A Distributed Geoprocessing Concept for Enhancing Terrain Analysis for Environmental Modeling

Geographic Information Systems (GIS) are well suited to support environmental modeling for dealing with space. However, some of the limitations of current GIS are the lack of tools for comprehensive documentation of the models, the inadequate representation of fields, and the deficient methodology for comprehensive management of uncertainty. Using Digital Terrain Modeling and Analysis as an example, this paper proposes an enhanced approach to overcome these drawbacks. It suggests implementing sophisticated functionality for modeling and analysis of fields in special-purpose modules outside monolithic GIS. These modules include three components: (1) an extensive framework for metainformation that allows a sound assessment of the fitness-for-use of digital field representations for environmental modeling applications, (2) an explicit digital representation of the field phenomenon equipped with the appropriate tools for the derivation of data, and (3) the methods to assess the quality of derived data. A standardized interface enables communication between the module and other software components. The presented modular approach combines the functionality of common GIS with highly specialized modeling and analysis tools encapsulating expert knowledge about the represented phenomena.     

On the Uncertainty of Local Shape of Lines and Surfaces

Modeling line or surface phenomena digitally involves two tasks: discretization of the phenomenon, which yields a finite set of data, and subsequent interpolation, which reconstructs the continuum. Many mathematical techniques exist for the latter task, and most methods require a number of parameters to be specified. The shape of digital line or surface models between the data points (that is, the local shape) and the information derived from these models both depend on the selected method and, possibly, on the specification of parameters. The reconstruction of the continuum thus introduces uncertainty. This paper examines the sources and effects of this type of uncertainty. For this purpose, the modeling of lines and surfaces is separated into an abstraction, an implementation, and measurement. The individual factors affecting uncertainty of local shape in each step are identified and discussed. The paper concludes that local shape uncertainty, unlike positional uncertainty of given data, cannot be numerically assessed. Instead, measures of plausibility have to be used to denote the quality of digital models of lines and surfaces. Finally, the concept and potential problems of future empirical investigations are discussed.     

The derivation of skeleton lines for terrain features

The geometric and physical analysis methods are conventional methods for the derivation of skeleton lines in the fields of cartography,digital photogrammetry,and related areas.this paper proposes a stepwise approach that uses the physical analysis method in the first stage and the geometric analysis method in the subsequent stage.The physical analysis method analyses the terrain globally to obtain a rough set of skeleton lines for a terrain surface.The rough skeleton lines help to structure the ordering of feature points by the geometric analysis method.     

Terrain complexity and reduction of topographic data

Digital terrain data are useful for a variety of applications in mapping and spatial analysis. Most available terrain data are organized in a raster format, among them being the most extensively-used Digital Elevation Models (DEM) of the U.S. Geological Survey. A common problem with DEM for spatial analysis at the landscape scale is that the raster encoding of topography is subject to data redundancy and, as such, data volumes may become prohibitively large. To improve efficiency in both data storage and information processing, the redundancy of the terrain data must be minimized by eliminating unnecessary elements. To what extent a set of terrain data can be reduced for improving storage and processing efficiency depends on the complexity of the terrain. In general, data elements for simpler, smoother surfaces can be substantially reduced without losing critical topographic information. For complex terrains, more data elements should be retained if the topography is to be adequately represented. In this paper, we present a measure of terrain complexity based on the behavior of selected data elements in representing the characteristics of a surface. The index of terrain complexity is derived from an estimated parameter which denotes the relationship between terrain representation (percentage surface representation) and relative data volume (percentage DEM elements). The index can be used to assess the required volume of topographic data and determine the appropriate level of data reduction. Two quadrangles of distinct topographic characteristics were examined to illustrate the efficacy of the developed methodology.     

The derivation of skeleton lines for terrain features

The geometric and physical analysis methods are conventional methods for the derivation of skeleton lines in the fields of cartography, digital photogrammetry, and related areas. This paper proposes a stepwise approach that uses the physical analysis method in the first stage and the geometric analysis method in the subsequent stage. The physical analysis method analyses the terrain globally to obtain a rough set of skeleton lines for a terrain surface. The rough skeleton lines help to structure the ordering of feature points by the geometric analysis method.     

