Global Grid System Research Articles

Constructing Efficient Mesh-Based Global Grid Systems with Reduced Distortions

Recent advancements in geospatial technologies have significantly expanded the volume and diversity of geospatial data, unlocking new and innovative applications that require novel Geographic Information Systems (GIS). (Discrete) Global Grid Systems (DGGSs) have emerged as a promising solution to further enhance modern geospatial capabilities. Current DGGSs employ a simple, low-resolution polyhedral approximation of the Earth for efficient operations, but require a projection between the Earth’s surface and the polyhedral faces. Equal-area DGGSs are desirable for their low distortion, but they fall short of this promise due to the inefficiency of equal-area projections. On the other hand, efficiency-first DGGSs need to better address distortion. We introduce a novel mesh-based DGGS (MBD) which generalizes efficient operations over watertight triangular meshes with spherical topology. Unlike traditional approaches that rely on Platonic or Catalan solids, our mesh-based method leverages high-resolution spherical meshes to offer greater flexibility and accuracy. MBD allows high-resolution polyhedra (HRP) to be used as the base polyhedron of a DGGS, significantly reducing distortion. To address the operational challenges, we introduce a new hash encoding method and an efficient barycentric indexing method (BIM). MBD extends Atlas of Connectivity Maps to the BIM to provide efficient spatial and hierarchical traversal. We introduce several new base polyhedra with lower areal and angular distortion, and we experimentally validate their properties and demonstrate their efficiency. Our experimentation shows that we achieve constant-time operations for high-resolution MBD, and we recommend polyhedra to be used as the base polyhedron for low-distortion DGGSs, compact faces, and efficient operations.

HierGP: Hierarchical Grid Partitioning for Scalable Geospatial Data Analytics

Application domains such as environmental health science, climate science, and geosciences—where the relationship between humans and the environment is studied—are constantly evolving and require innovative approaches in geospatial data analysis. Recent technological advancements have led to the proliferation of high-granularity geospatial data, enabling such domains but posing major challenges in managing vast datasets that have high spatiotemporal similarities. We introduce the Hierarchical Grid Partitioning (HierGP) framework to address this issue. Unlike conventional discrete global grid systems, HierGP dynamically adapts to the data’s inherent characteristics. At the core of our framework is the Map Point Reduction (MPR) algorithm, designed to aggregate and then collapse data points based on user-defined similarity criteria. This effectively reduces data volume while preserving essential information. The reduction process is particularly effective in handling environmental data from extensive geographical regions. We structure the data into a multilevel hierarchy from which a reduced representative dataset can be extracted. We compare the performance of HierGP against several state-of-the-art geospatial indexing algorithms and demonstrate that HierGP outperforms the existing approaches in terms of runtime, memory footprint, and scalability. We illustrate the benefits of the HierGP approach using two representative applications: analysis of over 289 million location samples from a registry of participants and efficient extraction of environmental data from large polygons. While the application demonstration in this work has focused on environmental health, the methodology of the HierGP framework can be extended to explore diverse geospatial analytics domains.

Spherical Magnetic Vector Forwarding of Isoparametric DGGS Cells with Natural Superconvergent Points

With the rapid advancement of satellite remote sensing technology, many scientists and organizations, including NASA, ESA, NAOC, and Roscosmos, observe and study significant changes in the geomagnetic field, which has greatly promoted research on the geomagnetic field and made it an important research direction in Earth system science. In traditional geomagnetic field research, tesseroid cells face degradation issues in high-latitude regions and accuracy limitations. To overcome these limitations, this paper introduces the Discrete Global Grid System (DGGS) to construct a geophysical model, achieving seamless global coverage through multi-level grid subdivision, significantly enhancing the processing capability of multi-source and multi-temporal spatial data. Addressing the challenges of the lack of analytical solutions and clear integration limits for DGGS cells, a method for constructing shape functions of arbitrary isoparametric elements is proposed based on the principle of isoparametric transformation, and the shape functions of isoparametric DGGS cells are successfully derived. In magnetic vector forwarding, considering the potential error amplification caused by Poisson’s formula, the DGGS grid is divided into six regular triangular sub-units. The triangular superconvergent point technique is adopted, and the positions of integration points and their weight coefficients are accurately determined according to symmetry rules, thereby significantly improving the calculation accuracy without increasing the computational complexity. Finally, through the forward modeling algorithm based on tiny tesseroid cells, this study comprehensively compares and analyzes the computational accuracy of the DGGS-based magnetic vector forwarding algorithm, verifying the effectiveness and superiority of the proposed method and providing new theoretical support and technical means for geophysical research.

