MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_0b333f12.8583.4039" ------=_NextPart_0b333f12.8583.4039 Content-ID: <20-040r3.htm> Content-Disposition: inline; filename="20-040r3.htm" Content-Type: text/html; charset="utf-8"
Open Geospatial Consortium
Submission Date: 2020-12-07
Approval Date: 2021-02-15
Publication Date: 2021-09-23
External identifier of this OGC® document: http://www.opengis.net/doc/AS/dggs/2.0
Internal reference number of this OGC® document: 20-040r3
Version: 2.0.0
Category: Abstract Specification Topic
Editor: Robert Gibb
Topic 21 - Discrete Global Grid Systems - Part 1 Core Reference system and Operations and Equal Area Earth Reference System
Copyright notice
Copyright
© 2021 Open Geospatial Consortium
To obtain additional rights of use, visit
http://www.ogc.org/legal/
Note
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. The Open Geospatial Consortium shall not be held responsible for identifying any or all such patent rights.
Recipients of this document are requested to submit, with their comments, notification of any relevant patent claims or other intellectual property rights of which they may be aware that might be infringed by any implementation of the standard set forth in this document, and to provide supporting documentation.
Notice
This document is not an OGC Standard. This document is an OGC Abstract Specification Topic and is therefore not an official position of the OGC membership. It is distributed for review and comment. It is subject to change without notice and may not be referred to as an OGC Standard.
Further, an OGC Abstract Specification Topic should not be referenced as required or mandatory technology in procurements.
Document number: 20-040r3 Document type: OGC® Abstract Specification Topic Document subtype: Document stage: Approved Document language: English |
License Agreement
Permission is hereby granted by the Open Geospatial Consortium, (“Licensor”), free of charge and subject to the terms set forth below, to any person obtaining a copy of this Intellectual Property and any associated documentation, to deal in the Intellectual Property without restriction (except as set forth below), including without limitation the rights to implement, use, copy, modify, merge, publish, distribute, and/or sublicense copies of the Intellectual Property, and to permit persons to whom the Intellectual Property is furnished to do so, provided that all copyright notices on the intellectual property are retained intact and that each person to whom the Intellectual Property is furnished agrees to the terms of this Agreement.
If you modify the Intellectual Property, all copies of the modified Intellectual Property must include, in addition to the above copyright notice, a notice that the Intellectual Property includes modifications that have not been approved or adopted by LICENSOR.
THIS LICENSE IS A COPYRIGHT LICENSE ONLY, AND DOES NOT CONVEY ANY RIGHTS UNDER ANY PATENTS THAT MAY BE IN FORCE ANYWHERE IN THE WORLD. THE INTELLECTUAL PROPERTY IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, AND NONINFRINGEMENT OF THIRD PARTY RIGHTS. THE COPYRIGHT HOLDER OR HOLDERS INCLUDED IN THIS NOTICE DO NOT WARRANT THAT THE FUNCTIONS CONTAINED IN THE INTELLECTUAL PROPERTY WILL MEET YOUR REQUIREMENTS OR THAT THE OPERATION OF THE INTELLECTUAL PROPERTY WILL BE UNINTERRUPTED OR ERROR FREE. ANY USE OF THE INTELLECTUAL PROPERTY SHALL BE MADE ENTIRELY AT THE USER’S OWN RISK. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR ANY CONTRIBUTOR OF INTELLECTUAL PROPERTY RIGHTS TO THE INTELLECTUAL PROPERTY BE LIABLE FOR ANY CLAIM, OR ANY DIRECT, SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING FROM ANY ALLEGED INFRINGEMENT OR ANY LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR UNDER ANY OTHER LEGAL THEORY, ARISING OUT OF OR IN CONNECTION WITH THE IMPLEMENTATION, USE, COMMERCIALIZATION OR PERFORMANCE OF THIS INTELLECTUAL PROPERTY.
This license is effective until terminated. You may terminate it at any time by destroying the Intellectual Property together with all copies in any form. The license will also terminate if you fail to comply with any term or condition of this Agreement. Except as provided in the following sentence, no such termination of this license shall require the termination of any third party end-user sublicense to the Intellectual Property which is in force as of the date of notice of such termination. In addition, should the Intellectual Property, or the operation of the Intellectual Property, infringe, or in LICENSOR’s sole opinion be likely to infringe, any patent, copyright, trademark or other right of a third party, you agree that LICENSOR, in its sole discretion, may terminate this license without any compensation or liability to you, your licensees or any other party. You agree upon termination of any kind to destroy or cause to be destroyed the Intellectual Property together with all copies in any form, whether held by you or by any third party.
Except as contained in this notice, the name of LICENSOR or of any other holder of a copyright in all or part of the Intellectual Property shall not be used in advertising or otherwise to promote the sale, use or other dealings in this Intellectual Property without prior written authorization of LICENSOR or such copyright holder. LICENSOR is and shall at all times be the sole entity that may authorize you or any third party to use certification marks, trademarks or other special designations to indicate compliance with any LICENSOR standards or specifications. This Agreement is governed by the laws of the Commonwealth of Massachusetts. The application to this Agreement of the United Nations Convention on Contracts for the International Sale of Goods is hereby expressly excluded. In the event any provision of this Agreement shall be deemed unenforceable, void or invalid, such provision shall be modified so as to make it valid and enforceable, and as so modified the entire Agreement shall remain in full force and effect. No decision, action or inaction by LICENSOR shall be construed to be a waiver of any rights or remedies available to it.
None of the Intellectual Property or underlying information or technology may be downloaded or otherwise exported or reexported in violation of U.S. export laws and regulations. In addition, you are responsible for complying with any local laws in your jurisdiction which may impact your right to import, export or use the Intellectual Property, and you represent that you have complied with any regulations or registration procedures required by applicable law to make this license enforceable.
Contents
TOC \o "1-2" \h \z \u Copyright notice . PAGEREF _Toc680687822 \h 1
Note . PAGEREF _Toc910153562 \h 1
License Agreement . PAGEREF _Toc323555406 \h 1
Notice . PAGEREF _Toc771549409 \h 1
I. Abstract . PAGEREF _Toc101631029 \h 1
II. Keywords . PAGEREF _Toc424006363 \h 1
III. Preface . PAGEREF _Toc151692478 \h 1
IV. Security considerations . PAGEREF _Toc969196652 \h 1
V. Submitting Organizations . PAGEREF _Toc595495716 \h 1
VI. Submitters . PAGEREF _Toc054889254 \h 1
VII. Foreword . PAGEREF _Toc759476779 \h 1
VIII. Introduction . PAGEREF _Toc487253636 \h 1
1. Scope . PAGEREF _Toc238804149 \h 1
2. Conformance . PAGEREF _Toc318129669 \h 1
3. Normative references . PAGEREF _Toc243650046 \h 1
4. Terms and definitions . PAGEREF _Toc005628760 \h 1
5. Conventions . PAGEREF _Toc189154057 \h 1
5.1. Abbreviated terms . PAGEREF _Toc866086681 \h 1
5.2. Universal Resource Identifiers . PAGEREF _Toc649137391 \h 1
5.3. Unified Modelling Language notation . PAGEREF _Toc271594518 \h 1
5.4. Naming conventions . PAGEREF _Toc544502498 \h 1
5.5. Attribute and association role status . PAGEREF _Toc844678394 \h 1
6. DGGS Specification Overview . PAGEREF _Toc054614794 \h 1
6.1. Package overview . PAGEREF _Toc562343214 \h 1
7. Common Spatio-temporal Classes Package . PAGEREF _Toc430972607 \h 1
7.1. Common Spatio-temporal Classes overview . PAGEREF _Toc450768100 \h 1
7.2. Temporal and Zonal Geometry package . PAGEREF _Toc480830453 \h 1
7.3. Temporal and Zonal RS using Identifiers package . PAGEREF _Toc898341060 \h 1
8. DGGS Core Reference System and Functions Package . PAGEREF _Toc769074186 \h 1
8.1. DGGS Core package conformance classes . PAGEREF _Toc447823321 \h 1
8.2. Core RS using Zonal Identifiers with Structured Geometry module . PAGEREF _Toc206495744 \h 1
8.3. DGGS Core functions . PAGEREF _Toc370476528 \h 1
9. DGGS Equal Area Earth Reference System Package . PAGEREF _Toc626460964 \h 1
9.1. Equal-Area Earth DGGS package . PAGEREF _Toc497105922 \h 1
Annex A (normative) Conformance Class Abstract Test Suite . PAGEREF _Toc605083762 \h 1
A.1. Common Spatio-temporal Classes package conformance categories . PAGEREF _Toc490611792 \h 1
A.2. DGGS Core package conformance categories . PAGEREF _Toc998567320 \h 1
A.3. Equal-Area Earth DGGS package conformance categories . PAGEREF _Toc016326681 \h 1
Annex B (informative) Equal area DGGS theory . PAGEREF _Toc919597929 \h 1
Annex C (informative) Background to DGGS . PAGEREF _Toc825812850 \h 1
C.1. DGGS as a digital information medium . PAGEREF _Toc379290483 \h 1
C.2. History . PAGEREF _Toc783184931 \h 1
C.3. Global grid taxonomy . PAGEREF _Toc985783403 \h 1
C.4. Criterion . PAGEREF _Toc755861768 \h 1
C.5. A digital spatial reference system . PAGEREF _Toc666143388 \h 1
C.6. Application . PAGEREF _Toc538185097 \h 1
D.1. General . PAGEREF _Toc579947327 \h 1
D.2. Geometry and topology . PAGEREF _Toc012214269 \h 1
D.3. Referencing by named periods . PAGEREF _Toc957482237 \h 1
Annex E (informative) Requirements crosswalk from Topic 21 v1.0 to v2.0 . PAGEREF _Toc208549505 \h 1
Annex F (normative) Revision History . PAGEREF _Toc390496448 \h 1
Bibliography . PAGEREF _Toc301839874 \h 1
List of Tables
TOC \h \z \t "TableTitle,tabletitle" Table 1 — Conformance classes for Common Spatio-temporal Classes package . PAGEREF _Toc929301087 \h 1
