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.     

LIDAR strip adjustment: Application to volcanic areas

DEMs derived from LIDAR data are nowadays largely used for quantitative analyses and modelling in geology and geomorphology. High-quality DEMs are required for the accurate morphometric and volumetric measurement of land features. We propose a rigorous automatic algorithm for correcting systematic errors in LIDAR data in order to assess sub-metric variations in surface morphology over wide areas, such as those associated with landslide, slump, and volcanic deposits. Our procedure does not require a priori knowledge of the surface, such as the presence of known ground control points. Systematic errors are detected on the basis of distortions in the areas of overlap among different strips. Discrepancies between overlapping strips are assessed at a number of chosen computational tie points. At each tie point a local surface is constructed for each strip containing the point. Displacements between different strips are then calculated at each tie point, and minimization of these discrepancies allows the identification of major systematic errors. These errors are identified as a function of the variables that describe the data acquisition system. Significant errors mainly caused by a non-constant misestimation of the roll angle are highlighted and corrected. Comparison of DEMs constructed using first uncorrected and then corrected LIDAR data from different Mt. Etna surveys shows a meaningful improvement in quality: most of the systematic errors are removed and the accuracy of morphometric and volumetric measurements of volcanic features increases. These corrections are particularly important for the following studies of Mt. Etna: calculation of lava flow volume; calculation of erosion and deposition volume of pyroclastic cones; mapping of areas newly covered by volcanic ash; and morphological evolution of a portion of an active lava field over a short time span.     

Rapid generation of Digital Elevation Models from topographic maps

Abstract

In this article we demonstrate that substantial gains in time can be made when using point sampling rather than contour line digitising for generation of Digital Elevation Models (DEMs). A simple sampling scheme, based on regularly distributed points, was used supplemented with points near break-lines in the terrain. An evaluation of surfaces created with three different interpolation methods at three different resolutions shows that the statistical distribution was better when using points as opposed to contours, and that the accuracy was comparable despite the much smaller amount of input data.     

Reconstructing pre-erosion topography using spatial interpolation techniques:A validation-based approach

Understanding the topographic context preceding the development of erosive landforms is of major relevance in geomorphic research, as topography is an important factor on both water and mass movement-related erosion, and knowledge of the original surface is a condition for quantifying the volume of eroded material. Although any reconstruction implies assuming that the resulting surface reflects the original topography, past works have been dominated by linear interpolation methods, incapable of generating curved surfaces in areas with no data or values outside the range of variation of inputs. In spite of these limitations, impossibility of validation has led to the assumption of surface representativity never being challenged. In this paper, a validation-based method is applied in order to define the optimal interpolation technique for reconstructing pre-erosion topography in a given study area. In spite of the absence of the original surface, different techniques can be nonetheless evaluated by quantifying their capacity to reproduce known topography in unincised locations within the same geomorphic contexts of existing erosive landforms. A linear method (Triangulated Irregular Network, TIN) and 23 parameterizations of three distinct Spline interpolation techniques were compared using 50 test areas in a context of research on large gully dynamics in the South of Portugal. Results show that almost all Spline methods produced smaller errors than the TIN, and that the latter produced a mean absolute error 61.4% higher than the best Spline method, clearly establishing both the better adjustment of Splines to the geomorphic context considered and the limitations of linear approaches. The proposed method can easily be applied to different interpolation techniques and topographic contexts, enabling better calculations of eroded volumes and denudation rates as well as the investigation of controls by antecedent topographic form over erosive processes.     

The simulation of surface flow dynamics using a flow-path network model

This paper proposes a flow-path network (FPN) model to simulate complex surface flow based on a drainage-constrained triangulated irregular network (TIN). The TIN was constructed using critical points and drainage lines extracted from a digital terrain surface. Runoff generated on the surface was simplified as ‘water volumes’ at constrained random points that were then used as the starting points of flow paths (i.e. flow source points). The flow-path for each ‘water volume’ was constructed by tracing the direction of flow from the flow source point over the TIN surface to the stream system and then to the outlet of the watershed. The FPN was represented by a set of topologically defined one-dimensional line segments and nodes. Hydrologic variables, such as flow velocity and volume, were computed and integrated into the FPN to support dynamic surface flow simulation. A hypothetical rainfall event simulation on a hilly landscape showed that the FPN model was able to simulate the dynamics of surface flow over time. A real-world catchment test demonstrated that flow rates predicted by the FPN model agreed well with field observations. Overall, the FPN model proposed in this study provides a vector-based modeling framework for simulating surface flow dynamics. Further studies are required to enhance the simulations of individual hydrologic processes such as flow generation and overland and channel flows, which were much simplified in this study.     

