不同地形下的大地水准面插值方法的比较
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摘要
在物理大地测量中,大地水准面是非常重要的参考面.为比较不同地形情况下大地水准面插值精度的差异,快速选定特定地形下大地水准面的最优插值方法.选取了平原、高原与山地等三种不同地形区域,利用地球重力场模型EGM2008计算的大地水准面格网值与GPS水准点数据,分别采用Kriging法、反距离加权法、样条函数法和自然邻点法四种方法进行内插实验,并通过模型值对插值结果进行检核,结果表明:样条函数法在不同地形区域都表现出了一定的优越性;不同地形情况下的插值误差相差较大,平原地区仅为1.59 mm,高原地区可达3.79 mm,而山地地区插值精度相对较差,误差约为1 cm.
Geoid is a very important reference surface in physical geodesy.In order to compare the accuracy of geoid height interpolation on different topography and obtain an optimal method for specific topography,this paper selects three different topographies such as plain,highland and mountainous region,then uses grid values of geoid calculated by EGM2008 earth gravity field model and GPS leveling data to conduct interpolation experiments by adopting Kriging,inverse distance weighting,spline function and natural adjacent point methods.The result checked by model values shows that spline function has certain superiority on different topography.The interpolation error varies on different topography,only 1.59 mm in plain areas and 3.79 mm in plateau areas,while the interpolation accuracy is relatively poor in mountainous areas with an error about 1 cm.
Geoid is a very important reference surface in physical geodesy.In order to compare the accuracy of geoid height interpolation on different topography and obtain an optimal method for specific topography,this paper selects three different topographies such as plain,highland and mountainous region,then uses grid values of geoid calculated by EGM2008 earth gravity field model and GPS leveling data to conduct interpolation experiments by adopting Kriging,inverse distance weighting,spline function and natural adjacent point methods.The result checked by model values shows that spline function has certain superiority on different topography.The interpolation error varies on different topography,only 1.59 mm in plain areas and 3.79 mm in plateau areas,while the interpolation accuracy is relatively poor in mountainous areas with an error about 1 cm.
引文
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[2] 费龙,田秋艳.丘陵地貌区高程内插适宜方法选择——以长春净月潭为例[J].地理科学,2016,36(4):597-602.
[3] 徐潇,谭衢霖,王浩宇,等.复杂地貌地形图等高线内插DEM算法的精度分析[J].遥感信息,2013,28(6):111-115.
[4] 中国科学院地理研究所.中国1:1000000地貌图制图规范(试行)[M].北京:科学出版社,1987.
[5] HAINING R.Spatial data analysis in the social and environ-mental sciences[M].Great Britain:Cambridge University Press,1990:291-312.
[6] BOGAERT P,MAHAU P,BECKERS F.The spatial interpolation of agro-climatic data.Cokriging software and source code.User's manual.Version 1.0b November 1995[M].Iale Delle Terme Di Caracalla:Fao Agrometeorology,1995.
[7] MATHERON G.Principles of geostatistics[J].Economic Geology,1963,58(8):1246-1266.
[8] WEBSTER R,BURGESS T M.Optimal and Isarithmic Mapping of Soil Properties.3.Changing Drift and Universal Kriging[J].European Journal of Soil Science,1980,31(3):505-524.
[9] 缪坤,李少梅,郭健,等.Surfer软件中高程数据内插方法比较分析[J].测绘科学技术学报,2014(4):431-435.
[10] HUSAR R B,FALKER S R.Uncertainty in the spatial interpolation of PM10 monitoring data in Southern California[J].DRAFT,1997:35-51.
[11] 李新,程国栋.空间内插方法比较[J].地球科学进展,2000,15(3):260-265.
[12] 黄杏元,马劲松.地理信息系统概论[M].北京:高等教育出版社,2008.
[13] 张伟,覃庆炎,简兴祥.自然邻点插值算法及其在二维不规则数据网格化中的应用[J].物探化探计算技术,2011,33(3):291-295.
[14] WATSON D F,PHILLP G M.Neighborhood-based interpolation[J].Geobyte,1987,2(2):12.
[15] WATSON D F.Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes[J].Computer Journal,1981,24(2):167-172.