【作者】 卢华兴；

【导师】 刘学军； 汤国安；

【作者基本信息】 南京师范大学 ， 地图学与地理信息系统， 2008， 博士

【摘要】 数字高程模型(Digital Elevation Model,DEM)是GIS空间数据库中赖以进行地学模拟和分析最为重要的基础空间数据。自1958年DEM概念首次提出以来,其质量问题就受到广泛的关注和研究。随着空间信息技术的发展,DEM在数据采样方法与数据精度评价上有了长足进步,然而,由于DEM数据的多源性、地形表面的不确定性和DEM建模的复杂性,DEM不确定性问题的研究相对落后于应用的要求.各类DEM误差的存在,不同程度地降低了GIS分析与应用结果的准确性,特别是当DEM及其地形参数作为各类地学模型的输入数据时。目前,基于4D产品的空间信息服务和GIS与地学分析模型的结合已成为GIS发展的基本趋势.日益复杂的地学模型对多重地理要素数据的计算要求,以及各类空间信息服务对基础数据的质量要求,使得作为4D产品之一的DEM的重要性和应用范围日益扩大,同时也对DEM质量的分析和评估提出了更高的要求。加强DEM不确定性的理论研究,为空间信息服务、地学分析和模拟提供科学、合理的质量标准,是十分必要而紧迫的任务。本文对目前DEM精度研究现状进行了较为系统的回顾和剖析,指出了传统的DEM全局精度指标和DEM误差模型的不足,在此基础上研究了DEM理论误差模型,旨在刻画DEM误差的空间分布特征,为用户提供全面的DEM精度描述信息.本文从DEM插值原理入手,剖析了DEM插值机理和本质,提出了DEM统一插值模型,并在统一插值模型的框架内,利用空间统计和误差传播理论,构建了DEM误差模型,揭示了DEM误差的空间分布特征,并进一步研究了DEM误差空间相关特征对地形分析的影响。本文所做主要研究工作如下:1、DEM统一插值模型构建在对常用DEM插值模型分析归纳基础上,分析了DEM插值模型的数学机理和物理机理,分析了DEM插值的本质和共性,发现了DEM插值模型研究核心是插值核函数的构建;在此基础上,论证了常用的DEM插值模型其实都是已知点权重分配的过程,即每个已知点都有其特定的插值基函数,根据这一原则,构建了DEM插值的统一概念模型,结合DEM插值参数和插值基函数的论述,实现了常用DEM插值模型的统一描述。2、基于统一插值模型的DEM误差模型构建考虑到现有的DEM误差模型大多是基于具体的DEM插值模型,缺乏通用性。本文在DEM统一插值模型的框架下,利用空间统计和误差传播等相关理论,构建了DEM误差模型,推导了DEM精度场的数学表达式(包括噪声精度场△场、逼近精度场ε场、合成精度场α场),从而解决了DEM局部精度(像元精度)的定量化描述问题,并对DEM误差模型的可靠性进行了实验分析。3、DEM误差的空间结构评价基于DEM误差模型,从理论分析角度进一步证明了DEM误差存在特定的空间自相关性。在DEM精度场模型的基础上,结合空间统计学的相关理论,论述了DEM精度场的空间结构评价方法,构建了DEM精度场的空间自相关模型,从而形成了DEM精度的全局、局部描述以及空间结构描述的DEM精度分析指标系列。4、顾及DEM误差自相关的地形参数精度分析以坡度、坡向作为研究对象,顾及DEM精度场的空间结构,推导了坡度、坡向的理论精度模型,并分析了各种差分方式下的坡度精度和坡向精度模型,最后从DEM误差传播角度,在前面实验分析基础上,对坡度、坡向的精度场(β场)数据进一步统计分析,分析了顾及和不顾及DEM误差空间结构两种情形下的β场数据,从而进一步揭示了DEM误差的空间结构对数字地形分析的影响规律。本研究完善了DEM的误差描述体系,为DEM使用者提供较为全面的DEM精度描述信息,以及为DEM的地学分析及应用的安全性和可靠性提供理论支撑,同时本文的研究也为空间数据的不确定性研究、地学模型的可靠性分析提供有益的参考。更多还原