Variable resolution block kriging using a hierarchical spatial data structure

Abstract

Kriging is an optimal method of spatial interpolation that produces an error for each interpolated value. Block kriging is a form of kriging that computes averaged estimates over blocks (areas or volumes) within the interpolation space. If this space is sampled sparsely, and divided into blocks of a constant size, a variable estimation error is obtained for each block, with blocks near to sample points having smaller errors than blocks farther away. An alternative strategy for sparsely sampled spaces is to vary the sizes of blocks in such away that a block's interpolated value is just sufficiently different from that of an adjacent block given the errors on both blocks. This has the advantage of increasing spatial resolution in many regions, and conversely reducing it in others where maintaining a constant size of block is unjustified (hence achieving data compression). Such a variable subdivision of space can be achieved by regular recursive decomposition using a hierarchical data structure. An implementation of this alternative strategy employing a split-and-merge algorithm operating on a hierarchical data structure is discussed. The technique is illustrated using an oceanographic example involving the interpolation of satellite sea surface temperature data. Consideration is given to the problem of error propagation when combining variable resolution interpolated fields in GIS modelling operations.     

A Point-Based Intelligent Approach to Areal Interpolation

Areal interpolation is the data transfer from one zonal system to another. A survey of previous literature on this subject points out that the most effective methods for areal interpolation are the intelligent approaches, which often take two-dimensional (2-D) land use or one-dimensional (1-D) road network information as ancillary data to give insight on the underlying distribution of a variable. However, the 2-D or 1-D ancillary information is not always applicable for the variable of interest in a specific study area. This article introduces a point-based intelligent approach to the areal interpolation problem by using zero-dimensional (0-D) points as ancillary data that are locationally associated with the variable of interest. The connection between zonal variables and point locations can be modeled with a linear or a nonlinear exponential function, which incorporates the distribution of the variables in the transferring of the information from the source zone to the target zone. An experimental study interpolating the population data at a suburbanized area suggests that the proposed method is an attractive alternative to other areal interpolation solutions based on the evaluation of its resulting accuracy and efficiency.     

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.     

Book reviews

A digital elevation model (DEM), which is used to represent a terrain surface, is normally constructed by applying an interpolation method on given sample elevation points. Interpolation methods can be classified into two classes: linear methods, which have a low time cost and are suitable for terrains where there is little change in elevation, and nonlinear methods, which normally consume comparatively more time and are more suitable for terrains where there are frequent changes in elevation. A hybrid interpolation method, which involves both a linear method and a nonlinear method of interpolation, is proposed in this paper. The proposed method aims to integrate the advantages of both linear and nonlinear interpolation methods for the refinement of regular grid DEM. Here, the bilinear is identified as the linear method, and the bi‐cubic is taken to be the nonlinear interpolation method. The hybrid method is an integration of a linear model and nonlinear interpolation model with a parameter that defines the weights for each of the models. The parameter is dependent on the complexity of the terrain, for which a DEM is to be interpolated. The experimental results in this study demonstrate that the hybrid method is effective for interpolating DEMs for various types of terrain.     

