基于误差传播定律的地形复杂度误差估计  

Error estimation of terrain complexity based on error propagation law

作　　者：周访滨[1,2] 杨自强 朱衍哲 马国伟 钟绍平 ZHOU Fangbin;YANG Ziqiang;ZHU Yanzhe;MA Guowei;ZHONG Shaoping(School of Transportation Engineering,Changsha University of Science&Technology,Changsha 410114,China;Key Laboratory of Special Environment Road Engineering of Hunan Province,Changsha University of Science&Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学交通学院,湖南长沙410114 [2]长沙理工大学特殊环境道路工程湖南省重点实验室,湖南长沙410114

出　　处：《长沙理工大学学报(自然科学版)》2025年第1期40-48,61,共10页Journal of Changsha University of Science & Technology:Natural Science

基　　金：国家自然科学基金项目(41671446);湖南省自然科学基金项目(2021JJ30702);长沙市自然科学基金(kq2402013)。

摘　　要：【目的】解决现有地形复杂度误差评价方法主观性强、缺少误差解析式的问题。【方法】利用误差传播定律推导了局部高差、局部标准差、局部褶皱度和局部全曲率的中误差表达式,依据复合地形因子误差传递规律构建了复合地形复杂度指标(compound terrain complexity index,CTCI)提取的误差估计模型(error estimation model for CTCI,CEEM)。通过模拟数字高程模型(digital elevation model,DEM)试验验证了该模型的有效性,并采用三个不同地貌区域的实体DEM进行CEEM泛化试验。【结果】在不同噪声影响下,CEEM平均误差、均方差、残差和平均绝对百分比误差最大值分别为-2.1×10^(-3)、7.99×10^(-6)、8.4×10^(-3)和22.8%,决定系数均在0.961以上,CEEM整体误差微小;不同地貌类型的地形复杂度提取误差存在差异,试验统计结果表明误差由大到小依次为高山、中山、丘陵。【结论】CEEM能定量化描述地形复杂度的提取误差,可为不同复杂地形地貌区域提取复合地形复杂度指标提供参考。[Purposes]This paper aims to address the issue that the existing terrain complexity error evaluation methods are subjective and lack error analytic formulas.[Methods]The mean square error expressions for local relief,local standard deviation,local rugosity,and local total curvature were derived by using error propagation law.The error estimation model for compound terrain complexity index(CTCI),namely CEEM was constructed by error transfer of compound terrain factors.The effectiveness of CEEM was verified by the simulated digital elevation model(DEM),and the generalization experiment of CEEM was carried out by using the entity DEM of three different landform regions.[Findings]Under the influence of different noises,the maximum values of CEEM’s mean error,mean square error,residual error,and mean absolute percentage error are -2.1×10^(-3),7.99×10^(-6),8.4×10^(-3),and 22.8%,respectively,with an absolute coefficient of above 0.961.The overall error of CEEM is small.There are differences in the extraction error of terrain complexity of different landform types,and the experimental statistical results show that the error size in descending order is high mountain,middle mountain,and hill.[Conclusions]The extraction error of terrain complexity can be quantitatively described by CEEM,which provides a reference for extracting compound terrain complexity index in different complex landform regions.

关 键 词：数字地形分析 栅格DEM 误差估计模型 误差传播定律 复合地形复杂度指标 

分 类 号：U412[交通运输工程—道路与铁道工程] P217[天文地球—测绘科学与技术]