基于DEM分形特征的坡度尺度变换模型
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摘要
利用DEM提取坡度具有明显的尺度依赖性,探求DEM在不同尺度下表现出的规律关系,建立多尺度变换模型,以实现不同尺度间的转换是地形分析研究的热点和难点。本文阐释了DEM表面与地表粗糙度分形维数值的地学意义及内在关系,并利用分形对象的自相似性原理,建立了一种基于DEM分形特征的坡度尺度变换模型。选取四川丘陵地区某小流域为研究区,进行坡度尺度变换实验和误差分析,结果表明该模型能有效实现坡度尺度变换:在非平坦地区(坡度>1°)一般重采样方法变换得到的坡度误差为该方法的1.86倍;从信息熵理论分析,经该方法转换后的坡度信息得到了显著恢复。对于无1︰1万及以上精度地形数据的西南山区,利用该方法获取高精度坡度数据具有重要的理论价值和现实意义。
Gradient slope, as a basic topographic parameter, has an important influence on the transfer of the land surface material and energy in watershed. It is one of the most important model parameters for distributed hydrological models and soil erosion models. However topographic parameters extracted from DEMs have distinct scale effect, which can lead strong uncertainty to application results of those models. It is a hotspot and a difficult point in terrain analysis to explore the regularity of DEM at different scales and additionally establish re-scaling model between different scales. This research expounded the geological significance and intrinsic relationship of fractal dimension between the DEM surface and the surface roughness. Moreover, a slope re-scaling model based on the fractal features of DEM was established using the self-similarity principle of the fractal object. A small watershed in the hilly area of Sichuan Province in China was selected as the study area. The slope re-scaling experiment and error analysis were carried out. The results showed that the model could effectively achieve the slope re-scaling; in the non-flat area(slope > 1 °), the slope error obtained by general resampling method was 1.86 times of the re-scaling method. From the perspective of information entropy theory, the slope information converted by the re-scaling method had been significantly recovered. This method had important theoretical and practical significance for obtaining high-precision slope data in the southwestern mountainous area for scale of 1∶10 000 and more accurate terrain data.
Gradient slope, as a basic topographic parameter, has an important influence on the transfer of the land surface material and energy in watershed. It is one of the most important model parameters for distributed hydrological models and soil erosion models. However topographic parameters extracted from DEMs have distinct scale effect, which can lead strong uncertainty to application results of those models. It is a hotspot and a difficult point in terrain analysis to explore the regularity of DEM at different scales and additionally establish re-scaling model between different scales. This research expounded the geological significance and intrinsic relationship of fractal dimension between the DEM surface and the surface roughness. Moreover, a slope re-scaling model based on the fractal features of DEM was established using the self-similarity principle of the fractal object. A small watershed in the hilly area of Sichuan Province in China was selected as the study area. The slope re-scaling experiment and error analysis were carried out. The results showed that the model could effectively achieve the slope re-scaling; in the non-flat area(slope > 1 °), the slope error obtained by general resampling method was 1.86 times of the re-scaling method. From the perspective of information entropy theory, the slope information converted by the re-scaling method had been significantly recovered. This method had important theoretical and practical significance for obtaining high-precision slope data in the southwestern mountainous area for scale of 1∶10 000 and more accurate terrain data.
引文
[1]刘昌明,李道峰,田英,等.基于DEM的分布式水文模型在大尺度流域应用研究[J].地理科学进展,2003,22(5):437-445[LIU Changming,LI Daofeng,TIAN Ying,et al.An application study of DEM based distributed hydrological model on macroscale watershed[J].Progress in Geography,2003,22(5):437-445]
[2]范建容,刘飞,郭芬芬,等.基于遥感技术的三峡库区土壤侵蚀量评估及影响因子分析[J].山地学报,2011,29(03):306-311[FAN Jianrong,LIU Fei,GUO Fenfen,et al.Soil erosion assessment and cause analysis in Three Gorges Reservoir Area based on remote sensing[J].Mountain Research,2011,29(03):306-311]
