Global Grid System Research Articles

An open-source web service for creating quadrilateral grids based on the rHEALPix Discrete Global Grid System

ABSTRACT The foundation of modern Digital Earth frameworks is the Discrete Global Grid System (DGGS). To standardize the DGGS model, the Open Geospatial Consortium (OGC) recently created the DGGS Specification, which also aims to increase usability and interoperability between DGGSs. To support these demands and aid future research, open implementations are necessary. However, several OGC conformant DGGSs are not available for researchers to use. This has motivated us to develop an open-source web service that allows users to create quadrilateral grids based on the rHEALPix DGGS. In this paper, we describe the implementation of the web service, including issues and limitations, and demonstrate how discrete global grids and regional grids can be created. Lastly, we present examples that show how vector data sets can be modeled and integrated at different levels of resolution – a key benefit of the DGGS model.

Geovisualization of complex origin-destination flow maps using Discrete Global Grid Systems

Abstract. Flow maps, where counts of people or things are shown travelling between origin-destination pairs with paths or arrows, are difficult to draw well, mostly because they rapidly get cluttered as more and more paths are added. Researchers in cartographic and information visualization fields have sought to mitigate these problems in various ways, including cluster detection and edge bundling (Buchin, Speckmann, & Verbeek, 2011; Guo, 2009), force-directed path placement (Holten & van Wijk, 2009; Jenny et al., 2017), use of network topological space instead of planimetric space (Xiao & Chun, 2009), interactive spatial filtering of flows (Vrotsou, Fuchs, Andrienko, & Andrienko, 2017), and by changing the drawing medium to accommodate flows that arc through 3D space (Raposo, 2017; Yang et al., 2019; Zhang, Zhang, Li, & Li, 2018). Other geovisualization techniques recently developed involve and use of matrixes or grids to store and visualize flows; Wood, Dykes, & Slingsby (2010) use spatial tessellation and a set of small multiples of the same tessellation representing origin and destination spaces, respectively, creating a sort of travel heat map when tiles are colored as a choropleth. A comparable approach is taken by Yang et al. (2017) in a system that combines an abstract matrix of flow records with inflow and outflow maps.This early-stage project builds on previous matrix-based flow visualization methods while leveraging the power of Discrete Global Grid Systems (DGGS), which present a naturally Earth-oriented hierarchical tessellation upon which a matrix of origins and destinations can be stored and visualized. DGGS (Sahr, White, & Kimerling, 2003; Raposo, Robinson, & Brown, in press) partition the round Earth into nested tiles in a manner similar to quad-trees, and have the desirable properties of covering the whole spherical globe in equal-area (or near equal-area) tiles, and of being hierarchical to an arbitrary number of levels. The hierarchical quality allows flows in a DGGS to be naturally bundled by origin and destination points as a function of grid size; greater or lesser detail (i.e., more or less bundling) in the overall pattern of flows is effected by descending or ascending DGGS levels. As DGGS are becoming increasingly popular for geospatial data computation and collection in movement analysis (Brodsky, 2018), the present work provides a natural bridge to the visualization of such data when it pertains to movement phenomena.The present research will develop a suite of flow visualization techniques upon an existing open-source DGGS rendering platform (Raposo, Robinson, & Brown, in press): 1) grid facet coloring in a choropleth scheme to indicate magnitudes of flow into or out of a particular facet; 2) vertical-space cubic spline flow arcs, and 3) tabular representation of the flow data. All three visualization techniques will function across multiple spatial resolutions, corresponding to each of the hierarchical levels of our chosen DGGS, so that users can interact both with each of the three visualizations of the data as well as the spatial granularity to which the data are displayed. All views will be interactive and linked.We use Dutton’s (1999) quaternary triangular mesh (QTM), being a DGGS based on recursively subdividing the faces of an octahedron over the globe (Figure 1). Our method begins by finding, at many nested QTM levels, the facets of the QTM with which each origin and destination point intersects; in practice, we use up to 16 levels, as the triangles at that level in the QTM are small enough to address typical individual buildings. Importantly, point-in-polygon intersection is calculated geodetically, and not in 2D projected space, since failing to do this can cause topological errors (Raposo, Robinson, Brown, in press). At each QTM facet and at each level, we build two lists: one of all the other facets at that level that contain an origin point for a flow that arrives at this facet, and another of those that contain a destination point for flows originating in this facet. These lists are stored to each facet as polygon attributes. A flow path curving through vertical space via a cubic spline is also derived for each origin-destination pair and stored as a renderable 3D solid.The QTM is then plotted in our software on a virtual globe using NASA’s World Wind application programming interface. As users select any one QTM facet, its attributes are read to find all the other facets either contributing or receiving flows to or from the selected facet; these are then colored according to a choropleth scheme to visualize magnitudes of flow (Figure 2). Coloration is controlled for various descriptive statistics on the flows (e.g., total, mean, maximum, etc.). Linear paths curving up and around the globe (Figure 3) will also be available to be toggled on or off, giving users multiple redundant symbolizations of travel paths.

