坡度和坡长尺度效应与尺度变换研究
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摘要
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（1:1000000）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4544.92t×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5118.15t×km~(-2)×a~(-1)增加到6590.29t×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。
Slope gradient and slope length are two of the most important terrain indexes whichinfluence soil erosion. These two indexes are normally extracted from DEMs with lowerresolution in the research of regional soil erosion. However, slope gradient tends to decreaseand slope length tends to increase as resolution becomes coarser. These make the calculatedslope gradient and slope length not accurate enough to describe the real relief of terrain. Thusthe accuracy of hydrology and soil erosion model is declined. With the comprehensiveapplication of wavelet analysis theory, digital image analysis and digital terrain analysis, thispaper firstly realizes the multi-scale representation of DEM by using the multi-resolutionanalysis method of wavelet. By systematically analyzing the relationship between the soilerosion terrain factor and resolution, it then deeply reveals that slope gradient decreases andthe slope length increases as the resolution of DEMs becomes coarser. Thirdly, the paperestablishes the slope gradient and slope length re-scaling mathematical model by using themethod of histogram matching. Next, taking Shannxi province as research area, we transformthe slope gradient and slope length extracted from the low-resolution DEMs. We also useChinese Soil Loess Equation (CSLE) to calculate the soil erosion volume, and validate thesuitability of the slope gradient and slope length re-scaling model in assessment of regionalsoil erosion. The main conclusions are as follows.
1. Based on the multi-resolution analysis of wavelet, the multi-scale representation ofsoil erosion terrain is realized.
A database of DEM is established, which has a gradually-changing resolution and aunified position control base, and effective ability in representing the overall topographiccharacteristics and landform macro structure. The database is generated by using the multi-resolution analysis method of wavelet, and the biorthogonal wavelet function Bior4.4was selected as the wavelet basis function. The Radical Law Selection Principles, traditionallyused in cartographic generalization, was used to set different scale parameters during thethreshold processing on the wavelet high frequency coefficients. Meanwhile, the research areais a typical small-scale watershed, i.e., XianNanGou mountains and gully district, and theoriginal 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 increasesas the resolution of DEMs becomes coarser.
(1) Taking the Hc-DEM data with the resolution of10m,25m and50m in XianNanGouwatershed as reference data, the paper evaluates the quality of the generated DEMs, whichhave different scalar parameters and obtained by using wavelet transform method. Then, therelationship between the scale parameter and resolution of DEMs is established. Hence, thegeneration of DEMs with arbitrary coarser resolutions is realized.
(2) Based on the multi-resolution database obtained by using wavelet transform, thevariation pattern of terrain along with the changing of resolution is analyzed. With thereduction of DEM resolution, the gully elevation is rising, while the Liang and Mao topelevation is decreasing, and the small-scale gully, Liang and Mao top are graduallydisappeared. Average slope shows a linearly decreasing trend with the reduction of DEMresolution, and slope frequency and cumulative frequency curves are moving towards gentleslope. In general, the overall slope gradient is declined, and the declining mainly happens insteep slope and with a changing order from main channel to small gully. Average slope lengthhas a linearly increasing trend with the reduction of DEM resolution, and slope lengthcumulative frequency curve is moving towards larger value. In general, the overall slopelength 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 transformationmodels based on histogram matching principle.
(1) After scale transformation, in the area of complex topography, the value of slopegradient and slope length are more close to those derived from high-resolution DEMs: theslope become steeper and the slope length becomes shorter. Compared to the area of complextopography, 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 ofmountains and channels is corrected and the spatial pattern is kept without distortion. Scaletransformation can improve terrain interpretation ability.
(2) In drawing the maps of slope gradient and slope length with small-scale scalar, toomuch detail is kept and little overall characteristics is obviously shown when50m resolutionis chosen. This case gives a poor mapping quality. While, our experimental results show theresolution of250m can provide better representation of terrain macro-structure. However, itsreduction of slope gradient and the expansion of slope length seriously impacted theapplication in soil erosion assessment. So it was necessary to do scale transformation ofterrain indexes. The slope gradient and slope length after transform generally meet thereference standard. That is, the scale transformation results not only satisfy the requirement ofsmall-scale terrain indexes mapping but also improve calculated accuracy of soil erosionassessment.
4. The effectiveness of the slope gradient and slope length scale transformation model isassessed taking the application in Shaanxi province as an example.
Using CSLE in soil erosion intensities assessment, the soil erosion intensity without andwith the scale transformation are calculated and compared. The result showed that, in the flatarea, the soil erosion intensity is declined and the force of slope length enlarging is more thanthat of slope gradient. In the steep area of the north part of the loess gully of Northern Shaanxiprovince, the erosion intensity has a little increase, and the forces of slope length and gradientis equal. In the steep area of the QinBa mountain area, the erosion intensity module decreasesfrom4544.92t×km~(-2)×a~(-1)to3796.48×km~(-2)×a~(-1), and the forces of slope length enlarging is morethan that of the slope gradient declining. In the steep area of the south part of the loess gullyof Northern Shaanxi province, the erosion intensity module decreases from5118.15t×km~(-2)×a~(-1)to6590.29t×km~(-2)×a~(-1), and the forces of slope length enlarging is less than that of the slopegradient declining. These means the main impacts of scale transform depend on the mainforce 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 ofregional soil erosion in future.
