干热河谷冲沟DEM插值误差的空间分布研究
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摘要
为了分析云南元谋干热河谷典型冲沟插值误差的空间分布特征,采用反距离加权(inverse distance weighting,IDW)、局部多项式(local polynomial interpolation,LPI)、张力样条(spline with tension,ST)、析取克里格(disjunctive Kriging,DK)以及不规则三角网(triangulated irregular network,TIN)模型方法对高程采样点进行插值,用交叉验证法、相对差系数及沟谷线差异衡量其插值精度。遴选高程误差大于1 m的误差点,用变异系数(coefficient of variation,CV)、全局Moran指数和Getis-Ord G_i~*指数分析其空间格局特征。结果表明:TIN和DK精度较高,IDW精度最低;高程误差均呈聚集分布,聚集程度TIN>LPI>DK>ST>IDW;高程误差均呈空间正自相关,TIN模型插值误差的自相关程度最高;误差热点位于坡度大的区域。
To analyze the interpolation errors spatial distribution characteristics of the typical gully of Yuanmou dry-hot valley,the measured elevation points were interpolated by inverse distance weighting( IDW),local polynomial interpolation( LPI),spline with tension( ST),disjunctive Kriging( DK) and triangulated irregular network( TIN) model to generate DEM. Cross validation,relative difference coefficient and the valley lines discrepancy were used to evaluate the interpolation accuracy. The error points with elevation error greater than1 m were extracted,and their spatial distribution characteristics were analyzed by coefficient of variation(CV),global Moran's index and Getis-Ord G_i~* index. The results show that DK and TIN model had higher interpolation accuracy,the height error points of five interpolation methods were overall aggregating distribution,and the degree was TIN>LPI>DK>ST>IDW. Height errors were significantly positive spatial autocorrelation and TIN model had the highest autocorrelation degree,the hot spots of errors were distributed in the area with large slope.
To analyze the interpolation errors spatial distribution characteristics of the typical gully of Yuanmou dry-hot valley,the measured elevation points were interpolated by inverse distance weighting( IDW),local polynomial interpolation( LPI),spline with tension( ST),disjunctive Kriging( DK) and triangulated irregular network( TIN) model to generate DEM. Cross validation,relative difference coefficient and the valley lines discrepancy were used to evaluate the interpolation accuracy. The error points with elevation error greater than1 m were extracted,and their spatial distribution characteristics were analyzed by coefficient of variation(CV),global Moran's index and Getis-Ord G_i~* index. The results show that DK and TIN model had higher interpolation accuracy,the height error points of five interpolation methods were overall aggregating distribution,and the degree was TIN>LPI>DK>ST>IDW. Height errors were significantly positive spatial autocorrelation and TIN model had the highest autocorrelation degree,the hot spots of errors were distributed in the area with large slope.
引文
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[14]Li Jinyang,Fan Jianrong,Xu Jinghua.Research on Precision Comparison of Interpolation DEM Based on the Point Cloud Data[J].Geomatics&Spatial Information Technology,2013,36(1):37-40(李瑾杨,范建容,徐京华.基于点云数据内插DEM的精度比较研究[J].测绘与空间地理信息,2013,36(1):37-40)
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[17]Qing Yalan,Luo Mingliang,Zhang Bin,et al.Effects of Interpolation Parameters in Radial Basis Function on DEM Accuracy in Dry-Hot Valleys[J].Science of Surveying and Mapping,2015,40(7):113-117(青亚兰,罗明良,张斌,等.径向基函数对干热河谷冲沟DEM构建的影响[J].测绘科学,2015,40(7):113-117)
[18]Chen Juan,Luo Mingliang,Zhang Bin,et al.Effects of Interpolation Parameters in Inverse Distance Weighted Method on DEM Accuracy in Dry-Hot Valleys of Yuanmou[J].Science of Soil and Water Conservation,2015,13(1):29-34(陈娟,罗明良,张斌,等.反距离加权插值参数变化对元谋冲沟DEM构建的影响[J].中国水土保持科学,2015,13(1):29-34)
