论DEM地形分析中的尺度问题

DEM及其地形分析具有强烈的尺度依赖特征。本文以黄高原地区的研究为例,结合地学建模和地学模拟的需求,重点讨论DEM地形分析中的尺度问题。文中从DEM建立与应用出发,首先建立了DEM地形分析中的尺度概念体系,剖析了各类尺度之间的关系,其次讨论了尺度所引起的各种地形分析效应问题,最后探讨了DEM地形分析中的尺度转换类型和方法。     

数字高程模型的制作及应用

本文结合工作实践,首先总结概括了数字高程模型(DEM)的制作方法及过程,其次阐述了DEM的质量监控,最后简述DEM在实际生产中面临的问题及在实际生产生活中的应用。     

数字高程模型在活动断层位置及地表变形变位特征提取研究中的应用

活动断层的位置分布及其地表变形变位特征的准确识别是研究和评价活动断层的基础,国内外学者利用数字高程模型(DEM)对断层提取进行了大量研究。本文基于DEM的活动断层位置的提取方法进行综述,总结了DEM提取断层位置的地貌形态特征分析、图像处理以及综合处理提取方法,突出介绍了高分辨率DEM在详细的断层位置分布提取中的优势,DEM在断层地表变形变位及其特征参数提取研究中的最新应用进展。随着高分辨率DEM的快速发展,DEM及其空间分析技术已成为一种常见的地学研究方法,将其与野外调查、遥感、测年等技术结合进行综合分析,能够促进对活动断层的深入研究,并成为断层定量化研究强有力的技术手段。     

DEM 点位地形信息量化模型研究

针对DEM 点位, 首先应用微分几何法对其所负载的语法信息量进行测度, 其次根据地形特征点类型及地形结构特征确定其语义信息量, 然后基于信息学理论构建了DEM 点位地形信息综合量化模型。在此基础上, 以黄土丘陵沟壑区作为实验样区, 对DEM 点位地形信息量提取方法及其在地形简化中的初步实例应用进行了探讨和验证。实验结果显示, 所提出的DEM 点位地形信息量化方案可行;基于DEM 地形信息量指数的多尺度DEM 构建方案, 具有机理明确、易于实现的特点, 并通过优先保留地形骨架特征点, 可以有效减少地形失真, 从而满足不同层次的多尺度数字地形建模和表达要求。对DEM 点位地形信息进行有效量化, 为认识DEM 地形信息特征提供了一个新的切入点, 同时为多尺度数字地形建模提供理论依据与方法支持。     

DEM地面形态重构方法的精度差异特征研究

依据DEM地形建模过程,阐述了DEM地面形态重构概念,并以黄土丘陵1∶5万DEM数据为例,采用高程数值误差场和局地坡面形态误差场相结合的分析技术,实验分析了双线性、三次卷积、局部二次多项式、规则样条函数等常用插值方法在基于加密格网的DEM地面形态重构过程中的精度差异,以及DEM地面形态可重构的基本条件等问题。研究表明:在高程数值误差的极值大小、离散程度、空间分布等方面,规则样条函数插值法具有最好的地面形态重构精度,其次为局部二次多项式、三次卷积和双线性插值法;对于已确定综合尺度的地形,存在满足高保真地面形态描述要求的最佳DEM格网分辨率阈值,只有当实际DEM格网分辨率等于或高于该阈值时,才有可能无歧义、高精度地重构出DEM所描述的综合地形的地面形态。     

DEM地形信息量计算的不确定性研究

DEM地形信息量的准确度量是判定DEM数据应用适宜性与限制性关键。以黄土丘陵沟壑区DEM及其派生的坡度、坡向DTM为例进行实验,研究子集划分与分级数对DEM信息量估算精度的影响。结果表明,DEM地形信息量是实际地形信息和子集划分策略共同作用的结果,现有DEM信息量计算存在不确定性,DEM子集划分算法和分级数的选择直接影响DEM信息量的计算结果。文章借助最大熵定理的基本思路构建DEM地形信息量分级判定模型,可客观获得连续型栅格地形数据在信息量计算上最优分级,为有效估算DEM地形信息量提供科学依据。     

