地理科学  2017 , 37 (11): 1764-1770 https://doi.org/10.13249/j.cnki.sgs.2017.11.019

Orginal Article

基于GIS的斜坡单元划分方法改进与实现

颜阁, 梁收运, 赵红亮

西部灾害与环境力学教育部重点实验室/兰州大学土木工程与力学学院地质工程系,甘肃 兰州 730000

An Approach to Improving Slope Unit Division Using GIS Technique

Yan Ge, Liang Shouyun, Zhao Hongliang

Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, Department of Geological Engineering, School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, Gansu, China

中图分类号:  P931;TP75;P642.22

文献标识码:  A

文章编号:  1000-0690(2017)11-1764-07

通讯作者:  通讯作者:梁收运,教授。E-mail:liangsy@lzu.edu.cn

收稿日期: 2016-09-25

修回日期:  2016-12-13

网络出版日期:  2017-11-20

版权声明:  2017 《地理科学》编辑部 本文是开放获取期刊文献,在以下情况下可以自由使用:学术研究、学术交流、科研教学等,但不允许用于商业目的.

基金资助:  国家重点基础研究发展计划(2014CB744701)和国家自然科学基金(41272326)资助

作者简介:

作者简介:颜阁(1990-),男,江苏南京人,硕士,主要从事GIS、地貌与地质灾害研究。E-mail:yang13@lzu.edu.cn

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摘要

斜坡单元已广泛应用于滑坡易发性制图和地质灾害评价。然而在山间盆地或大型宽谷处,常规方法划分出的斜坡单元与地貌背景难以匹配。依据高程及其衍生变量的基本形态系统和曲率的流域分割原理,基于ArcGIS技术,通过叠加曲率和反转曲率的流域边界,改进了斜坡单元划分方法。结果表明:与常规方法相比,改进方法不仅能够使用山脊线和山谷线以划分斜坡单元,还能利用台地边界和宽谷边界以分割水平地表与倾斜地表;划分出的单元大小相对均匀,单元形状总体介于圆形和正三角形之间。对于水平成分较多的地区,如黄土塬区和水库库区,该方法与传统方法相比,具有较好的应用前景。

关键词: 斜坡单元 ; 划分方法 ; 平均曲率 ; 流域分割 ; ArcGIS

Abstract

In recent years, slope units have been widely utilized in landslide susceptibility mapping and geological hazard assessment. Slope units automatically derived from high-quality DTMs, partition the territory into hydrological regions between drainage and divide lines. The division method of slope units conducts subwatershed segmentation on elevation and the reversal to extract ridge lines and valley lines, then overlays these terrain feature lines. However, these resultant units are unable to match with geomorphology background where intermountain basins or large open valleys exist. In this article, according to the basic morphometic system of elevation and the derived variables, slope is derivative of elevation while curvature is that of slope, thus the break of slope should be indicated by curvature instead of elevation. The disability of indicating variation of slope is regarded as the main reason for the limitation in the conventional method. According to the theory of watershed segmentation of mean curvature, the division method of slope units is improved by overlaying watershed boundaries on curvature and the reversal in ArcGIS. Firstly, the DEM should be smoothed twice with a 5×5 average filter in order to reduce the effect of noise and small scale variation in the DEM. The curvature is then calculated from the filtered DEM using the Arctool named Curvature. After that, watershed boundaries are generated mainly through computing flow direction, scouting sink and dividing watershed in the curvature image, and this image should be reversed for watershed boundaries on the reversal curvature. Finally, slope units can be separated from each other by these two kinds of boundaries which are further combined into the boundaries of slope units. Giving an example from Huachi County of Gansu Province, elevation layer in the resolution of 20 m was used as input data, and both two methods were then applied for slope unit division. Compared with the conventional method, the revised approach not only uses ridge lines and valley lines to segment slope units, but also utilizes tableland boundaries and open valley boundaries to separate horizontal surface from the inclined. The revised approach may give a new definition that slope units should be divided by ridge lines, valley lines, tableland boundaries and open valley boundaries. Also the revised method utilizes watershed segmentation on curvature instead of subwatershed division on DEM where filling sinks perhaps causes the serious change of reversal elevation. Furthermore, the resultant units have relatively uniform size and shape, more than 80% of them with the area from 0.1×104 to 6×104m2 and about 60% between circle and triangle shape, which are more suitable for landslide hazard evaluation. It is worth mentioning that the revised method would be more competitive than the original in some regions with large area of horizontal surface, just like Loess Tableland and reservoir surface.

Keywords: slope units ; division method ; mean curvature ; watershed segmentation ; ArcGIS

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颜阁, 梁收运, 赵红亮. 基于GIS的斜坡单元划分方法改进与实现[J]. 地理科学, 2017, 37(11): 1764-1770 https://doi.org/10.13249/j.cnki.sgs.2017.11.019

Yan Ge, Liang Shouyun, Zhao Hongliang. An Approach to Improving Slope Unit Division Using GIS Technique[J]. Scientia Geographica Sinica, 2017, 37(11): 1764-1770 https://doi.org/10.13249/j.cnki.sgs.2017.11.019

近几十年来,滑坡作为世界上最具破坏性的地质灾害[1,2],造成了巨大的财产损失和严重的人员伤亡。为减轻滑坡危害,许多学者已经致力于滑坡易发性制图、滑坡灾害评价和预防措施的研究。进行滑坡易发性制图首先需选择合适的制图单元。“单元”指代地表的一部分,包含了一系列与相邻单元不同的地面条件[3]。目前制图单元的划分方法可分为以下5种:栅格单元(grid-cells)、地貌单元(terrain units)、独特条件单元(unique-condition units)、斜坡单元(slope-units)以及地形单元(topographic units)[4]。其中,斜坡单元是将目标区域划分成由山谷线和山脊线共同分割的图元[5,6]。将斜坡单元应用于以滑坡为主的地质灾害评价日益引起众多学者的关注,如:地质灾害易发程度分区[7],滑坡易发性分区[8~10]和斜坡稳定性分析[11,12]

