基于组合熵权RSR法的董志塬沟谷发育评价

doi:10.13866/j.azr.2023.03.14

摘要/Abstract

摘要：

黄土沟谷的发育演化进程研究对于发掘沟谷形成与土壤侵蚀的内在机理，指导黄土地区生态修复有深刻的指导意义。基于沟谷水平空间、气候、沟谷点线面特征选取10个沟谷发育程度量化指标，利用组合熵权RSR法优异的多因子综合性分档评价能力建立董志塬沟谷发育阶段分级评价模型，探究黄土沟谷的发育演化及分布规律。研究发现：（1）基于熵权法计算归一化植被指数（NDVI）所占权重最高为16.08%，其次为沟谷密度（15.621%），两者是判断沟谷发育程度的重要指标。（2）基于组合熵权RSR法将董志塬82条沟谷发育程度分为幼年期、青年期、壮年期和老年期，壮年期和老年期沟谷面积占比为88.48%，董志塬东部及北部发育程度较高，对于塬面侵蚀强烈。（3）沟谷发育程度与其下伏古地貌、构造地质和黄土厚度有着高度相关性。（4）模型方差一致性检验显著性水平P<0.001，线性回归拟合优度R²为0.986，评价模型表现良好。

关键词: 黄土, 量化指标体系, 组合熵权RSR法, 沟谷发育分级评价, 董志塬

Abstract:

As a typical erosion geomorphic unit in the loess areas, gullies continuously erode loess surface under the action of internal and external forces, rainfall, and other factors. There are significant differences in the degree of development of gullies and valleys. Evaluating the development pattern of gullies and valleys can enhance the understanding of their organized, systematic formation and evolution. In addition, comprehensive quantitative indexes can facilitate the understanding of the longitudinal, lateral, and horizontal characteristics of gullies and valleys from multiple perspectives, which can help in the accurate and effective implementation of gully consolidation and loess protection projects, and reduce the constraints on development caused by this fragile geological environment. Evaluating the development of loess valleys is also crucial for exploring the intrinsic mechanism of valley formation, soil erosion, and guiding the ecological restoration of loess areas. In this study, ten quantitative indicators of gully development were selected based on the horizontal spatial, climatic, and point-line characteristics of the gullies, and used to establish an indexed evaluation model of the developmental stages of Dongzhi Loess Plateau gullies based on the efficient multi-factor comprehensive indexing evaluation capacity of the combined entropy-weight rank-sum ratio (RSR) method. Results showed that: (1) The highest weight of 16.08% could be attributed to the normalized vegetation index (NDVI) based on the entropy weighting method, followed by gully density (15.621%), both of which are important indicators for predicting the degree of gully development. (2) The combined entropy weighting RSR method could classify the 82 gullies of Dongzhi Loess Plateau into juvenile, youth, prime, and old age categories, with the percentage of gully area under the prime and old age categories accounting for 88.48% and 88.48%, respectively, while the eastern and northern parts of Dongzhi Loess Plateau exhibited more developed features and strong erosion on the loess surface. (3) The degree of gully development was highly correlated with the underlying palaeomorphology, tectonic geology, and loess thickness. (4) A significant model variance consistency test at P<0.001, with a linear regression R² fit of 0.986 was observed, which indicated a good performance of the model.

Key words: loess, quantitative index system, combined entropy-weighted RSR method, graded evaluation of gully development, Dongzhi Loess Plateau

崔帅, 许强, 袁爽, 蒲川豪, 陈婉琳, 纪续. 基于组合熵权RSR法的董志塬沟谷发育评价[J]. 干旱区研究, 2023, 40(3): 481-491.

CUI Shuai, XU Qiang, YUAN Shuang, PU Chuanhao, CHEN Wanlin, JI Xu. Evaluation of Dongzhi Loess Plateau Gully development based on combined entropy weight Rank-Sum Ratio method[J]. Arid Zone Research, 2023, 40(3): 481-491.