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。     

一种基于TIN的DEM表面插值模型

针对目前基于TIN的DEM存在的表面模型单一、表面不光滑、达不到更高的精度等问题,该文利用二元泰勒公式、顶点法向量、插值函数等,提出一种基于TIN的DEM表面插值模型,并利用数学曲面评估模型精度。结果表明,该模型具有较好的光滑效果和精度,扩展了基于TIN的DEM表达方式,为DEM的应用提供了更多的选择。     

三角网的生成与简化算法

在三维地理信息系统的开发与研究中 ,要求三角网模型的支持 ,而高效的三角网生成算法是三角网模型的基础。该文综述各类三角网的生成算法 ,对以往被人忽视但简明高效的算法———径向扫描算法进行阐释 ,并对它的实现进行改进 ;对地形数据的简化及建立地形层次对象模型是实现高效的三维地理信息系统的关键 ,而三角网的简化是地形数据简化的基石之一 ,文中提供三种简化三角网的算法供同行讨论 ;并在微机上实现上述算法。     

Historic reconstruction of reservoir topography using contour line interpolation and structure from motion photogrammetry

The geometry of impounded surfaces is a key tool to reservoir storage management and projection. Yet topographic data and bathymetric surveys of average-aged reservoirs may be absent for many regions worldwide. This paper examines the potential of contour line interpolation (TOPO) and Structure from Motion (SfM) photogrammetry to reconstruct the topography of existing reservoirs prior to dam closure. The study centres on the Paso de las Piedras reservoir, Argentina, and assesses the accuracy and reliability of TOPO- and SfM- derived digital elevation models (DEMs) using different grid resolutions. All DEMs were of acceptable quality. However, different interpolation techniques produced different types of error, which increased (or decreased) with increasing (or decreasing) grid resolution as a function of their nature, and relative to the terrain complexity. In terms of DEM reliability to reproduce area–elevation relationships, processing-related disagreements between DEMs were markedly influenced by topography. Even though they produce intrinsic errors, it is concluded that both TOPO and SfM techniques hold great potential to reconstruct the bathymetry of existing reservoirs. For areas exhibiting similar terrain complexity, the implementation of one or another technique will depend ultimately on the need for preserving accurate elevation (TOPO) or topographic detail (SfM).     

基于Hash函数的TIN拓扑关系重建

STL模型是CAD、景观造型器等图形处理软件中常用的三角形网络文件格式,该文件由于不带有三角形的拓扑关系,使其不便与GIS中的地形模型(如TIN)进行叠置分析等操作。提出一种基于Hash函数的STL模型的三角形拓扑重建算法,讨论Hash函数设计和评价,给出基于Hash函数的TIN拓扑重建算法和拓扑检查方法,并通过实例对该算法进行验证。     

Special Issue on parallel processing in GIS

This paper explores three theoretical approaches for estimating the degree of correctness to which the accuracy figures of a gridded Digital Elevation Model (DEM) have been estimated depending on the number of checkpoints involved in the assessment process. The widely used average‐error statistic Mean Square Error (MSE) was selected for measuring the DEM accuracy. The work was focused on DEM uncertainty assessment using approximate confidence intervals. Those confidence intervals were constructed both from classical methods which assume a normal distribution of the error and from a new method based on a non‐parametric approach. The first two approaches studied, called Chi‐squared and Asymptotic Student t, consider a normal distribution of the residuals. That is especially true in the first case. The second case, due to the asymptotic properties of the t distribution, can perform reasonably well with even slightly non‐normal residuals if the sample size is large enough. The third approach developed in this article is a new method based on the theory of estimating functions which could be considered much more general than the previous two cases. It is based on a non‐parametric approach where no particular distribution is assumed. Thus, we can avoid the strong assumption of distribution normality accepted in previous work and in the majority of current standards of positional accuracy. The three approaches were tested using Monte Carlo simulation for several populations of residuals generated from originally sampled data. Those original grid DEMs, considered as ground data, were collected by means of digital photogrammetric methods from seven areas displaying differing morphology employing a 2 by 2 m sampling interval. The original grid DEMs were subsampled to generate new lower‐resolution DEMs. Each of these new DEMs was then interpolated to retrieve its original resolution using two different procedures. Height differences between original and interpolated grid DEMs were calculated to obtain residual populations. One interpolation procedure resulted in slightly non‐normal residual populations, whereas the other produced very non‐normal residuals with frequent outliers. Monte Carlo simulations allow us to report that the estimating function approach was the most robust and general of those tested. In fact, the other two approaches, especially the Chi‐squared method, were clearly affected by the degree of normality of the residual population distribution, producing less reliable results than the estimating functions approach. This last method shows good results when applied to the different datasets, even in the case of more leptokurtic populations. In the worst cases, no more than 64–128 checkpoints were required to construct an estimate of the global error of the DEM with 95% confidence. The approach therefore is an important step towards saving time and money in the evaluation of DEM accuracy using a single average‐error statistic. Nevertheless, we must take into account that MSE is essentially a single global measure of deviations, and thus incapable of characterizing the spatial variations of errors over the interpolated surface.     