丘陵或山区主要发育倾斜的地表,然而也不可避免地存在一些近水平成分,表现为近水平的宽谷或近水平的台地,这部分地表本质上并非斜坡。在黄土高原地区,这样的地表较为常见,如:黄土塬或残塬、河流阶地和大型宽谷等。常规方法划分的斜坡单元一般不区分水平地表和倾斜地表,往往将水平地表机械式地并入到倾斜地表之中,使得同一单元内可能包含倾斜地表和水平地表两种截然不同的地貌区域,按单元提取的地形因子与实际情况就会存在明显的误差。Guzzetti等[4]曾提出当存在山间盆地或大型宽谷时,斜坡单元与斜坡失稳的局部地貌背景不匹配。此外,常规方法还打破了区域水系形成的自身规律[11],存在强行提取反转高程子流域的问题。据此,本文将对常规的斜坡单元划分方法进行改进,使得在划分斜坡单元的同时,能够区分出相对的水平地表与倾斜地表。

1 斜坡单元划分的改进方法

1.1 方法原理

高程及其衍生形态变量之间的等级关系构成了如下的基本形态系统[13~15]

M={(0)M={z}, (1)M={zi}, (2)M={zji}, (3)M={zijk},…} (1)

式中M表示所有局部形态变量的一个集合,并且在地表的每个点上都能定义[16](0)M表示M的一个子集仅包含高程元素(z);(1)M 表示由第一级形态变量(zi)组成的子集,定义为高程在方向i上的第一方向导数;(2)M 表示由第二级形态变量(zji)组成的子集,定义为子集(1)M的变量在方向j上的方向导数,以此类推。(1)M中包含了坡度和坡向等变量,通过对高程在任意方向上求一次导数得到。子集(2)M中包含了各种曲率(如正切曲率和剖面曲率),通过对高程在任意方向上求二次导数得到[17,18]。子集(3)M包含了用以表达曲率变化的变量,以此类推。它们之间的等级关系建立在求导的基础上,下一级变量可以描述上一级变量的变化,而上一级变量则无法刻画下一级变量。

常规方法依赖于水系提取和子流域分割,分别用高程和反转高程的子流域边界代表山脊线和山谷线,通过山谷线与山脊线的叠加划分斜坡单元[5,6],已集成到了ArcGIS的Spatial Analyst Tools- Hydrology工具箱中。具体划分步骤包括(图1):① 对高程数据进行洼地填充,以便让区域内部的所有水流从区域的边界流出。根据填洼后的高程,求解流向。根据流向计算上游集水单元格数(汇流面积),作为流量。把河网视作流量达到某一阈值后形成的,设定上游集水单元格数阈值提取河网。依节点将河网分解成枝干,作为局部汇流洼地。以流向为底图,以上一步洼地为集水点,计算子流域。矢量化子流域栅格得到凹形子流域边界,视为山脊线。② 反转高程数据,重复得到凸形子流域边界,视为山谷线。再用矢量合并工具合并2个边界,得到斜坡单元。此划分方法以高程为处理对象,难以准确反映坡度的变化,即使在坡度发生明显转折的部位(如各种台地边缘和宽谷与坡脚的分界),一般也不对应于所划分的单元边界线。

图1   常规方法划分斜坡单元的流程

Fig.1   Flow chart of conventional method to divide slope units

已有研究证明,剖面曲率(kv)是坡度在流线上的导数[17],其极大值和极小值分别指示台地边缘和宽谷边缘。正切曲率(kh)与等高线曲率有相似的作用,可描述等高线的弯曲程度。正切曲率的极大值或极小值部位也是坡向发生突变的部位,分别指示山脊和山谷。根据 Euler原理,正切曲率与剖面曲率的平均值即为平均曲率(H)。平均曲率是正切曲率与剖面曲率的简单综合,其极大值与极小值可同时指示坡向和坡度突变的位置,因而,在指示山脊线、山谷线的同时,也可反映出台地边缘和宽谷边缘。

Romstad[19]和Etzelmüller[20]曾经利用Matlab编程技术,对平均曲率进行流域分割,寻找曲率极大值点构成凹形地貌元素边界,并对反转的平均曲率进行流域分割,寻找凸形地貌元素的边界。这2个边界均位于曲率的极值点部位,其中凹形地貌元素边界位于极大值点,凸形地貌元素边界位于极小值点。据此可以设想,通过提取并叠加2种地貌元素边界,以改进斜坡单元划分的方法,便可达到合理划分斜坡单元并能够区分相对水平地表和倾斜地表的目的。

极大值(或极小值)并不是相对于四周的点而言的,而是在某一方向上的极大值(或极小值),如分水岭(或山谷)。

1.2 实现过程

ArcGIS可直接计算平均曲率,而不必考虑正切曲率和剖面曲率的求解。同时,ArcGIS能够进行曲率的流域分割,如此便可实现对常规斜坡单元划分方法作进一步的改进,具体过程如下(图2和3)。

图2   改进方法划分斜坡单元的流程

Fig.2   Flow chart of improved method to divide slope units

图3   某黄土地区改进方法提取斜坡单元示意图

Fig.3   Diagram of improved method to extract slope units in a certain loess area

1) 在坡面侵蚀作用下,倾斜地表往往不平整;溪流的发育使水平地表在局部位置下凹,这些都增大原高程(图3a)的粗糙度。在求解曲率之前,应先进行适当的均值过滤,以去除高程数据的小尺度变化。用过滤后的高程数据求解每个栅格的平均曲率值(图3b)。

2) 将平均曲率假想成描述地形起伏的数值或高程,求解流向数据。再依据流向数据,求解洼地单元。然后以流向为底图,以洼地为集水点求解流域。矢量化流域栅格数据后,得到凹形地貌元素边界(图3c)。

3) 反转平均曲率数据,重复步骤2,计算反转曲率数据得到凸形地貌元素边界(图3d)。再用矢量合并工具合并两类边界,即得到斜坡单元(图3e或3f)。

2 实例验证

以甘肃省东部华池县1:50 000地形等高线作为数据源,制备20 m分辨率的高程数据作为“图1图2”的输入,分别采用常规方法和改进方法提取斜坡单元,并从定性和定量的角度比较2种方法的差异。