Datacubes: A Discrete Global Grid Systems Perspective

Datacubes are increasingly being implemented to manage big data workflows efficiently, particularly those for processing geospatial data. However, there is confusion in both the definition of the term “datacube” and the choices for how it is implemented. This and the conventional approach to managing spatial data (i.e., in map-projected data sets) have led to a restricted set of datacube implementations that are each tightly coupled to the spatial constraints of the data and how they are stored on disc – resulting in barriers to interoperability, particularly on global scales. This article discusses options and how it is possible to implement a datacube based on discrete global grid systems, while using the same topologies as conventional datacubes. These provide a flexible spatial data infrastructure that leverages the same topological advantages as conventional geospatial datacubes, while reducing barriers to data interoperability of both raster and vector data and providing additional functionality. Also, they potentially provide a very efficient approach to connecting to big data sources in order to extract datasets on demand prior to proceeding to multi-level intelligent big data processing, mining, machine learning, and visualizations.

Geospatial Data Organization Methods with Emphasis on Aperture-3 Hexagonal Discrete Global Grid Systems

Digital Earth frameworks deal with data sets of different types collected from various sources. To effectively store, retrieve, and transmit these data sets, efficient multi-scale data representations that are compatible with the underlying structure of the Digital Earth framework are required. In this article, we describe several such techniques and their properties: namely, how to represent data in the multi-scale cell hierarchy of a discrete global grid system (DGGS) or in the multi-scale hierarchy of a customized wavelet transform. We also discuss how these techniques can be tuned to be applicable to the A3H DGGS.

Utilizing a Discrete Global Grid System for Handling Point Clouds with Varying Locations, Times, and Levels of Detail

Discrete global grid systems (DGGSs) have emerged in recent years as a new specification for working with global heterogeneous data sets in a Digital Earth framework. Point clouds originating from different sources usually have varying initial characteristics. This research aims to analyze to what extent a DGGS can be used to handle point clouds having varying coordinate systems, acquired at different levels of detail (densities), and at different times in the creation of a global map of point clouds. DGGSs, which are currently limited to a 2D (surface) space, are extended into 3D and 4D spaces to fully harness the multidimensional nature of point clouds. A continuous spatial indexing strategy, based on a space-filling curve, is then developed on an ellipsoidal model of the Earth and used to efficiently cluster and retrieve DGGS-based point clouds stored in a database. Finally, the queried points are visualized in a Web browser. The hierarchical, multi-resolution nature of a DGGS is exploited to achieve a variable-scale smooth-zoom visualization. The challenges and opportunities of point cloud integration in a DGGS are presented.