Table 2 — Conformance classes for DGGS Core package . PAGEREF _Toc272595751 \h 1
Table 3 — Categories of conformance for Equal-Area Earth DGGS package . PAGEREF _Toc276430300 \h 1
Table 4 — Module names used in UML diagrams in this document . PAGEREF _Toc613499101 \h 1
Table 5 — Elements of Temporal Geometry and Topology::Duration . PAGEREF _Toc755706250 \h 1
Table 6 — Elements of Temporal Geometry and Topology::EdgeT . PAGEREF _Toc528075880 \h 1
Table 7 — Elements of Temporal Geometry and Topology::Instant . PAGEREF _Toc915996814 \h 1
Table 8 — Elements of Temporal Geometry and Topology::Interval . PAGEREF _Toc437185734 \h 1
Table 9 — Elements of Temporal Geometry and Topology::NodeT . PAGEREF _Toc034490341 \h 1
Table 13 — Elements of Temporal Geometry and Topology::TemporalGeometry . PAGEREF _Toc470092648 \h 1
Table 16 — Elements of Temporal Geometry and Topology::TemporalTopology . PAGEREF _Toc405813099 \h 1
Table 19 — Elements of Zonal Geometry and Topology::ZoneGeometry . PAGEREF _Toc239577468 \h 1
Table 20 — Elements of Zonal Geometry and Topology::ZoneSimpleGeometry . PAGEREF _Toc086241272 \h 1
Table 21 — Elements of Zonal Geometry and Topology::ZoneSimpleTopology . PAGEREF _Toc848196637 \h 1
Table 22 — Elements of Zonal Geometry and Topology::ZoneTopology . PAGEREF _Toc539699726 \h 1
Table 23 — Elements of Spatial Location::LocationS . PAGEREF _Toc671093901 \h 1
Table 24 — Elements of Temporal RS using Identifiers::Period . PAGEREF _Toc897069412 \h 1
Table 25 — Elements of Temporal RS using Identifiers::PeriodClass . PAGEREF _Toc537025259 \h 1
Table 26 — Elements of Temporal RS using Identifiers::PeriodIdentifier . PAGEREF _Toc269731163 \h 1
Table 31 — Elements of Zonal RS using Identifiers::ZonalIdentifier . PAGEREF _Toc732375597 \h 1
Table 34 — Elements of Zonal RS using Identifiers::Zone . PAGEREF _Toc216512662 \h 1
Table 35 — Elements of Zonal RS using Identifiers::ZoneClass . PAGEREF _Toc934738028 \h 1
Table 36 — Elements of Zonal RS using Identifiers::ZoneClassComplex . PAGEREF _Toc046307672 \h 1
Table 37 — Elements of Zonal RS using Identifiers::ZoneClassPrimitive . PAGEREF _Toc648632208 \h 1
Table 38 — Elements of Zonal RS using Identifiers::ZoneCompound . PAGEREF _Toc979126956 \h 1
Table 39 — Elements of Zonal RS using Identifiers::ZonePrimitive . PAGEREF _Toc061548407 \h 1
Table 48 — Elements of Core Quantization Functions::DGG_Observation . PAGEREF _Toc162847021 \h 1
Table 49 — Elements of Core Quantization Functions::QuantizationContext . PAGEREF _Toc839120053 \h 1
Table 51 — Elements of Core Quantization Functions::Quantization . PAGEREF _Toc210764885 \h 1
Table 53 — Elements of Core Topological Query Functions::ZoneQuery . PAGEREF _Toc220936548 \h 1
Table 55 — Elements of Interoperation::InteroperationFunctions . PAGEREF _Toc413646816 \h 1
Table 56 — Elements of Interoperation Query::QueryComponents . PAGEREF _Toc631012188 \h 1
Table 57 — Elements of Interoperation Query::QueryFunctions . PAGEREF _Toc689353669 \h 1
Table 58 — Elements of Interoperation Query::QueryResult . PAGEREF _Toc683627360 \h 1
Table 59 — Elements of Interoperation Query::QueryType . PAGEREF _Toc725024089 \h 1
Table 60 — Elements of Interoperation Broadcast::BroadcastFunctions . PAGEREF _Toc701544184 \h 1
Table 61 — Elements of Interoperation Broadcast::BroadcastType . PAGEREF _Toc622488433 \h 1
Table 62 — Elements of Interoperation Broadcast::TranslationType . PAGEREF _Toc021608734 \h 1
Table 63 — Elements of Equal-Area Earth RS::EA_DGG_ReferenceSystem . PAGEREF _Toc063962469 \h 1
Table 64 — Elements of Equal-Area Earth RS::EA_GlobeGeometry . PAGEREF _Toc896514771 \h 1
Table 65 — Elements of Equal-Area Earth RS::EA_ReferenceSystemType . PAGEREF _Toc312443091 \h 1
Table 67 — Elements of Equal-Area Tessellation::EA_BaseUnitPolyhedron . PAGEREF _Toc685724734 \h 1
Table 68 — Elements of Equal-Area Tessellation::EA_DiscreteGlobalGrid . PAGEREF _Toc093556071 \h 1
Table 73 — Elements of Equal-Area Cell::EA_BoundaryData . PAGEREF _Toc495456652 \h 1
Table 74 — Elements of Equal-Area Cell::EA_Cell . PAGEREF _Toc310138833 \h 1
Table 75 — Elements of Equal-Area Cell::EA_Zone . PAGEREF _Toc974780246 \h 1
Table 76 — Elements of Equal-Area Cell::EA_BoundaryType . PAGEREF _Toc436534788 \h 1
Table A.2 — Conformance classes for DGGS Core package . PAGEREF _Toc048832048 \h 1
Table A.3 — Categories of conformance for Equal-Area Earth DGGS package . PAGEREF _Toc200339140 \h 1
Table B.1 . PAGEREF _Toc189875965 \h 1
Table B.2 . PAGEREF _Toc375448888 \h 1
Table B.3 . PAGEREF _Toc122028734 \h 1
Table C.1 . PAGEREF _Toc287330009 \h 1
Table C.2 . PAGEREF _Toc831465148 \h 1
Table E.1 — Requirements crosswalk from Topic 21 v1.0 to v2.0 . PAGEREF _Toc623172886 \h 1
Table E.2 — Requirements crosswalk from Topic 21 v2.0 to v1.0 . PAGEREF _Toc760515872 \h 1
Table F.1 . PAGEREF _Toc264661468 \h 1
List of Figures
TOC \h \z \t "FigureTitle,figuretitle" Figure 1 — Referencing by identifiers with structured geometry . PAGEREF _Toc762968097 \h 1
Figure 2 — DGGS Package Diagram . PAGEREF _Toc404237260 \h 1
Figure 3 — Primitives of Temporal Geometry and Topology . PAGEREF _Toc268787876 \h 1
Figure 4 — ISO 19107:2019 Context for Temporal Geometry and Topology . PAGEREF _Toc971561622 \h 1
Figure 5 — Components of Zonal Geometry and Topology module . PAGEREF _Toc011342747 \h 1
Figure 6 — Context for LocationS . PAGEREF _Toc693374366 \h 1
Figure 7 — Context for Temporal RS using Identifiers module . PAGEREF _Toc086928530 \h 1
Figure 8 — Primitives of ZonalIdentifier . PAGEREF _Toc733205806 \h 1
Figure 9 — Primitives of Zone . PAGEREF _Toc045410688 \h 1
Figure 10 — Primitives of ZoneClass . PAGEREF _Toc076223218 \h 1
Figure 11 — Primitives of RSUsingZonalIdentifiers . PAGEREF _Toc316065551 \h 1
Figure 12 — Components of RSUsingZonalIdentifiers . PAGEREF _Toc010210548 \h 1
Figure 14 — Components of the Core Quantization Functions module . PAGEREF _Toc155253812 \h 1
Figure 15 — Examples of parent, child, and sibling query operations . PAGEREF _Toc488085235 \h 1
Figure 16 — Components of Topological Zonal Query Functions module . PAGEREF _Toc260773967 \h 1
Figure 17 — Components of Core Interoperation Functions module . PAGEREF _Toc468789352 \h 1
Figure 18 — Components of Interoperation Query module . PAGEREF _Toc161962405 \h 1
Figure 19 — Interoperation Broadcast . PAGEREF _Toc263237135 \h 1
Figure 20 — Components of Equal-Area Earth RS module . PAGEREF _Toc371310143 \h 1
Figure 21 — Components of Equal-Area Tessellation module . PAGEREF _Toc800945298 \h 1
Figure 22 — Components of Equal-Area Cell module . PAGEREF _Toc628218430 \h 1
Figure B.3 — Planar square grid with nested child cells. . PAGEREF _Toc614363466 \h 1
Figure B.5 — Tessellations of the Earth to equal-area cells. . PAGEREF _Toc024335030 \h 1
Figure B.6 — Using Morton space filling curve for defining. . PAGEREF _Toc480110904 \h 1
Figure C.1 — Global Grid Taxonomy (Based on Figure 4 in [2]). . PAGEREF _Toc154890238 \h 1
List of Recommendations
TOC \h \z \t "RecommendationTitle,recommendationtitle" Requirement 1 . PAGEREF _Toc824919795 \h 1
Requirement 2 . PAGEREF _Toc763449827 \h 1
Requirement 3 . PAGEREF _Toc453118764 \h 1
Requirement 4 . PAGEREF _Toc993483820 \h 1
Requirement 5 . PAGEREF _Toc059958673 \h 1
Requirement 6 . PAGEREF _Toc345626124 \h 1
Requirement 7 . PAGEREF _Toc575820091 \h 1
Requirement 8 . PAGEREF _Toc251090899 \h 1
Requirement 9 . PAGEREF _Toc353153979 \h 1
Requirement 10 . PAGEREF _Toc808293498 \h 1
Requirement 11 . PAGEREF _Toc724852510 \h 1
Requirement 12 . PAGEREF _Toc106635058 \h 1
Requirement 13 . PAGEREF _Toc033140503 \h 1
Requirement 14 . PAGEREF _Toc555323005 \h 1
Requirement 15 . PAGEREF _Toc493049724 \h 1
Requirement 16 . PAGEREF _Toc907821247 \h 1
Requirement 17 . PAGEREF _Toc638498565 \h 1
Requirement 18 . PAGEREF _Toc515037832 \h 1
Requirement 19 . PAGEREF _Toc868333976 \h 1
Requirement 20 . PAGEREF _Toc262414305 \h 1
Requirement 21 . PAGEREF _Toc491169554 \h 1
Requirement 22 . PAGEREF _Toc636116783 \h 1
Requirement 23 . PAGEREF _Toc983350780 \h 1
Requirement 24 . PAGEREF _Toc092980776 \h 1
Requirement 25 . PAGEREF _Toc490813420 \h 1
Requirement 26 . PAGEREF _Toc797540667 \h 1
Requirement 27 . PAGEREF _Toc395951613 \h 1
Requirement 28 . PAGEREF _Toc281508377 \h 1
Requirement 29 . PAGEREF _Toc553576080 \h 1
This Abstract Specification lays the foundations for Discrete Global Grid Systems (DGGS). It defines Common classes for spatio-temporal geometry, topology, and reference systems using identifiers, a DGGS Core Reference system as a reference system using zonal identifiers with structured geometry that may be spatio-temporal, a suite of DGGS Core Functions, and it specifies Equal-Area Earth DGGS. The OGC DGGS Abstract Specification supports the specification of standardized DGGS infrastructures that enable the integrated analysis of very large, multi-source, multi-resolution, multi-dimensional, distributed geospatial data. Interoperability between OGC DGGS implementations is anticipated through implementation standards, and extension interface encodings of OGC Web Services.
The following are keywords to be used by search engines and document catalogues.
ogcdoc, OGC document, Discrete Global Grid System, DGGS, Digital Earth, DGGS-core, Spatial Reference System, Global Data Structure, Geographic Information Systems, DE-9IM, standard, specification
This document is consistent with the first edition ISO 19170-1:2020, Geographic Information — Discrete Global Grid Systems Specifications — Core Reference System and Operations, and Equal Area Earth Reference System. ISO/DIS 19170-1:2020 was prepared by Technical Committee ISO/TC 211, Geographic information/Geomatics, in close collaboration with the Open Geospatial Consortium (OGC). It replaces the first OGC edition published as document 15-104r5.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. The Open Geospatial Consortium shall not be held responsible for identifying any or all such patent rights.
