An alternative approach to transverse and profile terrain curvature

Terrain curvature is one of the most important parameters of land surface topography. Well-established methods used in its measurement compute an index of plan or profile curvature for every single cell of a digital elevation model (DEM). The interpretation of these outputs may be delicate, especially when selected locations have to be analyzed. Furthermore, they involve a high level of simplification, contrasting with the complex and multiscalar nature of the surface curvature itself. In this paper, we present a new method to assess vertical transverse and profile curvature combining real-scale visualization and the possibility to measure these two terrain derivatives over a large range of scales. To this purpose, we implemented a GIS tool that extracts longitudinal and transverse elevation profiles from a high-resolution DEM. The performance of our approach was compared with some of the most commonly used methods (ArcMap, Redlands, CA, USA; ArcSIE, Landserf) by analyzing the terrain curvature around charcoal production sites in southern Switzerland. The different methods produced comparable results. While conventional methods quickly summarize terrain curvature in the form of a matrix of values, they involve a loss of information. The advantage of the new method lies in the possibility to measure and visualize the shape and size of the curvature, and to obtain a realistic representation of the average curvature for different subsets of spatial points. Moreover, the new method makes it possible to control the conditions in which the index of curvature is calculated.

地形曲率是陆地表面地形最为重要的参数之一。现有成熟的地形曲率测量方法，均针对数字高程模型（Digital Elevation Model，DEM）的每个栅格单元，计算平面曲率或剖面曲率指标。对这些计算结果的解读往往较为复杂，当需要针对特定点位进行分析时难度尤甚。此外，这类方法往往进行了高度简化，而地表曲率本身具有复杂且多尺度的本质特性，二者形成鲜明反差。

本文提出一种全新的地形曲率评估方法，可结合真实尺度可视化能力，并支持在大范围尺度区间内测量两种地形派生曲率——垂直横向曲率与剖面曲率。为此，我们开发了一款地理信息系统（Geographic Information System，GIS）工具，可从高分辨率数字高程模型中提取纵向与横向高程剖面。

本文以瑞士南部木炭生产遗址周边的地形曲率为分析对象，将所提方法的性能与数种主流方法（ArcMap，美国加利福尼亚州雷德兰兹市；ArcSIE，Landserf）进行了对比。不同方法所得结果具有较好的一致性。传统方法多以数值矩阵的形式快速概括地形曲率，但在此过程中会丢失部分信息。本新方法的优势在于，可实现曲率形态与尺度的测量与可视化，并能针对不同空间点子集获取平均曲率的真实表征结果。此外，新方法还支持对曲率指标的计算条件进行精准调控。