A Virtual Globe Using a Discrete Global Grid System to Illustrate the Modifiable Areal Unit Problem

In the same way that discrete global grid systems (DGGS) are used to index data on the spherical Earth, they can aggregate point data, with their spherical polygons serving as bins. DGGS are particularly useful at multiple map scales because they are spatially hierarchical and exist on the sphere or ellipsoid, allowing large or small scale binning without projection distortion. We use DGGS in a free and open-source pedagogical tool for teaching students about the modifiable areal unit problem (MAUP). Our software application uses Dutton’s quaternary triangular mesh (QTM) to bin global data points geodesically with counts or measures of any theme at multiple levels. Users can interactively select the level to which the data are binned by the QTM, as well as translate the whole tessellation east or west so that points fall into and out of different bins. These two functions illustrate the scaling and zoning aspects of the MAUP with dynamically-drawn choropleths on the surface of a virtual globe that the user can zoom and rotate, allowing visualization at virtually any cartographic scale. Users may also select various quantile classifications to further explore issues in visualizing aggregate data. In addition to presenting this new tool, we highlight the importance, especially at smaller scales, of using geodesic point-in-polygon intersection detection, rather than the projected 2D methods typically used by geographic information systems.

Central Place Indexing: Hierarchical Linear Indexing Systems for Mixed-Aperture Hexagonal Discrete Global Grid Systems

Hexagonal discrete global grid systems (DGGSs) with integer spatial indexes are a promising new approach to designing geospatial data structures and location reference systems. Central place indexing (CPI) is a class of multi-precision hierarchical linear spatial indexing systems for pure and mixed-aperture hexagonal DGGSs. Definitions for CPI systems are given both on the plane and on the polyhedral surfaces of geodesic DGGSs, and examples of real-world DGGSs indexed using CPI are described. The semantic advantages of CPI systems are discussed, including their ability to exactly represent their own geometries.

Duality and Dimensionality Reduction Discrete Line Generation Algorithm for a Triangular Grid

Vectors are a key type of geospatial data, and their discretization, which involves solving the problem of generating a discrete line, is particularly important. In this study, we propose a method for constructing a discrete line mathematical model for a triangular grid based on a “weak duality” hexagonal grid, to overcome the drawbacks of existing discrete line generation algorithms for a triangular grid. First, a weak duality relationship between triangular and hexagonal grids is explored. Second, an equivalent triangular grid model is established based on the hexagonal grid, using this weak duality relationship. Third, the two-dimensional discrete line model is solved by transforming it into a one-dimensional optimal wandering path model. Finally, we design and implement the dimensionality reduction generation algorithm for a discrete line in a triangular grid. The results of our comparative experiment indicate that the proposed algorithm has a computation speed that is approximately 10 times that of similar existing algorithms; in addition, it has better fitting effectiveness. Our proposed algorithm has broad applications, and it can be used for real-time grid transformation of vector data, discrete global grid system (DGGS), and other similar applications.

A novel identifier scheme for the ISEA Aperture 3 Hexagon Discrete Global Grid System

ABSTRACTGeospatial data is often spatially aggregated by the use of Discrete Global Grid Systems. References to grid cells are needed for the communication of such data, and different identifier schemes have accordingly been introduced in literature. These schemes suffer, however, from being hard to understand for non-experts, and the geometry of a cell cannot be inferred from its identifier without complex computations. In this article, a novel identifier scheme that encodes the geographic coordinates of the centroid of a cell is proposed, which comes at the cost of potentially being ambiguous in case of a very fine-grained grid. We reason and computationally demonstrate that ambiguity does though not occur for real-world applications. The novel identifier scheme minimizes the amount of data to be communicated, for example, between a server and a client application, and it allows to infer approximate geometries of the cells only by their identifiers.

The rHEALPix Discrete Global Grid System: considerations for Canada

Geospatial data is ubiquitous. However, the geographic grid is not designed to manage, store, or integrate huge volumes of heterogeneous geospatial data. One possible solution to these challenges is a Discrete Global Grid System (DGGS), which was recently announced as a new standard by the Open Geospatial Consortium (OGC). If Canada plans to utilize a DGGS in the future to reference geospatial data, research is needed to explore characteristics and suitability of different DGGSs. Although hexagonal- and triangular-based DGGSs are popular, the square-based rHEALPix DGGS mirrors the geographic grid more closely and has many advantages. This paper reviews key features of the rHEALPix DGGS, outlines recent work, and qualitatively considers cell shape and cell orientation with respect to Canada, including how variations can be avoided or exploited by rotating the grid.