Comparison of existing triangulation methods for regularly and irregularly spaced height fields

Over the last two decades, the Delaunay triangulation has been the only choice for most geographical information system (GIS) users and researchers to build triangulated irregular networks (TINs). The classical Delaunay triangulation for creating TINs only considers the 2D distribution of data points. Recent research efforts have been devoted to generating data-dependent triangulation which incorporate information on both distribution and values of input data in the triangulation process. This paper compares the traditional Delaunay triangulations with several variant data-dependent triangulations based on Lawson's local optimization procedure (LOP). Two USGS digital elevation models (DEMs) are used in the comparison. It is clear from the experiments that the quality of TINs not only depends on the vertex placement but also on the vertex connection. Traditonal two step processes for TIN construction, which separate point selection from the triangulation, generate far worse results than the methods which iteratively select points during the triangulation process. A pure data-dependent triangulation contains a large amount of slivers and steep triangles, which greatly affect the quality of TINs constructed. Among the triangulation methods tested, the classical Delaunay triangulation is still the most successful technique for constructing TINs for approximating natural terrain surfaces.     

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。     

顾及风向和风速的气温空间插值方法

当前气温插值方法多将高程、经纬度等作为影响因素,无法解决风向、风速对气温空间分布的影响问题。该文提出一种顾及风向和风速的气温空间插值方法:1)根据气象观测站点的风向、风速数据进行插值,生成连续的风场表面;2)基于该风场数据利用高斯扩散模型构建成本表面;3)利用Dijkstra最短路径算法计算观测点与待求点的累计移动成本最短路径(SPOCMC);4)将SPOCMC作为协变量进行薄盘光滑样条插值以实现气温插值。为验证该方法的有效性和可靠性,选取山东省109个气象观测点样本数据,以SPOCMC、DEM和SPOCMC-DEM分别作为协变量对气温数据进行薄盘光滑样条插值,结果显示:SPOCMC-DEM法的MAE和RMSE均值(分别为0.517、0.779)略低于SPOCMC法(0.583、1.016),显著低于DEM法(0.809、1.231),表明添加SPOCMC作为协变量可有效提高气温空间插值的准确性。在江苏省与贵州省的插值实验结果证明了该方法的普适性。     

Comparison of existing methods for building triangular irregular network,models of terrain from grid digital elevation models

Abstract

Triangulated irregular networks (TINs) are increasingly popular for their efficiency in data storage and their ability to accommodate irregularly spaced elevation points for many applications of geographical information systems. This paper reviews and evaluates various methods for extracting TINs from dense digital elevation models (DEMs) on a sample DEM. Both structural and statistical comparisons show that the methods perform with different rates of success in different settings. Users of DEM to TIN conversion methods should be aware of the strengths and weaknesses of the methods in addition to their own purposes before conducting the conversion.     

DEM空间插值方法对土壤侵蚀模拟的影响研究——以USPED分析干热河谷典型冲沟为例

为探索不同空间插值方法得到的DEM如何影响土壤侵蚀模拟效果,本文选择金沙江干热河谷区典型冲沟为研究对象,利用野外测量高程数据,采用反距离加权(IDW)、析取克里格(DK)、局部多项式(LPI)和张力样条函数(ST)4种方法构建高精度DEM。基于USPED模型模拟冲沟的土壤侵蚀,对比不同空间插值方法的精度、土壤侵蚀的空间分布,采用相对差系数对比不同插值在土壤侵蚀研究中的相似性。结果表明：DEM空间插值的精度排序为ST相似文献