研究地表面积统计数学模型及其影响因素,消除不同分辨率DEM计算所得地表面积的差异,对综合利用多尺度DEM数据精确统计和监测地表面积具有重要意义.本文研究提出了一种顾及复杂地形因子的地表面积统计方法.该方法首先利用泰勒级数逼近原理对微观地形因子进行最小二乘估计,然后利用这些地形因子对DEM和多边形区域边界进行加密,最后利用加密后的DEM和多边形边界构建地表三角网统计地表面积.试验表明,在局部地形因子显著的山区或丘陵地区,使用不同分辨率DEM所统计的地表面积存在较大的差异,而顾及地形因子的地表面积统计方法可明显提高低分辨率DEM地表面积统计精度.
Mitigating the differences of the surface areas computed by DEM data with different resolutions is meaningful in precisely doing area statistics and monitoring area changes. In this paper, we discuss the mathematical models to the surface area computation and give the influences to the computational accuracy. An area computation method of polygons on the landscape surface is proposed and this method has taken local terrain factors into account. Firstly, the least squares estimation of these local terrain factors is achieved by employing the Taylor series expansion of the spatial function, then these estimated terrain factors are applied to the DEM interpolation. Finally, the regular triangulated network is structured to approximate the theoretical area of the landscape surface. Experiments show that, in the mountainous area or hilly region where the nonlinear topographic signal is prominent, the computational area heavily relies on the space resolution of the DEM data and the impact to the surface area computation is very serious. However, due to the using of terrain factors estimated, the area computation strategy proposed can significantly improve the precision of the computed area from the low resolution DEM.
[1] LI Deren,SUI Haigang, SHAN Jie.Discussion on Key Technologies of Geographic National Conditions Monitoring[J]. Geomatics and Information Science of Wuhan University, 2012(5):505-512. (李德仁,眭海刚,单杰.论地理国情监测的技术支撑[J]. 武汉大学学报:信息科学版, 2012(5): 505-512.)
[2] CHEN Junyong. Study Notes on National Condition Monitoring[J]. Acta Geodaetica et Cartographica Sinica, 2012,41(5):633-635. (陈俊勇.地理国情监测的学习札记[J]. 测绘学报, 2012,41(5):633-635.)
[3] CAO Zhenyu, TAN Mingjian, SHEN Yanmin. Study on Polygon Area Calculation Methods in Geodetic Coordinate System[J]. Bulletin of Surveying and Mapping, 2012(S1): 570-572. (曹振宇, 谭明建,沈艳敏.大地坐标系中多边形面积计算方法研究[J]. 测绘通报, 2012(S1): 570-572.)
[4] QIAO Chaofei. Review of Overseas National Condition Monitoring[J]. Bulletin of Surveying and Mapping, 2011(11): 81-83. (乔朝飞.国外地理国情监测概况与启示[J]. 测绘通报, 2011(11): 81-83.)
[5] American Society for Photogrammetry and Remote Sensing.Digital Elevation Model Technologies and Applications: The DEM Users Manual[M]. Bethesda ASPRS Publications,2007.
[6] SJöBERG L E. Determination of Areas on the Plane, Sphere and Ellipsoid[J]. Survey Review, 2006. 38(301): 583-593.
[7] GILLISSEN I. Area Computation of a Polygon on an Ellipsoid[J]. Survey Review,1993,32(248): 92-98.
[8] WANG Jiexian, YU Zhenwu. Area Calculation Error Caused by Gauss Projection[J]. Bulletin of Surveying and Mapping, 2003(4): 5-6. (王解先,俞振武.高斯投影引起的面积计算误差[J]. 测绘通报, 2003(4): 5-6.)
[9] PEDZICH P, KUZ＇MA M. Application of Methods for Area Calculation of Geodesic Polygons on Polish Administrative Units[J]. Geodesy and Cartography, 2012, 61(2): 105-115.
[10] JI Bing, BIAN Shaofeng.Calculation of Surface Area of Triaxial Ellipsoid[J]. Journal of Naval University of Engineering, 2008(4): 21-24.(纪兵,边少锋.三轴椭球表面积的计算[J]. 海军工程大学学报, 2008(4): 21-24.)
[11] ZHANG Y. Surface Area Processing in GIS for Different Mountain Regions[J]. Forestry Studies in China, 2011,13(4): 311-314.
[12] JENNESS J S. Calculating Landscape Surface Area from Digital Elevation Models[J]. Wildlife Society Bulletin, 2004,32(3): 829-839.
[13] JIANG Fan, LU Xiaohua, WANG Zhonglan. The Analysis of DEM Surface Area Based on Composed Calculus Algorithms[J]. Journal of Institute of Surveying and Mapping, 2005(4): 263-265. (江帆, 吕晓华, 王仲兰.基于复化公式的DEM表面积算法分析[J]. 测绘学院学报, 2005(4): 263-265.)
