DEM数据谷地分维值的估算
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摘要
提出了一种基于DEM数据的谷地分维估算方法,该方法以汇水量阈值为标度,基于谷地形态的自相似性确定汇水量的无标度区间,在无标度区间内通过谷底线长度与汇水量阈值的线性拟合计算谷地的长度分维,通过谷地平均分叉比与平均长度比的比值逼近谷地网络的结构分维值。实验表明,基于本文方法计算的谷地分维值符合不同地貌类型流域水系的形态结构特征。
In this paper,we present an approach to estimate the valley fractal dimension value based on DEM data.The flow accumulation is selected as scale and the scale-free range is selected based on the valley shape self-similarity analysis.Within scale-free range,the length fractal dimension of valley line is calculated by the linear fitting of the threshold value and the valley length,the structure fractal dimension is calculated by the average fractal dimension of multi-scale drainage networks.Experimental studies show that the approach of estimating the valley fractal dimension value proposed in this paper can better meet the morphological structure of basin water.
In this paper,we present an approach to estimate the valley fractal dimension value based on DEM data.The flow accumulation is selected as scale and the scale-free range is selected based on the valley shape self-similarity analysis.Within scale-free range,the length fractal dimension of valley line is calculated by the linear fitting of the threshold value and the valley length,the structure fractal dimension is calculated by the average fractal dimension of multi-scale drainage networks.Experimental studies show that the approach of estimating the valley fractal dimension value proposed in this paper can better meet the morphological structure of basin water.
引文
[1]Tarboton D G,Bras R L,Rodriguez-Iturbe I.The Fractal Nature of River Networks[J].Water Resource Research,1988,24:1 317-1 322
[2]Li Jingzhong,Ai Tinghua,Wang Hong.The DEM Generalization Based on the Filling Valley Coverage[J].Acta Geodaetica et Cartographica Sinica,2009,38(3):272-275(李精忠,艾廷华,王洪.一种基于谷地填充的DEM综合方法[J].测绘学报,2009,38(3):272-275)
[3]Wang Qiao,Wu Jitao.Fractal Transformation of Square Root Model in Cartographic Generalization[J].Acta Geodaetica et Cartographica Sinica,1996,25(2):104-109(王桥,吴纪桃.制图综合方根规律模型的分形扩展[J].测绘学报,1996,25(2):104-109)
[4]Mandelbrot B B.The Fractal Geometry of Nature[M].San Francisco:Frecman Press,1982
[5]La Barbera P,Rosso R.On the Fractal Dimensions of Stream Network[J].Water Resource Research,1989,25(4):735-741
[6]Feng Ping,Feng Yan.Calculation on Fractal Dimension of River Morphology[J].Acta Geographica Sinica,1997,52(4):324-330(冯平,冯焱.河流形态特征的分维计算方法[J].地理学报,1997,52(4):324-330)
[7]Horton R E.Erosion Development of Streams and Drainage Basins:Hydrophysical Approach to Quantitative Morphology[J].Bulletin of the Geological Society of America,1945,56(3):275-370
[8]O’Callaghan J F,Mark D M.The Extraction of Drainage Networks from Digital Elevation Data[J].Computer Vision,Graphics and Image Processing,1984,28(3):323-344
[9]Zhu Qing,Tian Yixiang,Zhang Yeting.The Extraction of Catchment and Subcatchment from Regular Grid DEMs[J].Acta Geodaetica et Cartographica Sinica,2005,34(2):129-133(朱庆,田一翔,张叶廷.从规则格网DEM自动提取汇水区域及其子区域的方法[J].测绘学报,2005,34(2):129-133)
