ISWC OpenIR  > 水保所知识产出(1956---)
黄土高原小流域侵蚀沟道空间频谱分析
王雷
Subtype博士
Thesis Advisor李 锐
2013-05
Degree Grantor中国科学院研究生院
Place of Conferral北京
Keyword数字高程模型 侵蚀沟道 格网尺寸 频谱 傅里叶分析
Abstract

目前,数字高程模型(DEM),特别是规则格网 DEM,已经成为土壤侵蚀以及其他
与地形相关的研究的主要数据源。众多的研究表明,DEM 的格网尺寸大小对于地形分
析结果有着重要的影响。但对于多大格网尺寸的 DEM 究竟能够表达怎样的地形信息,
即 DEM 的格网尺寸与地形的表达能力之间的关系仍不明确。这一问题使得在应用 DEM
进行土壤侵蚀或地形分析中存在一定的盲目性。针对上述问题,本研究基于陕西省绥德
县窑家湾沟的全数字摄影测量和野外实测的高精度 DEM 数据,以黄土高原侵蚀沟道为
研究对象,应用傅里叶频谱分析方法,首先研究了 DEM 数据的高程精度与格网尺寸的
关系,进而分析了利用 DEM 提取沟道网络时格网尺寸的影响。基于 DEM 提取的沟道
数据,布设了 24 个剖面,并利用一维频谱分析方法,分析了不同等级沟道的空间频率
特征,总结出了各侵蚀沟道的空间频率范围。最后将一维频谱分析结果推广至二维频谱
分析,并以此为依据对实验数据进行二维频率低通滤波。通过对滤波后的 DEM 数据与
各格网尺寸 DEM 进行对照,将侵蚀沟道的空间尺度与 DEM 格网尺度对应起来,以解
决 DEM 的格网尺寸与地形的表达能力之间的对应关系。论文的主要研究结果如下:
1.DEM 的高程精度与格网尺寸的关系
格网尺寸对规则格网 DEM 高程精度的影响表现在:上坡方向低估格网高程,下坡
方向则高估。因此格网上的高程误差大小取决于地形坡度,其空间分布的复杂程度取决
于格网尺寸大小。利用直接采样获得一系列 DEM 格网上高程误差的分析结果表明,
DEM 高程中误差和最大误差与格网尺寸存在近似线性的二次函数关系,随着格网尺寸
增大,DEM 高程误差增大,且格网上的最大高程误差远超出 2 倍中误差水平。
2.DEM 格网尺寸与沟道网络提取及其基本特征的关系
利用不同格网尺寸 DEM 提取的沟道网络的特征分析的结果表明,DEM 格网尺寸对
沟道网络的提取主要体现在对水流方向的影响与水流累积阈值的影响两方面。在地形发
生较为显著变化的部位,格网尺寸的变化会使水流方向有较为剧烈的变化;通过对水流
累积阈值和格网尺寸关系的分析,认为合理的水流累积阈值与格网尺寸存在二次幂指数
递减关系。总体来讲,当确定了适宜的水流累积阈值,格网尺寸的变化并不影响沟道网络的整体结构特征,但会使沟道的空间位置发生变化,具体形态特征也发生变化。格网
尺寸越大,沟道网络形态越概括。
3.基于剖面的沟道一维频谱特征
1)通过对实验区域布设的基本垂直于沟道延伸方向的剖面的空间特征及其一维频
谱特征的对照,级别较高的侵蚀沟道,其空间形态通常起伏较大,间隔较宽,对应的空
间频率较低,周期较长,振幅较大;而级别较低的侵蚀沟道,其空间形态一般起伏较小,
间隔较窄,其对应频率较高,周期越短,振幅较小。从频谱分析结果中可以清楚反映不
同振幅的起伏变化的空间频率,并能与沟道的实际起伏情况对应。
2)通过对不同频率组分的空间信号重建结果与原始沟道剖面数据的比对,侵蚀沟
道的主要空间频率集中在较为低频的部分。不同等级的沟道对应的空间频率范围不同。
包括细沟在内微小的地形起伏,空间频率大于 0.1 周/米;在约 0.03——0.1 周/米之间,
基本对应坡面上的各种浅沟;在约 0.015——0.085 周/米之间,基本对应各种规模切沟;
小于约 0.015 周/米的,主要是各种冲沟及更大规模沟道。
3)根据对不同格网尺寸 DEM 提取的剖面数据的频谱特征分析,在利用傅里叶分析
方法进行地形剖面特征分析时,需尽可能采用较小格网尺寸 DEM,并尽可能布设较长
剖面。
4.二维频谱特征分析及 DEM 格网尺寸与 DEM 沟道信息表达能力的关系
1)根据对实验区域 DEM 数据的二维频谱特征的分析,二维频谱能够反映地表的各
种尺度与规模的地形起伏,但直接利用二维频谱特征与空间特征建立对应关系是较为困
难的。因此,本研究结合沟道延伸方向的统计结果,将一维剖面频谱分析结果通过频率
分解至水平与垂直方向,得出实验区域各等级沟道的二维空间频率范围,并以此为依据
设计二维频域低通滤波器。
2)对实验区域 DEM 数据进行低通滤波,逐步滤掉包括细沟的微小起伏、浅沟及切
沟信息。根据滤波结果与各格网尺寸 DEM 的对比,得出格网尺寸与 DEM 沟道信息表
达能力的关系:大于等于 2m 的格网尺寸,无法表达地面上包括细沟在内的微小的地形
起伏的;格网尺寸大于 5m,则很难表现坡面上浅沟特征;格网尺寸超过 10m,切沟的
特征也基本消失。
关键词:数字高程模型,侵蚀沟道,格网尺寸,频谱,傅里叶分析

Other Abstract

At Present,Digital Elevation Models(DEMs), especially the GRID DEMs, is the main
data sources for the research of soil erosion and terrain analysis. Numerous studies show that
the grid size of DEMs greatly influences the results of terrain analysis. However, up to now, it
is not clear and definite how large the grid size of the DEMs is required to demonstrate fully