Recipients of this document are requested to submit, with their comments, notification of any relevant patent claims or other intellectual property rights of which they may be aware that might be infringed by any implementation of the standard set forth in this document, and to provide supporting documentation.
The following organizations submitted this Document to the Open Geospatial Consortium (OGC):
Manaaki Whenua - Landcare Research, New Zealand
Geoscience Australia, Joint Research Centre (JRC), Pangaea Innovations Pty Ltd
Peking University Collaborative Innovation Center for Geospatial Big Data
University of Calgary
All questions regarding this submission should be directed to the editor or the submitters:
This second OGC edition of Abstract Specification Topic 21 — Discrete Global Grid Systems replaces the first edition (OGC 15-104r5), which has been technically revised.
The changes in this edition compared to the previous OGC edition are:
separation into DGGS Core and a specification for Equal Area Earth DGGS;
explicit handling of Dynamic vs Static datums for Equal Area Earth DGGS;
remodelling of the Core to incorporate new editions of ISO 19107, ISO 19111 & ISO 19112;
remodelling of the Core reference system to more explicitly include metadata elements;
extension of the Core to support up to three spatial dimensions;
extension of the Core to support up to one temporal dimension;
extension of the Core to support DGGS reference systems with conformal, or axis aligned cells;
additional modelling of temporal geometry and temporal reference systems sufficient for spatio-temporal DGGS, introducing the concept of a zone as a region of space-time equivalent to a location or an era;
change in name from ‘DGGS Reference Frame’ to ‘Referencing using zonal identifiers with structured geometry’, due to the inclusion of non-spatial geometry, reference systems, spatio-temporal zones and the new capabilities in ISO 19107:2019, ISO 19111:2019 & ISO 19112:2019.
remodelling of algebraic functions, to extensions of ISO 19107 Query, now referred to as topological query functions
DGGSs (Discrete Global Grid Systems) provide a new way to organise, store and analyse spatio-temporal data. This document contains a normative definition for DGGS and informative annexes. Annex B discusses the theoretical basis for equal area Earth DGGS, and Annex C discusses DGGS’s historical background. At the heart of DGGS is a new Referencing system. Spatial and temporal RSs described elsewhere by ISO/TC211 and the OGC (Open Geospatial Consortium) fall into two types:
Referencing by coordinates (ISO 19111:2019), and
Referencing by identifiers (geographic in ISO 19112:2019 & ordinal era in ISO 19108:2002).
In spatial Referencing by identifiers, the only required geometry is an extent, which may be expressed as a simple bounding box. Formal geometry need not be defined and sometimes follows societal whim. Similarly in ordinal temporal RSs, the topology of ordinal era’s are known, but the start and finish times are often only an estimation and are not required by the data model. DGGSs introduce a third type — Referencing by identifiers with structured geometry, illustrated in Figure 1. A single parent global geometry is chosen to define the dimensionality and orientation of the region of space-time occupied by the DGGS — it’s global world.
The structure for the DGGS geometry is provided by a strictly controlled process of recursive tessellation of the parent geometry that creates the DGGS RS’s units of geometry. The region occupied by each unit of geometry is called a zone. Each zone is given a unique name, called a zonal identifier. Each zonal identifier is associated with a representative spatio-temporal position in a base CRS (coordinate reference system) defined by a datum for the DGGS’s global world. Best practice is for a zonal identifier to be an encoding of both its position and its topology. Referencing by identifiers with structured geometry gives rise to RSs using zonal identifiers with structured geometry. Geographic information is inherently four-dimensional and includes time. So, a unified spatio-temporal data model for coordinate systems, geometry, topology, identifiers and RSs using identifiers is a pre-requisite for spatio-temporal DGGSs.
The approach taken in this document to specifying spatio-temporal data classes is to apply the spatio-temporal data model pattern in ISO 19111:2019 to spatial data classes in both ISO 19107:2019 and ISO 19112:2019 to produce their spatio-temporal equivalents. The set of common spatio-temporal classes for geometry, topology, identifiers, and RSs using identifiers specified in this document are therefore consistent with spatio-temporal CRS and coordinate systems in ISO 19111. Like ISO 19111, the temporal data model in this document does not reference ISO 19108:2002. The similarities and differences are described in Annex D.
In this document the spatio-temporal scope is constrained to spatial classes that are invariant through all time, and to temporal classes that are invariant throughout space. While this approach excludes certain spatio-temporal situations, it is flexible enough for a very large body of social and environmental modelling. Oceanic, climate and weather modelling often need geometries with a constant mass of gaseous fluid under changing pressure and temperature. These models can be run outside a DGGS. However, the results coming from these environmental models can be stored in a DGGS for efficient later use with other data.
This document specifies data models for a consistent set of common spatio-temporal classes, a DGGS core built on the common spatio-temporal classes, and a DGGS EAERS (equal-area Earth RS). The Common Spatio-temporal Classes, DGGS Core, and Equal-Area Earth DGGS packages each have their own conformance classes with their associated specifications and requirements.
The DGGS Core package is comprised of a RS, and functions for quantization, topological query and interoperability.
The DGGS Core RS is a RS using zonal identifiers with structured geometry located in its real world by coordinates in a base CRS. The DGGS Core RS is designed to support:
temporal, surface, volumetric and spatio-temporal DGGS,
DGGS with different grid constraints,
DGGS with different refinement strategies, and
DGGS refencing either the Earth or other celestial bodies.
The RS in Equal-Area Earth DGGS is a specialization of the DGGS Core RS. It describes a RS, comprising:
a base unit polyhedron,
a discrete hierarchical sequence of global grids,
global grids with equal-area zones each with a unique identifier, and
located in a geodetic CRS, that is typically also a geographic CRS.
This document does not prescribe any specific Earth surface model, base polyhedron or class of polyhedra, but is intended to allow for a range of options that produce DGGSs with compatible and interoperable functional characteristics.
Future additions to the OGC Topic 21 / ISO 19170 series are intended to cover:
Part 2 — Three-dimensional and equal-volume Earth RS.
Part 3 — Spatio-temporal Earth RS.
Part 4 — Axis-aligned RS with all zone edges parallel to the base CRS’s axes.
Specification for a DGGS-API to formalise client-server, and server-server operations, both between DGGSs and between DGGSs and non-DGGS architectures.
Creation of a register system for DGGS definitions analogous to the register for CRSs.
Additions to other specifications, such as for OWS OGC 05-042r2, OGC 17-089r1 architectures, spatial features and data formats to support DGGS data structures.
Topic 21 - Discrete Global Grid Systems - Part 1 Core Reference system and Operations and Equal Area Earth Reference System
This document supports the definition of:
A DGGS core comprising:
a RS using zonal identifiers with structured geometry, and
functions providing import, export and topological query,
Common spatio-temporal classes for geometry, topology, RS using zonal identifiers, zonal identifiers and zones, based on ISO 19111 CRS. The spatio-temporal scope is constrained to
spatial elements that are invariant through all time, and
temporal elements that are invariant across all space.
EAERS for equal-area Earth DGGS.
This standard defines the conformance classes listed in tables Table 1–Table 3
Table 1 — Conformance classes for Common Spatio-temporal Classes package
Conformance class | Requirement tests |
Temporal geometry and topology | Annex A.1, Requirement test A.1 |
Temporal reference systems using period identifiers | Annex A.1, Requirement test A.4 |
Spatial zone geometry and topology | Annex A.1, Requirement test A.2 |
Spatial reference systems using zonal identifiers | Annex A.1, Requirement test A.3, & Annex A.1, Requirement test A.5 |
Spatio-temporal zone geometry and topology | Annex A.1, Requirement test A.1, & Annex A.1, Requirement test A.2 |
Spatio-temporal reference systems using zonal identifiers | Annex A.1, Requirement test A.3, Annex A.1, Requirement test A.4, & Annex A.1, Requirement test A.5 |
Table 2 — Conformance classes for DGGS Core package
Conformance class | Requirement tests |
Spatial DGGS Core | Annex A.1, Requirement test A.2, Annex A.1, Requirement test A.3, Annex A.1, Requirement test A.5, and all Core requirements in Annex A.2.1, Requirement test A.6–Annex A.2.2, Requirement test A.19. |
Spatio-temporal DGGS Core | Annex A.1, Requirement test A.1, Annex A.1, Requirement test A.2, Annex A.1, Requirement test A.3, Annex A.1, Requirement test A.4, Annex A.1, Requirement test A.5, and all Core requirement tests in Annex A.2.1, Requirement test A.6–Annex A.2.2, Requirement test A.19. |
Table 3 — Categories of conformance for Equal-Area Earth DGGS package
Conformance class | Requirement tests |
Equal-Area Earth DGGS | Annex A.1, Requirement test A.2, Annex A.1, Requirement test A.3, & Annex A.1, Requirement test A.5, and all Core requirement tests in Annex A.2.1, Requirement test A.6–Annex A.2.2, Requirement test A.19, and all EAERS requirement tests in Annex A.3, Requirement test A.20–Annex A.3, Requirement test A.29. |
Conformance with this standard shall be checked using the relevant tests specified in Annex A (normative) of this document. The framework, concepts, and methodology for testing, and the criteria to be achieved to claim conformance are specified in the OGC Compliance Testing Policies and Procedures and the OGC Compliance Testing web site.
All requirements-classes and conformance-classes described in this document are owned by the standard(s) identified.
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
ISO: ISO 19103:2015, Geographic information — Conceptual schema language. International Organization for Standardization, Geneva (2015). https://www.iso.org/standard/56734.html
ISO: ISO 19107:2019, Geographic information — Spatial schema. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/66175.html
The following pair of OGC and ISO documents are identical in normative content:
Roger Lott: OGC 18-005r5, Topic 2 — Referencing by coordinates Corrigendum. Open Geospatial Consortium (2021). https://docs.ogc.org/as/18-005r5/18-005r5.html
ISO: ISO 19111:2019, Geographic information — Referencing by coordinates. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/74039.html
ISO: ISO 19112:2019, Geographic information — Spatial referencing by geographic identifiers. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/70742.html
The following pair of OGC and ISO documents are identical in normative content:
ISO: OGC 11-111r1, Topic 11 — Metadata. Open Geospatial Consortium (2016). http://www.iso.org/iso/home/store/catalogue_ics/catalogue_detail_ics.htm?csnumber=53798
ISO: ISO 19115-1:2014, Geographic information — Metadata — Part 1: Fundamentals. International Organization for Standardization, Geneva (2014). https://www.iso.org/standard/53798.html
The following pair of OGC and ISO documents are identical in normative content:
Simon Cox: OGC 10-004r3, Topic 20 — Observations and Measurements. Open Geospatial Consortium (2010). https://portal.ogc.org/files/?artifact_id=41579
ISO: ISO 19156:2011, Geographic information — Observations and measurements. International Organization for Standardization, Geneva (2011). https://www.iso.org/standard/32574.html
This document uses the terms defined in OGC Policy Directive 49, which is based on the ISO/IEC Directives, Part 2, Rules for the structure and drafting of International Standards. In particular, the word “shall” (not “must”) is the verb form used to indicate a requirement to be strictly followed to conform to this standard and OGC documents do not use the equivalent phrases in the ISO/IEC Directives, Part 2.