三维动态交互式可视化模型─-地理信息系统中的三维表示与分析

针对当前计算机图形技术的发展和GIS多专业应用需求的特点,本文以吉奥之星（Geostar）地理信息系统平台为例,研究了在当前二维系统中如何考虑三维或者2．5维表面表示与分析的问题。提出了集成数字高程模型（DEM）、数字正射影像、常规的矢量数据和各种属性信息在一起,建立一体化的三维数据输入、操作与可视化机制,并在此基础上提出了二维与三维混合表示的空间查询与分析模型。该模型扩展了可视化概念,将可视化技术贯穿于整个GIS运行过程。     

A procedural footprint enhancement of global topographic surface with multiple levels of detail

ABSTRACT

Virtual globes are technologies for visual navigation through a three-dimensional, multi-resolution model of the entire planet. Data representations used in virtual globes, however, lack geometric flexibility at high-resolution levels of the planet-wide terrain surface. This is a problem especially if boundaries between individual geospatial features and the terrain are important. A novel integration of individual polygonal boundaries with a specific multi-resolution representation of the planet-wide terrain is developed in this article. In the preparation stage, the integration relies on an original simplification algorithm applied to the polygonal boundaries between geospatial features and the terrain. Its output is a multiple level-of-detail (LOD) geometry, which can be combined with a known multi-LOD representation of the terrain that uses run-time triangulation. This data representation is suitable for storage in existing database systems, avoids any data redundancy across LODs, and is even independent of the subdivision schema that partitions the planet's surface for the sake of dealing with LODs. At run-time, a novel reconstruction algorithm stitches geometric parts from different LODs together in a manner that augments the multi-LOD representation of the terrain. Within a certain proximity range from a given position, the method reconstructs a scene that preserves topological relations between the boundaries of geospatial features with the terrain. The method also guarantees that certain nearest proximity to the given position consists of the best geometries that correspond to the original datasets. Such properties of the method close up the gap between a mere exploratory visualization of static, pre-generated models and the models supporting geospatial analysis, which is deemed crucial for applications in Geographic Information Systems, Building Information Modelling and other software industries. A prototype implementation and experiment results that prove this method are also presented.     

An improved ANUDEM method combining topographic correction and DEM interpolation

Void filling and anomaly replacement in conjunction with auxiliary sources of data have been widely used to improve the quality of existing problematic high-resolution digital elevation models. However, the traditional interpolation methods used for this purpose have always failed to eliminate the discrepancies between different data-sets. In this paper, an improved ANUDEM method is presented for DEM interpolation, which incorporates the idea of topographic correction using high correlation of topological structure between contour lines (CLs) from multi-scale digital elevation models (DEM). Firstly, the terrain topological structure is extracted from the CLs of a low-resolution DEM. The topographic surface correction is then undertaken based on the extracted structure, which recovers the topographic information of the sharp depressions and eminences to fit the high-resolution representation. Finally, the breaklines of the terrain surface are distilled and integrated into the denser DEM generation. The experiments undertaken confirmed the superiority of the proposed method over the other DEM interpolation methods. It is shown that the proposed method can provide results with a higher accuracy, as well as a better visual quality.     

Scree Representation on Topographic Maps

Abstract

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Scree patterns are an important element of mountain maps in Swiss style. The size and density of scree dots vary with the exposition towards a source of illumination, which makes the dots extremely labour intensive to map without specialized algorithms. This paper identifies design principles for the symbolisation of scree fields on mountain slopes and presents a digital method for the quick placement of dot symbols requiring only minimal interventions by a cartographer. When digitally produced scree is combined with a shaded relief and a rock drawing, the terrain appears as a continuous three-dimensional surface to the reader. The described method is implemented in Scree Painter, a specialized free open-source software application. Scree patterns produced with Scree Painter match the quality standards of manually generated scree representations.     

A bilinear approximation of the surface relief in terrain correction computations

A new method is presented for the computation of the gravitational attraction of topographic masses when their height information is given on a regular grid. It is shown that the representation of the terrain relief by means of a bilinear surface not only offers a serious alternative to the polyhedra modeling, but also approaches even more smoothly the continuous reality. Inserting a bilinear approximation into the known scheme of deriving closed analytical expressions for the potential and its first-order derivatives for an arbitrarily shaped polyhedron leads to a one-dimensional integration with – apparently – no analytical solution. However, due to the high degree of smoothness of the integrand function, the numerical computation of this integral is very efficient. Numerical tests using synthetic data and a densely sampled digital terrain model in the Bavarian Alps prove that the new method is comparable to or even faster than a terrain modeling using polyhedra.     