2.1 定性分析

一般情况下,常规方法提取的单元边界与台地边界和宽谷边界明显地不吻合,难以区分出相对的水平地表和倾斜地表,而是将2种地表生硬地合并到同一单元中(图4a)。其次,常规方法需要在反转高程上提取子流域边界作为山谷线。有时候反转高程代表的地形与实际水系的分布缺乏关联性,难以保证水流能从边界流出。换言之,反转高程会存在一些大型洼地,与实际的山峰相对应。虽然可以通过填洼处理来消除洼地影响[21,22],但填洼极易人为地造出大片平地,而平地上提取的河网易出现平行部分[23]或伪河道[24],个别地方还出现近似直角河道形态特征[25]。基于河网提取的流域边界也会呈平行状。反之,平行流域边界指示了平地的范围。反转高程在提取流域的过程中对地形的改造比较大,凸形子流域边界的平行部分可能会明显超出台地的范围,在山脊的部位也会大量存在,说明很多非平地的区域在提取河网的过程中也被改造成了平地(图4a)。当研究区范围较大时,常规方法的划分结果不仅需要繁重的人工修编工作,其结果的合理性尚需要进一步商榷。

图4   华池县某部位基于2种方法划分的斜坡单元效果

Fig.4   Effects of slope units using two kinds of methods in a certain section of Huachi County

一般认为斜坡单元是由山脊线与山谷线共同包围的区域。当不存在平地(台地或宽谷)或平地范围小到可以忽略时,改进方法在倾斜地表上提取的单元边界由山脊线和山谷线所构成,符合斜坡单元的一般认识;当存在平地或平地范围大到不能忽略时,改进方法在倾斜地表上提取的单元边界将由山脊线、山谷线、台地边界线和宽谷边界线所构成,与常规方法相比,改进方法进一步利用台地边界和宽谷边界将水平地表与倾斜地表分离(图4b),将倾斜地表上的单元看作斜坡单元也应该是合理的。从改进方法可以给“斜坡单元”重新定义:斜坡单元是由山脊线、山谷线、台地边界和谷底边界共同分割的区域。此外,改进方法使用了流域分割方法,而不是子流域分割技术(图2),不需进行洼地填充和河网提取,避免了平行边界的产生(图4b)。由于相对的水平地表上会存在轻微的起伏,平均曲率在水平地表上也存在山脊和山谷的“假象”。这些“假象”对水平地表进一步分割,使得水平地表内划分的单元尺寸更加趋于合理(图3e,图4b)。总之,与常规方法提取的单元边界相比有明显差异,改进方法所提取的单元,不仅更为精细地刻画了倾斜地表,也区分出了平地的分布。由此可见,改进方法是对常规斜坡单元划分方法的拓展与进一步合理化。

2.2 定量比较

改进方法和常规方法的定量差异,可通过2种方法所划分的单元大小与形态来表征。单元大小对地质灾害易发性制图十分重要,因为描述地质环境因子的各种指标是按单元来提取的,为了使每个单元的环境因子具有可比性,各个单元所覆盖的区域大小应该大体上是相近的。大小均匀性可通过单元面积的分布来反映。以甘肃省东部华池县县境20 m分辨率的高程为数据源,统计结果为:改进方法划分的单元面积集中在0.1×104~6×104m2,超过全区总单元数的80%,面积在0.1×104m2以下和6×104m2以上的单元数量均不足总数的10%;常规法划分的单元面积在0.1×104m2以下和6×104m2以上的数量均超过总数的20% (图5a)。可见,改进方法划分的单元大小较为均一,而常规方法划分的单元碎块比较多。

图5   华池县改进方法与常规方法划分的斜坡单元的形态特征统计

Fig.5   Morphological feature statistics of slope units using improved method and conventional method in Huachi County

单元形态可用周长平方与面积的比值描述。圆形的比值最小为12,正方形和正三角形适中,分别为16和20。如果单元过扁或存在长条形部分,比值便会大大增大。同样以华池县为例进行统计:改进方法划分的单元的比值主要集中在16~20,占全区总单元数量的60%,比值在12~16和20~24的单元均较多,分别占总数的16%和14%,比值大于28的单元(可近似看成长宽比为5:1的单元)小于总数的10%;常规方法划分的单元近45%的比值都大于28 (图5b)。表明改进方法划分的单元形状多数介于圆形和正三角形之间,很少呈长条形。而常规方法划分的单元近一半呈长条形,需要繁杂的人工修编。

总之,改进方法划分的单元大小相对均匀,满足对制图单元大小相近的要求;单元形状多数介于圆形和正三角形之间,也避免繁杂的人工修编,因此,改进方法比常规方法更适合划分滑坡易发性制图单元。

3 结论

斜坡单元已广泛应用于滑坡易发性制图及其灾害评价。常规的斜坡单元划分方法是对高程与反转高程进行子流域分割以获得山脊线和山谷线,叠加这2种地形特征线来划分斜坡单元。然而,在山间盆地或大型宽谷处,划分出的斜坡单元与地貌背景无法匹配。

本文以高程及其衍生变量的基本形态系统为背景,分析出高程无法反映坡度变化是造成常规方法局限性的主要原因,进而基于Romstad和Etzelmüller的曲率的流域分割原理,提出了借助ArcGIS进行斜坡单元划分的改进方法:对平均曲率进行流域分割,寻找山脊线和台地边界,对反转曲率流域分割,寻找山谷线和宽谷边界。

与常规方法相比,改进方法不仅使用山脊线和山谷线以划分斜坡单元,而且能够依靠台地边界和宽谷边界以分割出相对的水平地表与倾斜地表。相比常规方法划分的制图单元多长条形、多碎块,改进方法所划分的制图单元大小较为均一,形状较为规则,避免繁杂的人工修编。

对于黄土塬区和水库库区等那些水平成分较大的地区,改进方法所划分的斜坡单元更为合理,更适于滑坡易发性制图及其灾害评价。

The authors have declared that no competing interests exist.


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基于斜坡单元的区域斜坡稳定性评价方法

[J]. 地理科学, 2013, 33(11): 1400-1405.

URL      Magsci      [本文引用: 1]      摘要

<p>为对大范围区域斜坡的稳定性进行有效、定量的评价,提出一个耦合二维力学分析模型的区域斜坡稳定性评价方法。选择宝鸡市金台区的一段黄土沟谷作为研究区,对文章提出的方法进行验证。首先,利用GIS 实现斜坡单元的划分;然后,利用钻探及调查得到的地层数据形成区域的多层Grid 模型;在此基础上,开发程序,完成计算剖面生成、滑面搜索、稳定性评价等工作;最后,根据各单元的稳定性系数,生成区域斜坡稳定性分区图。这种方法以二维极限平衡方法为基础,即可得到研究区域的二维安全系数分布图,又可求得最危险滑动面的位置和规模。</p>

[Gu Tianfeng, Wang Jiading, Fu Xinping.