[3]汤国安,赵牡丹,李天文,等.DEM提取黄土高原地面坡度的不确定性[J].地理学报,2003,58(6):824-830[TANG Guoan,ZHAO Mudan,LI Tianwen,et al.Modeling slope uncertainty derived from DEMs in Loess Plateau[J].Acta Geographica Sinica,2003,58(6):824-830]
[4]杨勤科,贾大韦,李锐,等.基于DEM的坡度研究---现状与展望[J].水土保持通报,2007,27(1):146-150[YANG Qinke,DAVID J,LI Rui,et al.Researches on DEM derived slope:a review and prospective[J].Bulletin of Soil and Water Conservation,2007,27(1):146-150]
[5]ZHOU Qiming,LIU Xuejun.Error analysis on grid-based slope and aspect algorithm[J].Photogrammetric Engineering and Remote Sensing,2004,70(8):957-962
[6]汤国安.我国数字高程模型与数字地形分析研究进展[J].地理学报,2014,69(9):1305-1325[TANG Guoan.Progress of DEM and digital terrain analysis in China[J].Acta Geographica Sinica,2014,69(9):1305-1325]
[7]ZHANG Xiaoyang,DRAKE N A,JOHN W.Comparison of slope estimates from low resolution DEMs:scaling issues and a fractal method for their solution[J].Earth Surface Processes and Landforms,1999,2(7):763-779
[8]汤国安,杨勤科,张勇,等.不同比例尺DEM提取地面坡度的精度研究:以在黄土丘陵沟壑区的试验为例[J].水土保持通报,2001,21(1):53-56[TANG Guoan,YANG Qinke,ZHANGYong,et al.Research on accuracy of slope derived from DEMs of different map scales[J].Bulletin of Soil and Water Conservation,2001,21(1):53-56]
[9]刘晓,赵荣,梁勇,等.顾及地貌与DEM分辨率的坡度算法适应性研究[J].测绘科学,2017,42(3):29-34[LIU Xiao,ZHAORong,LIANG Yong,et al.Research of algorithms for deriving slope based on different geomorphic types and DEM resolution[J].Science of Surveying and Mapping,2017,42(3):29-34]
[10]刘飞.基于DEM的小流域坡度尺度变换研究[D].北京:中国科学院研究生院,2012[LIU Fei.Scaling research of slope based on DEM in watershed[D].Beijing:Graduate School of Chinese Academy of Sciences,2012]
[11]郭兰勤,杨勤科,胡洁,等.基于分形的中低分辨率坡度降尺度变换方法研究[J].西北农林科技大学学报(自然科学版),2011,39(12):173-180[GUO Lanqin,YANG Qinke,HU Jie,et al.Research on method of re-scaling coarser resolution slope based on fractal analysis approach[J].Journal of Northwest University of Agriculture and Forestry Science and Technology(Natural Science Edition),2011,39(12):173-180]
[12]YANG Xin,TANG Guoan,ZHANG Yong.Scale effect and transformation model of slope based on DEMs[J].Geoinformatics2007.International Society for Optics and Photonics,2007:675322
[13]YANG Qinke,DAVID J,LI Rui,et al.Re-scaling lower resolution slope by histogram matching[J].Advances in Digital Terrain Analysis.Berlin:Springer Berlin Heidelberg,2008:193-210
[14]CHEN Yumin,ZHOU Qiming.A scale-adaptive DEM for multiscale terrain analysis[J].International Journal of Geographical Information Science,2013,27(7):1329-1348
[15]GAO Jing,JAMES E B,ZHU Axing.Neighborhood size and spatial scale in raster-based slope calculations[J].International Journal of Geographical Information Science,2012,26(10):1959-1978
[16]杨昕.基于DEM地形指数的尺度效应与尺度转换[D].南京:南京师范大学,2007[YANG Xin.Scale effect and scale transformation based on DEM topographic index[D].Nanjing:Nanjing Normal University,2007]
[17]徐静,任立良,程媛华,等.不受DEM空间分辨率影响的地形指数计算[J].清华大学学报:自然科学版,2008,48(6):983-986,990[XU Jing,REN Liliang,CHENG Yuanhua,et al.Topographic index calculation that is independent of the DEMspatial resolution[J].Journal of Tsinghua University:Natural Science Edition 2008,48(6):983-986,990]
[18]PRADHAM N R,TACHIKAWA Y,TAKARA K.A downscaling method of topographic index distribution for matching the scales of model application and parameter identification[J].Hydrological Processes,2006,20(6):1385-1405
[19]BENOIT B M.The Fractal Geometry of Nature[M].New York:W.H.Freeman and Company,1983:247-276
[20]曹颖.基于DEM的地貌分形特征研究---以陕北黄土高原部分样区为例[D].西安:西北大学,2007[CAO Yin.A research on fractal dimensions characteristics of landform based on DEM-sampled on several regions of Loess Plateau[D].Xi'an:Northwestern University,2007]
[21]曾珍,罗怀斌,范建容,等.四川宝兴森林分布及受损特征[J].山地学报,2014,32(3):284-292[ZENG Zhen,LUO Huaibin,FAN Jianrong,et al.Calculating surface area of forest vegetation and distribution characters of damaged forest in Baoxing of Sichuan,China[J].Mountain Research,2014,32(3):284-292]
[22]HUNTER G J,GOODCHILD M F.Modeling the uncertainty of slope and aspect estimates derived from spatial databases[J].Geographical Analysis,1997,29(1):35-49
[2]范建容,刘飞,郭芬芬,等.基于遥感技术的三峡库区土壤侵蚀量评估及影响因子分析[J].山地学报,2011,29(03):306-311[FAN Jianrong,LIU Fei,GUO Fenfen,et al.Soil erosion assessment and cause analysis in Three Gorges Reservoir Area based on remote sensing[J].Mountain Research,2011,29(03):306-311]
