Vector geometry based method for the extraction of slope of aspect by using DEMs

doi:10.11947/j.AGCS.2019.20180447

Abstract

Abstract: Aspect matrix, as the source data for calculating the slope of aspect (SOA), has the characteristic of directionality. Thus, misunderstanding and error would be produced if SOA was calculated by scalar method because its source data has the directional property. On a basis of the mathematical Gaussian surface and 5 m resolution DEM data of different loess landform sample areas, the mathematical vector method is proposed to calculate SOA with a full consideration of directional property of the aspect matrix. In this method, the original aspect matrix has been transformed into the polar coordinate system, and the vector geometric representation of aspect matrix could be achieved. Then the SOA is calculated on a basis of this vector transformed aspect data. In the end, a comparative analysis is conducted among the proposed method and traditional scalar methods. The results show that SOA calculated by the proposed method could effectively avoid the extreme error in the north direction and the inaccuracy when the aspect difference exceeds 180°. Meanwhile, a more reasonable SOA result could be achieved in the other main areas, and a more stable result can be obtained by using our method in different resolution DEMs. The proposed vector geometry method could help to provide a reference for accurate digital terrain analysis, and it is also an important practice to solve problem in DTA by mathematical vector geometry.

Key words: DEM, slope of aspect, aspect, vector geometry method

CLC Number:

P208

HU Guanghui, XIONG Liyang, TANG Guoan. Vector geometry based method for the extraction of slope of aspect by using DEMs[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(11): 1404-1414.