Regional slope stability analysis method based on the slope unit.

Scientia Geographica Sinica, 2013, 33(11): 1400-1405.]

URL      Magsci      [本文引用: 1]      摘要

<p>为对大范围区域斜坡的稳定性进行有效、定量的评价,提出一个耦合二维力学分析模型的区域斜坡稳定性评价方法。选择宝鸡市金台区的一段黄土沟谷作为研究区,对文章提出的方法进行验证。首先,利用GIS 实现斜坡单元的划分;然后,利用钻探及调查得到的地层数据形成区域的多层Grid 模型;在此基础上,开发程序,完成计算剖面生成、滑面搜索、稳定性评价等工作;最后,根据各单元的稳定性系数,生成区域斜坡稳定性分区图。这种方法以二维极限平衡方法为基础,即可得到研究区域的二维安全系数分布图,又可求得最危险滑动面的位置和规模。</p>
[13] Krcho J.

Morphometric analysis of relief on the basis of geometric aspect of field theory

[M]. Bratislava: Acta UC, 1973.

[本文引用: 1]     

[14] Evans I S.General geomorphometry, derivatives of altitude, and descriptive statistics[C]//In:Chorley R J.Spatial Analysis in Geomorphology. New York: Harper and Row, 1972:17-90.

[15] Minár J.

Morfometrická analýza polí a jej využitie v geoekológii

[J]. Geografický časopis, 1999, 51(3): 261-277.

[本文引用: 1]     

[16] Shary P A, Sharaya L S, Mitusov A V.

Fundamental quantitative methods of land surface analysis

[J]. Geoderma, 2002, 107(1/2): 1-32.

https://doi.org/10.1016/S0016-7061(01)00136-7      URL      [本文引用: 1]      摘要

Effective quantitative land surface analyses in soil science need scale-free land surface attributes (morphometric variables, MVs) to be introduced for making comparable results obtained at different scales. To investigate the problem in more detail, a conceptual scheme and curvatures studied earlier in Shary (1995) [Math. Geol. 27 (1995) 373] are further developed in this paper, formulae for a complete system of 12 curvatures and some other MVs are given, and modified Evans oung algorithm for curvature calculation is described that does not emphasize grid directions. The conceptual scheme is based on that MVs often describe not the land surface itself, but rather the system and surface+vector field , where vector fields of common interest are gravitational field and solar irradiation. Correspondingly, morphometric variables and concepts may (1) refer to this system description (field-specific), or (2) be invariant with respect to any vector field (field-invariant), that is, describing the land surface itself, its geometrical form. From the other side, MVs and concepts may be (1) local, (2) regional, which need extended portions of a restricted part of land surface for their determination at a given point, or (3) global (planetary), when elevations of all the Earth are needed for their determination at a given point. Global MVs do not consist subject of this paper; so, the four classes of MVs are considered here: class A (local field-specific MVs), class B (regional field-specific), class C (local field-invariant), and class D (regional field-invariant). MVs of these classes permit description of geometrical land form, pre-requisits of surface runoff, thermal regime of slopes, and altitude zonality. Class A contains three independent MVs expressed by first derivatives of elevation Z by plan coordinates (slope steepness, slope direction, solar insolation) and seven curvatures expressed by second derivatives of Z ; class C contains five curvatures; class B contains two variables (catchment and dispersal areas); MVs of class D are not introduced yet. Also, some non-system MVs of class A are described, sense of all MVs is described, and interrelationships between MVs are shown. Three curvatures are independent, not two, as this is often implied. It is experimentally shown that average depth of a depression defined in class B may not depend upon scale, while local MVs may not have limit values for large scales. Scale-free morphometric variables are defined here as those that have limit values for large scales. It is experimentally shown that maximal catchment area (class B) is a scale-free variable for thalwegs. These results show that local MVs are scale-specific (except elevation), but scale-free regional MVs might be introduced as a generalization of curvature concept. Two surface runoff accumulation mechanisms are considered in their relation to local and regional field-specific MVs; although the first one is generalized to a regional MV (catchment area), there is no regional MV for the second one description, although it is of great importance in soil science as describing slow profile changes. Geometrical forms were little studied in soil science; arguments are given that they may be useful for studying memory in soils, which is determined by temporal shifts between land surface formation and soil formation processes. The following topics are discussed: the current state of morphometry, an ambiguity in land form definitions, and a possibility to generalize curvature concept for regional scale-free MVs. The consideration is restricted by methods of the general geomorphometry; partial approaches are considered only by selection.
[17] Shary P A.

Land surface in gravity points classification by a complete system of curvatures

[J]. Mathematical Geology, 1995, 27(3): 373-390.

https://doi.org/10.1007/BF02084608      URL      [本文引用: 2]      摘要

A general theory of land surface in a gravitational field is being developed. The four classes of topographic variables are defined: local (class A) and global (class B) that have no sense without gravity, and local (class C) and global (class D) which are gravity invariant. A complete system of curvatures is introduced for a general situation of nonuniform gravity. The curvatures refer to classes A and C, the latter being subject of the differential geometry of surfaces, the former being subject of this work in a special section of mathematics concerned with surfaces in a vector field. The svstem of curvatures consists of 7 known ones of the classes A and C and 5 new curvatures of the class A (difference, horizontal excess, vertical excess, total ring, and total accumulation curvatures). Seven new theorems show in which way curvatures can reflect landforms and their ability to influence substance flows, and the relationship between them. Land surface in gravity-points classification is constructed based on signs of curvatures, which includes known curvature-based classifications as partial situations, and 12 main types (from total 48) are shown to form open subsets of the surface with equal probability to meet them for the land surface as indicated by a new statistical hypothesis. A central-point method for local variables calculation in uniform gravity approximation is described for a computer Digital Elevation Models treatment .
[18] Shary P A, Sharaya L S, Mitusov A V.

The problem of scale-specific and scale-free approaches in geomorphometry

[J]. Geografia Fisica e Dinamica Quaternaria, 2005, 28(1): 81-101.

