复杂网络理论在黄土高原沟谷地貌特征研究中的应用

doi:10.12082/dqxxkx.2021.200639

摘要/Abstract

摘要：

沟谷侵蚀是塑造黄土地表侵蚀形态的主要动力,沟谷的发育过程深刻地影响着黄土地貌的发育及演化。本文在黄土高原选择6个典型地貌样区,以样区的数字高程模型为基本数据源提取沟谷系统。将沟谷系统中的沟谷节点、沟谷源点和流域出水口点作为网络节点,网络节点之间的空间拓扑关系为边,高程差为权值,构建黄土高原沟谷加权复杂网络模型。对黄土沟谷地貌的节点特征和空间结构进行定量刻画和分析,得到黄土高原不同地貌类型网络特征的空间格局及其变化,并进一步映射地貌的发育过程及演化机理。研究结果表明：① 黄土高原沟谷加权网络的点强度累积概率分布呈指数分布,相关性系数皆达到0.80以上,该网络正处于向无标度网络转化的过渡期;② 样区从南到北,沟谷特征点的点强度值呈现逐渐减小的态势,且点强度的分布具有不对称性,沟谷右侧侵蚀强度较高,点强度分布较多;③ 平均路径长度和网络结构熵值在绥德一带最大,分别为30.94、6.31,并向南北两侧呈减少的趋势,网络密度值的变化与之相反;3个指标分别从网络结构的连通性、稳定性和紧密性反映了不同沟谷地貌类型的侵蚀程度以及地貌系统的演化机理;④ 网络指标与传统地貌指标的相关性系数均超过0.85,其可以科学、准确地表达地貌形态的复杂性及地貌的发育阶段,有望作为沟谷地貌地学特征研究的参数。该方法考虑了沟谷地貌的空间拓扑关系以及系统的整体性,为复杂表面形态的地貌研究提出了一种新的思路和方法。

关键词: 黄土高原, 复杂网络, 加权, 沟谷地貌, 拓扑关系, 空间结构, 数字高程模型, 网络指标

Abstract:

Gully erosion has been identified as a major driver of the formation of loess surface erosion, and the development process of the gully profoundly affects the development and evolution of the loess landform. In this study, six typical geomorphological plots of the Loess Plateau were selected, and the digital elevation model of these plots were used as the basic data source to extract the gully system. The weighted complex network model of the gully in the Loess Plateau was constructed using the gully nodes, gully source points, and water outlet points as the network nodes, the spatial topological relationship between the network nodes as the network edges, and the elevation difference as the weight. Through quantitative description and analysis of the nodal characteristics and spatial structure of the loess gully in the Loess Plateau, the spatial pattern and changes of the network characteristics of different landform types of the Loess Plateau were obtained. We further analyzed the development process and evolution mechanism of the loess valley landform. The results show that: ① The cumulative probability of the node strength of the gully weighted networks in the Loess Plateau was exponentially distributed. Correlation coefficients were all above 0.80, and the complex networks were in the transition period from random network to scale-free network; ② From the south to the north plots, the node strength values of the characteristic points of the gully showed a gradually decreasing trend, and the distribution was asymmetric, with higher erosion intensity and more node distribution on the right side of the gully; ③ The average path length and the network structure entropy in Suide area reached the maximum of 30.94 and 6.31, respectively, and gradually decreased at the north and south sides. The change curve of network density was the opposite. The connectivity, stability, and compactness of the network structure reflected the erosion degree of different gully geomorphic types and evolution mechanism of the geomorphic system; ④ The correlation coefficient between network index and traditional geomorphic index was more than 0.85. This parameter emphasized the attribute characteristics and spatial topological relationship of different valley feature points and the differences of feature points in spatial relationship. It can scientifically and accurately express the complexity and development stage of the geomorphology and is expected to be used as an important parameter to study the geomorphological characteristics of the gully. Our method considered the spatial topological relationship of the gully topography and the integrity of the system and provided a new idea for the research of complex surface morphology.

Key words: The Loess Plateau, complex network, weighted, gully landform, topological relationship, spatial structure, DEM, network index

贺卓文, 陈楠. 复杂网络理论在黄土高原沟谷地貌特征研究中的应用[J]. 地球信息科学学报, 2021, 23(7): 1196-1207.DOI:10.12082/dqxxkx.2021.200639

HE Zhuowen, CHEN Nan. Feature Analysis of Gully Landforms in the Loess Plateau based on Complex Networks[J]. Journal of Geo-information Science, 2021, 23(7): 1196-1207.DOI:10.12082/dqxxkx.2021.200639

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指标名称	单位	地学含义
点强度	无量纲	该指标从沟谷地貌高程极差的角度探究了沟谷网络的空间结构特征
平均路径长度	无量纲	该指标在一定程度上反映了沟谷网络的连通性,进而揭示了沟谷系统中支沟的发育程度
网络密度	无量纲	从沟谷网络节点连接的紧密程度出发反映沟谷地貌侵蚀、发育的特征指标
网络结构熵	无量纲	该指标表达了沟谷地貌的稳定性,指标值越大,沟谷网络越稳定,沟谷整体的发育程度越高

样区	地貌类型	平均坡度/°	平均海拔/m	沟壑密度/（km/km²）	发育阶段^[35]
神木	风沙-黄土过渡区	9	1197	4.12	壮年早期
绥德	黄土峁状丘陵沟壑区	29	995	8.44	壮年晚期
延川	黄土墚峁状丘陵沟壑区	31	1089	6.92	壮年晚期
富县	黄土墚峁状丘陵沟壑区	30	1299	6.61	壮年早期
宜君	黄土残塬区	19	987	5.55	壮年早期
淳化	黄土塬区	12	1044	1.06	幼年期

样区	指数函数			幂函数
样区	拟合方程	R²	残差平方和	拟合方程	R²	残差平方和
淳化	Y=188.65e^-0.018^x	0.881	9.240	Y=2372.12x^-0.969	0.573	32.994
宜君	Y=180.71e^-0.023^x	0.951	8.521	Y=1571.62x^-0.969	0.580	73.067
富县	Y=212.97e^-0.023^x	0.920	11.383	Y=1398.23x^-0.904	0.505	70.540
延川	Y=146.23e^-0.021^x	0.983	3.349	Y=3493.97x^-1.188	0.710	56.348
绥德	Y=235.25e^-0.037^x	0.953	11.860	Y=3535.60x^-1.307	0.606	99.334
神木	Y=205.29e^-0.041^x	0.958	3.791	Y=4705.84x^-1.386	0.726	24.481