Regular Grid Digital Elevation Model Research Articles

Fast approximate viewshed analysis based on the regular-grid digital elevation model: X-type partition proximity-direction-elevation spatial reference line algorithm

Viewshed analysis using regular-grid digital elevation models (DEM) is the basis of many analysis applications in geographic information systems. However, XDraw and reference plane, which have, until recently, acted a foundation of many viewshed analysis methods, have problems with accuracy and error-point aggregation. The proximity-direction-elevation spatial reference line (PDERL) algorithm, which is twice as slow as XDraw, has no accuracy problem, but not all applications can sacrifice speed for absolute accuracy. This study developed an “X-type partition PDERL” (XPDERL) algorithm based on PDERL by adjusting the partition mode of the PDERL and the combination mode of its partition results to maintain or even exceed the computational speed of traditional approximate fast algorithms while improving accuracy. The computational speed of XPDERL is stable at elevated heights from ground, slightly faster than XDraw and slightly slower than the reference plane algorithm; however, at lower elevations, it is significantly faster than both, especially in mountainous areas near the ground. In addition, the algorithm does not produce false-negative errors (identifying visible points as non-visible points) and can significantly reduce the error rate and degree of error-point aggregation. XPDERL can effectively alleviate the longstanding contradiction between speed and accuracy in viewshed analysis algorithms while providing a possible means for accurate and reliable large-scale viewshed analysis.

PDERL: an accurate and fast algorithm with a novel perspective on solving the old viewshed analysis problem

Viewshed analysis based on the regular grid digital elevation model (DEM) is one of the basic functions of geographic information systems. Traditional viewshed analysis algorithms are mainly carried out in a geospatial coordinate system, that create complexities when it is necessary to accurately express a perspective relationship. Moreover, it can only reduce the amount of calculation by using approximation methods, which result in decreased accuracy. We found that the error ratio of approximation algorithms is low but uneven and thereby highly likely to result in continuous area visibility errors. Despite the quality of DEM data having improved significantly in the last decade, traditional approximation algorithms have been unable to take full advantage of the improved data. Finding a fast and accurate algorithm has therefore become an urgent task. This study takes a new perspective to solve this problem by establishing a ‘proximity-direction-elevation’ (PDE) coordinate system and proposing a PDE spatial reference line (PDERL) algorithm within it. Many experiments prove that the accuracy of PDERL is the same as the R3 algorithm and its speed is about half that of the XDraw and reference plane algorithms, but much faster than R3. Due to the speed of PDERL, it is now possible and practical to do an accurate large-area DEM-based viewshed analysis.

Regular Grid DEM Data Processing Based on Hadoop

Digital Elevation Model (DEM) has been widely used in various sectors. But its data structure is special, and the amount of data is large. When it comes to big data or large-scale data simulation, the data processing of stand-alone mode often fails to meet the needs of users. This paper focuses on the Hadoop cloud computing platform for large data parallel processing and its built-in data types is limited, study the organization method of the regular grid DEM in the cloud computing platform, and designs the data types that applicable to the regular grid DEM processing in MapReduce framework. Finally, realize the parallelization processing of DEM and use non-source flood analysis as an example to verify the feasibility of data types.