基于光学立体和InSAR的Grove山地区DEM建立和分析

本文分别利用光学立体和In SAR技术生成了东南极Grove山地区15 m分辨率的ASTER DEM和20 m分辨率的In SAR DEM。在利用ASTER立体像对生成DEM的过程中引入ICESat测高数据作为高程控制以减少错误匹配,提高DEM垂直精度;而在利用ERS tandem数据生成DEM后,选取ICESat测高数据对In SAR DEM进行倾斜面纠正,以消除基线不精确估计等带来的影响。通过与未作控制的ICESat测高数据进行比较,评价了两种DEM的精度并对误差进行了分析。同时,比较了两种DEM的差异,并分析了造成这些差异的原因,探讨了两种技术生成南极冰盖DEM的优势和不足。最后结合两DEM的优势,融合生成了Grove山地区高精度的DEM。     

基于小波多尺度分析的DEM数据综合及尺度转换

DEM综合是其描述的地形表面细节逐渐舍去、轮廓不断呈现的连续过程。该文运用小波变换和方根模型模拟这一过程,将小波高频系数作为DEM综合的对象,以方根模型作为阈值设定的理论依据,对小波分解各层按不同等级进行取舍实现DEM综合。以1∶1万地形图建立的DEM进行试验,派生一系列不同复杂度的DEM,并用等高线分布特征、坡度和剖面曲率、地形叠加等进行对比分析。结果表明,随着DEM综合程度增大,生成的DEM逐步舍去地形表面细节,同时较好保持了原DEM山体轮廓、山脊和谷地的走向等地貌形态特征。最后,运用回归分析方法建立了派生DEM与相应空间分辨率之间的关系,为DEM尺度效应的应用提供方法和数据支持。     

DEM不确定性影响评价中的填洼分析

洼地广泛存在于DEM实现中,洼地的处理会影响DEM不确定性评价结果。该文利用蒙特卡罗方法模拟DEM不确定性,用偏差指标评价DEM不确定性对坡度和地形指数的影响,将填洼与不填洼情况下的偏差指标相减来量化填洼对DEM不确定性评价的影响。研究发现,洼地对不同参数DEM不确定性影响评价作用不同,随着DEM不确定性的增大,洼地的影响也增大。     

单流向法地形湿度指数尺度效应的不同地形区差异分析

利用DEM提取地形湿度指数(Topographic Wetness Index,TWI),以满足既定地理模型构建,需考虑不同地形区TWI提取的尺度效应。该文根据实际应用中的DEM分辨率尺度,生成1m、2.5m、5m、10m、20m、30m分辨率尺度的6景DEM;利用单流向算法提取研究区TWI;通过定性和定量方法分析了在不同DEM分辨率尺度中,居民地、梯田、湖泊和自然地形区4种地形区域中TWI值分布特征。结果表明:不同地形区TWI的尺度效应差异较大;随着DEM尺度增大,TWI值域逐渐缩小,变异程度逐渐增强,反映地表形态变化的能力逐渐减小;当DEM尺度大于5m时,TWI基本不能反映人工地形区域;自然地形区的TWI变化规律与研究区整体TWI变化规律相当,居民地与梯田的TWI变化规律大致相同,湖泊区域的TWI变化相对稳定。     

薄盘光滑样条插值中三种协变量方法的降水量插值精度比较

在薄盘光滑样条插值中,高相关协变量的选取决定了插值结果的精确性。以2001-2009年全国728个气象站点日降水为数据源,提取年降水量数据,在分析多年平均降水量与两协变量高程（DEM）和距海岸线距离（DCL）的空间相关性基础上,利用ANUSPLIN软件,比较不同协变量下降水量插值结果精度在全国尺度以及区域尺度上的差异。以DEM、DCL及DEM-DCL分别为协变量对降水量数据进行空间插值发现：①在全国尺度上,DEM法的平均绝对误差（MAE）为47.79,略低于DEM-DCL法（48.90）,但显著低于DCL法（55.54）;且DEM法的平均相对误差和均方根误差也明显低于其它两种方法。②在区域尺度上,除西藏地区外的其他7个区域,3种方法的插值误差与全国尺度上相一致。西藏地区降水插值结果以DCL法的精度最高,而DEM法则较差。研究建议除在西藏地区的降水量插值研究中采用DCL法,在全国其他大部分区域采用DEM法。     

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS-related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system and light detection and ranging have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.     