图/表 14

图1

表1

沟谷发育评价正向指标"

指标名称	计算公式	解释	指标意义
边界维数	$D = 2 l n N - C l n M$	M为沟谷面积；N为沟谷沿线周长；C为沟谷周长	反映水平方向上沟谷空间展布的复杂程度和沟谷的发育程度。指标值越大，说明局部沟谷与整体沟谷网络的相似程度越高,沟谷形态结构越复杂,发育程度越高。
沟谷密度	$D l = ∑ i = 1 n l i A$	$D l$ 为沟谷密度； $l i$ 为流域内各条沟谷的长度；A为流域面积	反映沟头前进及沟谷侵蚀发育程度的重要指标。指标值越大，说明沟头前进程度越大，即沟谷生长延伸程度越大，发育程度越高。
地表切割深度	$G i$ = $H m e a n - H m i n$	$G i$ 为地表切割深度； $H m e a n$ 为地面某点一定邻域范围内的平均高程； $H m i n$ 为该点同一邻域范围内的最低高程	直观反映了沟谷下切发育程度和地表被侵蚀切割的程度。指标值越大，地表侵蚀切割越剧烈,沟谷下切发育程度越高。
平均坡度	$s l o p e = a r c t a n f x 2 + f y 2 × 180 π$	$f x$ 为x方向的高程变化率； $f y$ 为y方向的高程变化率	在一定程度上反映沟谷地貌的发育程度。沟谷发育初期,沟谷发育以下切为主，指标值逐渐增大，随着沟谷发育程度的增加,沟谷在深切的同时也在横向展宽，指标值反而有所下降。
月平均降雨	$R i = R A 12$	$R i$ 为月平均降雨； $R A$ 为年总降雨	气候影响因素之一，降雨的多少一定程度上影响水流侵蚀的剧烈程度。

表1

表2

沟谷发育评价负向指标"

指标名称	计算公式	解释	指标意义
主沟支沟比	$R = L 0 L$	R为主沟支沟比； $L 0$ 为主沟谷长度； $L$ 为沟谷总长度	从沟谷长度的角度反映沟谷系统中支沟的发育程度。指标值越小，沟谷系统中支沟发育越明显，说明沟谷系统整体发育程度越高。
土地利用程度综合指标	$L a = 100 × ∑ j = 1 n A i × C i$	$L a$ 为土地利用程度综合指数；A_i为第i级的土地利用程度分级指数；C_i为第i级土地利用程度分级面积百分比	是针对一个具体年份内所有土地利用类型整体反映的土地利用集约化程度。通过对土地利用程度的分级,量化人类活动对于土地系统的影响程度,定量地描述该地区土地利用的综合水平和变化趋势，是衡量指定区域内土地利用情况的一个重要指标。
主沟纵比降	$J = H s - H 0 l$	$J$ 为主沟道纵比降, $H s$ 为主沟道出水口点的高程； $H 0$ 为主沟道沟头点的高程； $l$ 为主沟道长度	反映沟谷整体侵蚀势能,是描述沟谷在垂直方向上侵蚀发育程度的重要指标。指标值越小，说明沟谷的侵蚀能量越低，沟谷越趋近于稳定的宽谷，发育程度越高。
归一化植被指数	$N D V I = N I R - R N I R + R$	NIR为近红外波段的反射值；R为红光波段的反射值	反映土地覆盖植被状况的一种遥感指标，定义为近红外通道与可见光通道反射率之差与之和的商。
圆度率	$e i = 4 π S i C i$	$e i$ 为圆度率； $S i$ 为沟谷面积； $C i$ 为沟沿线长度	反应水平方向上沟谷接近圆的程度，其值越接近1，则越接近圆，其发育程度越低。

表2

图2

图3

图4

图5

表3

图6

表4

表5

图7

图8

图9

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发育阶段	百分位临界值	Probit	秩和比临界值（拟合值）	频数	面积/km²	面积占比
幼年期	<6.681	<3.5	<0.3106	5	10.04	0.63%
青年期	6.681~50	3.5~5	0.3106~0.4692	36	177.61	10.89%
壮年期	50~93.319	5~6.5	0.4692~0.6277	35	799.58	49.06%
老年期	>93.319	>6.5	>0.6277	6	642.44	39.42%

	非标准化系数		标准化系数	t	P	VIF	R²	调整R²	F
	B	标准误	Beta
常数	-0.059	0.007	-	-8.173	0.001	-	0.986	0.986	5567.72
Probit	0.106	0.001	0.993	74.617	0.001	1	0.986	0.986	5567.72