DEM分辨率对提取东北地区坡度的影响研究

刘佳轩; 高瑞; 师黎静

doi:10.11899/zzfy20210202

DEM分辨率对提取东北地区坡度的影响研究

doi: 10.11899/zzfy20210202

刘佳轩^1,,
高瑞^2, ,,
师黎静¹

1.
中国地震局工程力学研究所，地震工程与工程振动重点实验室，哈尔滨 154200
2.
黑龙江科技大学，建筑工程学院，哈尔滨 154200

基金项目: 国家重点研发计划（2018YFC1504601）；国家自然科学基金面上项目（51978635）

详细信息

作者简介:
刘佳轩，男，生于1995年。硕士研究生。主要从事工程抗震方面的研究。E-mail：liujiaxuanhit@163.com

通讯作者:
高瑞，男，生于1993年。硕士研究生。主要从事工程抗震方面的研究。E-mail：gaoruihy@163.com

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出版历程
- 收稿日期: 2021-04-26
- 刊出日期: 2021-06-30

Research on the Influence of DEM Resolution on the Slope Extraction in Northeast, China

Liu Jiaxuan^1
,,
Gao Rui^{2
, ,},
Shi Lijing¹

1.
Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 154200, China
2.
Department of Civil Engineering, Heilongjiang University of Science and Technology, Harbin 154200, China

摘要

摘要: 目前国内外广泛采用的坡度-等效剪切波速关系模型中，坡度主要基于30″分辨率数字高程数据的提取。DEM分辨率对坡度的提取具有重要影响，且对于不同地区、地貌单元的影响不同。本文以我国东北地区1″、3″、30″分辨率DEM为基础，分别提取研究区域内公里网格点的百分比坡度，分析不同分辨率下提取坡度差异的原因。区分平原、丘陵和山地统计分析坡度随分辨率变化特征，通过比较多种拟合模型的拟合优度和坡度分级平均相对差值，给出不同分辨率下的最佳坡度转换关系。研究结果表明，坡度体现计算面积的平均特性，随着分辨率的增大，栅格计算面积减小，导致坡度有所差异，区域坡度变化越大差异越大；在我国东北地区，随着DEM分辨率的降低，坡度-频率分布曲线向低坡度段移动，且均值、方差及值域变小，不同地貌的坡度-频率分布曲线向低坡度方向移动，且峰值区域变窄，其中平原地貌变化趋势性显著，丘陵次之，山地最小；平原及山地地貌最佳坡度拟合为线性拟合，丘陵地貌下1″、3″与30″分辨率下最佳坡度拟合分别为线性拟合和多项式拟合。
- DEM分辨率 /
- 地貌 /
- 坡度 /
- 坡度转换 /
- 场地分类
Abstract: The regional site classification method based on the slope has been successfully applied. The relationship model of slope-equivalent shear wave velocity based on 30 arc-second DEM is widely used at home and abroad. DEM resolution influences the extraction of the slope, and this influence is different in varying regions and landforms. Based on 1 arc-second, 3 arc-second, and 30 arc-second resolution DEM in Northeast China, this paper extracts the percentage slopes of the kilometer grid points and analyzes the reasons for the different slopes. Analyzing the characteristics of slope change with resolution in varying landforms, comparing the goodness of fit and the average relative difference, the best grade conversion relationship for different resolutions is selected. The results indicate the slope reflects the average characteristics of the calculated area. As the resolution increases, the grid area for slope calculation becomes smaller, which is the main reason for the different slopes. And the greater the slope of the area, the more significant the difference. With the decrease of DEM resolution, the frequency distribution curve of slope shifts to the low slope section, and the mean, variance, and range of values become smaller. The frequency distribution curves of varying landforms also move to the low slopes section, and the peak area becomes narrower. Among them, the changing trend of plain landforms is significant, followed by hills and mountains. The best fits for the slopes of plain and mountainous landforms are linear fitting. The best fits for slopes of 1 arc-second, 3 arc-seconds and 30 arc-seconds of hilly landforms are linear fitting and polynomial fitting, respectively.
- DEM resolution /
- Landform /
- Slope /
- Slope conversion /
- Site classification

HTML全文

图 1 东北地区不同分辨率下高程数据模型图

Figure 1. Elevation maps of 1 arc second, 3 arc second, and 30 arc second resolution in the Northeast, China