Bias estimation and correction for triangle-based surface area calculations

The calculation of surface area is meaningful for a variety of space-filling phenomena, e.g., the packing of plants or animals within an area of land. With Digital Elevation Model (DEM) data we can calculate the surface area by using a continuous surface model, such as by the Triangulated Irregular Network (TIN). However, just as the triangle-based surface area discussed in this paper, the surface area is generally biased because it is a nonlinear mapping about the DEM data which contain measurement errors. To reduce the bias in the surface area, we propose a second-order bias correction by applying nonlinear error propagation to the triangle-based surface area. This process reveals that the random errors in the DEM data result in a bias in the triangle-based surface area while the systematic errors in the DEM data can be reduced by using the height differences. The bias is theoretically given by a probability integral which can be approximated by numerical approaches including the numerical integral and the Monte Carlo method; but these approaches need a theoretical distribution assumption about the DEM measurement errors, and have a very high computational cost. In most cases, we only have variance information on the measurement errors; thus, a bias estimation based on nonlinear error propagation is proposed. Based on the second-order bias estimation proposed, the variance of the surface area can be improved immediately by removing the bias from the original variance estimation. The main results are verified by the Monte Carlo method and by the numerical integral. They show that an unbiased surface area can be obtained by removing the proposed bias estimation from the triangle-based surface area originally calculated from the DEM data.     

中国区域SRTM90m数字高程数据空值区域的填补方法比较

本文对中国地区SRTM90m分辨率的数字高程数据的空值区域做了提取和分析,在此基础上尝试了4种内插填补的方法,并对各种处理方法的过程及结果做了比较,从而确定先从SRTM90m数据中直接提取等高线,再内插生成DEM,用内插出来的值填补原始数据的方法在目前较为适用。此外本文还提出了一些后期处理方法以完善数据。     

Influence of survey strategy and interpolation model on DEM quality

Accurate characterisation of morphology is critical to many studies in the field of geomorphology, particularly those dealing with changes over time. Digital elevation models (DEMs) are commonly used to represent morphology in three dimensions. The quality of the DEM is largely a function of the accuracy of individual survey points, field survey strategy, and the method of interpolation. Recommendations concerning field survey strategy and appropriate methods of interpolation are currently lacking. Furthermore, the majority of studies to date consider error to be uniform across a surface. This study quantifies survey strategy and interpolation error for a gravel bar on the River Nent, Blagill, Cumbria, UK. Five sampling strategies were compared: (i) cross section; (ii) bar outline only; (iii) bar and chute outline; (iv) bar and chute outline with spot heights; and (v) aerial LiDAR equivalent, derived from degraded terrestrial laser scan (TLS) data. Digital Elevation Models were then produced using five different common interpolation algorithms. Each resultant DEM was differentiated from a terrestrial laser scan of the gravel bar surface in order to define the spatial distribution of vertical and volumetric error. Overall triangulation with linear interpolation (TIN) or point kriging appeared to provide the best interpolators for the bar surface. Lowest error on average was found for the simulated aerial LiDAR survey strategy, regardless of interpolation technique. However, comparably low errors were also found for the bar-chute-spot sampling strategy when TINs or point kriging was used as the interpolator. The magnitude of the errors between survey strategy exceeded those found between interpolation technique for a specific survey strategy. Strong relationships between local surface topographic variation (as defined by the standard deviation of vertical elevations in a 0.2-m diameter moving window), and DEM errors were also found, with much greater errors found at slope breaks such as bank edges. A series of curves are presented that demonstrate these relationships for each interpolation and survey strategy. The simulated aerial LiDAR data set displayed the lowest errors across the flatter surfaces; however, sharp slope breaks are better modelled by the morphologically based survey strategy. The curves presented have general application to spatially distributed data of river beds and may be applied to standard deviation grids to predict spatial error within a surface, depending upon sampling strategy and interpolation algorithm.     

