基于DEM的黄土沟谷横剖面形态特征研究——以宜君、延安、绥德为例

doi:10.13249/j.cnki.sgs.2020.03.014

地理科学 ›› 2020, Vol. 40 ›› Issue (3): 455-465.doi: 10.13249/j.cnki.sgs.2020.03.014

基于DEM的黄土沟谷横剖面形态特征研究——以宜君、延安、绥德为例

周毅^1,², 王泽涛^1,², 杨锋³

^1. 陕西师范大学地理科学与旅游学院,陕西西安 710119
^2. 地理学国家级实验教学示范中心,陕西西安 710119
^3. 北京师范大学地理科学学部遥感科学与工程研究院,北京 100875

收稿日期:2019-02-04 修回日期:2019-06-12 出版日期:2020-03-10 发布日期:2020-05-13
作者简介:周毅（1984-），男，河南南阳人，副教授，博士，主要从事GIS空间分析算法与黄土高原数字地形分析研究。E-mail: zhouyilucky@snnu.edu.cn
基金资助:
国家自然科学基金项目(41871288);国家自然科学基金项目(41930102);中央高校基本科研业务费专项资金项目资助(GK202003064);中央高校基本科研业务费专项资金项目资助(2018CSLZ002)

Morphological Characteristics of Gully Cross-section in the Loess Region Based DEM: Taking Yijun, Yan’an and Suide as Cases

Zhou Yi^1,², Wang Zetao^1,², Yang Feng³

^1. School of Geography and Tourism, Shaanxi Normal University, Xi’an 710119, Shaanxi, China;
^2. National Teaching Demonstration Center for Geography, Xi’an 710119, Shaanxi, China;
^3. Institute of Remote Sensing Science and Engineering, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China

Received:2019-02-04 Revised:2019-06-12 Online:2020-03-10 Published:2020-05-13
Supported by:
National Natural Science Foundation of China(41871288);National Natural Science Foundation of China(41930102);The Fundamental Research Funds for the Central Universities(GK202003064);The Fundamental Research Funds for the Central Universities(2018CSLZ002)

摘要/Abstract

摘要：

选用1:10 000高精度5.0 m分辨率的DEM数据,在陕北地区,按黄土地貌演化序列次序,遴选分别代表黄土残塬沟壑、梁状丘陵沟壑、峁状丘陵沟壑地貌的宜君、延安、绥德3个流域,研究其中1 831个沟谷横剖面19个因子的形态特征,利用主成分分析法确立核心因子,分析结果表明：① 沟谷深度、宽度、横剖面面积、宽深比、侵蚀度与不对称性指标的主成分累积贡献率为95.02%,为黄土沟谷横剖面核心指标;② 随级别的增加,3个流域沟谷宽度、横剖面积、宽深比、侵蚀度均呈现总体增加的态势,与黄土地貌发育阶段具有明显的空间耦合性,尤其是宽深比与侵蚀度指标,反映出低级别黄土沟谷溯源侵蚀现象明显,以下切侵蚀为主,而高级别沟谷沟沿线后移,以侧向侵蚀拓宽为主的规律;③ 随级别增加沟谷深度呈现先增后降的态势,并在中级别沟谷出现拐点,与实地调研发现沟谷在中级别下切侵蚀遇到基岩的现象相吻合。

关键词: DEM, 沟谷横剖面, 宽深比, 侵蚀度, 黄土高原

Abstract:

Loess gully cross-sections carry greatly important information on evolution of loess landforms, gully erosion and sediment yield. However, systematically quantifying morphological characteristics of loess gully remains been poorly understood. The objectives of this study are to: 1) Analyze the characteristics of gully cross-section indexes (including basic gully cross-section indexes and compounded gully cross-section indexes) for different ranks of gully in the same sub-watershed, and for the same rank of gully in different sub-watersheds. 2) Reveal the relation of gully cross-section and loess landforms in different evolution stage. In this study, we choose Loess Broken Tableland (Yijun Watershed), Loess Ridge (Yan’an Watershed) and Loess Hill (Suide Watershed) as the study test sites, and classify the three watersheds into 5 ranks according to Strahler’s method. Our original studied data are 5 m-resolution Digital Elevation Models (DEMs) and the matched Digital Orthophoto Maps (DOMs) with 1 m-resolution. The DEMs and DOMs met the national standards of China; the DOM data was conducted by using of 5 m-resolution DEM. Based on 5 m DEM, we measured 19 indexes for 1 831 loess gully cross-sections in Yijun, Yan’an and Suide using GIS platform. Futher, we applied the principal component analysis method (PCA) to obtain 7 key indexes: namely, depth, width, cross-section eroded area, the ratio of width/depth, erosion degree, asymmetry ratio of side width and asymmetry ratio of side area of loess gully. The results demonstrate that: 1) The principle component analysis test showed that the cumulative contribution rate of depth, width, cross-section eroded area, the ratio of width/depth, erosion degree, asymmetry ratio of side width and asymmetry ratio of side area of loess gully already reaches to 95.02%. These indexes act as key indexes for characterizing loess gully cross-section. 2) With the increase of loess gully-rank, obvious increasing trends were detected in width, cross-section area, width/depth ratio, erosion degree of loess gullies. Besides, the trends of width/depth ratio and gully depth indexes indicate that low-ranks loess gullies present obvious downward erosion, whereas high-ranks loess gullies present lateral erosion accompanying with shoulder-lines retreating. 3) With the increase of loess gully-rank, the depth presents a trend of increasing firstly and then decreasing, and the turning points occur at intermediate-levels gully. The trend confirms the fact that intermediate-levels gullies have started to incise into bedrock.

