ISWC OpenIR  > 水保所知识产出(1956---)
坡度和坡长尺度效应与尺度变换研究
郭伟玲
Subtype博士
Thesis Advisor李 锐
2012-11
Degree Grantor中国科学院研究生院
Place of Conferral北京
KeywordDem多尺度表达 坡度和坡长尺度效应 坡度和坡长尺度变换 土壤侵蚀
Abstract

坡度和坡长是影响土壤侵蚀的两个重要地形因子,在区域尺度土壤侵蚀研究中,坡
度和坡长一般是通过中低分辨率 DEM 来提取,但随着 DEM 分辨率的降低,提取的坡
度发生衰减,坡长发生扩张,这种衰减和扩张致使基于中低分辨率 DEM 提取的坡度表
面和坡长表面不能如实表现地形起伏状况,因之也不能有效地提取与坡度、坡长有关的
侵蚀地形参数,进而影响了土壤侵蚀评价的计算精度。本研究针对以上问题,综合应用
了小波分析理论、数字图像处理、数字地形分析等方法,首先利用小波多分辨率分析方
法实现 DEM 多尺度表达;其次通过对土壤侵蚀地形因子与分辨率关系的系统分析,深
入探讨了随着 DEM 分辨率的降低,坡度衰减和坡长扩张的规律;第三应用直方图匹配
原理,构建了坡度和坡长尺度变换的数学模型;第四以陕西省为例对粗分辨率 DEM 提
取的坡度和坡长进行变换,并利用中国土壤流失方程(CSLE)计算了土壤侵蚀量,进
而分析了坡度和坡长尺度变换模型对区域土壤侵蚀评价的适用性。论文主要研究结果如
下:
1. 基于小波多分辨率分析方法实现了对侵蚀地形的多尺度表达
在黄土丘陵沟壑区县南沟典型小流域,选取双正交小波 Bior4.4 作为小波基函数,
以方根规律作为小波高频系数阈值处理方法,以 2.5m 分辨率 Hc-DEM 为基础,基于小
波多分辨率分析方法,获得一系列具有统一定位控制基础、不同分辨率的 DEM,能够
较好的反映地形整体起伏状况和地形宏观结构。
2. 深入探讨了随着 DEM 分辨率的降低,坡度衰减和坡长扩张的规律
(1)以县南沟流域 10m、25m、50m 分辨率 Hc-DEM 为参照,对小波变换生成的
不同比例尺参数 DEM 进行质量评价,建立比例尺参数与分辨率之间的关系式,从而可
实现对任意规定的粗分辨率 DEM 数据的生成。
(2)以小波变换生成的不同分辨率 DEM 作为数据源,分析地形因子随分辨率变化
的情况。随着分辨率的不断降低,沟道高程不断升高、梁峁顶高程不断下降,细小的沟
道和梁峁逐渐消失。坡度平均值与分辨率之间呈较好的线性递减关系,坡度频率和累积
频率曲线逐渐向低坡度段移动,整体坡度以衰减为主,且发生衰减的部位主要分布在陡坡,发生顺序是从主沟道到细小的沟和梁。而平均坡长与分辨率之间呈较好的线性递增
关系,坡长累积频率逐渐向坡长较大值方向移动,整体坡长以扩张为主,且发生扩张的
部位主要分布在坡面中下部。
3. 构建了基于直方图匹配原理的坡度和坡长尺度变换模型
(1)粗分辨率坡度经变换后,地形复杂地区的坡度整体变陡,坡长整体变短,更
加接近高分辨率 DEM 上提取的数值;而地形平坦地区的坡度对 DEM 分辨率不敏感,
实际应用中可不对平坦地区坡度进行变换。变换后的坡度和坡长图的梁峁正地形和沟道
负地形轮廓相对关系正确,空间格局没有发生畸变,对地形起伏表达的能力有了很大提
高。
(2)利用小比例尺(1:1 000 000)进行坡度和坡长制图时,由于50m分辨率坡度和
坡长制图中表现出的细节信息过多,一些宏观特征不能被清晰表达,图面结构特征比较
差。而经试验250m分辨率坡度和坡长能够更好的表现地形宏观结构特征,但其上坡度衰
减和坡长扩张会影响其在土壤侵蚀评价中的应用,因此,需要对250m分辨率坡度和坡长
进行尺度变换。经变换后,坡度和坡长值从总体上达到了参考坡度和坡长的统计特征,
既满足了小比例尺地形指标制图的要求,又满足了土壤侵蚀评价的计算精度。
4. 以陕西省为例,分析了坡度和坡长尺度变换模型对区域土壤侵蚀评价的影响
以中国土壤流失方程(CSLE)为土壤侵蚀强度评价方法,由 50m 分辨率坡度、坡
长经变换后,地形较平坦地区的土壤侵蚀强度减弱,坡长扩张大于坡度衰减的影响作用。
而在地形复杂地区,陕北黄土丘陵北部的土壤侵蚀强度略有增加,但变化不明显,坡度
衰减和坡长扩张的影响相当;秦巴山地比变换前侵蚀模数由 4544.92 t×km -2 ×a -1 减少到
3796.48×km -2 ×a -1 ,坡长扩张的影响作用大于坡度衰减的影响作用;陕北黄土丘陵南部土
壤侵蚀模数由 5118.15 t×km -2 ×a -1 增加到 6590.29 t×km -2 ×a -1 ,坡度衰减的影响作用大于坡长
扩张的影响作用。也即在地形复杂地区经坡度和坡长变换后,对土壤侵蚀强度评价的影
响取决于该地区是由坡度衰减或坡长扩张起主要影响作用。因此在土壤侵蚀强度评价中
对坡度和坡长进行尺度变换是有必要的。
关键词 :DEM多尺度表达;坡度和坡长尺度效应;坡度和坡长尺度变换;土壤侵蚀

Other Abstract

Slope gradient and slope length are two of the most important terrain indexes which
influence soil erosion. These two indexes are normally extracted from DEMs with lower
resolution in the research of regional soil erosion. However, slope gradient tends to decrease