and correctly the terrain information. This question has not answered clearly in the previously
studies. In another word, the relationship between the grid size of DEMs and the ability to
describe the terrain information of DEMs is still not clear. This problem to some extent leads
to the blindness in the practical application of DEMs in the analysis of soil erosion and terrain.
Based on the DEM generated by the full digital photogrammetry and field measurements in
Yaojiawangou watershed, Suide, Shaanxi Province, and taking the gullies of loess plateau as
the studying objects, this paper uses the Fourier Analysis to solve the problem mentioned
above. Firstly, this paper discusses the relationship between the elevation error of DEMs and
grid size. According to this result, it analyzes the influence of grid size on the extraction of
erosion gullies network from DEM. Secondly, the paper analyzes the spatial frequency
characters of different grade gullies and summaries the spatial frequency range of each grade
gully with the analysis of spectrum on one dimension of 24 profiles lying on the gullies
network. At last, the paper extends the results of spectrum analysis of one dimension profiles
to two-dimensional spectral analysis, and then designs the two-dimensional frequency
low-pass filter to filter the information of each grade gully. According to the comparison
between the filtered DEMs and the original DEMs with different grid size, the study matches
spatial scale of erosion gullies with the grid size of DEMs. The conclusion of this paper solves
the corresponding relationship between the expression ability of the terrain information for  DEMs and the grid size of DEMs.
The main conclusions of this paper are as follows:
1. The relationship between the elevation error of DEMs and the grid size
The influence of grid size on the elevation error of DEMs is shown as follows: the
elevation on a grid is overestimated in down-slope direction, while underestimated in
up-slope direction. As a result, the value of elevation error on a grid is decided by the slope
gradient, while the complication of distribution of elevation error is decided by the size of
grid. The analysis of elevation error calculated from the DEMs series generated by sampling
directly shows that The RMSE and the maximum error of elevation DEMs increases with the
grid size in the way that is quadratic function which is very similar with a linear relationship.