Comparing the accuracy of estimated terrain elevations across spatial resolution

ABSTRACTTerrain is modelled in Geographic Information Science on a grid, assuming that elevation values are constant within any single pixel of a Digital Elevation Model (DEM). Pixels are considered flat and rigid, for computational simplicity (a ‘rigid pixel’ paradigm). This paradigm does not account for the slope and curvature of terrain within each pixel, generating imprecise measurements, particularly as pixel size increases or in uneven terrain. This paper relaxes the rigid pixel assumption, allowing for possible sub-pixel variations in slope and curvature (a ‘surface-adjusted’ paradigm). This paper compares different interpolation methods to investigate sub-pixel variations for estimating elevation of arbitrary points given a regular grid. Tests interpolating elevation values for 20,000 georeferenced off-centroid random points from a regular grid DEM are presented, using a variety of exact and inexact local deterministic interpolation methods within contiguity configurations incorporating first and second order neighbours. The paper examines the accuracy of surface-adjusted estimations across a progression of spatial resolutions (10 m, 30 m, 100 m, and 1,000 m DEMs) and a suite of terrain types varying in latitude, altitude, slope, and roughness, validating off-centre estimates against direct elevation measurements on 3 m resolution lidar DEM. Results illustrate that the Bi-quadratic and Bi-cubic interpolation methods outperform Weighted Average, Linear, and Bi-linear methods at coarse resolutions and in rough or non-uniform terrain. In smooth or flat terrain and at finest resolutions, the interpolation method impacts estimation accuracy less or not at all. The type of contiguity configuration appears to play a role in estimation errors as well, with tighter neighbourhoods exhibiting higher accuracy. The analysis also examined regularized mathematical surfaces, adding autocorrelated randomly distributed noise to simulate terrain. The results of experiments based on regularized smooth mathematical surfaces do not translate directly to terrain modelling. The analysis also considers the balance between the increased computation times needed to measure surface-adjusted elevation against improvements in accuracy.

Uncertainty modeling and analysis of surface area calculation based on a regular grid digital elevation model (DEM)

ABSTRACTIn the field of digital terrain analysis (DTA), the principle and method of uncertainty in surface area calculation (SAC) have not been deeply developed and need to be further studied. This paper considers the uncertainty of data sources from the digital elevation model (DEM) and SAC in DTA to perform the following investigations: (a) truncation error (TE) modeling and analysis, (b) modeling and analysis of SAC propagation error (PE) by using Monte-Carlo simulation techniques and spatial autocorrelation error to simulate DEM uncertainty. The simulation experiments show that (a) without the introduction of the DEM error, higher DEM resolution and lower terrain complexity lead to smaller TE and absolute error (AE); (b) with the introduction of the DEM error, the DEM resolution and terrain complexity influence the AE and standard deviation (SD) of the SAC, but the trends by which the two values change may be not consistent; and (c) the spatial distribution of the introduced random error determines the size and degree of the deviation between the calculated result and the true value of the surface area. This study provides insights regarding the principle and method of uncertainty in SACs in geographic information science (GIScience) and provides guidance to quantify SAC uncertainty.

Uncertainty modelling and analysis of volume calculations based on a regular grid digital elevation model (DEM)

The accuracy of earthwork calculations that compute terrain volume is critical to digital terrain analysis (DTA). The uncertainties in volume calculations (VCs) based on a DEM are primarily related to three factors: 1) model error (ME), which is caused by an adopted algorithm for a VC model, 2) discrete error (DE), which is usually caused by DEM resolution and terrain complexity, and 3) propagation error (PE), which is caused by the variables' error. Based on these factors, the uncertainty modelling and analysis of VCs based on a regular grid DEM are investigated in this paper. Especially, how to quantify the uncertainty of VCs is proposed by a confidence interval based on truncation error (TE). In the experiments, the trapezoidal double rule (TDR) and Simpson's double rule (SDR) were used to calculate volume, where the TE is the major ME, and six simulated regular grid DEMs with different terrain complexity and resolution (i.e. DE) were generated by a Gauss synthetic surface to easily obtain the theoretical true value and eliminate the interference of data errors. For PE, Monte-Carlo simulation techniques and spatial autocorrelation were used to represent DEM uncertainty. This study can enrich uncertainty modelling and analysis-related theories of geographic information science.

A Robust Algorithm of Multiquadric Method Based on an Improved Huber Loss Function for Interpolating Remote-Sensing-Derived Elevation Data Sets