This document also uses terms defined in the OGC Standard for Modular specifications (OGC 08-131r3), also known as the ‘ModSpec’. The definitions of terms such as standard, specification, requirement, and conformance test are provided in the ModSpec.
For the purposes of this document, the following additional terms and definitions apply.
This document uses the terms defined in Sub-clause 5.3 of OGC 06-121r9, which is based on the ISO/IEC Directives, Part 2, Rules for the structure and drafting of International Standards. In particular, the word “shall” (not “must”) is the verb form used to indicate a requirement to be strictly followed to conform to this standard.
4.1. boundary child ADMITTED compound CRS ADMITTED CRS ADMITTED reference frame ADMITTED DGGS ADMITTED dynamic CRS ADMITTED dynamic datum ADMITTED geodetic CRS ADMITTED geographic CRS ADMITTED global ADMITTED parent ADMITTED sibling ADMITTED spatio-temporal CRS ADMITTED static CRS ADMITTED static datum ADMITTED temporal CRS ADMITTED
set that represents the limit of an entity
Note 1 to entry: Boundary is most commonly used in the context of geometry, where the set is a collection of points or a collection of objects that represent those points. In other domains, the term is used metaphorically to describe the transition between an entity and the rest of its domain of discourse.
[SOURCE: ISO 19107:2019, Clause 3.6]
<DGGS> spatial, spatio-temporal or temporal unit of geometry with dimension greater than 0, associated with a zone (Clause 4.52)
Note 1 to entry: All cells within a DGGS (Clause 4.13) share the dimensionality of the DGGS’s parent global (Clause 4.24) geometry. DGGS with dimensionality of 0, are not supported.
Note 2 to entry: Cells are the unit of geometry in a DGGS, and the geometry of the region of space-time occupied by a zone is a cell.
Note 3 to entry: While the terms cell and zone are often used interchangeably, strictly zone is the preferred term. Cell is entirely appropriate when specifically discussing a zone’s geometry or topology.
<DGGS> process of subdividing parent cells (Clause 4.33) into descendant child cells (Clause 4.4) using a specified refinement ratio (Clause 4.38) and suite of refinement strategies
Note 1 to entry: Iterative application of cell refinements creates a hierarchy of descendant discrete global grids (Clause 4.12).
Note 2 to entry: Cell refinement methods may result in child cells that each have a single parent or that have multiple parents.
<DGGS> immediate descendant of a parent cell (Clause 4.33)
Note 1 to entry: Child cells are either within a single parent cell or overlapped by multiple parent cells
description of a set of objects that share the same attributes, operations, methods, relationships, and semantics
Note 1 to entry: A class may use a set of interfaces to specify collections of operations it provides to its environment. The term was first used in this way in the general theory of object-oriented programming, and later adopted for use in this same sense in UML.
[SOURCE: ISO 19103:2015, Clause 4.7, modified — Note 1 to entry has been added from clause 4.2]
4.6. compound coordinate reference system
coordinate reference system (Clause 4.7) using at least two independent coordinate reference systems
Note 1 to entry: Coordinate reference systems are independent of each other if coordinate values in one cannot be converted or transformed into coordinate values in the other.
[SOURCE: ISO 19111:2019, Clause 3.1.3]
4.7. coordinate reference system
coordinate system that is related to an object by a datum (Clause 4.10)
Note 2 to entry: For geodetic and vertical datums, the object will be the Earth. In planetary applications, geodetic and vertical reference frames may be applied to other celestial bodies.
[SOURCE: ISO 19111:2019, Clause 3.1.9]
set of mathematical rules for specifying how coordinates are to be assigned to points
[SOURCE: ISO 19111:2019, Clause 3.1.11]
specification of a value (Clause 4.49) domain with operations allowed on values in this domain
Note 1 to entry: Data types include primitive predefined types and user-definable types. All instances of a data type lack identity.
Example
[SOURCE: ISO 19103:2015, Clause 4.14, modified — Note 1 to entry has been added from ISO 19156:2011, Clause 4.3]
parameter or set of parameters that realize the positions of the origin, the scale, and the orientation of a coordinate system (Clause 4.8)
[SOURCE: ISO 19111:2019, Clause 3.1.15]
group of multiple realizations of the same terrestrial or vertical reference system that, for approximate spatial referencing purposes, are not significantly different
Note 1 to entry: Datasets referenced to the different realizations within a datum ensemble may be merged without coordinate transformation.
Note 2 to entry: ‘Approximate’ is for users to define but typically is in the order of under 1 decimetre but may be up to 2 metres.
Example
“WGS 84” as an undifferentiated group of realizations including WGS 84 (TRANSIT), WGS 84 (G730), WGS 84 (G873), WGS 84 (G1150), WGS 84 (G1674) and WGS 84 (G1762). At the surface of the Earth these have changed on average by 0.7 m between the TRANSIT and G730 realizations, a further 0.2 m between G730 and G873, 0.06 m between G873 and G1150, 0.2 m between G1150 and G1674 and 0.02 m between G1674 and G1762).
[SOURCE: ISO 19111:2019, Clause 3.1.16]
<DGGS> set of cells (Clause 4.2) at the same refinement level (Clause 4.37), that uniquely and completely cover a globe (Clause 4.24)
Note 1 to entry: the set of cell zonal identifiers (Clause 4.50) comprising a discrete global grid form a single Zone Class with its associated refinement level.
Note 2 to entry: the configuration of the set of cells comprising a discrete global grid satisfy at least one grid constraint in the DGG_GridConstraint codelist.
4.13. discrete global grid system
integrated system comprising a hierarchy (Clause 4.26) of discrete global grids (Clause 4.12), spatio-temporal referencing (Clause 4.42) by zonal identifiers (Clause 4.50) and functions for quantization (Clause 4.36), zonal query (Clause 4.51), and interoperability (Clause 4.28)
non-negative quantity of time equal to the difference between the final and initial instants (Clause 4.29) of a time interval (Clause 4.30)
Note 1 to entry: The duration is one of the base quantities in the International System of Quantities (ISQ) on which the International System of Units (SI) is based. The term “time” instead of “duration” is often used in this context and also for an infinitesimal duration.
Note 2 to entry: For the term “duration”, expressions such as “time” or “time interval” are often used, but the term “time” is not recommended in this sense and the term “time interval” is deprecated in this sense to avoid confusion with the concept of “time interval”.
Note 3 to entry: The exact duration of a time scale unit depends on the time scale used. For example, the durations of a year, month, week, day, hour or minute, may depend on when they occur [in a Gregorian calendar, a calendar month can have a duration of 28, 29, 30, or 31 days; in a 24-hour clock, a clock minute can have a duration of 59, 60, or 61 seconds, etc.]. Therefore, the exact duration can only be evaluated if the exact duration of each is known.
Note 4 to entry: This definition is closely related to NOTE 1 of the terminological entry “duration” in IEC 60050-113:2011, 113-01-13.
[SOURCE: ISO 8601-1:2019, Clause 3.1.1.8]
4.15. dynamic coordinate reference system
coordinate reference system (Clause 4.7) that has a dynamic reference frame (Clause 4.16)
Note 1 to entry: Coordinates of points on or near the crust of the Earth that are referenced to a dynamic coordinate reference system may change with time, usually due to crustal deformations such as tectonic motion and glacial isostatic adjustment.
Note 2 to entry: Metadata for a dataset referenced to a dynamic coordinate reference system should include coordinate epoch information.
[SOURCE: ISO 19111:2019, Clause 3.1.19]
reference frame (Clause 4.10) in which the defining parameters include time evolution
[SOURCE: ISO 19111:2019, Clause 3.1.20]
<metric> statement of or methodology for describing the nature and magnitude of the errors which affect the results of a calculation
[SOURCE: ISO 19107:2019, Clause 3.35, modified — Note 1 to entry has been removed]
abstraction of real-world phenomena
Note 1 to entry: A feature can occur as a type or an instance. In this document, feature instance is meant unless otherwise specified.
[SOURCE: ISO 19101-1:2014, Clause 4.1.11, modified — Note 1 to entry has been added from ISO 19156:2011, Clause 4.6, and modified]
class (Clause 4.5) of features (Clause 4.18) having common characteristics
[SOURCE: ISO 19156:2011, Clause 4.7]
4.20. geodetic coordinate reference system
three-dimensional coordinate reference system (Clause 4.7) based on a geodetic reference frame and having either a three-dimensional Cartesian or a spherical coordinate system
Note 1 to entry: In this document a CRS based on a geodetic reference frame and having an ellipsoidal coordinate system is geographic.
[SOURCE: ISO 19111:2019, Clause 3.1.31]
4.21. geographic coordinate reference system
coordinate reference system (Clause 4.7) that has a geodetic reference frame and an ellipsoidal coordinate system
[SOURCE: ISO 19111:2019, Clause 3.1.35]
spatial reference (Clause 4.41) in the form of a label or code that identifies a location (Clause 4.31)
Example
[SOURCE: ISO 19112:2019, Clause 3.1.2]
geometric object representing a single, connected, homogeneous (isotropic) element of space
Note 1 to entry: Geometric primitives are non-decomposed objects that present information about geometric configuration. They include points, curves, surfaces, and solids. Many geometric objects behave like primitives (supporting the same interfaces defined for geometric primitives) but are actually composites composed of some number of other primitives. General collections may be aggregates and incapable of acting like a primitive (such as the lines of a complex network, which is not connected and thus incapable of being traceable as a single line). By this definition, a geometric primitive is topological open, since the boundary (Clause 4.1) points are not isotropic to the interior points. Geometry is assumed to be closed. For points, the boundary is empty.
[SOURCE: ISO 19107:2019, Clause 3.50]
<DGGS> region of space-time enclosing a celestial body
Note 1 to entry: In this document globe is used in its most general form to refer to any celestial body or region of space-time enclosing a celestial body that may be referenced by a DGGS (Clause 4.13). When a specific body, such as the Earth is referred to, an explicit term is used.
network composed of two or more sets of curves in which the members of each set intersect the members of the other sets in an algorithmic way
[SOURCE: ISO 19123:2005, Clause 4.1.23]
<DGGS> organization and ranking of successive levels of cell refinement (Clause 4.3) of discrete global grids (Clause 4.12)
4.27. initial discrete global grid
<DGGS> discrete global grid tessellation created by circumscribing a defined path along the chosen surface model of the Earth between the vertices of the scaled base unit polyhedron
capability to communicate, execute programmes, or transfer data among various functional units in a manner that requires the user to have little or no knowledge of the unique characteristics of those units
Note 1 to entry: in this document interoperability specifically refers to functions that initiate and process transfers of data from a DGGS (Clause 4.13).
[SOURCE: ISO/IEC 2382:2015, Clause 2121317, modified — The original domain and Notes to Entry have been deleted. A Note 1 to entry has been added.]
<DGGS> temporal geometry primitive representing a point in time
Note 1 to entry: On temporal coordinate systems (Clause 4.46) as specified in ISO 19107:2019, the temporal geometric primitives (Clause 4.23) instant and interval (Clause 4.30) are the equivalent of points and lines as specified in ISO 19107:2019.