Utilizing serverless framework for dynamic visualization and operations in geospatial applications

ABSTRACT While substantial efforts have been invested in the development of Discrete Global Grid Systems (DGGS) spatial operations and their potential applications in the geospatial domain, it has become evident that there is a demand for an efficient and scalable system to handle the visualization of large-scale DGGS data. This study demonstrated the potential of DGGS in conjunction with the serverless framework for dynamic visualization at various resolutions, which is based on data storage and effective querying using PostgreSQL integrated into Amazon Aurora Serverless. The use of Amazon Web Services (AWS) Lambda for on-the-fly generation of hexagon geometries significantly reduced the storage requirements and improved the speed of the visualization process. In addition, we implemented on-the-fly spatial operations including point binning, thresholding, aggregation, and neighborhood operations in the DGGS, highlighting the capabilities of DGGS in vector and raster processing. The proposed system has shown promising results in terms of efficiency, scalability, and adaptability, making it a viable solution for large-scale geospatial data processing and visualization. Case studies using flood risk data and terrain data further illustrate the system’s practical applicability in on-the-fly spatial operations and rapid visualization.

Arctic seas data cube based on discrete global grid system

Arctic seas data cube based on discrete global grid system

DGGSTools: An Open Source Python Package for the Manipulation of Vector and Raster Datasets in the rHEALPix Discrete Global Grid System

DGGSTools: An Open Source Python Package for the Manipulation of Vector and Raster Datasets in the rHEALPix Discrete Global Grid System

Employing discrete global grid systems for reproducible data obfuscation

Archaeological heritage worldwide is threatened through deliberate destruction in particular site looting making the location of archaeological sites potentially sensitive data. At the same time, public information about site locations are important for heritage management, as well as agricultural and urban development. Finding a balance between revealing detailed site locations and not providing data at all is a difficult task. Here we provide an approach to obfuscate archaeological site location data facilitated through a Discrete Global Grid System. We then apply the new obfuscation method to the global p3k14c data set. Veiling the locations of heritage sites with a Discrete Global Grid System allows tiered accuracy access for different stakeholders tailored to their respective needs as well as legal constraints and requirements of administrations. Discrete Global Grid System based obfuscation is globally scalable, consistent, reproducible, and can address the current heterogeneity of obfuscation methods.

A general modeling scheme for spatiotemporal DGGS with emphasis on encoding and operating multiscale time grids

AbstractOne of the basic scientific problems concerning geographic information science is how to rapidly organize, query, and compute spatiotemporal big data. The spatiotemporal discrete global grid system (DGGS) provides a homogenized discrete structure for processing multiscale and multitype spatiotemporal data. To date, most research in spatiotemporal DGGS has focused on spatial discretization while neglecting temporal discretization. Here, we propose a general modeling scheme for spatiotemporal DGGS with emphasis on encoding and operating multiscale time grids. We subdivide continuous time into multiscale temporal grids, which are then encoded as integers. Moreover, we designed integer code operations, including hierarchical traversal, neighborhood finding, and temporal relationship calculations. Compared to the multiscale time segment integer coding (MTSIC) approach, the proposed method resulted in 22% higher encoding efficiency, 10.92 times faster decoding, 2.81 times better parent code finding efficiency, 41% improved efficiency, 100% accuracy in finding children codes (compared to less than 100% with MTSIC), and a 62% enhancement in temporal relationship calculation efficiency. The application of querying spatiotemporal trajectory data validates the feasibility and practicality of substituting conventional string‐based time and floating‐point location coordinates with spatiotemporal integer codes to query data. The time encoding and operation methods proposed here indicate high efficiency, superior accuracy, and broad application prospects.

Exploring the possibility of adding DGGS support to the S-100 Universal Hydrographic Data Model

reference systems. A DGGS is a spatial reference system consisting of multiple layers of grids with increasing resolution which partition the globe into polygon shaped cells of equal area. Individual cells can be easily identified and basic Geographic Information System (GIS) operations can be performed on data stored within the cells. Advantages of using DGGS for spatial data include the ability to integrate data layers of different data types in a statistically uniform way, the possibility to avoid distortions caused from projection, and the capability to scale analysis across multiple resolution levels. The benefits of using DGGS for hydrographic data, specifically Electronic Navigational Charts (ENC) are examined. The addition of DGGS to S-100 would provide a uniform gridding system for ENC cells, and would eliminate distortions in the Polar Regions caused when projecting rectangular cells based on latitude and longitude. The Open Geospatial Consortium (OGC) led a pilot project for which one of the participants developed a server that offers S-100 marine protected area data organized according to DGGS. Because of this success and the availability of open-source software for the implementation of DGGS, the BSH (German Federal Maritime and Hydrographic Agency) investigated the feasibility and possible benefits of using Discrete Global Grid Systems for S-100 data. The outcome was successful. However, it is recognized that DGGS as a standard is not yet advanced enough and the available software tools are inadequate for wide implementation. More investigation needs to be done, and additionally the best grid shape, orientation and aperture for a uniform grid for hydrographic data need to be determined. Overall, DGGS should be considered for future versions of S-100, the new universal hydrographic data model, because the benefits for ENCs and hydrographic data are clear and in the future, it is expected that DGGS will revolutionize GIS.