Remote-sensing-derived elevation data sets often suffer from noise and outliers due to various reasons, such as the physical limitations of sensors, multiple reflectance, occlusions and low contrast of texture. Outliers generally have a seriously negative effect on DEM construction. Some interpolation methods like ordinary kriging (OK) are capable of smoothing noise inherent in sample points, but are sensitive to outliers. In this paper, a robust algorithm of multiquadric method (MQ) based on an Improved Huber loss function (MQ-IH) has been developed to decrease the impact of outliers on DEM construction. Theoretically, the improved Huber loss function is null for outliers, quadratic for small errors, and linear for others. Simulated data sets drawn from a mathematical surface with different error distributions were employed to analyze the robustness of MQ-IH. Results indicate that MQ-IH obtains a good balance between efficiency and robustness. Namely, the performance of MQ-IH is comparative to those of the classical MQ and MQ based on the Classical Huber loss function (MQ-CH) when sample points follow a normal distribution, and the former outperforms the latter two when sample points are subject to outliers. For example, for the Cauchy error distribution with the location parameter of 0 and scale parameter of 1, the root mean square errors (RMSEs) of MQ-CH and the classical MQ are 0.3916 and 1.4591, respectively, whereas that of MQ-IH is 0.3698. The performance of MQ-IH is further evaluated by qualitative and quantitative analysis through a real-world example of DEM construction with the stereo-images-derived elevation points. Results demonstrate that compared with the classical interpolation methods, including natural neighbor (NN), OK and ANUDEM (a program that calculates regular grid digital elevation models (DEMs) with sensible shape and drainage structure from arbitrarily large topographic data sets), and two versions of MQ, including the classical MQ and MQ-CH, MQ-IH has a better ability of maximally reducing the impact of outliers, while faithfully preserving terrain features. Theoretically, MQ-IH is not a promising interpolation method, and some side effects can be found from its simulation results. For example, the contours of MQ-IH are coarser than ANUDEM in some locations of the real-world study site, and its hill shade may not strictly agree with the real-world surface at rough terrain. Furthermore, the computing cost of MQ-IH is much bigger than that of the classical interpolation methods. However, compared with the classical interpolation methods, MQ-IH has significant potential for interpolating remote-sensing-derived elevation data sets.

High Accuracy Regular Grid Digital Elevation Model Modeling Based on 3D Triangulated Irregular Network Using Total Station Measured Points

High Accuracy Regular Grid Digital Elevation Model Modeling Based on 3D Triangulated Irregular Network Using Total Station Measured Points

The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution

When topography is represented by a simple regular grid digital elevation model, the analytical rectangular prism approach is often used for a precise gravity field modelling at the vicinity of the computation point. However, when the topographical surface is represented more realistically, for instance by a triangular irregular network (TIN) model, the analytical integration using arbitrary polyhedral bodies (the analytical line integral approach) can be implemented directly without additional data pre-processing (gridding or interpolation). The analytical line integral approach can also facilitate 3-D density models created for complex geometrical bodies. For the forward modelling of the gravitational field generated by the geological structures with variable densities, the analytical integration can be carried out using polyhedral bodies with a varying density. The optimal expression for the gravitational attraction vector generated by an arbitrary polyhedral body having a linearly varying density is known. In this article, the corresponding optimal expression for the gravitational potential is derived by means of line integrals after applying the Gauss divergence theorem.

DEM generation from SPOT-5 3-fold along track stereoscopic imagery using autocalibration

This paper describes the derivation and accuracy assessment of Digital Elevation Models (DEM) from 3-fold along-track stereoscopic SPOT-5 imagery. The work was conducted in the scope of the HRS (Haute Résolution Stéréoscopique)-Scientific Assessment Program, organized by the Centre National d'Études Spatiales (CNES) and the International Society of Photogrammetry and Remote Sensing (ISPRS). The orientation of the SPOT-5 image scene is reconstructed by bundle adjustment using ground control points. The functional model is based on correction polynomials and permits autocalibration. At 17 independent check points a RMS-error of 2 m was achieved. DEM are produced in two different ways: The more rigorous way employs an automatic region growing image matching process generating a dense point cloud in image space, transforms it into the object space using the estimated model parameters and converts it into a regular grid DEM. In a second approach the commercial software ISAE and rational functions are applied. The comparison with a digital terrain model (DTM) of superior accuracy yields standard deviations better than 5 m in flat and moderate terrain and better than 10 m in mountainous regions. With ISAE a DEM for the entire image area (approx. 60 × 80 km) is produced with a standard deviation of approximately 8 m. All grid points were generated fully automatically, i.e. the presented standard deviations still include the effect of large differences between the produced DEM and the DTM.

A hybrid interpolation method for the refinement of a regular grid digital elevation model

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.