The maximum error on a grid far exceeds the 2 times of RMSE.
2. The relationship between the characters of gullies network extracted from DEMs and
the grid size
By means of analyzing the characters of gullies network extracted from DEMs series
which have different grid sizes, the main influence of the grid size on the extraction of gullies
network is reflected in two aspects --- the flow direction and the threshold of flow
accumulation. The change of grid size causes the flow direction’s turning dramatically in the
complicated topography area. The relationship between the grid size and the threshold of flow
accumulation shows that the reasonable threshold decreases while the grid size increases by
the way of negative second order power function. Generally, the change of grid size doesn’t
influence the structure of the gullies network while the reasonable flow accumulation
threshold is determined. However, the position of gullies will move from the original position
and the shape of gullies will be changed. The larger the grid size is, the simpler the shape of
gullies.
3. One-dimensional spectrum of gullies based on profile data
1)The comparison between the spatial characters of profiles which are perpendicular
with the direction of the gullies and its One-dimensional spectrum shows that: the gully which
is in higher level, in general, has the greater depth and the wider interval, meanwhile, the
corresponding spatial frequency is lower, the period is longer and the amplitude is larger. On
the contrary, the lower the level of gully is, the smaller the fluctuation, the narrower the
interval, the higher the frequency, the shorter the period, the smaller the amplitude. The  spectrum could reflect the spatial frequency with varying amplitude clearly, and could
correspond to the spatial characters of fluctuation of gullies.
2)According to the result of comparison between the profiles reconstructed by the
varying spatial frequency and the original profiles, the main spatial frequency range of
erosion gullies is concentrated in the low frequency part. The gullies with different grades
correspond to the different spatial frequency: The minor fluctuation including rills on the
slope has the frequency range higher than 0.1 cycle per meter; the frequency range of shallow
furrow is from 0.03 to 0.1 cycle per meter; the gully has the frequency range from 0.015 to
0.085 cycle per meter, while the gullies which are in higher grade correspond to the frequency
range lower than 0.015 cycle per meter.
3)In terms of the spectrum of profiles extracted from the DEMs data series which have
different grid size, the analysis of profile characters using Fourier transformation requires that
the DEMs should have smaller grid size, and that profile line should be as longer as possible.
4. Two-dimensional spectrum Analysis and the relationship between the expression
ability of the terrain information for DEMs and the grid size
1)Based on the analysis of two-dimensional spectrum of DEMs of the studied area, the
two-dimensional spectrum could reflect the scale of the relief. However, it is difficult to
obtain the corresponding relationship between the two-dimensional spectrum and spatial
characters. Therefore, according to the statistic of directions of gullies, the result of analysis
of one-dimensional spectrum is decomposed to the horizontal and vertical direction to achieve
the two-dimensional frequency range of gullies with different grades. This spatial range is the
basic parameter to design the two-dimensional frequency low-pass filter.
2)Using the two-dimensional frequency low-pass filters to remove the gullies
information step by step, three DEMs which do not contain the information of the rills ,
shallow furrows, gullies basically could be obtained respectively. The Comparison between
these three DEMs and the DEMs with varying grid sizes indicates the relationship between
the expression ability of the terrain information for DEMs and the grid size: the fluctuation
including rills nearly could not be described on the DEMs whose grid size is larger than about
2 meters. When the grid size of DEMs is larger than about 5 meters, the shallow furrows
could be represented clearly. If the grid size of DEMs is larger than about 10 meters, the
gullies information will nearly disappear.  

Language中文
Document Type学位论文
Identifierhttp://ir.iswc.ac.cn/handle/361005/8978
Collection水保所知识产出(1956---)
Recommended Citation
GB/T 7714
王雷. 黄土高原小流域侵蚀沟道空间频谱分析[D]. 北京. 中国科学院研究生院,2013.
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