Spherical Gravity Forwarding of Global Discrete Grid Cells by Isoparametric Transformation

For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular at the poles, i.e., degradation phenomena. Unlike other spherical discrete grids (e.g., square, triangular, and rhombic grids) that can fit the curvature, the Discrete Global Grid System (DGGS) grid can not only fit the curvature but also effectively avoid degradation phenomena at the poles. In addition, since it has only edge-adjacent grids, DGGS grids have consistent adjacency and excellent angular resolution. Hence, DGGS grids are the best choice for discretizing the sphere into cells with an approximate shape and continuous scale. Compared with the tesseroid, which has no analytical solution but has a well-defined integral limit, the DGGS cell (prisms obtained from DGGS grids) has neither an analytical solution nor a fixed integral limit. Therefore, based on the isoparametric transformation, the non-regular DGGS cell in the system coordinate system is transformed into the regular hexagonal prism in the local coordinate system, and the DGGS-based forwarding algorithm of the gravitational field is realized in the spherical coordinate system. Different coordinate systems have differences in the integral kernels of gravity fields. In the current literature, the forward modeling research of polyhedrons (the DGGS cell, which is a polyhedral cell) is mostly concentrated in the Cartesian coordinate system. Therefore, the reliability of the DGGS-based forwarding algorithm is verified using the tetrahedron-based forwarding algorithm and the tesseroid-based forwarding algorithm with tiny tesseroids. From the numerical results, it can be concluded that if the distance from observations to sources is too small, the corresponding gravity field forwarding results may also have ambiguous values. Therefore, the minimum distance is not recommended for practical applications.

Bidirectional mapping between rhombic triacontahedron and icosahedral hexagonal discrete global grid systems

ABSTRACT The icosahedron is currently the mainstream polygon in research and application of discrete global grid systems (DGGS). However, compared to the rhombic triacontahedron (RT), the icosahedron has disadvantages, such as lower sphere-fitting accuracy, greater projection distortion, and difficulty in incorporating the matrix structure for geospatial data storage. More importantly, the special positional relationship between the rhombic triacontahedron and the Earth enables it to effectively support event simulations related to geographical locations. To this end, bidirectional mapping of the hexagonal grid between the RT and icosahedron was proposed, which can efficiently integrate the existing datasets and algorithms of icosahedral DGGS into RT DGGS, thereby achieving seamless conversion between heterogeneous grid systems. We established geometric and topological correlations between the RT and icosahedron, abstracted the spatial algebraic structures of hexagonal grids on the two different polygons, and constructed mapping relationships between them. Finally, conversion between heterogeneous grid indices was achieved using dual quaternions. Experiments revealed that the proposed method was 3.9150 and 2.8151 times more efficient at grid conversion from RT to icosahedron and from icosahedron to RT, respectively, than was a method using latitude/longitude coordinates as a medium.

Encoding and operation scheme for the rhombic triacontahedron aperture 4 hexagonal discrete global grid system

ABSTRACT Discrete Global Grid System (DGGS) is a hierarchical structure with seamless global coverage, supporting processing and analysis of heterogeneous geospatial data. Compared with the most commonly used icosahedron, the rhombic triacontahedron (RT) approximates Earth better and can improve the accuracy of data modeling and expression. However, current RT DGGS studies have adopted a single-resolution integer coordinate scheme within a single surface that cannot achieve multilevel grid analysis. To this end, three adjacent surfaces are combined and a three-axis integer coordinate system is established to reduce the number of times crossing the surface. Then, the principle for partitioning aperture 4 hexagonal grids and a quadtree hierarchical encoding scheme are proposed. Further, this study establishes a fast transformation between the code and three-axis coordinates, implements hierarchical and neighbor code operations, and designs a transformation between the code and geographic coordinates. Experimental results indicate that, compared with the icosahedral hexagonal DGGS, the proposed scheme has a significant efficiency advantage in the transformation between the code and geographic coordinates, while the neighbor code operation efficiency can reach 40.97 times that of HLQT and 4.35 times that of HHUT. The proposed scheme provides a more suitable framework for organizing and analyzing global geospatial data.