GPU ray casting method for visualizing 3D pipelines in a virtual globe

ABSTRACTPipelines are an important part of urban infrastructure development. As part of a virtual globe (VG), the high-efficiency and high-quality visualization of 3D large-scale and high-density urban pipelines is of great importance. This paper proposes a GPU-based pipeline ray casting method for the visualization of urban-scale pipelines in the framework of a VG. The method involves the initial partitioning of the pipeline data into tiles, based on the relationship between the pipeline layer scale and the discrete global grid system (DGGSs). The pipeline centerline in each tile is then segmented and encoded, and a coarser pipeline bounding volume is subsequently constructed using a geometry shader. Finally, the fine 3D pipeline is rendered using a pixel shader. The results of the experimental implementation of the proposed method show that it satisfies the requirements for the multiscale visualization of pipelines in a VG. Moreover, compared with the traditional polygon-based method, the method facilitates a 20% increase in rendering frame rate for the same pixel level accuracy display effect. It also enables the visualization of the thickness of the 3D pipeline without any obvious effect on the rendering efficiency.

After the Map: Cartography, Navigation, and the Transformation of Territory in the Twentieth Century by William Rankin

Reviewed by: After the Map: Cartography, Navigation, and the Transformation of Territory in the Twentieth Century by William Rankin Amber J. Bosse After the Map: Cartography, Navigation, and the Transformation of Territory in the Twentieth Century William Rankin. The University of Chicago Press, Chicago, IL, 2016. 416 pp.13 color plates, 144 halftones, notes, and index. $55.00 cloth (ISBN 978-0-226-33936-8) Many of us are, at a minimum, tangentially familiar with many of the acronyms that have emerged throughout the development of the mapping sciences. William Rankin’s first book explores three such acronyms: IMW, UTM, and GPS. By painting a sophisticated mural depicting the histories surrounding these nine letters, Rankin ensures that readers will never again be at risk of forgetting what they stand for. At the foundation of this project is Rankin’s drive to search for breakages, undulations, and transformations in “geo-epistemology”, a term Rankin engages to describe the search for the “how” surrounding geospatial information (how it is known, how it is used). After attending to the mapping sciences archives with an astounding commitment to even the smallest details (if you don’t believe me, check out the book’s website where Rankin has made all the data, images, and references for the book available for download), Rankin crafts a narrative that allows readers to see how today’s geospatial knowledge is made possible not only through advancements of satellites, computers, and smart technology, but also through a “relatively broad change in attitudes, goals, and practices across the mapping sciences as a whole” (p. 209). Put another way, Rankins visualizes the lines of connection between geo-epistemologies of bounded territory, which rely on the search for “objectivity or truth,” and the geo-epistemologies of unbounded territory, which promote “convenience and efficiency” (p. 206). Rankin divides the book into three sections, each with two chapters. Chapters are often organized by chronology as it specifically relates to the occurrence of WWI or WWII. Part I attends to the rise and fall of the International Map of the World, or IMW. This project, which was proposed in 1891, set out to “consolidate all existing geographic knowledge” by publishing uniformly symbolized maps at a scale of 1:1,000,000 for every country across the globe (p. 23). Rankin notes how the eventual termination of this project stems, not from lack of effort or vision from the project’s collaborators, but from the emergence of a new geo-epistemology. As the “universal map user” who benefited from a “view from nowhere” (the foundational audience and perspective of the IMW) [End Page 136] gave way to the post WWII map which privileged specialized, focused use cases. As is presented in Part II, the popularization of specialized maps was exacerbated by the emergence of the Euclidean coordinate system. This system establishes a flat and regional, rather than curved and global, locational reference point. Rankin is particularly interested in outlining the history of the US Army’s influential global grid system, also known as the Universal Transverse Mercator, or UTM. In addition to this history, Rankin questions the role and impact of the military in generating tools and techniques to be used for the advancement of geospatial knowledge. While geographers are already quite familiar with the discipline’s historical and present day entanglement with the military, Rankin manages to keep things interesting by discussing the practical applications of grids-for example, their use for aiming weapons. These applications, Rankin explains, promoted an “embedded geographic subjectivity” (p. 165). In the case of pre-WWII grids, this embeddedness reinforces national boundaries. For post WWII grids, and UTM in particular, such boundaries are dissolved as the gird worked to organize space across international dividers. Part III charts the development of radio navigation, electronic grid systems, and the well-known Global Positioning System (GPS). In doing so, Rankin exposes the mechanisms behind our current geo-epistemology, one which privileges points over areas. While delineating four different types of universalism accessible both before and after the launch of GPS, it becomes clear that Rankins wants to leave readers with two main points. First, he continues to stress that the boundaries between military, civilian...