<DGGS> temporal geometry primitive representing a line in time
Note 1 to entry: On temporal coordinate systems (Clause 4.46) as specified in (ISO 19107:2019), the temporal geometric primitives (Clause 4.23) instant (Clause 4.29) and interval are the equivalent of points and lines as specified in ISO 19107:2019.
Note 2 to entry: In the context of DGGS (Clause 4.13), locations have dimension greater than one, and so are not points.
Example
[SOURCE: ISO 19112:2019, Clause 3.1.3, modified — Note two has been added and an additional example provided]
act of measuring or otherwise determining the value (Clause 4.49) of a property
[SOURCE: ISO 19156:2011, Clause 4.11]
<DGGS> cell (Clause 4.2) in a higher refinement level of discrete global grid with immediate descendants
Note 1 to entry: parent cells either overlap or contain their child cells (Clause 4.4).
<DGGS> particular era or span of time
Note 1 to entry: Periods are intervals (Clause 4.30) named with a period identifier (Clause 4.35)
<DGGS> temporal reference in the form of a label or code that identifies a period (Clause 4.34)
Note 1 to entry: Period identifiers are the temporal equivalent of geographic identifiers (Clause 4.22) as specified in ISO 19112:2019
<DGGS> function assigning data from external sources to cell values
<DGGS> numerical order of a discrete global grid (Clause 4.12) in the tessellation sequence
<DGGS> ratio of the number of child cells (Clause 4.4) to parent cells (Clause 4.33)
Note 1 to entry: A positive integer ratio n refinement of DGGS (Clause 4.13) parent cells yield n times as many child cells as parent cells.
Note 2 to entry: For a two-dimensional DGGS (as defined for EAERS in this document) this is the surface area ratio.
Note 3 to entry: In DGGS literature [2] the term aperture has been used instead of refinement ratio. Refinement ratio is preferred because it is clearer in meaning to audiences outside the early DGGS community.
<DGGS> cell (Clause 4.2) in a discrete global grid with the same parent cell (Clause 4.33)
Note 1 to entry: all the child cells (Clause 4.4) of a parent cell are each-others’ sibling cells.
<topology, geometry> homogeneous (all points have isomorphic neighbourhoods) and with a simple boundary (Clause 4.1)
Note 1 to entry: The interior is everywhere locally isomorphic to an open disc in a Euclidean coordinate space of the appropriate dimension Dn = {P|‖P‖ < 1.0}. The boundary is a dimension one smaller. This essentially means that the object does not intersect nor touch itself. Generally used for a curve that does not cross not touch itself with the possible exception of boundary points. Simple closed curves are isomorphic to a circle.
[SOURCE: ISO 19107:2019, Clause 3.84]
description of position in the real world
[SOURCE: ISO 19111:2019, Clause 3.1.56]
4.42. spatio-temporal reference
system for identifying position in the real world that may include time
4.43. spatio-temporal coordinate reference system
compound coordinate reference system (Clause 4.6) in which one constituent coordinate reference system (Clause 4.7) is a spatial coordinate reference system and one is a temporal coordinate reference system (Clause 4.47)
[SOURCE: ISO 19111:2019, Clause 3.1.59]
4.44. static coordinate reference system
coordinate reference system (Clause 4.7) that has a static reference frame (Clause 4.45)
Note 1 to entry: Coordinates of points on or near the crust of the Earth that are referenced to a dynamic coordinate reference system do not change with time.
Note 2 to entry: Metadata for a dataset referenced to a static coordinate reference system does not require coordinate epoch information.
[SOURCE: ISO 19111:2019, Clause 3.1.61]
reference frame (Clause 4.10) in which the defining parameters exclude time evolution
[SOURCE: ISO 19111:2019, Clause 3.1.62]
4.46. temporal coordinate system
<geodesy> one-dimensional coordinate system where the axis is time
[SOURCE: ISO 19111:2019, Clause 3.1.64]
4.47. temporal coordinate reference system
coordinate reference system (Clause 4.7) based on a temporal datum
[SOURCE: ISO 19111:2019, Clause 3.1.63]
partitioning of a space into a set of conterminous subspaces having the same dimension as the space being partitioned
Note 1 to entry: A tessellation composed of congruent regular polygons or polyhedra is a regular tessellation. One composed of regular, but non-congruent polygons or polyhedra is a semi-regular tessellation. Otherwise the tessellation is irregular. Tessellations on curved surfaces cannot be congruent, so all tessellations in DGGS (Clause 4.13) are either semi-regular or irregular.
Example
Graphic examples of tessellations may be found in Figures 11, 13, 20, and 22 of [ISO19123].
[SOURCE: ISO 19123:2005, Clause 4.1.39, modified — Note 1 to entry has been modified and new notes to entry have been added.]
Note 1 to entry: A value considers a possible state of an object within a class (Clause 4.5) or type (domain).
Note 3 to entry: A value can use one of a variety of scales including nominal, ordinal, ratio and interval, spatial and temporal. Primitive datatypes can be combined to form aggregate datatypes with aggregate values, including vectors, tensors and images.
[SOURCE: ISO 19156:2011, Clause 4.18]
<DGGS> spatio-temporal reference (Clause 4.42) in the form of a label or code that identifies a zone (Clause 4.52)
Note 1 to entry: A zonal identifier may be a geographic identifier (Clause 4.22), period identifier (Clause 4.35), or a compound of the two.
Note 2 to entry: A zone’s ZonalIdentifier provides the coordinates of a representative position for the zone, and spatio-temporal feature (Clause 4.18) geometry is represented by sets of ZonalIdentifiers.
<DGGS> geometry or topology function using a cell’s zonal identifiers (Clause 4.50) to specify geometry
Note 1 to entry: ISO 19107:2019 specifies a suite of geometry and topology functions in the Query2D and Query3D classes, where geometry elements used in each function’s parameters are described by sets of coordinates. In DGGS (Clause 4.13) all geometry can be referenced as sets of cells (Clause 4.2) represented solely by a list (or set) of their zonal identifiers. This document specifies ZoneQuery to implement the operations in both Query2D and Query3D using zonal identifiers to reference each operation’s source and target geometry.
<DGGS> particular region of space-time
Note 1 to entry: The primitives of zone are spatial location (Clause 4.31) and temporal period (Clause 4.34).
Note 2 to entry: A zone may be either a single zonal primitive or a compound zone comprising one spatial location and one temporal period. Zones can be regions of space-time associated with any celestial body.
Note 3 to entry: Zones are the primary container for storing and retrieving data within a DGGS implementation. DGGSs reference zones by their zonal identifier (Clause 4.50), for instance in databases or through tile nomenclature.
Note 4 to entry: Each zone’s geometry is represented by a cell (Clause 4.2).
DE-9IM | |
EAERS | |
EC | |
ECEF | |
GEM | |
GIS | |
GUID | |
HPC | |
HPD | |
ICT | |
ISEA | |
ISEA3H | |
ISO | |
OGC | |
OWS | |
QTM | |
rHEALPix | |
RS | |
UML | |
URI |
The normative provisions in this specification are denoted by the URI:
http://www.opengis.net/spec/dggs/2.0
All requirements and conformance tests that appear in this document denoted by partial URIs are relative to this base.
In this document, the conceptual schema for describing DGGSs are presented in the UML. ISO 19103:2015 presents the specific profile of UML used in this document.
The UML diagrams in this document refer to classifiers in five other standards. Each standard has been assigned a colour that is used consistently across all UML diagrams. Each diagram has a key listing the standards referred to in that diagram and their colours. Interface names in the figure have the structure <module-name>::<interface-name>. For reference, Table 1 lists all the module names and the standard they belong to. Both colour and module name can be used as quick reference to a classifier’s standard.
Where possible, when a classifier represents the common behaviour of a set of defined things from the terms defined in Clause 3, the UML classifier will generally use the defined terms as its name. Since classifier names are capitalized and contain no space, and the defined term may contain several words, the classifier name will separate words using upper-camel-case concatenations (no spaces but each word beginning with a capital with all other letters in lowercase). Similarly, the name may be some simplified key phrase. This “UpperCamelCase” rule is generally followed but may be violated if clarity or consistency with other standards is improved by minor violations. For example:
Zone identifier values are represented by the interface ZonalIdentifier or stored using the datatype DirectPosition defined in ISO 19107:2019.
Instances of primitives will realize the interface Primitive in the package Common Spatio-temporal Classes and other interfaces for their specific dimension and interpolation mechanism. For example, Point, Instant, Interval, Line, NodeT, LocationS.
Any classifier name referenced from another standard retains its original format.
Classifier names for attributes and operations in the UML models may similarly use key phrases in lowerCamelCase (same as UpperCamelCase, but the first word begins in a lowercase letter). For example: parent; child; parentOf; childOf and relatePosition are all used as operation names.
Module and package names can contain spaces. In some situations, a phrase that has an abbreviation is used in its unabbreviated form as a package name. Where a package or module is referred to in the text, both the capitalisation and unabbreviated form are preserved. This distinguishes them from a phrase in general use. For example: DGGS Equal-Area Earth Reference System; Zone and Temporal Geometry; and Reference System defined in this standard and Coordinate Reference Systems defined in ISO 19111:2019.
In summary, the use of capitals for a term in the general text indicates a reference to a classifier from the UML
In this document, conceptual schema in Clauses 6–8 are defined by tables. In these tables:
attributes and association roles are given an Obligation status:
M: mandatory — this attribute or association role shall be supplied.
C: conditional — this attribute or association role shall be supplied if the condition (given in the description) is true. It may be supplied if the condition is false.
O: optional — this attribute or association role may be supplied.
the Maximum Occurrence column in the tables indicates the maximum number of occurrences of attribute values that are permissible, with * indicating no upper limit.
non-navigable associations are not included in the UML diagrams or tables.
The tables provide a summary of the UML diagrams. In particular, association roles, attributes, operations, and constraints that are inherited from another class unchanged are not described in the tables. In the event of any discrepancies between the UML diagrams and text, the UML shall prevail.
The specification for DGGSs is described in this document in the form of a UML model with supplementary defining tables and text. The UML data model is organised into three primary packages. The Common Spatio-temporal Classes package contains two UML sub-packages, DGGS Core contains four UML sub-packages, and DGGS Equal-Area Earth Reference System package is a single UML package, as shown in Figure 2.
Common Spatio-temporal Classes package contains
Zone and Temporal Geometry package, comprising temporal and spatio-temporal primitives for geometry and topology,
Zone, Identifier and RS package, comprising temporal and spatio-temporal RS using identifiers and their primitives.
DGGS Core package contains:
Core RS using zonal identifiers with structured geometry package,
Core Quantisation Functions package,
Core Query Functions package,
Core Interoperation Functions package.
Equal-Area Earth DGGS package.
In Figure 2, each box represents a package and contains the package name. Each arrowed line shows the normative dependency of one package upon another package (at the head of the arrow). The Common Spatio-temporal Classes, DGGS Core and Equal-Area Earth DGGS packages dependent on packages in five other ISO standards.
