基于DEM的坡度尺度效应研究
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摘要
坡度是水文和土壤侵蚀模型的重要参数,认识理解坡度随分辨率变化规律对于土壤侵蚀定量评价研究十分重要。本研究以黄土丘陵沟壑区的县南沟流域为研究区,基于1:1万地形图,利用ANUDEM软件生成多种分辨率DEM,并利用ARC/INFO中计算坡度的方法提取了各种分辨率的坡度。综合运用数字地形分析、地统计学等方法,对坡度及相关地形因子随分辨率的变化及其空间格局进行了分析。主要结论如下:
(1)分辨率对样点、地形特征线、正负地形等坡度提取结果的影响。随着DEM分辨率的降低,单个样点坡度值表现出不确定性,坡度较小的样点随分辨率变化的不确定性表现的更加明显,而坡度较陡的样点更表现出坡度衰减的趋势。沟沿线上坡度值随分辨率降低衰减速度最快,分水线和流水线上坡度缓慢下降。正负地形坡度均衰减,其中负地形坡度衰减比正地形快。较平缓坡度段(0～10°),平均坡度随分辨率降低表现为先升高后降低;中等坡度段(10～25°),分区平均坡度与DEM分辨率呈线性关系,其中10～12.5°坡度段,随DEM分辨率降低坡度几乎不变;陡坡段(>=25°),分区平均坡度与DEM分辨率呈对数变化。
(2)平均坡度、平均剖面曲率提取结果与分辨率的关系。随着DEM分辨率的降低,平均坡度呈下降趋势,并且二者具有对数关系。粗分辨率DEM上提取的缓坡地面积会有所增加,陡坡地面积减少。对DEM分辨率与平均剖面曲率进行回归分析,得到二者呈幂函数关系。随着分辨率的降低,粗分辨率DEM上剖面曲率降低,地形起伏程度变小。
(3)分辨率对地形因子频率曲线的影响。坡度累积频率曲线与分辨率有很大关系,随着分辨率的降低,坡度累积频率曲线向左上方移动,即坡度越来越向较小坡度值集中。随着分辨率的降低,剖面曲率频率曲线的峰值不断向左移动,剖面曲率越来越向较小曲率值集中。不同分辨率的坡向频率曲线均表现出“双峰”特征,并且差异比较小。
(4)地形信息空间结构与分辨率关系。地统计学分析表明,坡度表现为强烈的空间相关性,其变异函数的最佳理论模型为指数模型,基台值、块金值随分辨率的降低而减小,变程随分辨率降低有增加的趋势。不同分辨率剖面曲率变异函数模型的变程随分辨率的降低而增加,其最佳理论模型也是指数模型。随分辨率降低,剖面曲率的基台值下降明显。基于空间频率理论,对制图综合过程中损失的高频信息进行分析。结果表明,制图综合过程起到了“削峰填谷”的作用,即沟谷处高程略有增加,梁上高程略微降低。
Slope is an important parameter for hydrology and soil erosion model, understanding changes of slope with the changing resolution is very important for improving the precision of hydrological simulation. In this study, taking Xiannangou watershed, representing the loess hilly geomorphology landscape, as the test area, a series of hydrologically corrected DEMs were generated using ANUDEM based on the 1:10,000 digital topographic map. Different resolution slope gradients were extracted within the ARC/INFO slope calculation methods. By applying terrain analysis and geostatistical methods, changes of DEM-derived slope with horizontal resolution and their spatial distribution were systematically investigated. The main conclusions are as follows:
Research shows that with DEM resolution decreasing, slope at single point shows uncertainty. Slope at the edgeline decreases sharply, at borderline and streamline decrease slowly. slope at positive and negative terrain both decrease. Slope at negative terrain decrease faster than the positive terrain. low slope terrain increases at first and then decreases, middle slope terrain shows slight changes, and steep slope terrain decreases with logarithm greatly. With the decrease of DEM resolution, mean slope of the basin decreases with logarithm. With resolution reduction, ramp areas continue to increase while steep areas gradually decrease.With DEM resolution reduction, mean profile curvature of the watershed decreases with power function, profile curvature tend to concentrate at small values, topographic relief become smaller. The aspect frequency distribution with different resolutions both have“double peaks”.
Slope cumulative frequency distribution with resolution reduction, the peak continuously move to left. The peak of profile curvature frequency distribution also move to left with resolution reduction, it means profile curvature tend to concentrate at small values, topographic relief become smaller.
It is showed from the semi-variance analysis that slope is strongly spatially dependent, the exponential model can describe the spatial variability of slope. With DEM resolution reducing, sill and nugget decrease, range increases. The variograms of profile curvature have the similar laws.
Make an Analysis of high frequency information based on spatial frequency theory. The results show that the process of cartographic generalization played an effect that reducing peak and filling valley.
