插值条件下DEM误差的空间自相关模型研究

项目名称： 插值条件下DEM误差的空间自相关模型研究

项目编号： No.41471373

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 卢华兴

作者单位： 东南大学

项目金额： 84万元

中文摘要： DEM误差的空间自相关性已经被证明存在并显著影响DEM及数字地形分析的不确定性。针对目前DEM误差的空间自相关性及其应用研究中重随机模拟而轻理论建模，重单一误差描述而轻两类误差的统一描述的研究现状，本研究拟从DEM构建方式之一的DEM插值入手，分析DEM插值基函数和核函数的空间自相关性质，建立不同插值算法的空间自相关性的统一描述，降低DEM误差的空间自相关性建模的复杂性；在前期研究成果DEM统一误差模型框架下，利用误差传递和空间统计学等相关理论，引入局部M指数、局部G指数、邻域Cov等指标，建立DEM两类误差的空间自相关性的数学模型，对DEM误差的空间自相关性进行定量化描述，最后以样区实际数据和地形参数为实验对象对DEM误差的空间自相关模型进行检验，以提高模型的适用性和有效性。本研究有望进一步完善DEM误差特性的描述体系，为DEM及数字地形分析的不确定性分析和评价提供理论支撑。

中文关键词： 数字高程模型；误差；空间自相关；基函数；核函数

英文摘要： Digital Elevation Model (DEM) is known as the most important GIS fundamental data used in geo-simulation and terrain analysis, DEM and its derivatives uncertainty has gained widespread attention and extensive research ever since DEM concept was proposed in 1958. Due to terrain's inherent characteristics and interpolation impacts when generating DEM, DEM error has specific spatial autocorrelation property which has been proved that significantly influences the uncertainty of DEM and its derivatives. Recently enormous amount of related literatures that has taken DEM error autocorrelation as a factor when quantifying DEM and derivatives uncertainty, however, most of them use the empirical stochastic autocorrelation model, or just consider one type of DEM error, which will more or less produce biased results. Based on previous research results（DEM unified error model）, this study intends to investigate the interpolation spatial autocorelation principle and analyze the characteristics of interpolation kernel functions and base functions,then deduce the theoretical spatial autocorrelation model of DEM error on the condition of DEM interpolation. In order to quantify local DEM error autocorrelation, this study plans to introduce local correlation indices (Local M's I, Local G's I, Neighbor Cov), present series of quantitative method for accessing local spatial autocorrelation of grid DEM noise error and approximate error derived from DEM interpolation, and then, obain DEM error correlation grid fields. In order to testify spatial autocoreltion model, this research lastly plans to take DEM error autocorelation as a key factor to evaluate uncertainties of DEM derivatives, select typical test area and typical interpolation as cases, the goal of these cases are: 1）Evaluate regular patterns of relations between DEM error and interpolation attributes(base functions and kernel functions) 2）Testify how significantly the error autocorrelation influence DEM and its derivatives.This study intends to enhance the evaluation method of DEM error desciription system, provide more comprehensive description information of the DEM error for its users, give a theoretical support to the security and reliability of DEM when used in terrain analysis and engineering application, and simultaneously this research will provide a useful reference for other studies of the uncertainty of spatial data and reliability analysis of the geo-models.

英文关键词： DEM;Error;Spatial Autocorrelation;Base Function;Kernel Function