URL      [本文引用: 1]      摘要

ABSTRACT An extended system of 18 basic land surface attributes, or morphometric variables (MVs), is presented, together with formulae and computation algorithms. MVs and related methods, including those relevant to oil spills and natural hazards, are described. All MVs, both discovered and not, are classified into six non-overlapping classes, with the general properties of each class elucidated. The problem of MV precision is studied on the basis of the concept that MVs are scale-free if tended to some finite limit as grid mesh approaches to zero (with enlarging map scale), and they are scale-specific in the opposite case. MV plots against grid mesh are studied experimentally. Due to roughness in natural landscapes, some scale-specific land form types, such as those of Gaussian or Troeh's classifications, occupy predicted areas for any terrain, as described by Shary's statistical hypothesis [Shary, 1995]. This is validated experimentally for 17 terrains. The Evans' phenomenon [Evans, 1980] is explained as a consequence of natural landscape roughness. Some natural terrain-specific deviations from values predicted by MV methods are described. An example of scale-free land form classification is presented, in which some terrain-specific hydrologically important geomorphologic features are described directly. A new concept of distribution areas for studying hydrological phenomena generalizes the concept of flow-lines for the case of the real (non-smooth) land surface, and is applied to oil spills. Future prospects and forthcoming trends in geomorphometry are discussed.
[1] He Sanwei, Pan Peng, Dai Lan et al.

Application of kernel-based Fisher discriminant analysis to map landslide susceptibility in the Qinggan River delta, Three Gorges, China

[J]. Geomorphology, 2012, 171: 30-41.

https://doi.org/10.1016/j.geomorph.2012.04.024      URL      [本文引用: 1]      摘要

Kernel machines are widely applied in classification because of many typical advantages, such as a good capacity to deal with high-dimensional data, good generation performance, few parameters to adjust, explainable results, etc. The kernel-based Fisher discriminant analysis (KFDA) is a typical kernel-based method based on the statistical discriminant analysis and it includes both the training and testing process. The model is trained by a dataset of environmental factors that cause landslide occurrence and target output values. Furthermore, the trained model is tested by a separate set of testing samples. This approach utilizes a kernel function to map data from the original feature space to a high-dimensional space, through which a nonlinear problem is converted into a linear one. A typical landslide study area, namely Qinggan River delta, situated in Three Gorges, China, is selected for this study and the following environmental factors are determined as independent variables of the model ithology, elevation, normalized difference vegetation index (NDVI), slope, aspect, distance to rivers, plan curvature, and profile curvature. Judging from the accuracies of the training and testing samples, the sigmoid kernel performed better than the radial basis function kernel and the polynomial kernel. Using different ratios of landslide to non-landslide samples, the performance of KFDA is compared with the linear Fisher discriminant analysis (LFDA) and the logistic regression using a ROC/AUC validation. The results reveal that the average performance of KFDA for all ratios of samples is the most optimal with the mean AUC value as high as 0.911, while the mean AUC values of the logistic regression and LFDA are 0.867 and 0.089 respectively. Although the logistic regression performed slightly better than KFDA when the ratio of landslide to non-landslide samples was 2:1 and 3:1, its AUC values for other ratios of samples are much lower than the AUC values of KFDA. KFDA is more robust and less sensitive to different ratios of samples. The susceptibility map produced by KFDA shows that the regions around rivers are highly at risk to the occurrence of landslides in the study area.
[2] Hadji R, Boumazbeur A E, Limani Y A et al.

Geologic, topographic and climatic controls in landslide hazard assessment using GIS modeling: A case study of Souk Ahras region, NE Algeria

[J]. Quaternary International, 2013, 302: 224-237.

https://doi.org/10.1016/j.quaint.2012.11.027      URL      [本文引用: 1]      摘要

Landslides are the most common hazard in mountainous regions of northeast Algeria. In this study, landslide hazard zonation of Souk Ahras province was carried out using a Raster-based GIS and statistical processing. Landslide locations were defined from interpretation of aerial photographs and field surveys. Rotational, planar and complex landslides were identified. To reveal the controlling factors of landslides, a temporal distribution of 603 recognized landslides (1981 2011) is compared with the monthly precipitation variation, indicating a strong correlation between precipitation and landslide occurrence. The correlation between landslide and lithology, slope angle, and elevation shows the same results. Tabular data, maps and satellite images were collected, processed, and constructed into a spatial database in a GIS platform. The factors that influence landslide occurrence, such as slope angle, slope exposition and elevation were derived from the DEM; Lithology, soil deposits and faults were digitalized from the geologic maps; roads, streams and timber were extracted from Landsat image; precipitation was krigged from pluviometric measurement dataset. Different classes of thematic layers were assigned. A corresponding rating value as attribute information and an attribute map was generated for each data layer in the GIS. Landslide hazard areas were assessed and mapped using the landslide occurrence and permanent factor maps, by applying a probabilistic method with a logistic regression approach. The results of the analysis were verified using landslides location map, compared with the probability model. The resulting map can be used to mitigate this hazard, and to plan land use and urbanization.
[19] Romstad B, Etzelmüller B.Structuring the digital elevation model into landform elements through watershed segmentation of curvature[C]//In:Proceedings of Geomorphometry. Switzerland: University of Zurich, 2009:55-60.

[本文引用: 1]     

[20] Romstad B, Etzelmuller B.

Mean-curvature watersheds: A simple method for segmentation of a digital elevation model into terrain units

[J]. Geomorphology, 2012, 139: 293-302.

https://doi.org/10.1016/j.geomorph.2011.10.031      URL      [本文引用: 1]      摘要

Terrain segmentation is the process of subdividing a continuous terrain surface into discrete terrain units. If the resulting units represent meaningful geomorphic objects the approach may facilitate studies of not only landforms and land forming processes, but also the interaction among surface form, soil, vegetation, hydrology and topoclimatic regimes. Commonly used methods for terrain segmentation fail to produce terrain units with a potentially large, but cyclic variation in topographic attributes, such as uniformly curved areas bounded by topographic break-lines, although this topographic characterisation is common for a number of landforms. This paper describes a new method for terrain segmentation using mean-curvature ( MEC ) watersheds. The method produces objects that contain a cycle of MEC values. Thus the topographic variation within each object may be large, but due to the cyclic nature of the MEC variation a geometric simplicity is ensured. In a case study we show how the resulting terrain units correspond well with a number of landforms and surface types observed in the field, and conclude that the method can be expected to be of great value for a number of applications within geomorphology and related disciplines.
[3] Hansen A.Landslide hazard analysis[C]// In:Brunsden D,Prior D B. Slope Instability. New York:Wiley,1984:523-602.

