DEM in quantitative analysis of structural geomorphology: application and prospect
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摘要: 作为一种描述地形起伏特征的数据模型，数字高程模型（Digital Elevation Model，DEM）通过有限的地形高程数据实现对地形曲面的数字化模拟（即地形表面形态的数字化表示），为研究地表的演化过程提供了数据基础。文章归纳梳理了DEM在基本地形因子、流域地貌特征、古地貌面的重塑、构造地貌发育模式、地貌分类与制图以及地形特征提取算法等领域的应用现状。总的来看，DEM研究对象以陆地为重点，以河流地貌和山地地貌为主要内容；研究过程从早期对地貌形态的定性描述向多种地貌参数的半定量、定量分析转变；研究尺度空间上从某个小流域到整个造山带，时间上从数小时向百万年扩展。构造地貌演化时间序列的不确定性、地貌参数获取的复杂性、地形模型算法的多样化以及DEM生成过程中的误差因素，这些均影响构造地貌定量分析结果的准确度，因此在归纳梳理已有研究成果的同时，对DEM在构造地貌研究领域的应用进行了一些思考。Abstract: Digital elevation model (DEM) is used to realize the digital simulation of terrain surface (i.e. the digital representation of terrain surface shape) through the limited terrain elevation data. As a new tool to describe the terrain, it provides a new field of vision for people to study the evolution process of the earth's surface. The application status of DEM in many fields are summerized in this paper, including basic topographic factors, watershed geomorphological features, reconstruction of paleogeomorphology, tectonic geomorphological development model, tectonic activity classification, geomorphological classification and environmental assessment, geomorphological parameter algorithms and computing platform development. Our research generally focuses on land, with river geomorphology and mountain geomorphology as the main objects. The research process changes from the early qualitative description of geomorphology to the semi-quantitative and quantitative analysis of a variety of geomorphological parameters. The research scale extends from a small watershed to the whole orogenic belt in space and from a few hours to millions of years in time. However, many factors can influence the accuracy of quantitative analysis results of tectonic geomorphology, such as the uncertainty of the time series of tectonic geomorphology evolution, the complexity of the acquisition of geomorphological parameters, the diversification of terrain model algorithms and the error factors in the process of DEM generation. Therefore, while summarizing the previous research results, some thoughts are given on the application of DEM in tectonic geomorphology.
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Key words:
- tectonic geomorphology /
- DEM /
- geomorphological parameters /
- application progress
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图 1 构造、气候和侵蚀之间发生相互作用的关系简图(据刘静等, 2018修改)
a—造山带碰撞的构造模式; b—构造、气候、侵蚀三者之间的内在关联
Figure 1. Relationship diagram showing the interaction between structure, climate and erosion (modified after Liu et al., 2018)
(a) Tectonic model of the orogenic belt collision; (b) Interaction between structure, climate and erosion
图 2 河道高程与chi(χ)值的线性关系(据Whipple et al., 2017修改)
在设定不同流域的初始高程zb相同的情况下, 分水岭两侧χ值的差异主要受河道陡峭程度的影响, 标准河道陡峭指数Ksn大的一侧所对应的χ值较小, 标准河道陡峭指数Ksn较小的一侧所对应的χ值较大
Figure 2. Linear relationship between the channel height and chi (χ) value (modified after Whipple et al., 2017)
Under the same initial elevation zb of different watershed, the difference of χ values on both sides of watershed is mainly affected by channel steepness. The side with higher standard channel steepness index Ksn corresponds to a smaller χ value, while the side with lower standard channel steepness index Ksn corresponds to a larger χ value