[10]Wang Qiao.Research on Some Theory Problems of Fractal Geographical Map Handling[J].Journal of Wuhan Technical University of Surveying and Mapping,1996,21(4):382-386(王桥.分形地学图形处理中几个理论问题的研究[J].武汉测绘科技大学学报,1996,21(4):382-386)
[11]Liu Xuejun,Zhang Ping.Effective Scale of Slope and Aspect Derived from Grid-based Digital Elevation Model[J].Geomatics and Information Science of Wuhan University,2008,33(12):1 254-1 258(刘学军,张平.DEM坡度、坡向的有效尺度范围[J].武汉大学学报.信息科学版,2008,33(12):1 254-1 258)
[12]Li Jingzhong,Ai Tinghua,Ke Shu,et al.Effective Flow Accumulation Threshold of Extracting Valleyline from Grid-based Digital Elevation Model[J].Geomatics and Information Science of Wuhan University,2012,37(10):1 244-1 247(李精忠,艾廷华,柯舒,等.DEM提取谷底线的有效汇水量阈值范围[J].武汉大学学报·信息科学版,2012,37(10):1 244-1 247)
[2]Li Jingzhong,Ai Tinghua,Wang Hong.The DEM Generalization Based on the Filling Valley Coverage[J].Acta Geodaetica et Cartographica Sinica,2009,38(3):272-275(李精忠,艾廷华,王洪.一种基于谷地填充的DEM综合方法[J].测绘学报,2009,38(3):272-275)
[3]Wang Qiao,Wu Jitao.Fractal Transformation of Square Root Model in Cartographic Generalization[J].Acta Geodaetica et Cartographica Sinica,1996,25(2):104-109(王桥,吴纪桃.制图综合方根规律模型的分形扩展[J].测绘学报,1996,25(2):104-109)
[4]Mandelbrot B B.The Fractal Geometry of Nature[M].San Francisco:Frecman Press,1982
[5]La Barbera P,Rosso R.On the Fractal Dimensions of Stream Network[J].Water Resource Research,1989,25(4):735-741
[6]Feng Ping,Feng Yan.Calculation on Fractal Dimension of River Morphology[J].Acta Geographica Sinica,1997,52(4):324-330(冯平,冯焱.河流形态特征的分维计算方法[J].地理学报,1997,52(4):324-330)
[7]Horton R E.Erosion Development of Streams and Drainage Basins:Hydrophysical Approach to Quantitative Morphology[J].Bulletin of the Geological Society of America,1945,56(3):275-370
[8]O’Callaghan J F,Mark D M.The Extraction of Drainage Networks from Digital Elevation Data[J].Computer Vision,Graphics and Image Processing,1984,28(3):323-344
[9]Zhu Qing,Tian Yixiang,Zhang Yeting.The Extraction of Catchment and Subcatchment from Regular Grid DEMs[J].Acta Geodaetica et Cartographica Sinica,2005,34(2):129-133(朱庆,田一翔,张叶廷.从规则格网DEM自动提取汇水区域及其子区域的方法[J].测绘学报,2005,34(2):129-133)
[10]Wang Qiao.Research on Some Theory Problems of Fractal Geographical Map Handling[J].Journal of Wuhan Technical University of Surveying and Mapping,1996,21(4):382-386(王桥.分形地学图形处理中几个理论问题的研究[J].武汉测绘科技大学学报,1996,21(4):382-386)
[11]Liu Xuejun,Zhang Ping.Effective Scale of Slope and Aspect Derived from Grid-based Digital Elevation Model[J].Geomatics and Information Science of Wuhan University,2008,33(12):1 254-1 258(刘学军,张平.DEM坡度、坡向的有效尺度范围[J].武汉大学学报.信息科学版,2008,33(12):1 254-1 258)
[12]Li Jingzhong,Ai Tinghua,Ke Shu,et al.Effective Flow Accumulation Threshold of Extracting Valleyline from Grid-based Digital Elevation Model[J].Geomatics and Information Science of Wuhan University,2012,37(10):1 244-1 247(李精忠,艾廷华,柯舒,等.DEM提取谷底线的有效汇水量阈值范围[J].武汉大学学报·信息科学版,2012,37(10):1 244-1 247)