Algebraic encoding scheme for aperture 3 hexagonal discrete global grid system

Discrete Global Grid Systems (DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal (A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron, multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.

An Improved Identification Code for City Components Based on Discrete Global Grid System

City components are important elements of a city, and their identification plays a key role in digital city management. Various identification codes have been proposed by different departments and systems over the years, however, their application has been partly hindered by the lack of a unified coding framework. The use of a code identifying a city component for unified management and geospatial computation across systems is still problematic. In this paper, we put forward an improved identification code for city components based on the discrete global grid system (DGGS). According to their spatial location, city components were identified with one-dimensional integer codes. The results illustrated that this identification code could express the location information of city components explicitly, as well as indicate the spatial distance relationship and the spatial direction relationship between different components. The experiment showed that this code performed better than traditional codes in data query and geospatial computation. Therefore, we concluded that this improved identification code was conducive to the more efficient management of city components, and hence might be used to improve digital city management.

Efficient encoding and decoding algorithm for triangular discrete global grid based on Hybrid Transformation Strategy

Grid codes are an important part of a grid system and provide a unique identifier for the cells in the spherical triangular discrete global grid, where the transformation between geographic coordinates and grid codes is the basis of global spatial data integration and various analytical applications. Owing to the particularity of the topological properties, the spherical space cannot be continuously paved with the same grid cells as those in the plane space. Thus, the recursive approximation method is typically used to establish the transformation algorithm between the geographic coordinates and the grid codes. The efficiency of those algorithms that were based on recursive approximation obviously decreased with the increased grid subdivision level; thus, it is not conducive to the integration of massive high-resolution spatial data. Whereas the geometric properties of the grid cells in the spherical triangular discrete global grid differ during the initial subdivision levels, as the level increases, these geometric properties tend to be the same, along with the properties of the local regions similar to the plane. Considering this characteristic, this paper proposes a hybrid bidirectional transformation algorithm. In the proposed algorithm, the recursive approximation method is used at the lower level where there is a large difference in the geometrical properties of the grid cells, and the direct mapping method using a similar plane grid is used at the higher level where the geometrical properties of the grid cells are virtually the same. In experiments conducted using the proposed algorithm with geographic coordinates at different scales and grid codes at different levels, the running time remained stable with no significant change throughout increases in the hierarchical level. Further, it was proven to satisfy the requirements of the absolute accuracy evaluation method. Compared with the traditional recursive approximation algorithm, the proposed algorithm has obvious advantages in the transformation between grid codes and geographic coordinates, as it can better support spatial data integration and various analytical applications in the spherical triangular discrete global grid system.