and slope length tends to increase as resolution becomes coarser. These make the calculated
slope gradient and slope length not accurate enough to describe the real relief of terrain. Thus
the accuracy of hydrology and soil erosion model is declined. With the comprehensive
application of wavelet analysis theory, digital image analysis and digital terrain analysis, this
paper firstly realizes the multi-scale representation of DEM by using the multi-resolution
analysis method of wavelet. By systematically analyzing the relationship between the soil
erosion terrain factor and resolution, it then deeply reveals that slope gradient decreases and
the slope length increases as the resolution of DEMs becomes coarser. Thirdly, the paper
establishes the slope gradient and slope length re-scaling mathematical model by using the
method of histogram matching. Next, taking Shannxi province as research area, we transform
the slope gradient and slope length extracted from the low-resolution DEMs. We also use
Chinese Soil Loess Equation (CSLE) to calculate the soil erosion volume, and validate the
suitability of the slope gradient and slope length re-scaling model in assessment of regional
soil erosion. The main conclusions are as follows.
1. Based on the multi-resolution analysis of wavelet, the multi-scale representation of
soil erosion terrain is realized.
A database of DEM is established, which has a gradually-changing resolution and a
unified position control base, and effective ability in representing the overall topographic
characteristics and landform macro structure. The database is generated by using the  multi-resolution analysis method of wavelet, and the biorthogonal wavelet function Bior4.4
was selected as the wavelet basis function. The Radical Law Selection Principles, traditionally
used in cartographic generalization, was used to set different scale parameters during the
threshold processing on the wavelet high frequency coefficients. Meanwhile, the research area
is a typical small-scale watershed, i.e., XianNanGou mountains and gully district, and the
original DEM data is the hydrological correct DEMs (hc-DEMs) of high resolution (2.5m).
2. This paper deeply reveals that slope gradient decreases and the slope length increases
as the resolution of DEMs becomes coarser.