Determination of complexity factor and its relationship with accuracy of representation for DEM terrain

Based on the estimating rule of the normal vector angles between two adjacent terrain units, we use the concept of terrain complexity factor to quantify the terrain complexity of DEM, and then the formula of terrain complexity factor in Raster DEM and TIN DEM is deduced theoretically. In order to make clear how the terrain complexity factor E _CF and the average elevation h affect the accuracy of DEM terrain representation RMSE _Et , the formula of Gauss synthetical surface is applied to simulate several real terrain surfaces, each of which has different terrain complexity. Through the statistical analysis of linear regression in simulation data, the linear equation between accuracy of DEM terrain representation RMSE _Et , terrain complexity factor E _CF and the average elevation h is achieved. A new method is provided to estimate the accuracy of DEM terrain representation RMSE _Et with a certain terrain complexity and it gives convincing theoretical evidence for DEM production and the corresponding error research in the future.     

DEM及数字地形分析中尺度问题研究综述

基于DEM尺度的概念与类型、DEM地形分析的尺度效应、DEM地形分析尺度研究的关键问题、DEM地形分析尺度研究的方法等几个方面的论述，分析了当前国内外在该领域的研究进展，并指出了今后应重点研究的方向，包括自然地面与DEM模拟地面之间的尺度匹配、尺度冲突与尺度耦合的关系；空间尺度参数对DEM地形分析影响的过程与机理；DEM格网单元地形分析的异质性效应。在尺度层面上，提出不同地形复杂度条件下的DEM地形分析的确定性与不确定性规律，建立以尺度为自变量的多尺度地形分析模型，建立DEM地形分析的尺度转换模型。     

Cartographic Symbol Design Considerations for the Space–Time Cube

The cartographic representation of geographic phenomena in the space–time cube comes with special challenges and opportunities when compared with two-dimensional maps. While the added dimension allows the display of attributes that vary with time, it is difficult to display rapidly varying temporal data given the limited display height. In this study, we adapt 2D cyclic point symbols to construct 3D surfaces designed along a helical path for the space–time cube. We demonstrate how these complex?3D helical surfaces can display detailed data, including data reported daily over 100 years and data reported in four-hour intervals over a year. To create the point symbols, each value is plotted along the curve of a helix, with each turn of the helix representing one year or week, respectively. The model is modified by varying the radii from the time axis to all points using the attribute value, in these cases maximum daily temperature and four-hourly ridership, and then creating a triangulated surface from the resulting points. Using techniques common to terrain representation, we apply hue and saturation to the surface based on attribute values, and lightness based on relief shading. Multiple surfaces can be displayed in a space–time cube with a consistent time interval facing the viewer, and the surfaces or viewer perspective can be rotated to display synchronized variations. We see this method as one example of how cartographic design can refine or enhance operations in the space–time cube.     

城市电子地图多尺度自动缩编方法

随着智慧城市、地理信息公共服务及地理国情数据等政务信息逐步公开,作为各类政务信息发布基础的城市电子地图在多尺度展现时,只能通过关闭、选取要素来实现,这种未进行制图综合的做法导致要素在逐级放大过程中,会出现跳跃性丢失和细节破碎的现象,既不符合地图表达要求也难以满足用户视觉体验。本文提出了一源数据多尺度自动缩编的技术方法,构建了最优化的"统一源头、一致派生、无级表达"技术体系,实现了城市电子地图联动更新和多尺度展现,节省了大量人力和物力,为最大限度地发挥测绘地理信息集成与服务能力提供保障。     

基于偏微分方程的小比例尺晕渲图地貌综合方法研究

基于高精度DEM数据的晕渲图中,破碎的地形细节破坏了晕渲法的立体塑造能力,但是采用传统的均值滤波法进行地貌综合时,在消除地形细节的同时,模糊了地貌特征。为了克服消除地形细节和保持地貌特征这一矛盾,利用偏微分方程各向异性的特点,采用基于经典总变分模型的偏微分方程法对地貌进行综合。实验结果证明偏微分方程法在综合地貌时能较好地保持地貌结构特征。     

提取山脊线和山谷线的一种新方法

在研究了现有的仅从山脊线和山谷线的几何特性或物理特性的单一方面设计的提取山脊线和山谷线的算法后 ,提出了一种基于地形表面流水分析与等高线几何分析相结合的提取山脊线和山谷线的方法。该方法把等高线几何分析的方法与地形表面流水模拟分析的方法有机地结合起来 ,能够克服各自所具有的弊端。实验结果表明 ,用本文方法所提取的山脊线和山谷线与实际地形相符合。     

Error assessment of grid‐based terrain shading algorithms for solar radiation modeling over complex terrain