[19]Liu Xuejun,Jin Bei,Wang Yanfang.Similarity Analysis of Flow Route Algorithms for Extracting Drainage Network from Grid-Based Terrain Model[J].Geographical Research,2008,27(6):1 347-1 357(刘学军,晋蓓,王彦芳.DEM流径算法的相似性分析[J].地理研究,2008,27(6):1 347-1 357)
[20]Yan Chaode,Bai Jianjun,Zhao Renliang.Voronoi Diagram’s Recursive Convergence Characteristic Along Preferred Possible Nearest Neighbor Objects and Its Application[J].Geomatics and Information Science of Wuhan University,2009,34(1):48-51(闫超德,白建军,赵仁亮.Voronoi图的首最邻近递归收敛特性及其应用[J].武汉大学学报·信息科学版,2009,34(1):48-51)
[21]Zhang Hong,Wang Xinsheng,Yu Ruilin.Voronoi Diagram to Study the Spatial Distribution Pattern of Point Sets[J].Journal of Central China Normal University(Natural Sciences),2005,39(3):422-426(张红,王新生,余瑞林.基于Voronoi图的测度点状目标空间分布特征的方法[J].华中师范大学学报(自然科学版),2005,39(3):422-426)
[22]Zhang Songlin,Zhang Kun.Comparison Between General Moran’s Index and Getis-Ord General G of Spatial Autocorrelation[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2007,46(4):93-97(张松林,张昆.全局空间自相关Moran指数和G系数对比研究[J].中山大学学报(自然科学版),2007,46(4):93-97)
[23]Li Xiang,Deng Qingchun,Zhang Bin,et al.Cha-racteristics and Controlling Factors of Rills in the Microwatershed of Yuanmou Dry-Hot Valley[J].Science of Soil and Water Conservation,2015,13(5):24-30(李响,邓青春,张斌,等.元谋干热河谷微流域细沟形态特征及控制因素[J].中国水土保持科学,2015,13(5):24-30)
[24]Wang Lei,Yang Qinke,Wang Chunmei,et al.Analysis of Relationship Among RMSE of Elevation,Grid Size and Data Density when Generate DEM[J].Geomatics and Information Science of Wuhan University,2012,37(3):366-369(王雷,杨勤科,王春梅,等.采样数据密度及栅格尺寸对高程中误差的影响分析[J].武汉大学学报·信息科学版,2012,37(3):366-369)
[2]Lu Huaxing.Research on DEM Error Model[D].Nanjing:Nanjing Normal University,2008(卢华兴.DEM误差模型研究[D].南京:南京师范大学,2008)
[3]Liu Xuejun,Bian Lu,Lu Huaxing,et al.The Accuracy Assessment on Slope Algorithms with DEM Error Spatial Autocorrelation[J].Acta Geodaetica et Cartographica Sinica,2008,37(2):200-206(刘学军,卞璐,卢华兴,等.顾及DEM误差自相关的坡度计算模型精度分析[J].测绘学报,2008,37(2):200-206)
[4]Liu Xuejun,Wang Yefei,Cao Zhidong,et al.A Study of Error Spatial Distribution of Slope and Aspect Derived from Grid DEM[J].Bulletin of Surveying and Mapping,2004(12):11-13(刘学军,王叶飞,曹志东,等.基于DEM的坡度坡向误差空间分布特征研究[J].测绘通报,2004(12):11-13)
[5]Tang Guoan,Gong Jianya,Chen Zhengjiang,et al.A Simulation on the Accuracy of DEM Terrain Representation[J].Acta Geodaetica et Cartographica Sinica,2001,30(4):361-365(汤国安,龚健雅,陈正江,等.数字高程模型地形描述精度量化模拟研究[J].测绘学报,2001,30(4):361-365)
[6]Tang Guoan,Zhao Mudan,Cao Han.An Investigation of the Spatial Structure of DEM Errors[J].Journal of Northwest University(Natural Science Edition),2000,30(4):351-352(汤国安,赵牡丹,曹菡.DEM地形描述误差空间结构分析[J].西北大学学报(自然科学版),2000,30(4):351-352)
[7]Wang Chun,Tang Guoan,Dai Shibao,et al.Quantitative Analysis of DEM Terrain Representation Error Field[J].Geomatics and Information Science of Wuhan University,2014,39(9):1 074-1 079(王春,汤国安,戴仕宝,等.DEM地形描述误差场量化分析研究[J].武汉大学学报·信息科学版,2014,39(9):1 074-1 079)
[8]Chen Yonggang,Tang Guoan,Zhu Shijie.Spatial Point Pattern of DEM Re-sampling Error and Difference Analysis of Influence Factor[J].Journal of China University of Mining&Technology,2011,40(4):653-659(陈永刚,汤国安,祝士杰.DEM重采样误差空间分布格局及差异性分析[J].中国矿业大学学报,2011,40(4):653-659)
[9]Jia Yini,Tang Guoan,Liu Xuejun.The Impact of Elevation Interpolation on the Accuracy of Gradient and Aspect from DEMs[J].Geo-Information Science,2009,11(1):36-42(贾旖旎,汤国安,刘学军.高程内插方法对DEM所提取坡度、坡向精度的影响[J].地球信息科学学报,2009,11(1):36-42)
[10]Zhou Xinghua,Yao Yiqiang,Zhao Jixian.Research on Interpolation and Accuracy Assessment of DEM[J].Science of Surveying and Mapping,2005,30(5):86-88(周兴华,姚艺强,赵吉先.DEM内插方法与精度评定[J].测绘科学,2005,30(5):86-88)