Оценка изменения количества информации в шестиугольных дискретных глобальных сеточных системах с апертурой семь

The authors analyze the change in the amount of information at each level of hexagonal discrete global grid systems with an aperture of 7. They provide mechanisms for sampling spatial data and changing their granularity through hierarchical transitions between levels. The resolution is related to the volume of spatial data that can be displayed with the current grid. Three metrics are used to estimate the parameter having quantitative findings on the built-up areas and qualitative land use-and-cover data as an example. The results showed that the amount of information decreases non-linearly with increasing grid cell size; the nature of the change differs for different data types and aggregation methods. The study led to the conclusion that it is possible to predict the number of levels within which the information content reduces insignificantly with a cutback in detail for a specific DGGS configuration and data type

Regional Accuracy Assessment of 30-Meter GLC_FCS30, GlobeLand30, and CLCD Products: A Case Study in Xinjiang Area

With the development of remote sensing technology, a number of fine-resolution (30-m) global/national land cover (LC) products have been developed. However, accuracy assessments for the developed LC products are commonly conducted at global and national scales. Due to the limited availability of representative validation observations and reference data, knowledge relating to the accuracy and applicability of existing LC products on a regional scale is limited. Since Xinjiang, China, exhibits diverse surface cover and fragmented urban landscapes, existing LC products generally have high classification uncertainty in this region. This makes Xinjiang suitable for assessing the accuracy and consistency of exiting fine-resolution land cover products. In order to improve knowledge of the accuracy of existing fine-resolution LC products at the regional scale, Xinjiang province was selected as the case area. First, we employed an equal-area stratified random sampling approach with climate, population density, and landscape heterogeneity information as constraints, along with the hexagonal discrete global grid system (HDGGS) as basic sampling grids to develop a high-density land cover validation dataset for Xinjiang (HDLV-XJ) in 2020. This is the first publicly available regionally high-density validation dataset that can support analysis at a regional scale, comprising a total of 20,932 validation samples. Then, based on the generated HDLV-XJ dataset, the accuracies and consistency among three widely used 30-m LC products, GLC_FCS30, GlobeLand30, and CLCD, were quantitatively evaluated. The results indicated that the CLC_FCS30 exhibited the highest overall accuracy (88.10%) in Xinjiang, followed by GlobeLand30 (with an overall accuracy of 83.58%) and CLCD (81.57%). Moreover, through a comprehensive analysis of the relationship between different environmental conditions and land cover product performance, we found that GlobeLand30 performed best in regions with high landscape fragmentation, while GLC_FCS30 stood out as the most outstanding product in areas with uneven proportions of land cover types. Our study provides a novel insight into the suitability of these three widely-used LC products under various environmental conditions. The findings and dataset can provide valuable insights for the application of existing LC products in different environment conditions, offering insights into their accuracies and limitations.

Advancing digital earth modeling: Hexagonal multi-structural elements in icosahedral DGGS for enhanced geospatial data processing

Discrete Global Grid Systems (DGGSs) employ uniform cells for hierarchical Earth surface representation. However, prevalent software systems stemming from DGGS only focus on grid centers and lack the modeling of vertices and edges, which hindering efficient geospatial data computation and analysis. Consequently, we propose a novel mathematical model for hexagonal centers, vertices and edges of an icosahedral DGGS and provide corresponding hierarchical indexing methods and conversion rules with respect to integer coordinates. The proposed method was incorporated into the open-source software DGGRID, thereby enhancing its capabilities by integrating data fusion into the computation framework and expanding its application scope. The results show that the introduction of multi-structural elements could lead to higher-precision modeling of raster and vector data.

Poster] Spatial modelling of midair collision risk using ADS-B data


 The airspace environment is a complex system that is only expected to continue increasing in complexity with the introduction of new types of air vehicles and operations, such as uncrewed aircraft, and the projected growth of air traffic volumes. This increase in complexity brings a need for investigating and developing new models of complex airspace environments to better understand their constituent parts. To address this need, this paper presents a methodology to create a geospatial model of complex airspace environments which can be used to study any geospatially distributed entity part of these environments. The methodology leverages Discrete Global Grid Systems (DGGS) for this purpose, a Geographic Information Systems framework previously utilized in geography and urban planning. The usefulness of the model is demonstrated on a case study geospatial entity which is the risk of midair collisions for many geospatially distributed points in an airspace region of interest. Since such a model needs to be able to work for any type of air vehicle and airspace region in a fully three-dimensional model that is capable of performing time varying analysis in a computationally efficient manner, a rudimentary midair collision risk model was also developed which satisfies these requirements. Air traffic data from the OpenSky Network was collected and integrated in the geospatial model and the midair collision risk model was used to calculate the risk of collisions for many geospatially distributed points in the airspace for four scenarios of ascending airspace complexity. The results from these four scenarios showed that the proposed methodology can be used to study the risk of midair collisions for different points in the airspace for any type of air vehicle and airspace region of interest in a fully three-dimensional model that is capable of performing time varying analysis in a computationally efficient manner.
 