【Abstract】 Digital Elevation Model (DEM) is known as the most important GIS fundamental data used in geo-simulation and spatial analysis, and its quality has gained widespread attention and extensive research ever since DEM concept was proposed in 1958. With the development of geoinformatics, a great progress has been made in DEM sampling method and accuracy assessment. However, due to the multiple data resources of DEM, uneven terrain surface, and complexity of DEM modeling, the research on DEM uncertainty relatively fell behind its application requirements. The various types of DEM errors, to some extent, reduce the precision of the GIS analysis and its application, especially when DEM and its derivatives serve as the input data of various types of topographical models.Nowadays, spatial information services (SIS) which is based on 4D products and especially on the combination of GIS and geo-models have become the main development trend of GIS. The increasingly complex geo-models ask for requirements of multi-feature data geocomputation as well as the quality of the GIS fundamental data. DEM as one of the important 4D products, its application has expanded into many fields, which simultaneously put forward higher requirements to DEM quality, In order to offer a sound quality standard for SIS, spatial analysis and geo-simulation, further theoretical study on the DEM accuracy is extremely essential.This thesis firstly gave a systematic review and assessment on literature, and pointed out the following limitations: global DEM accuracy model like root mean square error (RMSE) can not describe spatial distribution of DEM error, which can not provide overall accuracy information for users. Traditional error models can not give precised error prediction or lack of universality in use. Based on these limitations, this thesis started from the conventional DEM interpolation theory, analyzed the DEM interpolation mechanism and deduced DEM unified interpolation model (UIM). Under the framework of UIM, also by using geostatistic and error propagation theory, this thesis modeled DEM local accuracy (Pixel accuracy), proposed DEM accuracy field concept and model, which aimed at revealing the spatial characteristics of the DEM error distribution (spatial structure of DEM error), and investigating DEM error propagation in terrain analysis (take slope and aspect extraction as example) considered the impact of spatial structure of DEM error.The major contributions are as the following:1) DEM unified interpolation model (UIM)After introducing conventional DEM interpolation models, this thesis analyzed the mechanisms of the DEM interpolation models, investigated the nature and general character of the DEM interpolation algorithms, and lastly presented UIM. UIM demonstrates that conventional DEM interpolation model actually is a weight allocation process of each reference point, that is, each reference point has its own base function, and its base function relies on interpolation kernel. UIM is an abstract model that links each conventional DEM interpolation models.2) DEM error model based on UIMThe existing DEM error models are all based on specific interpolation model, thus, they lack the universality in use. Under the framework of the UIM, and by using the spatial statistics and the error propagation theory, this thesis constructed the DEM accuracy field model (including noise accuracy field: A field; approximated accuracy field: e field; synthesis accuracy field:αfield), DEM error model based on UIM is independent from specific interpolation model, thus its universality in use has been enhanced. Lastly, this thesis carried on experimental research analyzing the practicality of the DEM error model, results showed DEM error model presented in this thesis was sound in accuracy prediction. 3) The spatial structure of the DEM errorBased on DEM error model, this thesis theoretically testified that DEM error existed specific spatial autocorrelation, by using the theory of geostatistic, this thesis presented the methodology on how to describe spatial structure of DEM error, and constructed the spatial autocorrelation model of the DEM accuracy field, lastly formed the DEM accuracy evaluation criterion from the global to local description as well as spatial structure description.4) Terrain parameters accuracy analysis considered spatial structure of DEM accuracy fieldConsidered the spatial structure of the DEM accuracy field, this thesis took slope and aspect as study objects, inferred the theoretical precision model for the slope and aspect, and calculated slope and aspect accuracy field (βfield ) based on various DEM difference algorithms, testified the correctness of the slope and aspect accuracy model through experimentation, results further revealed the impact that spatial autocorrelation of DEM error on accuracy of digital terrain analysis was remarkable.This study enhanced the evaluation method of DEM accuracy, provided more comprehensive description information of the DEM accuracy for its users, gave a theoretical support to the security and reliability of DEM when used in terrain analysis and engineering application, and simultaneously this study provided a useful reference for the study of the uncertainty of spatial data and reliability analysis of the geo-models.更多还原