[3]汤国安,赵牡丹,李天文,等.DEM提取黄土高原地面坡度的不确定性[J].地理学报,2003,58(6):824-830[TANG Guoan,ZHAO Mudan,LI Tianwen,et al.Modeling slope uncertainty derived from DEMs in Loess Plateau[J].Acta Geographica Sinica,2003,58(6):824-830]
[4]杨勤科,贾大韦,李锐,等.基于DEM的坡度研究---现状与展望[J].水土保持通报,2007,27(1):146-150[YANG Qinke,DAVID J,LI Rui,et al.Researches on DEM derived slope:a review and prospective[J].Bulletin of Soil and Water Conservation,2007,27(1):146-150]
[5]ZHOU Qiming,LIU Xuejun.Error analysis on grid-based slope and aspect algorithm[J].Photogrammetric Engineering and Remote Sensing,2004,70(8):957-962
[6]汤国安.我国数字高程模型与数字地形分析研究进展[J].地理学报,2014,69(9):1305-1325[TANG Guoan.Progress of DEM and digital terrain analysis in China[J].Acta Geographica Sinica,2014,69(9):1305-1325]
[7]ZHANG Xiaoyang,DRAKE N A,JOHN W.Comparison of slope estimates from low resolution DEMs:scaling issues and a fractal method for their solution[J].Earth Surface Processes and Landforms,1999,2(7):763-779
[8]汤国安,杨勤科,张勇,等.不同比例尺DEM提取地面坡度的精度研究:以在黄土丘陵沟壑区的试验为例[J].水土保持通报,2001,21(1):53-56[TANG Guoan,YANG Qinke,ZHANGYong,et al.Research on accuracy of slope derived from DEMs of different map scales[J].Bulletin of Soil and Water Conservation,2001,21(1):53-56]
[9]刘晓,赵荣,梁勇,等.顾及地貌与DEM分辨率的坡度算法适应性研究[J].测绘科学,2017,42(3):29-34[LIU Xiao,ZHAORong,LIANG Yong,et al.Research of algorithms for deriving slope based on different geomorphic types and DEM resolution[J].Science of Surveying and Mapping,2017,42(3):29-34]
[10]刘飞.基于DEM的小流域坡度尺度变换研究[D].北京:中国科学院研究生院,2012[LIU Fei.Scaling research of slope based on DEM in watershed[D].Beijing:Graduate School of Chinese Academy of Sciences,2012]
[11]郭兰勤,杨勤科,胡洁,等.基于分形的中低分辨率坡度降尺度变换方法研究[J].西北农林科技大学学报(自然科学版),2011,39(12):173-180[GUO Lanqin,YANG Qinke,HU Jie,et al.Research on method of re-scaling coarser resolution slope based on fractal analysis approach[J].Journal of Northwest University of Agriculture and Forestry Science and Technology(Natural Science Edition),2011,39(12):173-180]
[12]YANG Xin,TANG Guoan,ZHANG Yong.Scale effect and transformation model of slope based on DEMs[J].Geoinformatics2007.International Society for Optics and Photonics,2007:675322
[13]YANG Qinke,DAVID J,LI Rui,et al.Re-scaling lower resolution slope by histogram matching[J].Advances in Digital Terrain Analysis.Berlin:Springer Berlin Heidelberg,2008:193-210
[14]CHEN Yumin,ZHOU Qiming.A scale-adaptive DEM for multiscale terrain analysis[J].International Journal of Geographical Information Science,2013,27(7):1329-1348
[15]GAO Jing,JAMES E B,ZHU Axing.Neighborhood size and spatial scale in raster-based slope calculations[J].International Journal of Geographical Information Science,2012,26(10):1959-1978
[16]杨昕.基于DEM地形指数的尺度效应与尺度转换[D].南京:南京师范大学,2007[YANG Xin.Scale effect and scale transformation based on DEM topographic index[D].Nanjing:Nanjing Normal University,2007]
[17]徐静,任立良,程媛华,等.不受DEM空间分辨率影响的地形指数计算[J].清华大学学报:自然科学版,2008,48(6):983-986,990[XU Jing,REN Liliang,CHENG Yuanhua,et al.Topographic index calculation that is independent of the DEMspatial resolution[J].Journal of Tsinghua University:Natural Science Edition 2008,48(6):983-986,990]
[18]PRADHAM N R,TACHIKAWA Y,TAKARA K.A downscaling method of topographic index distribution for matching the scales of model application and parameter identification[J].Hydrological Processes,2006,20(6):1385-1405
[19]BENOIT B M.The Fractal Geometry of Nature[M].New York:W.H.Freeman and Company,1983:247-276
[20]曹颖.基于DEM的地貌分形特征研究---以陕北黄土高原部分样区为例[D].西安:西北大学,2007[CAO Yin.A research on fractal dimensions characteristics of landform based on DEM-sampled on several regions of Loess Plateau[D].Xi'an:Northwestern University,2007]
[21]曾珍,罗怀斌,范建容,等.四川宝兴森林分布及受损特征[J].山地学报,2014,32(3):284-292[ZENG Zhen,LUO Huaibin,FAN Jianrong,et al.Calculating surface area of forest vegetation and distribution characters of damaged forest in Baoxing of Sichuan,China[J].Mountain Research,2014,32(3):284-292]
[22]HUNTER G J,GOODCHILD M F.Modeling the uncertainty of slope and aspect estimates derived from spatial databases[J].Geographical Analysis,1997,29(1):35-49
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