A Big Data Grided Organization and Management Method for Cropland Quality Evaluation

A new gridded spatio-temporal big data fusion method is proposed for the organization and management of cropland big data, which could serve the analysis application of cropland quality evaluation and other analyses of geographic big data. Compared with traditional big data fusion methods, this method maps the spatio-temporal and attribute features of multi-source data to grid cells in order to achieve the structural unity and orderly organization of spatio-temporal big data with format differences, semantic ambiguities, and different coordinate projections. Firstly, this paper constructs a dissected cropland big data fusion model and completes the design of a conceptual model and logic model, constructs a cropland data organization model based on DGGS (discrete global grid system) and Hash coding, and realizes the unified management of vector data, raster data and text data by using multilevel grids. Secondly, this paper researches the evaluation methods of grid-scale adaptability, and generates distributed multilevel grid datasets to meet the needs of cropland area quality evaluation. Finally, typical data such as soil organic matter data, road network data, cropland area data, and statistic data in Da’an County, China, were selected to carry out the experiment. The experiment verifies that the method could not only realize the unified organization and efficient management of cultivated land big data with multimodal characteristics, but also support the evaluation of cropland quality.

Designing aperture [formula omitted] hexagonal grids and their indexing as factor rings of Eisenstein integers

This paper proposes apertures of size 22k for hexagonal grids together with their indexing scheme, where k may be any positive integer. Hexagonal grid can be represented by an ideal I(2+ω) of a unit-ring Z(ω) of Eisenstein integers, where, for the set Z of integers and the cube root ω of 1, Z(ω) denotes {a+bω|a,b∈Z}, and, for any λ∈Z(ω), I(λ) denotes an ideal {κλ|κ∈Z(ω)} of Z(ω). We show that a factor ring I(2+ω)/I(2k(2+ω)) represents an aperture 22k hexagonal grid, and prove that it is isomorphic to a factor ring Z(ω)/I(2k). The latter represents a trigonal grid in a rhombus-shaped aperture with its edge length 2k, where we can address each of its 22k grid points as i+jω using two k-bit positive binary integers. We show that each grid point α=a+bω in I(2+ω)/I(2k(2+ω)) can be indexed by the address of its isomorphic image in Z(ω)/I(2k), and that this index is identical to the pair of the k-bit 2′s complements of a and b. Based on these findings, we clarify how indices may change for different resolutions, how to define the hierarchical indexing, how to geometrically interpret algebraic operations on indices, and, as one of the applications, how the quantization of trajectories of 106∼107 mobile objects on hexagonal grids may reduce the communication capacity required for their quasi-real-time simultaneous monitoring and sharing through the Internet. We also show how our indexing scheme can be applied to the design of DGGSs (Discrete Global Grid Systems) that cover the entire Earth's surface and 3D regular grids.

Construction of quality evaluation indicator system for diamond discrete global grid systems

ABSTRACT Although the uniformity of diamond discrete global grid is essential for calculations and searches, geometric deformations increase with the level of divisions. The Goodchild Criteria provides a basis for evaluating the quality of the global grid. However, some indicators in the criteria are redundant and contradictory, and the existing indicator system has limitations. Directly using the indicator system may render the evaluation of the diamond grid unreliable. In this study, we summarized the evaluation indicators for grid quality based on the Goodchild Criteria, calculated the correlations between these indicators using different diamond grid systems, and constructed reliable evaluation systems based on similarities and differences. The selected grid systems are classified into two groups: non-equal-area and equal-area grids. Their quality evaluation systems are composed of Size-Shape-Topology Factor and Geometry-Topology Factor, respectively. The proposed quality evaluation systems utilize a minimal number of indicators selected from each factor to provide a comprehensive description of the diamond grid’s characteristics. This approach simplifies the complexity of the evaluations while improving their reliability and credibility.

Interlevel information loss in hexagonal discrete global grid systems

Interlevel information loss in hexagonal discrete global grid systems