References 26

[1]	CARTER B J, CIOLKOSZ E J. Slope gradient and aspect effects on soils developed from sandstone in Pennsylvania[J]. Geoderma, 1991, 49(3-4):199-213.
[2]	YANG Xin, TANG Guoan, XIAO Chenchao, et al. Terrain revised model for air temperature in mountainous area based on DEMs[J]. Journal of Geographical Sciences, 2007, 17(4):399-408.
[3]	夏誉玲, 李小娟, 王涛. 基于数字高程模型的混合流向算法[J]. 测绘学报, 2018, 47(5):683-691. DOI:10.11947/j.AGCS.2018.20170614. XIA Yuling, LI Xiaojuan, WANG Tao. A hybrid flow direction algorithm for water routing on DEMs[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(5):683-691. DOI:10.11947/j.AGCS.2018.20170614.
[4]	汤国安, 李发源, 刘学军. 数字高程模型教程[M]. 2版. 北京:科学出版社, 2010. TANG Guoan, LI Fayuan, LIU Xuejun. Digital elevation model tutorial[M]. 2nd ed. Beijing:Science Press, 2010.
[5]	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. DOI:10.3321/j.issn:1001-1595.2005.02.007. 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. DOI:10.3321/j.issn:1001-1595.2005.02.007.
[6]	程维明, 周成虎, 申元村, 等. 中国近40年来地貌学研究的回顾与展望[J]. 地理学报, 2017, 72(5):755-775. CHENG Weiming, ZHOU Chenghu, SHEN Yuancun, et al. Retrospect and perspective of geomorphology researches in China over the past 40 years[J]. Acta Geographica Sinica, 2017, 72(5):755-775.
[7]	朱秋莲, 邢肖毅, 张宏, 等. 黄土丘陵沟壑区不同植被区土壤生态化学计量特征[J]. 生态学报, 2013, 33(15):4674-4682. ZHU Qiulian, XING Xiaoyi, ZHANG Hong, et al. Soil ecological stoichiometry under different vegetation area on loess hilly gully region[J]. Acta Ecologica Sinica, 2013, 33(15):4674-4682.
[8]	XIONG Liyang, TANG Guoan, LI Fayuan, et al. Modeling the evolution of loess-covered landforms in the Loess Plateau of China using a DEM of underground bedrock surface[J]. Geomorphology, 2014, 209:18-26.
[9]	LÜ Guonian, XIONG Liyang, CHEN Min, et al. Chinese progress in geomorphometry[J]. Journal of Geographical Sciences, 2017, 27(11):1389-1412.
[10]	汤国安, 那嘉明, 程维明. 我国区域地貌数字地形分析研究进展[J]. 测绘学报, 2017, 46(10):1570-1591. DOI:10.11947/j.AGCS.2017.20170388. TANG Guoan, NA Jiaming, CHENG Weiming. Progress of digital terrain analysis on regional geomorphology in China[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10):1570-1591. DOI:10.11947/j.AGCS.2017.20170388.
[11]	朱庆, 赵杰, 钟正, 等. 基于规则格网DEM的地形特征提取算法[J]. 测绘学报, 2004, 33(1):77-82. DOI:10.3321/j.issn:1001-1595.2004.01.014. ZHU Qing, ZHAO Jie, ZHONG Zheng, et al. The extraction of topographic patterns based on regular grid DEMs[J]. Acta Geodaetica et Cartographica Sinica, 2004, 33(1):77-82. DOI:10.3321/j.issn:1001-1595.2004.01.014.
[12]	QIN C, ZHU A X, PEI T, et al. An adaptive approach to selecting a flow-partition exponent for a multiple-flow-direction algorithm[J]. International Journal of Geographical Information Science, 2007, 21(4):443-458.
[13]	CHEN Yumin, ZHOU Qiming, LI Sheng, et al. The simulation of surface flow dynamics using a flow-path network model[J]. International Journal of Geographical Information Science, 2014, 28(11):2242-2260.
[14]	JONES K H. A comparison of algorithms used to compute hill slope as a property of the DEM[J]. Computers & Geosciences, 1998, 24(4):315-323.
[15]	MINÁR J, EVANS I S. Elementary forms for land surface segmentation:the theoretical basis of terrain analysis and geomorphological mapping[J]. Geomorphology, 2008, 95(3-4):236-259.
[16]	CHENG Guo, LIU Lu, JING Ning, et al. General-purpose optimization methods for parallelization of digital terrain analysis based on cellular automata[J]. Computers & Geosciences, 2012, 45(1):57-67.
[17]	褚永彬, 朱利东, 唐斌, 等. 疏勒河上游流域地面坡谱特征[J]. 干旱区地理, 2015, 38(2):345-350. CHU Yongbin, ZHU Lidong, TANG Bin, et al. Slope spectrum characteristics of the Shule River's upstream basin[J]. Arid Land Geography, 2015, 38(2):345-350.
[18]	焦贝贝, 石培基, 刘春芳, 等. 黄土高原低山丘陵区农村居民点分布与地形因子关系研究——以兰州市七里河区为例[J]. 资源科学, 2013, 35(8):1719-1727. JIAO Beibei, SHI Peiji, LIU Chunfang, et al. The distribution of rural settlements in relation to land form factors in low hilly land on the Loess Plateau[J]. Resources Science, 2013, 35(8):1719-1727.
[19]	谢轶群, 汤国安, 江岭. DEM提取坡向变率中的误差特征与消除方法[J]. 地理与地理信息科学, 2013, 29(2):49-53. XIE Yiqun, TANG Guoan, JIANG Ling. Characteristics and correcting methods of errors in extraction of SOA based on DEMs[J]. Geography and Geo-Information Science, 2013, 29(2):49-53.
[20]	FLORINSKY I V. Computation of the third-order partial derivatives from a digital elevation model[J]. International Journal of Geographical Information Science, 2009, 23(2):213-231.
[21]	MINÁR J, JENČO M, EVANS I S, et al. Third-order geomorphometric variables (derivatives):definition, computation and utilization of changes of curvatures[J]. International Journal of Geographical Information Science, 2013, 27(7):1381-1402.
[22]	李润超, 袁林旺, 李硕, 等. DEM坡向提取的向量场模板匹配方法[J]. 测绘学报, 2013, 42(6):922-928. LI Runchao, YUAN Linwang, LI Shuo, et al. A vector field template matching method of DEM slope extraction[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(6):922-928.
[23]	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. DOI:10.3321/j.issn:1001-1595.2004.03.014. 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. DOI:10.3321/j.issn:1001-1595.2004.03.014.
[24]	JIANG Sheng, TANG Guoan, LIU Kai. A new extraction method of loess shoulder-line based on Marr-Hildreth operator and terrain mask[J]. PLoS One, 2015, 10(4):e0123804.
[25]	李登科. 陕北吴起县退耕还林(草)成效的遥感监测分析[J]. 中国沙漠, 2009, 29(1):125-130, 200-201. LI Dengke. Remote sensing analysis on effect of tillage reverting to woodland or grassland in Wuqi, Shaanxi Province[J]. Journal of Desert Research, 2009, 29(1):125-130, 200-201.
[26]	XIONG Liyang, TANG Guoan, YAN Shijiang, et al. Landform-oriented flow-routing algorithm for the dual-structure loess terrain based on digital elevation models[J]. Hydrological Processes, 2014, 28(4):1756-1766.