[本文引用: 1]     

[4] Guzzetti F, Carrara A, Cardinali M et al.

Landslide hazard evaluation: a review of current techniques and their application in a multi-scale study, Central Italy

[J]. Geomorphology, 1999, 31(1/4): 181-216.

https://doi.org/10.1016/S0169-555X(99)00078-1      URL      [本文引用: 2]      摘要

In recent years, growing population and expansion of settlements and life-lines over hazardous areas have largely increased the impact of natural disasters both in industrialized and developing countries. Third world countries have difficulty meeting the high costs of controlling natural hazards through major engineering works and rational land-use planning. Industrialized societies are increasingly reluctant to invest money in structural measures that can reduce natural risks. Hence, the new issue is to implement warning systems and land utilization regulations aimed at minimizing the loss of lives and property without investing in long-term, costly projects of ground stabilization. Government and research institutions worldwide have long attempted to assess landslide hazard and risks and to portray its spatial distribution in maps. Several different methods for assessing landslide hazard were proposed or implemented. The reliability of these maps and the criteria behind these hazard evaluations are ill-formalized or poorly documented. Geomorphological information remains largely descriptive and subjective. It is, hence, somewhat unsuitable to engineers, policy-makers or developers when planning land resources and mitigating the effects of geological hazards. In the Umbria and Marche Regions of Central Italy, attempts at testing the proficiency and limitations of multivariate statistical techniques and of different methodologies for dividing the territory into suitable areas for landslide hazard assessment have been completed, or are in progress, at various scales. These experiments showed that, despite the operational and conceptual limitations, landslide hazard assessment may indeed constitute a suitable, cost-effective aid to land-use planning. Within this framework, engineering geomorphology may play a renewed role in assessing areas at high landslide hazard, and helping mitigate the associated risk.
[21] 朱庆, 田一翔, 张叶廷.

从规则格网DEM自动提取汇水区域及其子区域的方法

[J]. 测绘学报, 2005, 34(2): 129-133.

https://doi.org/10.3321/j.issn:1001-1595.2005.02.007      URL      [本文引用: 1]      摘要

从DEM自动提取的汇水区域及其子区域信息对进一步的水文分析有着重要的辅助作用.在经过洼地处理的DEM及得到水流方向矩阵的基础上,本文提出并实现了一种汇水区域及其子区域的提取算法.该算法首先提取整个DEM区域内每条河流的汇水区域,然后按照不同的要求划分子区域.经过试验,与现有的方法相比,该算法在提取效率和结果准确性方面都有明显提高.

[Zhu Qing, Tian Yixiang, Zhang Sheting.

The extraction of catchment and subcatchment from regular grid DEMs.

Acta Geodaetica et Cartographica Sinica, 2005, 34(2): 129-133.]

https://doi.org/10.3321/j.issn:1001-1595.2005.02.007      URL      [本文引用: 1]      摘要

从DEM自动提取的汇水区域及其子区域信息对进一步的水文分析有着重要的辅助作用.在经过洼地处理的DEM及得到水流方向矩阵的基础上,本文提出并实现了一种汇水区域及其子区域的提取算法.该算法首先提取整个DEM区域内每条河流的汇水区域,然后按照不同的要求划分子区域.经过试验,与现有的方法相比,该算法在提取效率和结果准确性方面都有明显提高.
[5] Xie M, Esaki T, Qiu C et al.

Spatial three-dimensional landslide susceptibility mapping tool and its applications

[J]. Earth Science Frontiers, 2007, 14(6): 73-84.

https://doi.org/10.1016/S1872-5791(08)60004-4      URL      [本文引用: 2]      摘要

There are three methods of zoning landslide susceptibility: qualitative,statistical methodologies and geotechnical model.Qualitative approaches are based on the judgment of those conducting the susceptibility or hazard assessment;the statistical approach uses a predictive function or index derived from a combination of weighted factors;and the deterministic,or physically based,models are based on the physical laws of conservation of mass,energy and momentum.Two-dimensional deterministic models are widely used in the design of civil engineering and the infinite slope model(one-dimensional) is employed in the deterministic model based landslide hazard mapping.This paper presents a new GIS(Geographic Information Systems)-based landslide susceptibility mapping system which can be used to identify the three-dimensional(3-D) landslide bodies from complex topography.All slope-related spatial information(vector or raster dataset) is integrated in the system,by dividing the study area into slope units and assuming the initial slip to be the lower part of an ellipsoid.The 3-D critical slip surface in the 3-D slope stability analysis is located by minimizing the 3-D safety factor using the Monte Carlo random simulation.The failure probability of the landslide is calculated using an approximate method in which effective cohesion,effective friction angle and 3-D safety factor are assumed to be in normal distribution.A computational program called 3-DSlopeGIS,in which a GIS Developer kit(ArcObjects of ESRI) is used to fulfill the GIS spatial analysis function and effective data management,has been developed to implement all the calculations of the 3-D slope problem.By using the spatial analysis functions,the data management and the visualization of GIS for processing the complicated slope-related data,the 3-D slope stability problem is easier to be studied through a friendly visual graphical user interface.The system has been applied for mapping the landslide susceptibility of three examples: the first one for city planning,the second for predicting the possible landslide influence around a past slope disaster,and the third for mapping landslide along a national route.Based on numerous Monte Carlo simulations,the possible critical landslide bodies have been identified which cannot be carried out by using the traditional slope stability analyses.
[6] Jia Ning, Mitani Y, Xie Mowen et al.

Shallow landslide hazard assessment using a three-dimensional deterministic model in a mountainous area

[J]. Computers and Geotechnics, 2012, 45: 1-10.

https://doi.org/10.1016/j.compgeo.2012.04.007      URL      [本文引用: 2]      摘要

Shallow landslides are common in mountainous areas after intense rainfall. Of all landslide hazard assessment methods, deterministic methods provide the best quantitative information on landslide hazard. However, they require a large amount of detailed in situ data, derived from laboratory tests and field measurements, and therefore it is difficult to apply them over large areas. One of the most important input parameters is soil depth. For large areas, it is impossible to obtain soil depth through field measurements. To overcome this difficulty, a statistics-based regression analysis is used to evaluate soil depths. All the terrain attributes that control soil depths are selected as influential factors. By using multi-linear regression, the soil depths at each location can be predicted. Slope stability analysis can then be performed using deterministic methods with the evaluated soil depths. The study area is divided into slope units. For each slope unit, Monte-Carlo simulation and a GIS-based 3D limit equilibrium model are used to locate the critical slip surface and calculate the corresponding safety factor. The effectiveness of the proposed method has been tested by applying it to a mountainous area in Japan.
[22] 朱庆, 赵杰, 钟正, .