A vector-based method for the extraction of catchment from grid DEMs

The methodology of catchment extraction especially from regular grid digital elevation models (DEMs) is briefly reviewed. Then an efficient algorithm, which combines vector process and traditional neighbourhood raster process, is designed for extracting the catchments and subcatchments from depressionless DEMs. The catchment area of each river in the grid DEM data is identified and delineated, then is divided into subcatchments as required. Compared to traditional processes, this method for identifying catchments focuses on the boundaries instead of the area inside the catchments and avoids the boundary intersection phenomena. Last, the algorithm is tested with a set of DEMs of different sizes, and the result proves that the computation efficiency and accuracy are better than existent methods.

Higher-order interpolation of regular grid digital elevation models

The fundamental aim of a digital elevation model (DEM) is to represent a surface accurately, such that elevations can be estimated for any given location. It is, therefore, necessary to have efficient and precise algorithms for the computation of surface elevations between given points. The hypothesis presented here, is that higher-order interpolation techniques will always be more accurate than the likes of the popular bilinear algorithm. This hypothesis will be evaluated through an assessment of the accuracy with which DEMs can be interpolated to higher spatial resolutions. A variety of interpolation techniques are assessed, ranging from the one-term level plane to the 36-term biquintic polynomial. In general, techniques that take account of the local terrain neighbourhood are more consistent and accurate, reducing the rms. error by up to 20% of the bilinear interpolant.

Kinematic routing using finite elements on a triangular irregular network

Automated extraction of geometry for hydraulic routing from digital elevation models (DEM) is a procedure that must be easily accomplished for widespread application of distributed hydraulically based rainfall excess‐runoff models. One‐dimensional kinematic routing on a regular grid DEM is difficult due to flow division and convergence. Two‐dimensional kinematic routing on a triangular irregular network (TIN) surmounts many of these difficulties. Because TIN DEMs typically require far fewer points to represent topography than regular grid DEMs, substantial computational economy is also realized. One‐dimensional routing using vector contour data overcomes the grid‐based routing disadvantages but often requires several orders of magnitude more storage points than a TIN. The methodology presented in this paper represents a compromise between slightly increased computational complexity and the economy of TIN topographic representation. We take the unique approach of subdividing each topographic triangle (TIN facet) into a set of coplanar triangular finite elements, performing routing on a single facet and then routing the resulting excess hydrograph to downstream facets and channels via upstream boundary conditions. Results indicate that shock conditions are readily handled, computed depths match analytic results to within ±3% and volume balances are typically within 1%. This modeling system illustrates the viability of kinematic routing over a TIN DEM derived directly from digital mapping data.

A new procedure for gridding elevation and stream line data with automatic removal of spurious pits

A morphological approach to the interpolation of regular grid digital elevation models (DEMs) from surface specific elevation data points and selected stream lines is described. The approach has given rise to a computationally efficient interpolation procedure which couples the minimization of a terrain specific roughness penalty with an automatic drainage enforcement algorithm. The drainage enforcement algorithm removes spurious sinks or pits yielding DEMs which may be used to advantage in hydrological process studies. The drainage enforcement algorithm has also been found to significantly increase the accuracy of DEMs interpolated from sparse, but well chosen, surface specific elevation data. Moreover, it facilitates the detection of errors in elevation data that would not be detected by more conventional statistical means and forms a sound physical basis for cartographic generalization.

Automated river-course, ridge and basin delineation from digital elevation data

Starting from a Digital Elevation Model (DEM) formed by a triangular irregular network (TIN) of facets, an algorithm that allows for the tracking of the path of steepest slope, downstream or upstream, from any point on the topographic surface has been developed. The analysis shows that when starting such a path in a downstream (upstream) direction from point P, down (up) to a point M, and then from point M in an upstream (downstream) direction and if the path returns to point P, then the segment PM corresponds to a “pure” streamline. Otherwise it corresponds to a river course (ridge). This property allows an easy way to delineate the network of river courses and ridges. Likewise, the repetitive use of this algorithm allows for the definition of basin and sub-basins, also called “contributing areas”, to any point on a river course. Finally, it is shown how a regular grid DEM can be treated as a particular case of the TIN-DEM, which gives generality to the presented procedures.