Packages are grouped in a hierarchy of sub-packages, with modules containing interfaces at the leaves of the hierarchy. In the UML diagrams that follow, interface names are often shown as <module-name>::<interface-name>. For reference, Table 4 lists all the module names that are referred in the diagrams and names the standard they come from.
Table 4 — Module names used in UML diagrams in this document
Conformance classes for the modules in the Common Spatio-temporal Classes, DGGS Core, and Equal-Area Earth DGGS packages are described in Annex A.
One product conformance class is also defined for an Equal-Area Earth DGGS product, that brings modules together as a system.
This clause specifies the common spatio-temporal classes to support temporal and spatio-temporal geometry, topology, zones, zonal identifiers, zonal query, and RSs using temporal or zonal identifiers.
These classes are defined here in such a way that they can be used in any context which requires an internally consistent set of temporal and spatio-temporal classes for use with spatial classes from ISO 19107, 19111 and 19112. They are further specialised in the DGGS Core for use in DGGS. In this restricted model for spatio-temporal systems, the spatio-temporal scope is constrained to spatial classes that are invariant through all time, and to temporal classes that are invariant throughout space.
The Common Spatio-temporal Classes are organized into two packages with five modules:
Temporal and Zonal Geometry package comprises:
Temporal Geometry and Topology module
Zonal Geometry and Topology module
RS using Temporal and Zonal Identifiers package comprises:
Spatial Location module
Temporal RS using Identifiers module
Zonal RS using Identifiers module
In each package separate spatial and temporal classes are defined first, followed by spatio-temporal classes that bring temporal and spatial classes together.
Temporal geometry is geometry constrained to one of the temporal coordinate systems, defined by TemporalCS in ISO 19111:2019. Temporal geometry primitives instant and interval implement the temporal analogues of point and line respectively in ISO 19107:2019. All geometry has topology, and the temporal topology primitives nodeT and edgeT implement the temporal analogues of node and edge respectively. These are shown in Figure 3.
Temporal interfaces paralleling the spatial geometry and topology interface structure are built from these temporal primitives. Each temporal interface has the same meaning and semantics as their equivalent spatial interface, with the constraint that all temporal interfaces are constrained to the same coordinate system as their temporal primitives. Figure 4 shows the spatial classes on the left and their temporal equivalents on the right.
Figure 4 — ISO 19107:2019 Context for Temporal Geometry and Topology
Table 5 — Elements of Temporal Geometry and Topology::Duration
Table 6 — Elements of Temporal Geometry and Topology::EdgeT
Table 7 — Elements of Temporal Geometry and Topology::Instant
Table 8 — Elements of Temporal Geometry and Topology::Interval
Table 9 — Elements of Temporal Geometry and Topology::NodeT
Table 10 — Elements of Temporal Geometry and Topology::TemporalGeometricCollection
Table 11 — Elements of Temporal Geometry and Topology::TemporalGeometricComplex
Table 12 — Elements of Temporal Geometry and Topology::TemporalGeometricPrimitive
Table 13 — Elements of Temporal Geometry and Topology::TemporalGeometry
Table 14 — Elements of Temporal Geometry and Topology::TemporalTopologicalComplex
Table 15 — Elements of Temporal Geometry and Topology::TemporalTopologicalPrimitive
Table 16 — Elements of Temporal Geometry and Topology::TemporalTopology
Table 5 — Elements of Temporal Geometry and Topology::Duration
Table 6 — Elements of Temporal Geometry and Topology::EdgeT
Table 7 — Elements of Temporal Geometry and Topology::Instant
Table 8 — Elements of Temporal Geometry and Topology::Interval
Table 9 — Elements of Temporal Geometry and Topology::NodeT
Table 10 — Elements of Temporal Geometry and Topology::TemporalGeometricCollection
Table 11 — Elements of Temporal Geometry and Topology::TemporalGeometricComplex
Table 12 — Elements of Temporal Geometry and Topology::TemporalGeometricPrimitive
Table 13 — Elements of Temporal Geometry and Topology::TemporalGeometry
Table 14 — Elements of Temporal Geometry and Topology::TemporalTopologicalComplex
Table 15 — Elements of Temporal Geometry and Topology::TemporalTopologicalPrimitive
Table 16 — Elements of Temporal Geometry and Topology::TemporalTopology
Referring to Figure 5, ZoneGeometry is either a primitive of ZoneSingleGeometry or a compound of two ZoneSingleGeometry primitives — one spatial and one temporal.
Zones exhibit topology of the same spatio-temporal dimension as their geometry.
Table 17 — Elements of Zonal Geometry and Topology::ZoneCompoundGeometry
Table 18 — Elements of Zonal Geometry and Topology::ZoneCompoundTopology
Table 19 — Elements of Zonal Geometry and Topology::ZoneGeometry
Table 20 — Elements of Zonal Geometry and Topology::ZoneSimpleGeometry
Table 21 — Elements of Zonal Geometry and Topology::ZoneSimpleTopology
Table 22 — Elements of Zonal Geometry and Topology::ZoneTopology
Table 17 — Elements of Zonal Geometry and Topology::ZoneCompoundGeometry
Table 18 — Elements of Zonal Geometry and Topology::ZoneCompoundTopology
ZoneCompoundTopology exhibits both spatial topology with respect to the spatial component of its geometry and temporal topology with respect to the temporal component of its geometry. | |||||||
Table 19 — Elements of Zonal Geometry and Topology::ZoneGeometry
Table 20 — Elements of Zonal Geometry and Topology::ZoneSimpleGeometry
Table 21 — Elements of Zonal Geometry and Topology::ZoneSimpleTopology
ZoneSimpleTopology is a one-, two- or three-dimensional spatial topology that is invariant over all time, OR a one-dimensional temporal topology that is invariant over all space. | |||||||
Table 22 — Elements of Zonal Geometry and Topology::ZoneTopology
ISO 19112:2019 describes spatial refencing by geographic identifiers, locations and location classes. The LocationS interface is a specialisation of the Location interface from ISO 19112:2019. See Figure 6. In the next section the Period interface is introduced as the temporal equivalent of LocationS.
Table 23 — Elements of Spatial Location::LocationS
Table 23 — Elements of Spatial Location::LocationS
Particular place or position. | |||||||
Semantically, the terms period and zone are defined as the temporal and spatio-temporal equivalents of a location. These are represented in the data model by the interfaces Period and Zone.
Referring to Figure 7 showing the spatial classes on the left and the temporal classes on the right, it is noted that Period is augmented by:
PeriodIdentifier data-type as the temporal equivalent of GeographicIdentifier,
Period interface as the temporal equivalent of LocationS, see Figure 6,
PeriodClass interface as the temporal equivalent of LocationClass, and
TemporalReferenceSystemusingPeriodIdentifiers interface as the temporal equivalent of SpatialReferenceusingGeographicIdentifiers.
Table 24 — Elements of Temporal RS using Identifiers::Period
Table 25 — Elements of Temporal RS using Identifiers::PeriodClass
Table 26 — Elements of Temporal RS using Identifiers::PeriodIdentifier
Table 27 — Elements of Temporal RS using Identifiers::TemporalReferenceSystemUsingPeriodIdentifiers
Table 24 — Elements of Temporal RS using Identifiers::Period
Table 25 — Elements of Temporal RS using Identifiers::PeriodClass
Table 26 — Elements of Temporal RS using Identifiers::PeriodIdentifier
Table 27 — Elements of Temporal RS using Identifiers::TemporalReferenceSystemUsingPeriodIdentifiers
Semantically zones are the spatio-temporal equivalent of periods and locations. Zones are represented in the data model by the interface Zone and along with it the following interfaces are also established.
ZonalIdentifier,
ZoneClass, and
RSUsingZonalIdentifiers.
Referring to Figure 8, a ZonalIdentifier is either a zonal identifier primitive or a compound of two zonal identifier primitives, one spatial and one temporal.
Referring to Figure 9, a Zone is either a zonal primitive or a compound of two zonal primitives, one spatial and one temporal.
Referring to Figure 10, a ZoneClass is either a zonal class primitive or a compound of two zonal class primitives, one spatial and one temporal.
Referring to Figure 11, an RSUsingZonalIdentifiers is either a zonal RS using identifiers primitive or a compound of two of its primitives, one spatial and one temporal.
Referring to Figure 12, Zone, ZonalIdentifier and ZoneClass come together to form RSUsingZonalIdentifiers.
Table 28 — Elements of Zonal RS using Identifiers::RSUsingZonalIdentifiers
Table 29 — Elements of Zonal RS using Identifiers::RSUsingZonalIdentifiersCompound
Table 30 — Elements of Zonal RS using Identifiers::RSUsingZonalIdentifiersPrimitive
Table 31 — Elements of Zonal RS using Identifiers::ZonalIdentifier
Table 32 — Elements of Zonal RS using Identifiers::ZonalIdentifierComplex
Table 33 — Elements of Zonal RS using Identifiers::ZonalIdentifierPrimitive
Table 34 — Elements of Zonal RS using Identifiers::Zone
Table 35 — Elements of Zonal RS using Identifiers::ZoneClass
Table 36 — Elements of Zonal RS using Identifiers::ZoneClassComplex
Table 37 — Elements of Zonal RS using Identifiers::ZoneClassPrimitive
Table 38 — Elements of Zonal RS using Identifiers::ZoneCompound
Table 39 — Elements of Zonal RS using Identifiers::ZonePrimitive
Table 28 — Elements of Zonal RS using Identifiers::RSUsingZonalIdentifiers
Table 29 — Elements of Zonal RS using Identifiers::RSUsingZonalIdentifiersCompound
A reference system using zonal identifiers compound is a compound of one spatial reference system using zonal identifiers and one temporal reference system using zonal identifiers primitives. | |||||||
Table 30 — Elements of Zonal RS using Identifiers::RSUsingZonalIdentifiersPrimitive
A reference system using zonal identifiers primitive is either a spatial reference system using geographic identifiers or a temporal reference system using period Identifiers. | |||||||
Table 31 — Elements of Zonal RS using Identifiers::ZonalIdentifier
Spatial, temporal or spatio-temporal reference in the form of a label or code that identifies a zone. | |||||||
Table 32 — Elements of Zonal RS using Identifiers::ZonalIdentifierComplex
Zonal identifier complex is a complex of two zonal identifier primitives, one geographic identifier and one period identifier. | |||||||
Table 33 — Elements of Zonal RS using Identifiers::ZonalIdentifierPrimitive
Table 34 — Elements of Zonal RS using Identifiers::Zone
Table 35 — Elements of Zonal RS using Identifiers::ZoneClass
Table 36 — Elements of Zonal RS using Identifiers::ZoneClassComplex
Zone class complex is a complex of two zone class primitives, one location class and one period class. | |||||||
Table 37 — Elements of Zonal RS using Identifiers::ZoneClassPrimitive
Table 38 — Elements of Zonal RS using Identifiers::ZoneCompound
Table 39 — Elements of Zonal RS using Identifiers::ZonePrimitive
This clause specifies the DGGS Core RS conformance class and the DGGS Core Functions conformance class. These cover:
DGGS Core RS — comprising parent global geometry, base CRS, and RS using zonal identifiers with structured geometry;
DGGS Core Functions — comprising quantization, topological query, and interoperation.