基于规则格网DEM的地形特征提取算法

[J]. 测绘学报, 2004, 33(1): 77-82.

https://doi.org/10.3321/j.issn:1001-1595.2004.01.014      URL      [本文引用: 1]      摘要

提出并实现了一种基于规则格网DEM的地形特征线提取算法,该算法在现有地表水流模拟方法的基础上将矢量操作与栅格操作结合起来对规则格网DEM中的洼地进行填平处理,采用邻域格网分组扫描方法确定平地水流方向,与以往算法相比在提取效率和结果准确性等方面都有了明显的改进,从而也使其更加适合于对大规模的DEM数据进行处理,采用各种尺度的DEM进行试验的结果验证了以上结论。

[Zhu Qing, Zhao Jie, Zhong Zheng et al.

The extraction of topographic patterns based on regular grid DEMs.

Acta Geodaetica et Cartographica Sinica, 2004, 33(1): 77-82.]

https://doi.org/10.3321/j.issn:1001-1595.2004.01.014      URL      [本文引用: 1]      摘要

提出并实现了一种基于规则格网DEM的地形特征线提取算法,该算法在现有地表水流模拟方法的基础上将矢量操作与栅格操作结合起来对规则格网DEM中的洼地进行填平处理,采用邻域格网分组扫描方法确定平地水流方向,与以往算法相比在提取效率和结果准确性等方面都有了明显的改进,从而也使其更加适合于对大规模的DEM数据进行处理,采用各种尺度的DEM进行试验的结果验证了以上结论。
[7] 霍艾迪, 张骏, 卢玉东, .

地质灾害易发性评价单元划分方法——以陕西省黄陵县为例

[J]. 吉林大学学报:地球科学版, 2011, 41(2): 523-528, 535.

[本文引用: 1]     

[Huo Aidi, Zhang Jun, Lu Yudong et al.

Method of classification for susceptibility evaluation unit for geological hazards: a case study of huangling county, Shaanxi, China.

Journal of Jilin University(Earth Science Edition), 2011, 41(2): 523-528, 535.]

[本文引用: 1]     

[23] 叶爱中, 夏军, 王纲胜, .

基于数字高程模型的河网提取及子流域生成

[J]. 水利学报, 2005, 36(5): 531-537.

https://doi.org/10.3321/j.issn:0559-9350.2005.05.004      URL      [本文引用: 1]      摘要

提出新的从DEM直接提取河网与划分子流域的方法(AEDNM).该方法与以往方法的不同之 处在于不再对DEM进行填洼处理,而是结合图论与水文学的思想,从流域的出口直接向上游搜索,通过图的遍历来确定流向,使全流域形成一个有向无环图,这样 提取的河网可以保证是连续的,同实际河网误差很小.根据河网划分的子流域大小也基本均匀,能够满足水文模型模拟的需求.经过黄河、泾河与白河流域的算例验 证,表明该法简单可行.

[Ye Aizhong, Xia Jun, Wang Gangsheng et al.

Drainage network extraction and subcatchment delineation based on digital elevation model.

Journal of Hydraulic Engineering, 2005, 36(5): 531-537.]

https://doi.org/10.3321/j.issn:0559-9350.2005.05.004      URL      [本文引用: 1]      摘要

提出新的从DEM直接提取河网与划分子流域的方法(AEDNM).该方法与以往方法的不同之 处在于不再对DEM进行填洼处理,而是结合图论与水文学的思想,从流域的出口直接向上游搜索,通过图的遍历来确定流向,使全流域形成一个有向无环图,这样 提取的河网可以保证是连续的,同实际河网误差很小.根据河网划分的子流域大小也基本均匀,能够满足水文模型模拟的需求.经过黄河、泾河与白河流域的算例验 证,表明该法简单可行.
[8] 程温鸣, 彭令, 牛瑞卿.

基于粗糙集理论的滑坡易发性评价——以三峡库区秭归县境内为例

[J]. 中南大学学报:自然科学版, 2013, 44(3): 1083-1090.

URL      [本文引用: 1]      摘要

以滑坡灾害突出的三峡库区秭归县境内为研究区,利用粗糙集理论将20个初始评价因子进行属性约简至12个核心评价因子,并对其组成的决策表进行知识挖掘获得滑坡与评价因子之间的规则集合。利用知识规则集合对决策表进行分类,得到以斜坡单元为基础的滑坡易发性图。研究结果表明:滑坡易发区面积占研究区总面积的21.7%,主要分布在斜坡结构为顺向坡,地层岩性为软岩、软硬相间岩,以及靠近水系及公路开挖的区域。粗糙集方法的预测精度为87%,其预测能力较KNN算法和Logistic模型的优。粗糙集理论是一种行之有效的区域滑坡易发性评价方法。

[Cheng Wenming, Peng Ling, Niu Ruiqing.

Landslide susceptibility assessment based on rough set theory:Taking Zigui County territory in Three Gorges Reservoir for example.

Journal of Central South University (Science and Technology), 2013, 44(3): 1083-1090.]

URL      [本文引用: 1]      摘要

以滑坡灾害突出的三峡库区秭归县境内为研究区,利用粗糙集理论将20个初始评价因子进行属性约简至12个核心评价因子,并对其组成的决策表进行知识挖掘获得滑坡与评价因子之间的规则集合。利用知识规则集合对决策表进行分类,得到以斜坡单元为基础的滑坡易发性图。研究结果表明:滑坡易发区面积占研究区总面积的21.7%,主要分布在斜坡结构为顺向坡,地层岩性为软岩、软硬相间岩,以及靠近水系及公路开挖的区域。粗糙集方法的预测精度为87%,其预测能力较KNN算法和Logistic模型的优。粗糙集理论是一种行之有效的区域滑坡易发性评价方法。
[24] 俞雷, 刘洪斌, 武伟.