In mountainous regions, solar radiation exhibits a strong spatial heterogeneity due to terrain shading effects. Terrain shading algorithms based on digital elevation models can be categorized into two types: area‐based and point‐specific. In this article, we evaluated two shading algorithms using designed mathematic surfaces. Theoretical shading effects over four Gauss synthetic surfaces were calculated and used to evaluate the terrain shading algorithms. We evaluated the area‐based terrain shading algorithm, Hillshade tool of ArcGIS, and the point‐specific shading algorithm from Solar Analyst (SA) in ArcGIS. Both algorithms showed shading overestimation, and Hillshade showed more accuracy with a mean absolute error (MAE) of 1.20%, as compared to the MAE of 1.66% of SA. The MAE of Hillshade increases exponentially as the spatial extent of the study area increases because the solar position for all locations on the surface is the same in Hillshade. Consequently, we suggest that the surface should be divided into more tiles in Hillshade when the discrepancy in the latitude of the whole surface is greater than 4°. Skyshed, which represents the horizon angle distribution in SA, is error‐prone over more complex terrain because horizon angle interpolation is problematic for such areas. We also propose a new terrain shading algorithm, with solar positions calculated using local latitude for each cell and the horizon angle calculated for every specific time interval, but without projections. The new model performs better than Hillshade and SA with an MAE of 0.55%.     

顾及“保真性”原则的双向滚动球变换DDM多尺度表达算法

在分析符合"安全性"要求的数字水深模型(DDM)正向滚动球变换应用局限的基础上,根据高保真DDM多尺度表达评价标准中对水深值准确性、严密有序性及地形信息等级嵌套性的要求,从顾及"保真性"原则的DDM多尺度表达需要出发,提出一种基于双向滚动球变换的DDM多尺度表达算法。分析了海底地貌特征点在DDM双向滚动球变换过程中的变化趋势,根据DDM正向滚动球变换的尺度依赖特性,计算出了一定尺度下海底地貌的横向分布范围与纵向分布高度,建立了DDM多尺度表达中细部(骨架)地貌的判定准则。通过保留给定尺度下DDM中的骨架地貌,使海底地形的整体变化趋势得到了保持,满足了DDM多尺度表达对水深值准确性的要求;论证了DDM单值曲面等距离面变换的水深序同构特性,通过对给定尺度下的细部地貌进行DDM双向滚动球变换的等距离面提取,使海底地形的局部起伏形态得到了保持,满足了DDM多尺度表达对水深值严密有序性的要求;从满足DDM多尺度表达对地形信息等级嵌套性的要求出发,分析了DDM双向滚动球变换中尺度因子与地形信息等级单元逻辑包含关系的不相关性,论证了任意尺度因子条件下具有的相应等级地形信息范围的一致性。试验结果表明该算法克服了DDM正向滚动球变换存在的无法保留负向骨架地貌和保持海底局部地形起伏形态等不足,可有效保留DDM中骨架地貌并综合细部地貌,满足顾及"保真性"原则的DDM多尺度表达要求。     

Elevation models for reproducible evaluation of terrain representation

ABSTRACT

This paper proposes elevation models to promote, evaluate, and compare various terrain representation techniques. Our goal is to increase the reproducibility of terrain rendering algorithms and techniques across different scales and landscapes. We introduce elevation models of varying terrain types, available to the user at no cost, with minimal common data imperfections such as missing data values, resampling artifacts, and seams. Three multiscale elevation models are available, each consisting of a set of elevation grids, centered on the same geographic location, with increasing cell sizes and spatial extents. We also propose a collection of single-scale elevation models of archetypal landforms including folded ridges, a braided riverbed, active and stabilized sand dunes, and a volcanic caldera. An inventory of 78 publications with a total of 155 renderings illustrating terrain visualization techniques guided the selection of landform types in the elevation models. The benefits of using the proposed elevation models include straightforward comparison of terrain representation methods across different publications and better documentation of the source data, which increases the reproducibility of terrain representations.     

Errors within the Inverse Distance Weighted (IDW) interpolation procedure

Interpolation procedure is broadly used in sciences that are concerned with spatial data and continuous phenomena that can be depicted on a spatial surface. Interpolation makes use of sampling data, which is accurate and qualitative, in order to produce a continuous representation of the phenomenon in question. The data's accuracy is transferred by the procedure to its results and should be known. This paper examines error propagation by the interpolation procedure, using the Inverse Distance Weighted (IDW) method in the case of the Earth's relief.