The DGGS Core RS shown in Figure 13 is a RS using zonal identifiers with structured geometry for a globe. It is defined by the attributes of the DGG_ReferenceSystem interface Table 41 and its metadata. In the context of the DGGS, and particularly in the DGGS Core, the term globe is used in its most general sense to represent a mathematical model of any planetary body and, depending on need, potentially its surroundings out to the orbit of a planet’s outer moons, and for spatio-temporal DGGS over a defined time span. The spatio-temporal extent of the entire globe is referred to as the domain of the DGGS. The DGGS Core itself is dimension agnostic.
The DGGS Core RS model in Figure 13 describes a hierarchy of paired elements — at each tier of the hierarchy a geometry element, shown on the left of the figure is paired with the equivalent zonal element, shown on the right of the figure.
At the root of the hierarchy, the globe’s reference model and base CRS for the DGGS are defined. A single parent geometry (GlobeGeometry) is defined to coincide with the globe’s reference model. The parent geometry’s dimensionality governs the dimensionality of the DGGS (See Clause 8.2.3). The parent global geometry is paired with a RS using zonal identifiers (RSUsingZonalIdentifiers).
A sequence of discrete global grids (DiscreteGlobalGrids), each paired with a ZoneClass, define the lower levels of the hierarchy.
Each DiscreteGlobaGrid is made up of Cells. Each Cell occupies a region of space-time (a Zone). The Zones corresponding to Cells in a DiscreteGlobaGrid all belong to the corresponding ZoneClass (See Clause 8.2.5).
Cells provide zones with geometry and topology, and zones provide cells with names in the form of zonal identifiers and representative positions in the base CRS in the form of direct positions (See Clause 8.2.4).
Each cell is the child of one or more parent cells in the parent discrete global grid in the level above in the hierarchy. The cells of a discrete global grid are topologically related to the cells in the parent(s) by the collection of refinement strategies defined in DGG_ReferenceSystem(DGGS_Refinement).
Each cell’s geometry, orientation and size is governed by the constraint defined in DGG_ReferenceSystem(DGGS_Grids) and by the sequence of refinement ratios defined in DGG_ReferenceSystem(DGGS_RefinementRatio). If a sequence of refinementRatio is defined, the values are applied to each level in the hierarchy in a recurring sequence starting at the top with the first refinementRatio in the sequence and working down through the levels in order.
Table 40 — Elements of Core RS using Zonal Identifiers with Structured Geometry::Cell
Table 41 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_ReferenceSystem
Table 42 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_ReferenceSystemType
Table 43 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DiscreteGlobalGrid
Table 44 — Elements of Core RS using Zonal Identifiers with Structured Geometry::GlobeGeometry
Table 45 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_GridConstraint
Table 46 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_RefinementStrategy
Table 40 — Elements of Core RS using Zonal Identifiers with Structured Geometry::Cell
Reference system unit of geometry associated with a Zone. As part of GlobeGeometry, it has the same spatial, temporal and topological dimensionality as GlobeGeometry. | |||||||
Table 41 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_ReferenceSystem
Table 42 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_ReferenceSystemType
Table 43 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DiscreteGlobalGrid
Ratio of the number of cells in the parent DiscreteGlobalGrid to the number in this DiscreteGlobalGrid. | |||||||
Table 44 — Elements of Core RS using Zonal Identifiers with Structured Geometry::GlobeGeometry
Table 45 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_GridConstraint
Table 46 — Elements of Core RS using Zonal Identifiers with Structured Geometry::DGG_RefinementStrategy
The following requirements apply:
Requirement 6 | |
---|---|
www.opengis.net/spec/DGGS/2.0/req/core/rs/harmonized_model | |
The data model for a DGGS RS and its element definitions shall comply with the DGGS Core RS data model in Figure 13 and definitions in Table 40–Table 46. |
The domain of the DGGS shall be defined as the entire globe, with cells that “exhaustively cover the globe without overlapping or underlapping” (Goodchild [7]). Applying these criteria to the cells in each discrete global grid, there shall be no gaps between cells and no positions that are covered by more than one cell.
Each cell inherits its dimensionality from the choice of geometry for the GlobalGeometry class, so a reference system that specifies a geometry and domain as the globe’s surface will have two-dimensional cells on the surface of the globe, and one that specifies a geometry and domain as a globe’s volume will have three-dimensional cells filling the globe. A reference system that specifies a linear geometry and domain, for instance for time, will result in one-dimensional cells.
The following requirements apply:
Requirement 9 | |
---|---|
www.opengis.net/spec/DGGS/2.0/req/core/rs/global_domain/complete | |
DGGS RS domain completeness — the level zero discrete global grid shall cover the entire global domain. |
Semantically, the terms cell and zone refer to different characteristics of the same region of space-time. Cells in a DGGS shall be geometrically simple. Simple geometries have the following properties:
they do not self-intersect;
they are topologically the same as a circle, or the circle’s equivalent in the dimension of the cell. e.g. to a sphere in three-dimensions; and
they enclose a region which is always measurable using a metric of the same dimensionality as the cell.
Each cell’s zone has a fixed representative position in the space of the base CRS, recorded as a direct position.
Each cell’s zone shall be assigned a unique address in the form of a zonal identifier. The value assigned to each address shall be structured on one or more of these four general indexing methods: hierarchy-based, space-filling curve based, coordinate [1] and encoded address schemas (such as those used for IP addresses [10]).
Cells at the same level in the tessellation hierarchy are aggregated into discrete global grids. The hierarchy of discrete global grids is an ordered sequence, typically also of decreasing cell size, representing the lowest resolution to higher resolutions. The discrete sequence of grids forms a multi-resolution grid hierarchy that is the basis for the DGGS RS.
The following requirements apply:
Requirement 14 | |
---|---|
www.opengis.net/spec/DGGS/2.0/req/core/rs/discrete_global_grid | |
A DGGS RS shall define discrete global grids as aggregations of all the cells at the same level in the hierarchy. |
A DGGS is defined based on the geometry of the globe in a data agnostic manner. Therefore, a DGGS specification shall define quantization methods for assigning data to cells so that the data is accessible for future use. Different quantization strategies may be used for sampling content into cells. For example, a single DGGS may be used as a data structure for integrating multiple datasets of different types (e.g. vector and raster datasets)[9] and in different ways (e.g. DGGS cells as data tiles, or one raster pixel per DGGS cell or DGGS cell indices as vector coordinate-pairs). This abstract specification makes use of the concepts defined by ISO 19156:2011 to facilitate the association of observations/spatial data to a DGGS cell(s). Some DGGS/polyhedron choices are more efficient for sampling than others (e.g. DGGS based on an icosahedron).
Multiple observation contexts are recognized for quantization, each corresponding to a distinct role for DGGS cells to play. In any particular DGGS specification, one or more (and potentially all) roles may be described for either internal or external use to support interoperability, as follows:
asDataTiles: In data tile quantization, spatial feature/observations (e.g. point clouds, images, vectors, etc.) are aggregated and clipped to cell boundaries and stored in tiles without any changes made to the feature type parameters. The cells of the DGGS provide a multi-, or single-resolution tiling schema with the cell index used as the identifier in the tile naming convention. In the context of “Big Data Analytics”, ‘asDataTile’ support will likely be the most efficient type of granularity for job submission on HPC/HPD or Cloud ICT infrastructure, particularly for dominantly embarrassingly parallel analyses. It is also likely to be the most efficient granularity for many data transfer requests.
asDataCells: In data cell quantization, the spatial features/observations (e.g. point clouds, images, vectors, etc.) are sampled to each DGGS cell by assignment of data value(s) using the cell’s geometry to govern the quantization operation.
asCoordinates: In coordinate quantization, each coordinate tuple from the spatial feature/observation is converted to a cell index of an appropriate level of precision. The cell data package will include appropriate vector topology to preserve the structure of the spatial feature in the context of the DGGS.
asTags: In tag quantization, cell index values are “tagged” to data objects in a similar fashion to social media records. The refinement level of the cell index is indicative of the precision with which the location of a spatial feature/observation and/or its spatial extent are known. This can be thought of as a convex hull with the same geometry of the DGGS cell surrounding the objects to be assigned to that cell.
asGraphicCells: In graphic cell quantization, data is rendered to cells, and refinement levels are leveraged to support corresponding levels of detail or zoom levels.
asGraphicTiles: In graphic tile quantization, graphic cells are tiled, and often cached for delivery to a display system. As with data tiles, the cell index is used as the identifier in the tile naming convention.
The extent of the data assigned at any time to a particular DGGS implementation, defines the DGGS’s extent. The extent is likely to vary over the DGGS’s lifecycle as the extent of data assigned to it changes. The domain of the DGGS, is however, always fixed and always defined over the entire surface model of the DGGS’s globe.
Figure 14 shows the key elements required to perform data quantization operations in a DGGS specification.
Table 47 — Elements of Core Quantization Functions::DataAssignmentProcess
Table 48 — Elements of Core Quantization Functions::DGG_Observation
Table 49 — Elements of Core Quantization Functions::QuantizationContext
Table 50 — Elements of Core Quantization Functions::QuantizationFunctions
Table 51 — Elements of Core Quantization Functions::Quantisation
Table 47 — Elements of Core Quantization Functions::DataAssignmentProcess
Table 48 — Elements of Core Quantization Functions::DGG_Observation
Table 49 — Elements of Core Quantization Functions::QuantizationContext
Table 50 — Elements of Core Quantization Functions::QuantizationFunctions
Table 51 — Elements of Core Quantization Functions::Quantization
The Topological Query Functions module implements the DE9IM [5] functionality defined in ISO 19107:2019 Geometry::Query2D and Geometry::Query3D for zonal topology. This is achieved through a single interface called ZoneQuery (Figure 16, Table 53). By default ZoneQuery operates at the dimensionality of the DGGS’s zones. Changes in dimensionality are controlled with an optional parameter projectTo that constrains ZoneQuery to a specified reference direction, surface or volume.
Two additional operations are provided that are based on the temporal concept of relative position. These are called relatePosition and relativePosition. These are generalized for use on any single reference direction specified by projectTo, not just the temporal direction.
Six additional operations are provided in ZoneQuery that leverage the ZoneClass hierarchy. These are called parent, child and sibling and parentOf, childOf and siblingOf.
