Vector algebra for Steep Slope Model analysis

Geographic Information Systems offer many algorithms that allow analysis of digital elevation models. They work with both GRID and TIN data, but they are limited to 2.5D models, where one planar (X,Y) position refers to only one vertical (Z) value. In mountainous regions, however, many steep, vertical and even overhung parts of rock walls and slopes occur. GRID and TIN models in a standard projection are not capable to deal with such a relief as they are not able to capture all complexity of steep slopes that can be observed from the terrestrial perspective. Such a perspective can be introduced into GIS via computer graphics software that allows 3D surface modelling by means of \mathit{mesh}, e.g. 3D triangular network. The paper presents a concept that implements 3D mesh in GIS and utilizes vector algebra to analyze such a surface. The idea is based on using normal vectors to compute slope and aspect of each triangle in a mesh. The computed values are saved as their attributes. Complete procedures are written in Python programming language and implemented into popular GIS software to work as a plug-in tool

Accuracy assessment in glacier change analysis

This thesis assesses the accuracy of digital elevation models (DEM) generated from contour lines and LiDAR points (Light Detection and Ranging) employing several interpolation methods at different resolutions. The study area is Jostefonn glacier that is situated in Sogn og Fjordane county, Norway. There are several ways to assess accuracy of DEMs including simple ways such as visual comparison and more sophisticated methods like relative and absolute comparison. Digital elevation models of the Jostefonn glacier were created from contour lines for years 1966 and 1993. LiDAR data from year 2011 was used as a reference data set. Of all the interpolation methods tested Natural Neighbours (NN) and Triangular Irregular Network (TIN) algorithms rendered the best results and proved to be superior to other interpolation methods. Several resolutions were tested (the cell size of 5 m, 10 m, 20 m and 50 m) and the best outcome was achieved by as small cell size as possible. The digital elevation models were compared to a reference data set outside the glacier area both on a cell-by-cell basis and extracting information at test points. Both methods rendered the same results that are presented in this thesis. Several techniques were employed to assess the accuracy of digital elevation models including visualization and statistical analysis. Visualization techniques included comparison of the original contour lines with those generated from DEMs. Root mean square error, mean absolute error and other accuracy measures were statistically analysed. The greatest elevation difference between the digital elevation model of interest and the reference data set was observed in the areas of a steep terrain. The steeper the terrain, the greater the observed error. The magnitude of the errors can be reduced by using a smaller cell size but that this is offset by a larger amount of data and increased data processing time.Popular science Glaciers are very sensitive indicators of climate change. The major cause of melting glaciers is global warming. This rapid rate of melting has serious negative impact on the earth causing flooding, leaving impact on flora and fauna, resulting in shortage of freshwater and hydroelectricity. The long-term monitoring of glaciers and the knowledge gained from it can help governments, environmental and water resource managers to make plans to cope with impacts of climate change. Results from glacier monitoring ought to be precise, showing the actual situation compared to the situation in the past as well as predicting possible glacier changes in the future. The aim of this thesis was to investigate how sensitive the results were to different methods used in glacier change detection focusing on the quality of Digital Elevation Models (DEMs). The study area of this thesis was the Jostefonn glacier situated in Sogn and Fjordane county, Norway. Digital elevation models were created from contour lines for years 1966 and 1993. LiDAR data from year 2011 was used as a reference data set. Several techniques were employed to estimate the accuracy of digital elevation models including visualization, statistical analysis, analysing the accuracy of digital elevation models for terrain on different slopes, comparison to a reference data set outside the glacier area that was considered to be stable and where no elevation change was expected. The original contour lines (1966 and 1993) were compared with the ones generated from the created terrain models (glacier area) as well as with the contour lines from the reference data set (outside the glacier area) by visualization techniques. Accuracy measures (Root Mean Square Error, Mean Absolute Error and others) were statistically analysed. Natural Neighbours and Triangular Irregular Network interpolators proved to be superior to other algorithms used to create the terrain models. The best outcome was achieved by using as small cell size as possible. 5 m resolution rendered the best results from the resolutions tested (5 m, 10 m, 20 m and 50 m). The greatest elevation differences were observed in the areas of a steep terrain. The steeper the terrain, the greater the elevation difference. The terracing effect was noticed in the digital elevation models due to the high density of elevation points on the contour lines and hardly any points between them. Useful information can be obtained by estimating accuracy of digital elevation models. The accuracy of terrain models determines the reliability of glacier change analysis and that is why the digital elevation model must represent the terrain as accurately as possible. The different methods used in this thesis rendered very similar results and that indicated that the results were reliable and the terrain models created with Natural Neighbours and Triangular Irregular Network interpolators (resolution of 5 m) can be employed in further glacier change analysis

Grid models versus TIN : geometric accuracy of multibeam data processing

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Exploring multiple viewshed analysis using terrain features and optimisation techniques

