Measuring distance “as the horse runs”: Cross-scale comparison of terrain-based metrics
Measuring distance “as the horse runs”: Cross-scale comparison of terrain-based metrics
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“当马奔跑时”测量距离：基于地形的指标的跨尺度比较
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发表时间：
2016
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影响因子：
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通讯作者：
Y. Qiang
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作者：
B. Buttenfield;M. Ghandehari;S. Leyk;L. Stanislawski;Meg Brantley;Y. Qiang
GIScience 2016 短文论文集“马奔跑时”测量距离：基于地形的度量的跨尺度比较 BP Buttenfield 1 、 M Ghandehari 1 、 S Leyk 1 、 LV Stanislawski 2 、 ME Brantley 1 和 Yi Gang 1 科罗拉多大学地理系，博尔德 CO 80309 电子邮件：{babs;梅赫兰·甘德哈里；斯特凡·莱克；玛格丽特·布兰特利； yi.qiang} @colorado.edu 美国地质调查局 (USGS)，地理空间信息科学卓越中心，Rolla MO 65401 电子邮件：lstan @usgs.gov 免责声明：任何贸易、公司或产品名称的使用均出于描述目的，并不意味着美国政府的认可。 1. 简介 距离度量在空间建模任务中发挥着重要作用，例如洪水泛滥（Tucker 和 Hancock 2010）、河流提取（Stanislawski 等人 2015）、电力线路布线（Kiessling 等人 2003）以及氮等地表污染物分析（Harms 等人 2009）。雪崩风险基于坡度、坡向和曲率，所有这些都直接根据距离度量计算得出（Gutierrez 2012）。距离度量锚定变异函数分析、核估计和空间插值（Cressie 1993）。采用多种方法来测量距离。平面度量测量两点之间的直线距离（“直线距离”），简单直观，但存在不确定性。平面度量假设数字高程模型 (DEM) 像素是刚性且平坦的，就像瓷砖的微小面近似连续地形表面一样。事实上，地形可以在每个像素内弯曲、扭曲和起伏。使用光探测和测距（激光雷达）数据或高分辨率地形来实现精确测量存在挑战，因为过滤可能会消除或扭曲重要特征（Passalacqua 等人，2015）。目前在发达国家，激光雷达数据的可用性还很不全面，在许多农村和欠发达地区也不存在。尽管计算取得了进步，但 DEM 的距离估计从未得到系统评估，因为假设改进很小，表面调整是没有根据的。对于单个像素来说，误差可能很小，但附加效应可能会急剧传播，特别是在像素跨越数十到数百公里的区域模型（例如灾难疏散）或全球模型（例如海平面上升）中（Usery et al 2003）。此类模型越来越普遍，为理解平面距离度量使用的缺点提供了令人信服的理由。研究人员研究了基于曲率的地形建模。珍妮等人。 (2011) 使用曲率生成分层地形模型。 Schneider (2001) 为 DEM 提取的结构线创建了一个“合理性”度量。 d’Oleire-Oltmanns 等人。 (2014) 采用基于对象的图像处理作为使用 DEM 的替代方法；承认将地形转换为对象模型所涉及的预处理是计算密集型的，并且对于某些应用程序来说可能不可行。本文将平面距离与表面调整距离进行比较，从“乌鸦飞”的距离演变为“马跑”的距离。对涵盖研究区域一系列分辨率的 DEM 的多种方法进行了比较，并根据 3 米 (m) 激光雷达数据基准进行了验证。误差大小随像素大小和表面调整方法的不同而变化。误差增加率也可能因景观类型（地形粗糙度、降水状况和土地沉降模式）而异。此处报告了单个研究区域的跨尺度分析。会议将介绍其他领域。 2. 数据和研究区域 研究区域面积为 7,885.94 平方公里（sq km），位于北卡罗来纳州西部（北纬 35.798 度，西经 81.473 度），横跨皮斯加国家森林。其位置位于
GIScience 2016 Short Paper Proceedings Measuring Distance “As the Horse Runs”: Cross-Scale Comparison of Terrain-Based Metrics BP Buttenfield 1 , M Ghandehari 1 , S Leyk 1 , LV Stanislawski 2 , ME Brantley 1 , and Yi Qiang 1 Department of Geography, University of Colorado, Boulder CO 80309 Email: {babs; mehran.ghandehari; stefan.leyk; margaret.brantley; yi.qiang} @colorado.edu U.S. Geological Survey (USGS), Center of Excellence for Geospatial Information Science, Rolla MO 65401 Email: lstan @usgs.gov Disclaimer: Any use of trade, firm, or product names is for descriptive purposes and does not imply endorsement by the U.S. Government. 1. Introduction Distance metrics play significant roles in spatial modeling tasks, such as flood inundation (Tucker and Hancock 2010), stream extraction (Stanislawski et al. 2015), power line routing (Kiessling et al. 2003) and analysis of surface pollutants such as nitrogen (Harms et al. 2009). Avalanche risk is based on slope, aspect, and curvature, all directly computed from distance metrics (Gutierrez 2012). Distance metrics anchor variogram analysis, kernel estimation, and spatial interpolation (Cressie 1993). Several approaches are employed to measure distance. Planar metrics measure straight line distance between two points (“as the crow flies”) and are simple and intuitive, but suffer from uncertainties. Planar metrics assume that Digital Elevation Model (DEM) pixels are rigid and flat, as tiny facets of ceramic tile approximating a continuous terrain surface. In truth, terrain can bend, twist and undulate within each pixel. Work with Light Detection and Ranging (lidar) data or High Resolution Topography to achieve precise measurements present challenges, as filtering can eliminate or distort significant features (Passalacqua et al. 2015). The current availability of lidar data is far from comprehensive in developed nations, and non-existent in many rural and undeveloped regions. Notwithstanding computational advances, distance estimation on DEMs has never been systematically assessed, due to assumptions that improvements are so small that surface adjustment is unwarranted. For individual pixels inaccuracies may be small, but additive effects can propagate dramatically, especially in regional models (e.g., disaster evacuation) or global models (e.g., sea level rise) where pixels span dozens to hundreds of kilometers (Usery et al 2003). Such models are increasingly common, lending compelling reasons to understand shortcomings in the use of planar distance metrics. Researchers have studied curvature-based terrain modeling. Jenny et al. (2011) use curvature to generate hierarchical terrain models. Schneider (2001) creates a ‘plausibility’ metric for DEM-extracted structure lines. d’Oleire- Oltmanns et al. (2014) adopt object-based image processing as an alternative to working with DEMs; acknowledging the pre-processing involved in converting terrain into an object model is computationally intensive, and likely infeasible for some applications. This paper compares planar distance with surface adjusted distance, evolving from distance “as the crow flies” to distance “as the horse runs”. Several methods are compared for DEMs spanning a range of resolutions for the study area and validated against a 3 meter (m) lidar data benchmark. Error magnitudes vary with pixel size and with the method of surface adjustment. The rate of error increase may also vary with landscape type (terrain roughness, precipitation regimes and land settlement patterns). Cross-scale analysis for a single study area is reported here. Additional areas will be presented at the conference. 2. Data and Study Area The study area is 7,885.94 square kilometers (sq km), located in western North Carolina, (35.798 degrees N and 81.473 degrees W) spanning the Pisgah National Forest. Its location at