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（1:1000000）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4544.92t×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5118.15t×km~(-2)×a~(-1)增加到6590.29t×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。
Slope gradient and slope length are two of the most important terrain indexes whichinfluence soil erosion. These two indexes are normally extracted from DEMs with lowerresolution in the research of regional soil erosion. However, slope gradient tends to decreaseand slope length tends to increase as resolution becomes coarser. These make the calculatedslope gradient and slope length not accurate enough to describe the real relief of terrain. Thusthe accuracy of hydrology and soil erosion model is declined. With the comprehensiveapplication of wavelet analysis theory, digital image analysis and digital terrain analysis, thispaper firstly realizes the multi-scale representation of DEM by using the multi-resolutionanalysis method of wavelet. By systematically analyzing the relationship between the soilerosion terrain factor and resolution, it then deeply reveals that slope gradient decreases andthe slope length increases as the resolution of DEMs becomes coarser. Thirdly, the paperestablishes the slope gradient and slope length re-scaling mathematical model by using themethod of histogram matching. Next, taking Shannxi province as research area, we transformthe slope gradient and slope length extracted from the low-resolution DEMs. We also useChinese Soil Loess Equation (CSLE) to calculate the soil erosion volume, and validate thesuitability of the slope gradient and slope length re-scaling model in assessment of regionalsoil erosion. The main conclusions are as follows.
1. Based on the multi-resolution analysis of wavelet, the multi-scale representation ofsoil erosion terrain is realized.
A database of DEM is established, which has a gradually-changing resolution and aunified position control base, and effective ability in representing the overall topographiccharacteristics and landform macro structure. The database is generated by using the multi-resolution analysis method of wavelet, and the biorthogonal wavelet function Bior4.4was selected as the wavelet basis function. The Radical Law Selection Principles, traditionallyused in cartographic generalization, was used to set different scale parameters during thethreshold processing on the wavelet high frequency coefficients. Meanwhile, the research areais a typical small-scale watershed, i.e., XianNanGou mountains and gully district, and theoriginal 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 increasesas the resolution of DEMs becomes coarser.
(1) Taking the Hc-DEM data with the resolution of10m,25m and50m in XianNanGouwatershed as reference data, the paper evaluates the quality of the generated DEMs, whichhave different scalar parameters and obtained by using wavelet transform method. Then, therelationship between the scale parameter and resolution of DEMs is established. Hence, thegeneration of DEMs with arbitrary coarser resolutions is realized.
(2) Based on the multi-resolution database obtained by using wavelet transform, thevariation pattern of terrain along with the changing of resolution is analyzed. With thereduction of DEM resolution, the gully elevation is rising, while the Liang and Mao topelevation is decreasing, and the small-scale gully, Liang and Mao top are graduallydisappeared. Average slope shows a linearly decreasing trend with the reduction of DEMresolution, and slope frequency and cumulative frequency curves are moving towards gentleslope. In general, the overall slope gradient is declined, and the declining mainly happens insteep slope and with a changing order from main channel to small gully. Average slope lengthhas a linearly increasing trend with the reduction of DEM resolution, and slope lengthcumulative frequency curve is moving towards larger value. In general, the overall slopelength 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 transformationmodels based on histogram matching principle.
(1) After scale transformation, in the area of complex topography, the value of slopegradient and slope length are more close to those derived from high-resolution DEMs: theslope become steeper and the slope length becomes shorter. Compared to the area of complextopography, 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 ofmountains and channels is corrected and the spatial pattern is kept without distortion. Scaletransformation can improve terrain interpretation ability.
(2) In drawing the maps of slope gradient and slope length with small-scale scalar, toomuch detail is kept and little overall characteristics is obviously shown when50m resolutionis chosen. This case gives a poor mapping quality. While, our experimental results show theresolution of250m can provide better representation of terrain macro-structure. However, itsreduction of slope gradient and the expansion of slope length seriously impacted theapplication in soil erosion assessment. So it was necessary to do scale transformation ofterrain indexes. The slope gradient and slope length after transform generally meet thereference standard. That is, the scale transformation results not only satisfy the requirement ofsmall-scale terrain indexes mapping but also improve calculated accuracy of soil erosionassessment.
4. The effectiveness of the slope gradient and slope length scale transformation model isassessed taking the application in Shaanxi province as an example.
Using CSLE in soil erosion intensities assessment, the soil erosion intensity without andwith the scale transformation are calculated and compared. The result showed that, in the flatarea, the soil erosion intensity is declined and the force of slope length enlarging is more thanthat of slope gradient. In the steep area of the north part of the loess gully of Northern Shaanxiprovince, the erosion intensity has a little increase, and the forces of slope length and gradientis equal. In the steep area of the QinBa mountain area, the erosion intensity module decreasesfrom4544.92t×km~(-2)×a~(-1)to3796.48×km~(-2)×a~(-1), and the forces of slope length enlarging is morethan that of the slope gradient declining. In the steep area of the south part of the loess gullyof Northern Shaanxi province, the erosion intensity module decreases from5118.15t×km~(-2)×a~(-1)to6590.29t×km~(-2)×a~(-1), and the forces of slope length enlarging is less than that of the slopegradient declining. These means the main impacts of scale transform depend on the mainforce 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 ofregional soil erosion in future.
引文
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