Key words: Digital Elevation Model, gully cross-section, width/depth ratio, erosion degree, the Loess Plateau

中图分类号:

P931.6

周毅, 王泽涛, 杨锋. 基于DEM的黄土沟谷横剖面形态特征研究——以宜君、延安、绥德为例[J]. 地理科学, 2020, 40(3): 455-465.

Zhou Yi, Wang Zetao, Yang Feng. Morphological Characteristics of Gully Cross-section in the Loess Region Based DEM: Taking Yijun, Yan’an and Suide as Cases[J]. SCIENTIA GEOGRAPHICA SINICA, 2020, 40(3): 455-465.

图/表 12

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样区名称	经纬度	平均坡度（°）	高差（m）	沟谷密度（km/km²）	面积高程积分	侵蚀模数 [t/(km²·a)]	地貌类型
宜君	109°18′45″~109°26′15″E, 35°25′00″~35°30′00″N	20.59	334.69	2.44	0.515	2569	黄土残塬
延安	110°18′30″~110°22′00″E, 37°33′00″~37°35′00″N	29.17	337.12	7.74	0.519	8104	黄土梁状丘陵沟壑
绥德	110°15′00″~110°22′30″E, 37°32′30″~37°37′30″N	29.77	319.90	9.39	0.484	8949	黄土峁状丘陵沟壑

参数	参数名称	参数计算方式及意义	参数	参数名称	参数计算方式及意义
w_t	沟谷顶部宽	w_t=w_l+w_r	s	沟谷横剖侵蚀面积	s=s_l+ s_r
w_1/4	沟谷底部宽	1/4最大深度处的宽度	A	沟谷横剖面面积	沟谷横剖面侵蚀、未侵蚀面积之和
w_l	沟谷左侧宽	左沟沿线到沟底的水平距离	s_bl	左侧未被侵蚀面积	沟谷左侧未被侵蚀的面积
w_r	沟谷右侧宽	右沟沿线到沟底的水平距离	s_br	右侧未被侵蚀面积	沟谷右侧未被侵蚀的面积
d_r	沟谷右侧深	沟谷右坡与沟沿线的交点	s_i	形状指数	描述沟谷形状,s_i= w_1/4/w_t
d_l	沟谷左侧深	沟谷左坡与沟沿线的交点	e	侵蚀度	描述沟谷侵蚀程度, e=s/A
d_g	沟谷线位置深	d_g=(w_l d_r+w_rd_l)/(w_r+w_l)	r_w/d	宽深比	描述侧向侵蚀与下切侵蚀的关系,r_w/d= w_t/d_g
d_m	沟谷均深	沟谷横剖面被侵蚀部分均深	s_a	面积不对称性	描述面积的差异性,s_a= s_r/s_l
s_l	沟谷左侧面积	沟谷左侧被侵蚀的面积	s_w	宽度不对称性	两侧侧向侵蚀差异性,s_w = w_r/w_l
s_r	沟谷右侧面积	沟谷右侧被侵蚀的面积

主分量	方差(%)	累积方差(%)
1	63.93	63.93
2	19.37	83.30
3	11.72	95.02

参数	主分量			参数	主分量
参数	1	2	3	参数	1	2	3
d₁	0.424	0.763	-0.185	S_br	0.872	0.322	0.073
d_r	0.733	0.618	0.095	S₁	0.988	-0.060	-0.084
d_m	0.353	0.916	-0.148	S_r	0.985	0.023	0.079
d_g	0.557	0.824	-0.004	S	0.996	-0.012	0.011
w₁	0.941	-0.294	-0.087	A	0.986	0.116	-0.036
w_r	0.964	-0.160	-0.059	e	0.920	-0.219	0.216
w_t	0.966	-0.218	-0.071	r_w/d	0.759	-0.621	-0.144
w_1/4	0.914	-0.393	0.044	S_w	0.137	0.178	0.948
S_i	0.726	-0.517	0.240	S_a	0.138	0.124	0.976
S_b₁	0.868	0.118	-0.381

	宜君流域					延安流域					绥德流域
级别	1级	2级	3级	4级	5级	1级	2级	3级	4级	5级	1级	2级	3级	4级	5级
d_g	22	40	46	38	42	30	43	39	33	33	25	36	34	34	31
w_t	52	102	128	182	196	86	136	142	161	224	75	98	104	114	166
s	525	2027	3264	4141	4279	1274	3068	2822	3137	4465	850	1667	1754	2096	3475
e	0.36	0.44	0.49	0.54	0.48	0.40	0.45	0.44	0.51	0.54	0.39	0.42	0.45	0.46	0.56
r_w/d	2.73	2.65	2.89	4.80	4.81	3.10	3.27	3.96	4.95	7.45	3.25	2.88	3.21	3.40	5.80
s_w	0.95	1.27	1.31	1.62	1.28	1.14	0.98	0.83	0.98	0.86	1.16	1.16	1.08	1.09	1.22
s_a	1.06	1.22	1.41	1.83	1.49	1.15	0.99	0.83	1.00	0.79	1.15	1.14	1.10	1.08	1.22

基于DEM的黄土沟谷横剖面形态特征研究——以宜君、延安、绥德为例

Morphological Characteristics of Gully Cross-section in the Loess Region Based DEM: Taking Yijun, Yan’an and Suide as Cases

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参考文献 30

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研究样区	沟谷级别						合计
研究样区		1	2	3	4	5	合计
宜君	沟谷数	28	19	6	2	1	56
宜君	横剖面	176	183	79	50	34	522
延安	沟谷数	26	18	12	2	1	59
延安	横剖面	181	150	122	69	21	543
绥德	沟谷数	25	29	17	4	1	76
绥德	横剖面	177	271	205	70	43	766

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