A discrete global grid system for earth system modeling

ABSTRACTTo support Earth system modeling, we propose a discrete global grid system that expresses multi-resolution spatial data. Specifically, a unified coding model that expresses a grid of nodes, edges, and cells is constructed for a triangular discrete global grid system. To fulfill the requirements of practical applications, we design a code-based topological query method for this grid system and an algorithm to transform between grid codes and geographic coordinates. We evaluate the Global Finite Volume Community Ocean Model (Global-FVCOM) on the triangular discrete global grid system in the proposed uniform coding model. The ocean tidal waves simulated by the Global-FVCOM running on the coded grid are then compared with results obtained using a traditional irregular spherical grid system, and the results display comparable accuracy. The uniform coding model proposed in this paper provides a triangular discrete global grid system that can represent multi-resolution spatial data and can be used in Earth system models. This unified coding model can also be applied to the geographic coordinate system made up of latitudes and longitudes, as well as diamond and hexagonal grids.

THE TRANSFORM BETWEEN GEOGRAPHIC COORDINATES AND LOCATION CODES OF APERTURE 4 HEXAGONAL GRID SYSTEM

Abstract. Discrete global grid system is a new data model which supports the fusion processing of multi-source geospatial data. In discrete global grid systems, all cell operations can be completed by codes theoretically, but most of current spatial data are in the forms of geographic coordinates and projected coordinates. It is necessary to study the transform between geographic coordinates and grid codes, which will support data entering and getting out of the systems. This paper chooses the icosahedral hexagonal discrete global system as a base, and builds the mapping relationships between the sphere and the icosahedron. Then an encoding scheme of planar aperture 4 hexagonal grid system is designed and applied to the icosahedron. Basing on this, a new algorithm of transforms between geographic coordinates and grid codes is designed. Finally, experiments test the accuracy and efficiency of this algorithm. The efficiency of code addition of HLQT is about 5 times the efficiency of code addition of HQBS.

Non-chemistry coupled PM10 modeling in Chiang Mai City, Northern Thailand: A fast operational approach for aerosol forecasts

The Weather Research and Forecasting (WRF v. 3.7) model was applied to model PM10 data in Chiang Mai city for 10-days during a high haze event utilizing updated land use categories from the Moderate Resolution Imaging Spectroradiometer (MODIS). A higher resolution meteorological lateral boundary condition (from 1 degree to 0.25 degree) was also used from the NCEP GDAS/FNL Global Tropospheric Analyses and Forecast Grid system. A 3-category urban canopy model was also added and the Thompson aerosol-aware microphysics parameterization scheme was used to model the aerosol number concentrations that were later converted to PM10 concentrations. Aerosol number concentration monthly climatology was firstly used as initial and lateral boundary conditions to model PM10 concentrations. These were compared to surface data obtained from two stations of the Pollution Control Department (PCD) of Thailand. The results from the modeled PM10 concentrations could not capture the variability (r = 0.29; 0.27 for each site) and underestimated a high PM10 spike during the period studied. The authors then added satellite data to the aerosol climatology that improved the comparison with observations (r = 0.45; 43). However, both model runs still were not able to capture the high PM10 concentration event. This requires further investigation.

Physical Visualization of Geospatial Datasets.

Geospatial datasets are too complex to easily visualize and understand on a computer screen. Combining digital fabrication with a discrete global grid system (DGGS) can produce physical models of the Earth for visualizing multiresolution geospatial datasets. This proposed approach includes a mechanism for attaching a set of 3D printed segments to produce a scalable model of the Earth. The authors have produced two models that support the attachment of different datasets both in 2D and 3D format.

G<sup>2</sup>EDPS's First Module & Its First Extension Modules

100% renewable worldwide power grid (Global Grid) system needs a Global Grid Electricity Demand Prediction System (G²EDPS) with very short, short, medium and long term forecasting consoles. This paper presents the 1^st core module and its 10 extension modules in the long term prediction console. A type 1 Mamdani like Fuzzy Inference System (FIS) with 7 triangle membership functions and 49 rules is designed for 2 input and 1 output variables for a 100 year forecasting period. The maximum absolute percentage errors (MAP), the mean absolute percentage errors (MAPE), and the Symmetric MAPE (SMAPE) of the best core module and its extension modules are respectively 0, 24; 0, 08; 0, 05 and 0, 22; 0, 07; 0, 05.