[14] JENSON S, DOMINGUE J.Extracting Topographic Structure from Digital Elevation Data for Geographic Information System Analysis[J]. Photogrammetric Engineering and Remote Sensing, 1988,54(11): 1593-1600.
[15] HOECHSTETTER S.Effects of Topography and Surface Roughness in Analyses of Landscape Structure—a Proposal to Modify the Existing Set of Landscape Metrics[J]. Landscape Online, 2008,3: 1-14.
[16] BEASOM S L, WIGGERS E P, GIARDINO J R. A Technique for Assessing Land Surface Ruggedness[J]. The Journal of Wildlife Management, 1983,47(4): 1163-1166.
[17] QIN Yanhong, LU Lin, WU Jitao.A Study on the Multi-resolution Representation of the Areas Based on Two-dimension Wavelet Transformation[J]. Mathematical Theory and Applications, 2005(2): 43-48. (秦艳红, 卢林, 吴纪桃.地形坡度面积的二维多分辨分析研究[J]. 数学理论与应用, 2005(2): 43-48.)
[18] AGUILAR F J.Effects of Terrain Morphology, Sampling Density, and Interpolation Methods on Grid DEM Accuracy[J]. Photogrammetric Engineering and Remote Sensing, 2005,71(7): 805.
[19] WISE S M. The Effect of GIS Interpolation Errors on the Use of Digital Elevation Models in Geomorphology[J]. Landform Monitoring, Modelling and Analysis, 1998,99: 139-164.
[20] CHILDS C. Interpolating Surfaces in ArcGIS Spatial Analyst[R].[S.l.]:ESRI Education Services, 2004.
[21] LI Xin, CHENG Guodong, LU Ling. Comparison of Spatial Interpolation Methods[J]. Advance in Earth Sciences, 2000, 15(3): 260-265. (李新, 程国栋, 卢玲.空间内插方法比较[J]. 地球科学进展, 2000, 15(3): 260-265.)
[22] THOMAS G B, FINNEY R L. Thomas' Calculus[M].[S.l.]:Addison Wesley Publishing Company,2002.
[23] DANG Yamin, CHENG Yingyan, XUE Shuqiang.Geodetic Coordinate System and Its Applications[M]. Beijing:Surveying and Mapping Press, 2010. (党亚民, 成英燕,薛树强.大地坐标系统及其应用[M]. 北京:测绘出版社, 2010.)
[24] ZHU Huatong. Establishment of Geodetic Coordinate System[M]Beijing:Surveying and Mapping Press, 1986. (朱华统.大地坐标系的建立[M].北京:测绘出版社, 1986.)
[25] ZHU Huiyi,LIU Shulin,JIA Shaofeng.Problems of the Spatial Interpolation of Physical Geographical Elements[J]. Geographical Research, 2004, 23(4): 425-432. (朱会义, 刘述林, 贾绍凤. 自然地理要素空间插值的几个问题[J]. 地理研究, 2004, 23 (4): 425-432.)
[26] XUE Shuqiang, YANG Yuanxi. Generalized Inverse Distance Weighting Method for Spatial Interpolation[J]. Geomatics and Information Science of Wuhan University, 2013,38(12):1435-1439.(薛树强,杨元喜. 广义反距离加权空间推估法[J]. 武汉大学学报:信息科学版,2013,38(12):1435-1439.)
[27] ZHU Qing, CHEN Chujiang. Quick Generation of TIN and Its Dynamic Updating[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1998(3): 18-21. (朱庆,陈楚江.不规则三角网的快速建立及其动态更新[J]. 武汉测绘科技大学学报, 1998(3): 18-21.)
[28] LIU Xuejun, GONG Jianya, ZHOU Qiming, et al. A Study of Accuracy and Algorithms for Calculating Slope and Aspect Based on Grid Digital Elevation Model(DEM)[J]. Acta Geodaetica et Cartographica Sinica, 2004,33(3):258-263. (刘学军,龚健雅,周启鸣,等. 基于DEM坡度坡向算法精度的分析研究[J]. 测绘学报,2004,33(3):258-263).
[29] LIU Xuejin, REN Zhifeng, WANG Yanfang, et al. Slope Model at Arbitrary Direction Derived from Grid-based DEM[J]. Areal Research and Development,2009(4):139-141. (刘学军,任志峰,王彦芳,等. 基于DEM的任意方向坡度计算方法[J]. 地域研究与开发,2009(4):139-141.)
[30] HE Dan. Window Analysis for Extraction of Terrain Factors from Different Resolution DEM[D]. Xi'an:Northwest University,2012. (贺丹. 不同分辨率DEM提取地形因子的适宜分析窗口研究[D].西安:西北大学,2012.)