(1)分辨率对样点、地形特征线、正负地形等坡度提取结果的影响。随着DEM分辨率的降低,单个样点坡度值表现出不确定性,坡度较小的样点随分辨率变化的不确定性表现的更加明显,而坡度较陡的样点更表现出坡度衰减的趋势。沟沿线上坡度值随分辨率降低衰减速度最快,分水线和流水线上坡度缓慢下降。正负地形坡度均衰减,其中负地形坡度衰减比正地形快。较平缓坡度段(0～10°),平均坡度随分辨率降低表现为先升高后降低;中等坡度段(10～25°),分区平均坡度与DEM分辨率呈线性关系,其中10～12.5°坡度段,随DEM分辨率降低坡度几乎不变;陡坡段(>=25°),分区平均坡度与DEM分辨率呈对数变化。
(2)平均坡度、平均剖面曲率提取结果与分辨率的关系。随着DEM分辨率的降低,平均坡度呈下降趋势,并且二者具有对数关系。粗分辨率DEM上提取的缓坡地面积会有所增加,陡坡地面积减少。对DEM分辨率与平均剖面曲率进行回归分析,得到二者呈幂函数关系。随着分辨率的降低,粗分辨率DEM上剖面曲率降低,地形起伏程度变小。
(3)分辨率对地形因子频率曲线的影响。坡度累积频率曲线与分辨率有很大关系,随着分辨率的降低,坡度累积频率曲线向左上方移动,即坡度越来越向较小坡度值集中。随着分辨率的降低,剖面曲率频率曲线的峰值不断向左移动,剖面曲率越来越向较小曲率值集中。不同分辨率的坡向频率曲线均表现出“双峰”特征,并且差异比较小。
(4)地形信息空间结构与分辨率关系。地统计学分析表明,坡度表现为强烈的空间相关性,其变异函数的最佳理论模型为指数模型,基台值、块金值随分辨率的降低而减小,变程随分辨率降低有增加的趋势。不同分辨率剖面曲率变异函数模型的变程随分辨率的降低而增加,其最佳理论模型也是指数模型。随分辨率降低,剖面曲率的基台值下降明显。基于空间频率理论,对制图综合过程中损失的高频信息进行分析。结果表明,制图综合过程起到了“削峰填谷”的作用,即沟谷处高程略有增加,梁上高程略微降低。
Slope is an important parameter for hydrology and soil erosion model, understanding changes of slope with the changing resolution is very important for improving the precision of hydrological simulation. In this study, taking Xiannangou watershed, representing the loess hilly geomorphology landscape, as the test area, a series of hydrologically corrected DEMs were generated using ANUDEM based on the 1:10,000 digital topographic map. Different resolution slope gradients were extracted within the ARC/INFO slope calculation methods. By applying terrain analysis and geostatistical methods, changes of DEM-derived slope with horizontal resolution and their spatial distribution were systematically investigated. The main conclusions are as follows:
Research shows that with DEM resolution decreasing, slope at single point shows uncertainty. Slope at the edgeline decreases sharply, at borderline and streamline decrease slowly. slope at positive and negative terrain both decrease. Slope at negative terrain decrease faster than the positive terrain. low slope terrain increases at first and then decreases, middle slope terrain shows slight changes, and steep slope terrain decreases with logarithm greatly. With the decrease of DEM resolution, mean slope of the basin decreases with logarithm. With resolution reduction, ramp areas continue to increase while steep areas gradually decrease.With DEM resolution reduction, mean profile curvature of the watershed decreases with power function, profile curvature tend to concentrate at small values, topographic relief become smaller. The aspect frequency distribution with different resolutions both have“double peaks”.
Slope cumulative frequency distribution with resolution reduction, the peak continuously move to left. The peak of profile curvature frequency distribution also move to left with resolution reduction, it means profile curvature tend to concentrate at small values, topographic relief become smaller.
It is showed from the semi-variance analysis that slope is strongly spatially dependent, the exponential model can describe the spatial variability of slope. With DEM resolution reducing, sill and nugget decrease, range increases. The variograms of profile curvature have the similar laws.
Make an Analysis of high frequency information based on spatial frequency theory. The results show that the process of cartographic generalization played an effect that reducing peak and filling valley.
引文
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Thompson, J., Bell, J., Butler, C. 2001. Digital elevation model resolution: effects on terrain attribute calculation and quantitative soil-landscape modeling. Geoderma, 100(1-2):67-89.
Walker, J., Willgoose, G. 1999. On the effect of digital elevation model accuracy on hydrology and geomorphology. Water Resources Research, 35(7):2259-2268.
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Thompson, J., Bell, J., Butler, C. 2001. Digital elevation model resolution: effects on terrain attribute calculation and quantitative soil-landscape modeling. Geoderma, 100(1-2):67-89.
Walker, J., Willgoose, G. 1999. On the effect of digital elevation model accuracy on hydrology and geomorphology. Water Resources Research, 35(7):2259-2268.
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Yue, T. X., Du, Z. P., Song, D. J., Gong, Y. 2007. A new method of surface modeling and its application to DEM construction. Geomorphology, 91(1-2):161-172.
Zevenbergen, L., Thorne, C. 1987. Quantitative analysis of land surface topography. Earth Surface Processes and Landforms, 12(1):47-56.
Zhang, W., Montgomery, D. R. 1994. Digital elevation model grid size, landscape representation, and hydrologic simulations. Water Resources Research, 30(4):1019-1028.
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