[11]Wang Yaoge,Wang Zhiwei,Zhu Changqing.Ana-lysis of Digital Terrain Error Based on Spatial Autocorrelation[J].Geomatics and Information Science of Wuhan University,2008,33(12):1 259-1 262(王耀革,王志伟,朱长青.DEM误差的空间自相关特征分析[J].武汉大学学报·信息科学版,2008,33(12):1 259-1 262)
[12]Liu Ling.Research on Creation and Visualization of Large-Scale Digital Elevation Model[D].Chongqing:Chongqing University,2001(柳玲.大比例尺数字高程模型的生成及可视化研究[D].重庆:重庆大学,2001)
[13]Duan Xiumei.Updating Method of 1∶50 000 Scale DEM Based on 1∶10 000 Scale Terrain Data[D].Hunan:Central South University,2012(段修梅.基于1∶1万地形数据更新1∶5万DEM的方法研究[D].湖南:中南大学,2012)
[14]Li Jinyang,Fan Jianrong,Xu Jinghua.Research on Precision Comparison of Interpolation DEM Based on the Point Cloud Data[J].Geomatics&Spatial Information Technology,2013,36(1):37-40(李瑾杨,范建容,徐京华.基于点云数据内插DEM的精度比较研究[J].测绘与空间地理信息,2013,36(1):37-40)
[15]Yang Qinke,Mc Vicar T R,van Niel T G,et al.Comparison of Hydro-geomorphology Representing Between DEMs by TIN and ANUDEM Approaches[J].Bulletin of Soil and Water Conservation,2006,26(6):84-88(杨勤科,Mc Vicar T R,van Niel T G,等.ANUDEM和TIN两种建立DEM方法的对比研究[J].水土保持通报,2006,26(6):84-88)
[16]Wang Ping,Li Hao,Chen Shuai,et al.Interpolation of Permanent Gully Density Based on Slope Steepness in Black Soil Area[J].Research of Soil and Water Conservation,2014,21(6):312-317(王平,李浩,陈帅,等.基于坡度的黑土区切沟密度协同克里格插值方法研究[J].水土保持研究,2014,21(6):312-317)
[17]Qing Yalan,Luo Mingliang,Zhang Bin,et al.Effects of Interpolation Parameters in Radial Basis Function on DEM Accuracy in Dry-Hot Valleys[J].Science of Surveying and Mapping,2015,40(7):113-117(青亚兰,罗明良,张斌,等.径向基函数对干热河谷冲沟DEM构建的影响[J].测绘科学,2015,40(7):113-117)
[18]Chen Juan,Luo Mingliang,Zhang Bin,et al.Effects of Interpolation Parameters in Inverse Distance Weighted Method on DEM Accuracy in Dry-Hot Valleys of Yuanmou[J].Science of Soil and Water Conservation,2015,13(1):29-34(陈娟,罗明良,张斌,等.反距离加权插值参数变化对元谋冲沟DEM构建的影响[J].中国水土保持科学,2015,13(1):29-34)
[19]Liu Xuejun,Jin Bei,Wang Yanfang.Similarity Analysis of Flow Route Algorithms for Extracting Drainage Network from Grid-Based Terrain Model[J].Geographical Research,2008,27(6):1 347-1 357(刘学军,晋蓓,王彦芳.DEM流径算法的相似性分析[J].地理研究,2008,27(6):1 347-1 357)
[20]Yan Chaode,Bai Jianjun,Zhao Renliang.Voronoi Diagram’s Recursive Convergence Characteristic Along Preferred Possible Nearest Neighbor Objects and Its Application[J].Geomatics and Information Science of Wuhan University,2009,34(1):48-51(闫超德,白建军,赵仁亮.Voronoi图的首最邻近递归收敛特性及其应用[J].武汉大学学报·信息科学版,2009,34(1):48-51)
[21]Zhang Hong,Wang Xinsheng,Yu Ruilin.Voronoi Diagram to Study the Spatial Distribution Pattern of Point Sets[J].Journal of Central China Normal University(Natural Sciences),2005,39(3):422-426(张红,王新生,余瑞林.基于Voronoi图的测度点状目标空间分布特征的方法[J].华中师范大学学报(自然科学版),2005,39(3):422-426)
[22]Zhang Songlin,Zhang Kun.Comparison Between General Moran’s Index and Getis-Ord General G of Spatial Autocorrelation[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2007,46(4):93-97(张松林,张昆.全局空间自相关Moran指数和G系数对比研究[J].中山大学学报(自然科学版),2007,46(4):93-97)
[23]Li Xiang,Deng Qingchun,Zhang Bin,et al.Cha-racteristics and Controlling Factors of Rills in the Microwatershed of Yuanmou Dry-Hot Valley[J].Science of Soil and Water Conservation,2015,13(5):24-30(李响,邓青春,张斌,等.元谋干热河谷微流域细沟形态特征及控制因素[J].中国水土保持科学,2015,13(5):24-30)
[24]Wang Lei,Yang Qinke,Wang Chunmei,et al.Analysis of Relationship Among RMSE of Elevation,Grid Size and Data Density when Generate DEM[J].Geomatics and Information Science of Wuhan University,2012,37(3):366-369(王雷,杨勤科,王春梅,等.采样数据密度及栅格尺寸对高程中误差的影响分析[J].武汉大学学报·信息科学版,2012,37(3):366-369)
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