插值条件下DEM误差的空间自相关模型研究

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.

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。

本课题拟解决DEM误差空间自相关定量化描述问题，从而丰富DEM误差的描述体系，最终目的是提高DEM数字地形分析中精度评价的可靠性。经过四年的研究，项目组基本完成了相应的研究任务，但项目进展不顺利，研究论文发表滞后。课题组依照研究内容和目标开展工作，完成了DEM各类插值算法的整理、归纳和分析，提出了DEM插值的权函数，归纳了全部DEM插值算法的权函数，并推导了部分隐式插值算方法的DEM权函数；完成了DEM噪声误差的空间自相关模型的建模、实验和验证，并获得DEM噪声空间自相关场数据。在DEM逼近误差空间自相关建模过程中，出现约8%左右的负相关以及相关系数大于1的情况，实验结果不理想；在估计DEM误差空间自相关的影响评价和分析方面，课题组完成坡度、坡向等地形因子提取的精度评价。后续研究将继续针对DEM逼近误差的获取、建模和分析，实现两类DEM误差的空间自相关性进行定量化描述，从而进一步完善 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。