图 3 沉积面恢复示意图(据张会平等, 2006修改)
虚线代表未发生侵蚀之前的地形面(恢复地形面), 与现今地形面做差值运算可得侵蚀量的大小
Figure 3. Schematic diagram showing the resteration of the sedimentary surface (modified after Zhang et al., 2006)
The dashed line represents the topographic surface before erosion (restoring the topographic surface), and the amount of erosion can be obtained by difference calculation with the current topographic surface
图 4 地形特征点和地形特征线提取示意图
Figure 4. Schematic diagram showing the extraction of terrain feature points and lines
表 1 全球数字高程(DEM)产品及其主要参数
Table 1. Global digital elevation products and the main parameters
DEM产品 发布时间/年 分辨率/m 覆盖范围 水平基准 垂直基准 数据来源 获取地址 ETOPO1 2008 30 90°S~90°N WGS84 MSL 数据融合 URL1 GTOPO30 1996 1000 90°S~90°N WGS84 MSL 数据融合 URL2 SRTM v1:2003
v2:2006
v3:201330
90 100056°S~60°N WGS84 EGM96 InSAR v1/v2:URL3
v3:URL4GMTED2010 2010 225
450 9090°S~84°N WGS84 EGM96 数据融合 URL2 ASTER GDEM v1:2009
v2:2011
v3:201930 83°S~83°N WGS84 EGM96 光学立体摄影测量 v2:URL5
v3:URL6AW3D30 v1:2016
v2:2017
v3:2018
v4:201930/12.5 82°S~82°N CRS80 EGM96 光学立体摄影测量 URL7 TanDEM-X DEM 2016 90 90°S~90°N WGS84-G1150 LE90 In SAR URL8 注: MSL—平均海平面、EMG96—1996地球引力模型、LE90—90%线概率误差
URL1: http://maps.ngdc.noaa.gov/viewers/wcs-client/
URL2: http://earthexplorer.usgs.gov/
URL3: http://dds.cr.usgs.gov/srtm/或http://www2.jpl.nasa.gov/srtm/
URL4: https://search.earthdata.nasa.gov/search?q=C1000000240-LPDAAC_ECS或https://lpdaac.usgs.gov/products/srtmgl1v003/
URL5: http://reverb.echo.nasa.gov/reverb/#utf8=%E2%9C%93&spatial_map=satellite&spatial_type=rectangle
URL6: https://search.earthdata.nasa.gov/search/granules?p=C1575726572-LPDAAC_ECS&fi=ASTER
URL7: https://www.eorc.jaxa.jp/ALOS/en/aw3d30/data/index.htm, URL8:https://download.geoservice.dlr.de/TDM90/files/
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表 2 常见的地形因子及其算法
Table 2. Common terrain factors and their algorithms
地形因子 算法 描述 坡度(slope) $ { slope }=arctan \sqrt{f_{x}^{2}+f_{y}^{2}}$ fx、fy分别代表x和y方向上的高程变化率。坡度即水平面与地形面之间的夹角, 可以描述地表的倾斜程度 坡向(aspect) $ { aspect }=180^{\circ}-arctan \frac{f_{x}}{f_{y}}+90^{\circ}\left|\frac{f_{y}}{f_{y}}\right|$ 坡向即地面一点的切平面的法线在水平面的投影与过该点的正北方向的夹角, 表征该点高程值改变量的最大变化方向 剖面曲率(Kv) $K_{\mathrm{v}}=\frac{p^{2} r+2 p q s+q^{2} t}{\left(p^{2}+q^{2}\right) \sqrt{1+p^{2}+q^{2}}}$ P为x方向的高程变化率, q为y方向的高程变化率, r为x方向上高程变化率的变化率, s为x方向高程变化率在y方向上的变化率, t为y方向高程变化率的变化率。剖面曲率是对地面坡度沿最大坡降方向地面高程变化率的度量 平面曲率(Kn) $K_{\mathrm{n}}=\frac{q^{2} r+2 p q s+p^{2} t}{\left(p^{2}+q^{2}\right) \sqrt{1+p^{2}+q^{2}}}$ 平面曲率可以描述地表曲面沿水平方向的弯曲变化情况 地形起伏度(RFi) $R F_{\mathrm{i}}=H_{\max }-H_{\min }$ Hmax、Hmin分别指某一固定分析窗口内的最大高程和最小高程。地形起伏度可反映水土流失区域的土壤侵蚀特征 地形粗糙度(R) $R=\frac{S_{\text {曲面 }}}{S_{\text {水平 }}}$ S曲面、S水平分别指某一地表单元的曲面面积与其在水平面上的投影面积。地形粗糙度可衡量地表的侵蚀程度 地表切割深度(Di) $D_{\mathrm{i}}=H_{\text {mean }}-H_{\min }$ Hmean、Hmin分别指某一固定分析窗口内的平均高程和最低高程。地表切割深度是反映地形起伏变化情况的指标 高程变异系数(V) $V=\frac{H_{\mathrm{std}}}{H_{\text {mean }}}$ Hstd、Hmean分别指某一固定分析窗口内的高程标准差与平均高程。高程变异系数对于区域内部的侵蚀切割情况和地形起伏有很好的反映 注: 公式中涉及相同的参数不做重复介绍, x、y为坐标系参数
Note: the formula involves the same parameters will not be repeated, x and y are in the xyz coordinate system.
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