2012 , Vol. 14 >Issue 3: 286 - 291

ARTICLES

The DEM Based 5-Node Second-order Finite Difference Model for Slope Computation

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• 1. Key Laboratory of Virtual Geographical Environment, Ministry of Education, Nanjing Normal University, Nanjing 210046, China;
2. School of Resource and Environmental Engineering, Hefei University of Technology, Hefei 230009, China

Revised date: 2012-04-05

Online published: 2012-06-25

Abstract

Slope is the most basic terrain parameter to construct geo-science models. The accuracy analysis of the computing model is one of the most important issues in the geo-science. A lot of studies focused on error analysis of the computing model over the past few decades. The source of the error and the relationship between the error and the other parameters were studied. However, few studies were aimed to put forward a new model to decrease the error, which is more important for high resolution DEMs. By analyzing the error source of the slope computing model, this paper put forward a new model called 5 Node Second-order Finite Difference (5N-2FD). The characteristic of this model is that it is able to consider the multi-distance neighbor node: firstly it builds two difference models using different grid sizes, and then combines the two models into one with different weights. It is proved that it can improve the accuracy of the results remarkably through mathematical analysis. In this paper, a mathematical surface is selected to verify the accuracy of the new model. In order to study the influence of the resolution to the accuracy of the slope, this paper generated DEMs from the mathematical surface with different resolution, one is 1m, and the other is 5m. The results show that the new model can significantly improve the accuracy of the result compared with the common models. This study enriched the method system of digital terrain analysis, and provided slope data of high accuracy for many geo-science models. In addition, besides slope, there are many terrain parameters which are calculated through finite difference, such as aspect and various kinds of curvature, and the methods of this paper could afford some useful references in improving the accuracy of such terrain parameters.

ZHAO Mingwei, TANG Guoan, ZHANG Lei, TIAN Jian, SONG Xiaodong . The DEM Based 5-Node Second-order Finite Difference Model for Slope Computation[J]. Journal of Geo-information Science, 2012 , 14(3) : 286 -291 .

References

[1] 刘学军. 基于规则格网数字高程模型解译算法误差分析与评价 . 武汉大学,2002.

[2] Jones K H. A comparison of algorithms used to compute hill slope as a property of the DEM[J]. Computer and Geosciences, 1998, 24(4):315-323.

[3] OCallaghan J F, Mark D M. The extraction of drainage networks from digital elevation data [J]. Computer Vision, Graphics, and Image Processing, 1984(28):323-344.

[4] Sharpnack D A, Akin G. An algorithm for computing slope and aspect from elevations[J]. Photogrammetric Survey, 1969(35): 247-248.

[5] Horn B K P. Hill shading and the reflectance map[J]. Proceedings of IEEE, 1981, 69(1): 14-47.

[6] 刘学军,卞璐,卢华星,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.

[7] Zhou Q M, Liu X J. Analysis of errors of derived slope and aspect related to DEM data properties[J]. Computer & Geosciences, 2004(30):369-378.

[8] 汤国安,赵牡丹,李天文,等. DEM提取黄土高原地面坡度的不确定性[J]. 地理学报,2003,58(6):824-830.

[9] 刘学军,龚健雅,周启鸣,等. DEM结构特征对坡度坡向的影响分析[J]. 地理与地理信息科学,2004,20(6):1-5.

[10] 贾敦新,汤国安,王春,等. DEM数据误差与地形描述误差对坡度精度的影响[J]. 地球信息科学,2009,11(1):43-49.

[11] Hodgson M E. What cell size does the computed slope/aspect angle represent?[J]. Photogrammetric Engineering and Remote Sensing, 1995(61): 513-517.

[12] Jones K H. A comparison of algorithms used to compute hill slope as a property of the DEM[J]. Computer and Geosciences, 1998, 24(4): 315-323.

[13] Carter J R. The effect of data precision on the calculation of slope and aspect using gridded DEMs[J]. Cartographica, 1992, 29(1): 22-34.

[14] 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,2009,11(1):36-42.

[15] 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.

[16] 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.

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