(1) Taking the Hc-DEM data with the resolution of 10m, 25m and 50m in XianNanGou
watershed as reference data, the paper evaluates the quality of the generated DEMs, which
have different scalar parameters and obtained by using wavelet transform method. Then, the
relationship between the scale parameter and resolution of DEMs is established. Hence, the
generation of DEMs with arbitrary coarser resolutions is realized.
(2) Based on the multi-resolution database obtained by using wavelet transform, the
variation pattern of terrain along with the changing of resolution is analyzed. With the
reduction of DEM resolution, the gully elevation is rising, while the Liang and Mao top
elevation is decreasing, and the small-scale gully, Liang and Mao top are gradually
disappeared. Average slope shows a linearly decreasing trend with the reduction of DEM
resolution, and slope frequency and cumulative frequency curves are moving towards gentle
slope. In general, the overall slope gradient is declined, and the declining mainly happens in
steep slope and with a changing order from main channel to small gully. Average slope length
has a linearly increasing trend with the reduction of DEM resolution, and slope length
cumulative frequency curve is moving towards larger value. In general, the overall slope
length is enlarged, and the enlarging mainly happens in the middle and bottom of slopes.
3. This work establishes slope gradient and slope length re-scaling transformation
models based on histogram matching principle.
(1) After scale transformation, in the area of complex topography, the value of slope
gradient and slope length are more close to those derived from high-resolution DEMs: the
slope become steeper and the slope length becomes shorter. Compared to the area of complex
topography, the effects of slope scale transformation is not crucial at the flat topography.
Therefore, it was not necessary to do the slope scale transformation in the regions with flat  topography. In addition, after scale transformation, the spatial distribution of outlines of
mountains and channels is corrected and the spatial pattern is kept without distortion. Scale
transformation can improve terrain interpretation ability.
(2) In drawing the maps of slope gradient and slope length with small-scale scalar, too
much detail is kept and little overall characteristics is obviously shown when 50m resolution
is chosen. This case gives a poor mapping quality. While, our experimental results show the
resolution of 250m can provide better representation of terrain macro-structure. However, its
reduction of slope gradient and the expansion of slope length seriously impacted the
application in soil erosion assessment. So it was necessary to do scale transformation of
terrain indexes. The slope gradient and slope length after transform generally meet the
reference standard. That is, the scale transformation results not only satisfy the requirement of
small-scale terrain indexes mapping but also improve calculated accuracy of soil erosion
assessment.
4. The effectiveness of the slope gradient and slope length scale transformation model is
assessed taking the application in Shaanxi province as an example.
Using CSLE in soil erosion intensities assessment, the soil erosion intensity without and
with the scale transformation are calculated and compared. The result showed that, in the flat
area, the soil erosion intensity is declined and the force of slope length enlarging is more than
that of slope gradient. In the steep area of the north part of the loess gully of Northern Shaanxi
province, the erosion intensity has a little increase, and the forces of slope length and gradient
is equal. In the steep area of the QinBa mountain area, the erosion intensity module decreases
from 4544.92 t×km -2
×a
-1 to 3796.48×km -2
×a
-1 , and the forces of slope length enlarging is more
than that of the slope gradient declining. In the steep area of the south part of the loess gully
of Northern Shaanxi province, the erosion intensity module decreases from 5118.15 t×km -2
×a
-1
to 6590.29 t×km -2
×a
-1 , and the forces of slope length enlarging is less than that of the slope
gradient declining. These means the main impacts of scale transform depend on the main
force type (the force of slope length enlarging or that of slope gradient declining). Therefore,
it is crucial to do the slope gradient and slope length scale transformation in the assessment of
regional soil erosion in future.
Keywords: DEM multi-scale representation, scale effect of slope gradient and slope length,
scale transformation of slope gradient and slope length, soil erosion

Language中文
Document Type学位论文
Identifierhttp://ir.iswc.ac.cn/handle/361005/8971
Collection水保所知识产出(1956---)
Recommended Citation
GB/T 7714
郭伟玲. 坡度和坡长尺度效应与尺度变换研究[D]. 北京. 中国科学院研究生院,2012.
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