基于格网DEM的等高线提取误差传播模型
|
摘要
从格网DEM的结构入手,根据误差传播定律,分析了格网点的高程误差对由其生成的等高线数据的位置偏移、长度及方向的影响,建立误差传播模型,以实际DEM为例对比了原始等高线和DEM内插产生的等高线的变化,并进行了模型验证。结果表明:等高点落在格网点时中误差最大,越接近中点,中误差越小;等高线折线的长度中误差是线元长度中误差的累计,其值随内插点的增多而增大;等高线折线的方向中误差与折线的起点和终点位置相关,与等高线的追踪路径无关。
Contour is an important approach to describe the terrain,and grid DEM has increasingly become the main data source of contour.According to the law of error propagation,this article analyzed the effects of contour point elevation error interpolating from grid DEM,as well as the change of length and direction of the contour line. Then the error propagation models were present. Finally,taking a typical DEM as an example,original contour and regenerative contour were compared,the models were examined and identified. The results show that the RMSE of contour point that fall at point of grid DEM will be the maximum,and that the middle will be the minimum. The RMSE of line segments' length will add up to make a total RMSE of polyline's length,and the RMSE of polyline's direction only relates to the location of starting point and ending point,unrelated to tracing path of contour.
Contour is an important approach to describe the terrain,and grid DEM has increasingly become the main data source of contour.According to the law of error propagation,this article analyzed the effects of contour point elevation error interpolating from grid DEM,as well as the change of length and direction of the contour line. Then the error propagation models were present. Finally,taking a typical DEM as an example,original contour and regenerative contour were compared,the models were examined and identified. The results show that the RMSE of contour point that fall at point of grid DEM will be the maximum,and that the middle will be the minimum. The RMSE of line segments' length will add up to make a total RMSE of polyline's length,and the RMSE of polyline's direction only relates to the location of starting point and ending point,unrelated to tracing path of contour.
引文
[1]汤国安,陶旸,王春.等高线套合差及在DEM质量评价中的应用研究[J].测绘通报,2007(7):65-67.
[2]LI Z L.Mathematical Models of the Accuracy of Digital Terrain Model Surfaces Linearly Constructed from Square Gridded Data[J].P hotogrammetric Record,1993,14(82):661-674.
[3]李国重,张国芹,朱长青.DEM线性建模过程中的高程误差传播[J].测绘科学技术学报,2009,26(4):283-287.
[4]钟剑龙,花向红,陈华安.TIN DEM线性内插不确定性的随机过程模型[J].武汉大学学报(信息科学版),2010,35(2):193-196.
[5]王耀革,王鑫,朱长青.基于双线性内插规则格网DEM地形误差模型[J].测绘科学技术学报,2007,24(6):419-421.
[6]HU P,LIU X,HU H.Accuracy Assessment of Digital Elevation Models Based on Approximation Theory[J].P hotogrammetric Engineering and Remote Sensing,2009,75(1):49-56.
[7]史巍巍,裘昱,戴宗友.数字高程模型与等高线质量相关性研究[J].测绘通报,2006(2):23-26.
[8]史文中,王斌,刘二永,等.基于双三次Hermite插值方法的DEM误差传播分析[J].测绘科学技术学报,2013,30(4):380-387.
[9]李毅,石豫川,王平,等.基于DEM的吉太曲流域水文信息分析[J].人民黄河,2015,37(9):32-34.
[10]周启鸣,刘学军.数字地形分析[M].北京:科学出版社,2006:94-95.
[2]LI Z L.Mathematical Models of the Accuracy of Digital Terrain Model Surfaces Linearly Constructed from Square Gridded Data[J].P hotogrammetric Record,1993,14(82):661-674.
[3]李国重,张国芹,朱长青.DEM线性建模过程中的高程误差传播[J].测绘科学技术学报,2009,26(4):283-287.
[4]钟剑龙,花向红,陈华安.TIN DEM线性内插不确定性的随机过程模型[J].武汉大学学报(信息科学版),2010,35(2):193-196.
[5]王耀革,王鑫,朱长青.基于双线性内插规则格网DEM地形误差模型[J].测绘科学技术学报,2007,24(6):419-421.
[6]HU P,LIU X,HU H.Accuracy Assessment of Digital Elevation Models Based on Approximation Theory[J].P hotogrammetric Engineering and Remote Sensing,2009,75(1):49-56.
[7]史巍巍,裘昱,戴宗友.数字高程模型与等高线质量相关性研究[J].测绘通报,2006(2):23-26.
[8]史文中,王斌,刘二永,等.基于双三次Hermite插值方法的DEM误差传播分析[J].测绘科学技术学报,2013,30(4):380-387.
[9]李毅,石豫川,王平,等.基于DEM的吉太曲流域水文信息分析[J].人民黄河,2015,37(9):32-34.
[10]周启鸣,刘学军.数字地形分析[M].北京:科学出版社,2006:94-95.