~1.564rad/m之间;在研究的三个样区,从东北样区、黄土塬区到黄土丘陵区,等高线曲率均值从东北较缓坡丘陵区的0.025rad/m逐渐增大到黄土丘陵沟壑区的0.086rad/m;从等高线曲率图形特征看,其空间分布与地形特征具有良好的对应关系,计算结果合理可信。文章还提出了有待研究解决的若干问题,包括曲率对地形凸凹变化的表达问题和等高线曲率与坡度等地形指标的关系等。

Contour curvature is one of the fundamental topographic indices in digital terrain analysis.Calculating contour curvature on contour lines directly is of great significance to quantitative analysis of contour complexity and definition of reasonable DEM resolutions.This paper developed an algorithm named circle fitting to calculate contour curvature using single contour according to the mathematic sense of curvature.Contour curvature is calculated and analyzed in loess hilly region,loess tableland region and undulated hilly region in northeast China.Preliminary results are as follows:(i)contour curvature is greater where contour line is more curved or where terrain is more complex,and smaller where contours are straighter or the landform is simpler,the range of contour curvature is 0.000/m to 1.564/m;(ii)the mean value of contour curvature increase from undulated hilly(0.025/m)in northeast,loess tableland sample region to loess hilly sample region(0.086/m);(iii)the spatial distribution of contour curvature well corresponds to terrain characteristic.The calculation result is reasonable.Issues to be further studied are also discussed,including the relationship between contour curvature and terrain convexity,relationship between contour curvature and other topographic indices.