The calculation of viewsheds is a routine operation in geographic information systems and is used in a wide range of applications. Many of these involve the siting of features, such as radio masts, which are part of a network and yet the selection of sites is normally done separately for each feature. The selection of a series of locations which collectively maximise the visual coverage of an area is a combinatorial problem and as such cannot be directly solved except for trivial cases. In this paper, two strategies for tackling this problem are explored. The first is to restrict the search to key topographic points in the landscape such as peaks, pits and passes. The second is to use heuristics which have been applied to other maximal coverage spatial problems such as location-allocation. The results show that the use of these two strategies results in a reduction of the computing time necessary by two orders of magnitude, but at the cost of a loss of 10% in the area viewed. Three different heuristics were used, of which Simulated Annealing produced the best results. However the improvement over a much simpler fast-descent swap heuristic was very slight, but at the cost of greatly increased running times. © 2004 Elsevier Ltd. All rights reserved

Airborne LiDAR for DEM generation: some critical issues

Airborne LiDAR is one of the most effective and reliable means of terrain data collection. Using LiDAR data for DEM generation is becoming a standard practice in spatial related areas. However, the effective processing of the raw LiDAR data and the generation of an efficient and high-quality DEM remain big challenges. This paper reviews the recent advances of airborne LiDAR systems and the use of LiDAR data for DEM generation, with special focus on LiDAR data filters, interpolation methods, DEM resolution, and LiDAR data reduction. Separating LiDAR points into ground and non-ground is the most critical and difficult step for DEM generation from LiDAR data. Commonly used and most recently developed LiDAR filtering methods are presented. Interpolation methods and choices of suitable interpolator and DEM resolution for LiDAR DEM generation are discussed in detail. In order to reduce the data redundancy and increase the efficiency in terms of storage and manipulation, LiDAR data reduction is required in the process of DEM generation. Feature specific elements such as breaklines contribute significantly to DEM quality. Therefore, data reduction should be conducted in such a way that critical elements are kept while less important elements are removed. Given the highdensity characteristic of LiDAR data, breaklines can be directly extracted from LiDAR data. Extraction of breaklines and integration of the breaklines into DEM generation are presented

Coverage And Visibility Problems On Topographic Surfaces

This thesis discusses and defines visibility coverage problems by using visibility information derived from topographic surfaces. Algorithms for extracting visibility information are developed and tested on both randomly generated and real topographic surfaces to solve visibility coverage problems, such as the determination of visible regions for specific viewpoints, the determination of a minimal set of viewpoints to see the entire surface. Problems are also extended to the cases of viewpoints whose heights are allowed to vary.;A triangulated irregular network (TIN) model was selected to represent topographic surfaces in this study. A drop heuristic algorithm for extracting TIN models from grid digital elevation models (DEM) was also developed and presented. Heuristic algorithms are used to solve visibility coverage problems and are compared for their performances. Solutions to visibility coverage problems suggested that peaks and vertices on ridge lines are found to be most likely good candidates as solution viewpoints. Relief variations on topographic surfaces are found to have a positive relationship with the number of viewpoints as well as the cost of building watchtowers required to see the entire surface. Parameters describing topographic surfaces, such as statistics of elevations and slopes of triangles, proportions of peak and ridge points in a set of vertices, the spatial autocorrelation coefficient, and the parameters of variograms are found to have similar relationship

Evaluating the Differences of Gridding Techniques for Digital Elevation Models Generation and Their Influence on the Modeling of Stony Debris Flows Routing: A Case Study From Rovina di Cancia Basin (North-Eastern Italian Alps)

Debris \ufb02ows are among the most hazardous phenomena in mountain areas. To cope with debris \ufb02ow hazard, it is common to delineate the risk-prone areas through routing models. The most important input to debris \ufb02ow routing models are the topographic data, usually in the form of Digital Elevation Models (DEMs). The quality of DEMs depends on the accuracy, density, and spatial distribution of the sampled points; on the characteristics of the surface; and on the applied gridding methodology. Therefore, the choice of the interpolation method affects the realistic representation of the channel and fan morphology, and thus potentially the debris \ufb02ow routing modeling outcomes. In this paper, we initially investigate the performance of common interpolation methods (i.e., linear triangulation, natural neighbor, nearest neighbor, Inverse Distance to a Power, ANUDEM, Radial Basis Functions, and ordinary kriging) in building DEMs with the complex topography of a debris \ufb02ow channel located in the Venetian Dolomites (North-eastern Italian Alps), by using small footprint full- waveform Light Detection And Ranging (LiDAR) data. The investigation is carried out through a combination of statistical analysis of vertical accuracy, algorithm robustness, and spatial clustering of vertical errors, and multi-criteria shape reliability assessment. After that, we examine the in\ufb02uence of the tested interpolation algorithms on the performance of a Geographic Information System (GIS)-based cell model for simulating stony debris \ufb02ows routing. In detail, we investigate both the correlation between the DEMs heights uncertainty resulting from the gridding procedure and that on the corresponding simulated erosion/deposition depths, both the effect of interpolation algorithms on simulated areas, erosion and deposition volumes, solid-liquid discharges, and channel morphology after the event. The comparison among the tested interpolation methods highlights that the ANUDEM and ordinary kriging algorithms are not suitable for building DEMs with complex topography. Conversely, the linear triangulation, the natural neighbor algorithm, and the thin-plate spline plus tension and completely regularized spline functions ensure the best trade-off among accuracy and shape reliability. Anyway, the evaluation of the effects of gridding techniques on debris \ufb02ow routing modeling reveals that the choice of the interpolation algorithm does not signi\ufb01cantly affect the model outcomes