基于DEM的重庆三峡库区水系提取试验研究

[J]. 地理科学, 2006, 26(5): 616-621.

[本文引用: 1]     

[Yu Lei, Liu Hongbin, Wu Wei.

Extraction of river networks in the Three Gorges Area in Chongqing based on DEM.

Scientia Geographica Sinica, 2006, 26(5): 616-621.]

[本文引用: 1]     

[9] 武雪玲, 任福, 牛瑞卿, .

斜坡单元支持下的滑坡易发性评价支持向量机模型

[J]. 武汉大学学报:信息科学版, 2013, 38(12): 1499-1503.

URL      摘要

针对传统滑坡预测手段数据源有限、数据更新周期长、难以发现隐藏在复杂滑坡系统中的规律等问题,本文以三峡库区为研究对象,从多源空间数据中提取滑坡孕灾环境和影响因素等信息,采用数字地形水文分析方法划分斜坡单元,对评价因子进行重采样,进而构建两类支持向量机模型.分析了多源影响因素与滑坡易发性的定量关系,并生成滑坡易发性分区图.采用成功率曲线和误差率评价预测结果,模型预测精度达到98.21%,与野外调查实际情况吻合较好.

[Wu Xueling, Ren Fu, Niu Ruiqing et al.

Landslide spatial prediction based on slope units and support vector machines.

Geomatics and Information Science of Wuhan University, 2013, 38(12): 1499-1503.]

URL      摘要

针对传统滑坡预测手段数据源有限、数据更新周期长、难以发现隐藏在复杂滑坡系统中的规律等问题,本文以三峡库区为研究对象,从多源空间数据中提取滑坡孕灾环境和影响因素等信息,采用数字地形水文分析方法划分斜坡单元,对评价因子进行重采样,进而构建两类支持向量机模型.分析了多源影响因素与滑坡易发性的定量关系,并生成滑坡易发性分区图.采用成功率曲线和误差率评价预测结果,模型预测精度达到98.21%,与野外调查实际情况吻合较好.
[25] 周德民, 程进强, 熊立华.

基于DEM的洪泛平原湿地数字水系提取研究

[J]. 地理科学, 2008, 28(6): 776-781.

Magsci      [本文引用: 1]      摘要

为了研究探索洪泛平原湿地区域基于DEM的地表水要素数字特征,采用ArcGIS9.0的Hydro Arc Tools模块,配合改进升值裂开算法编制的程序在三江平原洪河保护区1:1万比例尺的DEM基础上进行了数字水系提取研究,将研究区划分为6个数字集水区,提取出以沃绿兰河-浓江河为主的数字河网,以及大小82处泡沼和洼地。研究表明,在保持高精度DEM前提下,数字地表水系统可以通过基于DEM自动提取出来,但是存在河道偏移以及河网形态失真等问题,需要在进行数字提取前后进行多次修正。在DEM数字高程预处理过程中保持高程信息的水文特征不丢失,以及发展专业处理平坦区域和低洼地域的有效算法,将是进一步提高洪泛平原湿地区域数字水系提取效率和精度的关键。

[Zhou Demin, Cheng Jinqiang, Xiong Lihua.

Digital extraction of surface hydrological elements from DEM data in the wetland area of a flood plain.

Scientia Geographica Sinica, 2008, 28(6): 776-781.]

Magsci      [本文引用: 1]      摘要

为了研究探索洪泛平原湿地区域基于DEM的地表水要素数字特征,采用ArcGIS9.0的Hydro Arc Tools模块,配合改进升值裂开算法编制的程序在三江平原洪河保护区1:1万比例尺的DEM基础上进行了数字水系提取研究,将研究区划分为6个数字集水区,提取出以沃绿兰河-浓江河为主的数字河网,以及大小82处泡沼和洼地。研究表明,在保持高精度DEM前提下,数字地表水系统可以通过基于DEM自动提取出来,但是存在河道偏移以及河网形态失真等问题,需要在进行数字提取前后进行多次修正。在DEM数字高程预处理过程中保持高程信息的水文特征不丢失,以及发展专业处理平坦区域和低洼地域的有效算法,将是进一步提高洪泛平原湿地区域数字水系提取效率和精度的关键。
[10] 薛强, 张茂省, 李林.

基于斜坡单元与信息量法结合的宝塔区黄土滑坡易发性评价

[J]. 地质通报, 2015, 34(11): 2108-2115.

URL      [本文引用: 1]      摘要

滑坡易发性评价对滑坡灾害的防治与管理具有重要意义.为了评价延安宝塔区黄土滑坡易发性,以斜坡为基本评价单元,选取斜坡坡度、坡高、坡向、坡形、斜坡结构类型、植被和人类工程活动7个指标作为评价因子,在ArcGIS平台下,利用信息量模型对研究区的黄土滑坡进行易发性分区评价.评价结果表明,宝塔区滑坡高易发区面积1092.39km2,占全区面积的30.81%,主要分布于宝塔区的中部及北部地区,低易发区集中于宝塔区南部汾川河流域.以斜坡作为评价单元提高了与实际地形地貌的吻合度.应用信息量模型进行滑坡易发性评价具有较高的预测精度,已有滑坡点落在很高易发区和高易发区中的比例为95.7%,较真实地反映了客观实际.

[Xue Qiang, Zhang Maosheng, Li Lin.

Loess landslide susceptibility evaluation based on slope unit and information value method in Baota District, Yan'an.

Geological Bulletin of China, 2015, 34(11): 2108-2115.]

URL      [本文引用: 1]      摘要

滑坡易发性评价对滑坡灾害的防治与管理具有重要意义.为了评价延安宝塔区黄土滑坡易发性,以斜坡为基本评价单元,选取斜坡坡度、坡高、坡向、坡形、斜坡结构类型、植被和人类工程活动7个指标作为评价因子,在ArcGIS平台下,利用信息量模型对研究区的黄土滑坡进行易发性分区评价.评价结果表明,宝塔区滑坡高易发区面积1092.39km2,占全区面积的30.81%,主要分布于宝塔区的中部及北部地区,低易发区集中于宝塔区南部汾川河流域.以斜坡作为评价单元提高了与实际地形地貌的吻合度.应用信息量模型进行滑坡易发性评价具有较高的预测精度,已有滑坡点落在很高易发区和高易发区中的比例为95.7%,较真实地反映了客观实际.

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