下载: 全尺寸图片幻灯片

图 2 计算高程梯度变化率的像元窗口

Figure 2. 3×3 unit schematic diagram of slope calculation point

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图 3 东北地区不同分辨率下坡度图

Figure 3. Slope maps of 1 arc second, 3 arc second, and 30 arc second resolution in the Northeast, China

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图 4 不同DEM分辨率下的坡度统计

Figure 4. Slope statistics of different DEM resolutions

下载: 全尺寸图片幻灯片

图 5 地貌分布图

Figure 5. Landform distribution map

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图 6 不同分辨率下不同地貌单元坡度-频率分布曲线

Figure 6. Slope-frequency distribution curves of different topography at different resolutions

下载: 全尺寸图片幻灯片

图 7 不同地貌单元不同分辨率下坡度转换结果

Figure 7. Conversion results of DEM slopes with different resolutions under different landforms

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表 1 不同地貌单元回归模型拟合参数及评价参数（1″与30″分辨率下）

Table 1. Fitting and evaluation parameters of regression models for different landforms (1 arc second and 30 arc second)

地貌单元类型	拟合模型	拟合参数				R²	Δ_mean	K
地貌单元类型	拟合模型	a	b	c	d	R²	Δ_mean	K
平原	线性函数	0	0.085 63	—	—	0.313 40	0.535 7	0.585 0
	多项式函数	0.114 600	−0.154 80	0.090 50	0	0.322 20	0.763 9	0.421 7
	幂函数	0.047 160	0.658 50	0	—	0.080 00	0.892 3	0.089 6
丘陵	线性函数	0	0.132 57	—	—	0.552 50	0.320 8	1.722 2
	多项式函数	0.259 270	−0.736 80	0.711 46	0	0.610 81	0.486 5	1.255 5
	幂函数	0.043 249	0.329 23	0	—	0.077 8	0.842 3	0.092 3
山地	线性函数	0	0.199 24	—	—	0.598 49	0.345 1	1.734 2
	多项式函数	0.445 110	−0.996 52	0.686 59	0	0.687 30	0.714 8	0.961 5
	幂函数	0.079 990	0.287 73	0	—	0.092 45	0.965 3	0.095 7

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表 2 不同地貌单元回归模型拟合参数及评价参数（3″与30″分辨率下）

Table 2. Fitting and evaluation parameters of regression models for different landforms (3 arc second and 30 arc second)

地貌	拟合模型	拟合参数				R²	Δ_mean	K
地貌	拟合模型	a	b	c	d	R²	Δ_mean	K
平原	线性函数	0	0.180 0	—	—	0.313 40	0.106 7	2.937 20
	多项式函数	0.485 0	−1.476 0	1.646	0	0.322 20	0.324 4	0.993 20
	幂函数	0.160 0	0.713 0	0	—	0.080 00	0.525 9	0.152 10
丘陵	线性函数	0	0.246 0	—	—	0.552 50	0.385 1	1.434 70
	多项式函数	0.449 0	−1.695 0	2.337	0	0.610 81	0.410 1	1.489 40
	幂函数	0.082 1	0.465 0	0	—	0.077 80	0.579 9	0.134 10
山地	线性函数	0	0.279 8	—	—	0.598 49	0.354 1	1.690 10
	多项式函数	0.635 0	−2.104 0	2.366	0	0.687 30	0.716 0	0.959 90
	幂函数	0.103 6	0.360 2	0	—	0.092 45	0.782 7	0.118 11

下载: 导出CSV

表 3 不同地貌单元不同分辨率下坡度转换公式

Table 3. The slope conversion formula of different resolution DEM for different landforms

地貌单元类型	与30″的转换关系
地貌单元类型	1″（i=1″）	3″（i=3″）
平原	$ {S_{30}} = {\text{0}}{\text{.085 63}}{S_{{i}}} $	$ {S_{30}} = {\text{0}}{\text{.18}}{S_{{i}}} $
丘陵	$ {S_{30}} = {\text{0}}{\text{.132 57}}{S_{{i}}} $	$ {S_{30}} = {\text{0}}{\text{.449}}{S_{{i}}}{{ - 1}}{\text{.695}}{S_{{i}}}^{\text{2}}{\text{ + 2}}{\text{.337}}{S_{{i}}}^{\text{3}} $
山地	$ {S_{30}} = {\text{0}}{\text{.199 24}}{S_{{i}}} $	$ {S_{30}} = {\text{0}}{\text{.279 8}}{S_{{i}}} $

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