The impact of resolution on the accuracy of hydrologic data derived from DEMs

1 Introduction Automated extraction of drainage features from DEMs is an effective alternative to the tedious manual mapping from topographic maps. The derived hydrologic characteristics include stream-channel networks, delineation of catchment boundaries, catchment area, catchment length, stream-channel long profiles and stream order etc. Other important characteristics of river catchments, such as the stream-channel density, stream-channel bifurcation ratios, stream-channel order, number…     

The impact of resolution on the accuracy of hydrologic data derived from DEMs

Hydrologic data derived from digital elevation models (DEM) has been regarded as an effective method in the spatial analysis of geographical information systems (GIS). However, both DEM resolution and terrain complexity has impacts on the accuracy of hydrologic derivatives. In this study, a multi-resolution and multi-relief comparative approach was used as a major methodology to investigate the accuracy of hydrologic data derived from DEMs. The experiment reveals that DEM terrain representation error affects the accuracy of DEM hydrological derivatives (drainage networks and watershed etc.). Coarser DEM resolutions can usually cause worse results. However, uncertain result commonly exists in this calculation. The derivative errors can be found closely related with DEM vertical resolution and terrain roughness. DEM vertical resolution can be found closely related with the accuracy of DEM hydrological derivatives, especially in the smooth plain area. If the mean slope is less than 4 degrees, the derived hydrologic data are usually unreliable. This result may be helpful in estimating the accuracy of the hydrologic derivatives and determining the DEM resolution that is appropriate to the accuracy requirement of a particular user. By applying a threshold value to subset the cells of a higher accumulation flow, a stream network of a specific network density can be extracted. Some very important geomorphologic characteristics, e.g., shallow and deep gullies, can be separately extracted by means of adjusting the threshold value. However, such a flow accumulationbased processing method can not correctly derive those streams that pass through the working area because it is hard to accumulate enough flow direction values to express the stream channels at the stream's entrance area. Consequently, errors will definitely occur at the stream’s entrance area. In addition, erroneous derivatives can also be found in deriving some particular rivers, e.g., perched (hanging up) rivers, anastomosing rivers and braided rivers. Therefore, more work should be done to develop and perfect the algorithms.     

The impact of DEM data source on prediction of flooding and erosion risk due to sea-level rise

Digital elevation model (DEM) elevation accuracy and spatial resolution are typically considered before a given DEM is used for the assessment of coastal flooding, sea-level rise or erosion risk. However, limitations of DEMs arising from their original data source can often be overlooked during DEM selection. Global elevation error statistics provided by DEM data suppliers can provide a useful indicator of actual DEM error, but these statistics can understate elevation errors occurring outside of idealised ground reference areas. The characteristic limitations of a range of DEM sources that may be used for the assessment of coastal inundation and erosion risk are tested using high-resolution photogrammetric, low- and medium-resolution global positioning system (GPS)-derived and very high-resolution terrestrial laser scanning point data sets. Errors detected in a high-resolution photogrammetric DEM are found to be substantially beyond quoted error, demonstrating the degree to which quoted DEM accuracy can understate local DEM error and highlighting the extent to which spatial resolution can fail to provide a reliable indicator of DEM accuracy. Superior accuracies and inundation prediction results are achieved based on much lower-resolution GPS points confirming conclusions drawn in the case of the photogrammetric DEM data. This suggests a scope for the use of GPS-derived DEMs in preference to the photogrammetric DEM data in large-scale risk-mapping studies. DEM accuracies and superior representation of micro-topography achieved using high-resolution terrestrial laser scan data confirm its advantages for the prediction of subtle inundation and erosion risk. However, the requirement for data fusion of GPS to remove ground-vegetation error highlighted limitations for the use of side-scan laser scan data in densely vegetated areas.