ZoneQuery operations are defined in Figure 16 and Clause 8.3.4. The following parameters are shared by many of the operations as specified in <Table 53
another |
type ZonalIdentifier, mandatory. |
inheritID |
type Boolean, optional, default ⇐ False |
projectTo |
type directPosition[4], optional, default ⇐ (0,0,0,1) for relatePosition and relativePosition, otherwise (1,1,1,1) |
rangeRefine |
type refinementLevelRange, optional, default ⇐ [ min(source.refinementLevel,target.refinementLevel) : max(source.refinementLevel,target.refinementLevel) ]. |
levels |
type Integer, optional, default ⇐ 1 |
The following operations have the same topological meaning as their equivalent operations in ISO 19107:2019 Geometry::Query2D and Geometry::Query3D: distance, contains, crosses, disjoint, equals, intersects, overlaps, touches, within, withinDistance, difference, intersection, symDifference, union, and relate.
relativePosition: A.relativePosition(B, projectTo), returns the relativePosition enumerator that describes B‘s relative position to A with respect to the direction defined by projectTo.
relatePosition: A.relatePosition(B, relation, projectTo) returns whether B has the relative position to A given by relation with respect to the direction projectTo
parentOf: A.parentOf(B, inheritID, projectTo), returns whether A is a parent cell of B, optionally filtered by inheritID and projectTo.
childOf: A.childOf(B, inheritID, projectTo), returns whether A is a child cell of B, optionally filtered by inheritID and projectTo.
siblingOf: A.siblingOf(B, inheritID, projectTo), returns whether A is a sibling cell of B, optionally filtered by inheritID and projectTo.
parent: A.parent(inheritID, projectTo, levels), returns the unique «set» of zoneIdentifiers for zones that satisfy A.parentOf(B, inheritID, projectTo) applied recursively levels times up the parent hierarchy. The «set» will have at most one member from each level of the hierarchy if inheritID is True, and may have more than one if the cell refinementStrategy is not nested.
child: A.child(inheritID, projectTo, levels), returns the unique «set» of zoneIdentifiers for zones that satisfy A.parentOf(B, inheritID, projectTo) applied recursively levels times down the parent hierarchy.
sibling: A.sibling(inheritID, projectTo, levels), returns the unique «set» of zoneIdentifiers for zones that satisfy A.parentOf(B, inheritID, projectTo) applied recursively levels times outward on zones at the same refinement level. Multiple levels of sibling can also be thought of as the children of its parent(s) the specified number of levels up the hierarchy.
Further query and analysis functions may then be applied to the returned data through additional software bindings. This abstract specification does not specify any requirements for the binding or implementation of further, extension, query or analytic functions.
Table 52 — Elements of Core Topological Query Functions::refinementLevelRange
Table 53 — Elements of Core Topological Query Functions::ZoneQuery
Table 54 — Elements of Core Query Functions::RelativePosition
Table 52 — Elements of Core Topological Query Functions::refinementLevelRange
Table 53 — Elements of Core Topological Query Functions::ZoneQuery
Table 54 — Elements of Core Topological Query Functions::RelativePosition enumeration
Enumeration for the relative position of two geometries projected to a single uni-directional dimension, e.g. time. | |||||||
Definition: | |||||||
self.begin < another.begin AND self.end > another.begin AND self.end < another.end | |||||||
While the quantization and topological query functions enable a DGGS implementation to successfully operate internally, in order to facilitate connectivity with other spatial data infrastructures additional interoperation functions are required. As shown in Figure 17, the interoperation functions are split into two modules:
Interoperation Query: Interpret and translate external data queries sent to the DGGS implementation; and
Interoperation Broadcast: Convert the result set returned from a DGGS query operation from internal data format(s) (optimized for that DGGS implementation) to format(s) suitable for external data delivery.
This document does not specify the specific interface protocol encodings required to connect a DGGS implementation to an external client and to facilitate the transfer of information into and out of a DGGS. This abstract specification makes use of the tools available in ISO 19156:2011 to facilitate the linkage between external query operations and the data/observations assigned to the DGGS zone(s) of interest. Specific interface encodings are anticipated to be elaborated as extensions to this abstract specification.
Table 55 — Elements of Interoperation::InteroperationFunctions
Table 55 — Elements of Interoperation::InteroperationFunctions
External queries may originate from an external client application and range in syntax from natural language queries (e.g. ‘Where are the gas pipelines in Western Canada located?’, or ‘How has the Murray-Darling Basin in Australia changed over the past 27 years?’, or ‘Compute the watershed area of the Kawarau Catchment in New Zealand’), to an OWS ‘GetCapabilities’ or similar type of query, to an SQL (or similar) statement. To support interoperability, a DGGS specification shall define methods to receive, interpret and translate an external data query (or process) request into a form that can be processed by the internal DGGS data retrieval and query functions.
Figure 18 shows the key functional elements required for DGGS to translate and execute an external query or process operations.
Table 56 — Elements of Interoperation Query::QueryComponents
Table 57 — Elements of Interoperation Query::QueryFunctions
Table 58 — Elements of Interoperation Query::QueryResult
Table 59 — Elements of Interoperation Query::QueryType
Table 56 — Elements of Interoperation Query::QueryComponents
Table 57 — Elements of Interoperation Query::QueryFunctions
Table 58 — Elements of Interoperation Query::QueryResult
Table 59 — Elements of Interoperation Query::QueryType
Just as it is necessary for DGGS to be able to interpret and execute external data queries, DGGS shall also define methods to broadcast results from data queries to external client(s) or data infrastructure(s). External clients are anticipated to be web-based client(s), software client(s) on the same ICT infrastructure as the DGGS, or other DGGS.
Figure 19 shows basic elements required to translate the result set(s) returned from a DGGS data query into a suitable data format for transfer and broadcast the reformatted result set via one or a number of data or information transfer protocols.
Table 60 — Elements of Interoperation Broadcast::BroadcastFunctions
Table 61 — Elements of Interoperation Broadcast::TranslationType
Table 62 — Elements of Interoperation Broadcast::TranslationType
Table 60 — Elements of Interoperation Broadcast::BroadcastFunctions
Table 61 — Elements of Interoperation Broadcast::BroadcastType
Table 62 — Elements of Interoperation Broadcast::TranslationType
The following requirement applies:
Requirement 19 | |
---|---|
www.opengis.net/spec/DGGS/2.0/req/core/functions/interoperation/broadcast | |
A DGGS specification shall implement operations to translate data results from interoperation queries to standard data formats and broadcast the reformatted result set that conform to the data model in Figure 17 and Figure 19, and definitions in Table 55 and Table 60–Table 62. |
This clause specifies the Equal-Area Earth RS module.
For a DGGS RS that is conformant with the DGGS Core to be an EAERS, it shall satisfy all the requirements for the Equal-Area Earth DGGS package.
The data model supports DGGS EAERS based on either static or dynamic datums. Care shall be taken when implementing DGGS with static datums. Static CRS are by their nature only intended for use on one tectonic plate. However the definition for a DGGS always has a global domain. This apparent conundrum is resolved in two ways:
Orientation: Noting that some static CRS have one or more points on the Earth’s surface where the underlying mathematics is poorly behaved, orient the EA_BaseUnitPolyhedron so that areas, centroids, vertices, and edges can be computed; and
Precision: On the tectonic plate where the reference frame is static choose the level of DGGS precision to suit the intended use of the DGGS (typically in the range of millimetres to 10s of metres), and in areas of the Earth on plates that are moving with respect to the static reference frame choose the level of DGGS precision to reflect the larger of the constraints imposed by the mathematics and by plate tectonics (typically in the of range 10s to 100 000s of metres).
Dynamic datums present problems of a different form. The most frequently used is WGS 84, which is a datum ensemble. Care shall be taken to ensure that the error budget for EA_Cell’s area is set at a value that caters to the level of approximation in the WGS 84 definition.
Figure 20, Figure 21 and Figure 22 show the data models for modules in the Equal-Area Earth DGGS package.
See Clause 9.1.2 for definitions of elements in this Figure.
See Clause 9.1.4.5 for definitions of elements in this Figure.
See Clause 9.1.5.4 for definitions of elements in this Figure.
Table 63 — Elements of Equal-Area Earth RS::EA_DGG_ReferenceSystem
Table 64 — Elements of Equal-Area Earth RS::EA_GlobeGeometry
Table 65 — Elements of Equal-Area Earth RS::EA_ReferenceSystemType
Table 66 — Elements of Equal-Area Earth RS::EA_SurfaceInterpolation
Table 63 — Elements of Equal-Area Earth RS::EA_DGG_ReferenceSystem
Table 64 — Elements of Equal-Area Earth RS::EA_GlobeGeometry
Table 65 — Elements of Equal-Area Earth RS::EA_ReferenceSystemType
Table 66 — Elements of Equal-Area Earth RS::EA_SurfaceInterpolation class
For a DGGS RS to be an EAERS, the domain shall be defined as the entire surface of the Earth.
A multiresolution hierarchical tessellation of cells is created by constructing a sequence of discrete global grids, each with successively finer cell resolutions. First an initial discrete global grid is constructed as described in subclause Clause 9.1.4.2. The cells of this initial tessellation are then iteratively refined by application of cell refinement method(s) [2] to create finer resolution child cells. The initial tessellation, the cell shape, the refinement methods and indexing methods may all vary for different DGGSs.
The entire surface of the Earth is partitioned to a finite/discrete set of regions. Most methods initially approximate the Earth’s surface using a simple base unit polyhedron which is scaled so that all vertices are located on the surface model of the Earth, and the edges are warped so they also lie on the surface model. The resulting edges may be any of the types listed in EA_CurveType. These include geodesics, small circles, small ellipses and lines that project to a straight line on a plane. These all result from intersections of a plane and an ellipsoid. The initial discrete global grid tessellation has the same form as the base unit polyhedron. Each EA_Cell of the initial tessellation represents one face of the chosen base unit polyhedron mapped to the chosen surface model of the Earth. This document refers to the initial tessellation as a “polyhedral tessellation”. The most common choices for an initial base unit polyhedron are discussed in subclause Annex C.4 [2].
DGGS EAERS comprise a discrete sequence of global grids formed from recursive application of a tessellation method to refine the grid cells, so that each global grid has a progressively finer spatial resolution.
The following requirements apply:
Preservation of total surface area throughout the range of hierarchical tessellations is a necessary property of DGGSs in order to represent information consistently at successive resolutions. This requirement ensures that each level of grid refinement completely covers the Earth’s surface without cell overlaps.
The following requirement applies:
Table 67 — Elements of Equal-Area Tessellation::EA_BaseUnitPolyhedron
Table 68 — Elements of Equal-Area Tessellation::EA_DiscreteGlobalGrid
Table 69 — Elements of Equal-Area Tessellation::EA_DiscreteGlobalGridTessellation
Table 70 — Elements of Equal-Area Tessellation::EA_InitialDiscreteGlobalGrid
Table 71 — Elements of Equal-Area Tessellation::EA_PolyhedralTessellation
Table 72 — Elements of Equal-Area Tessellation::EA_RefinedDiscreteGlobalGrid
Table 67 — Elements of Equal-Area Tessellation::EA_BaseUnitPolyhedron
Table 68 — Elements of Equal-Area Tessellation::EA_DiscreteGlobalGrid
Table 69 — Elements of Equal-Area Tessellation::EA_DiscreteGlobalGridTessellation
Table 70 — Elements of Equal-Area Tessellation::EA_InitialDiscreteGlobalGrid
The EA_InitialDiscreteGlobalGrid is formed by applying the EA_PolyhedralTessellation method to a EA_BaseUnitPolyhedron. | |||||||
Table 71 — Elements of Equal-Area Tessellation::EA_PolyhedralTessellation
Table 72 — Elements of Equal-Area Tessellation::EA_RefinedDiscreteGlobalGrid
EA_Cells are simple polygons formed from an ordered set of boundary curves adhering to the geometric reference surface of the Earth model. EA_Cells are defined in three-dimensional space and are topologically two-dimensional. Different cell shapes can be used, typically triangle, quadrilateral, pentagon, hexagon, and octagon. Cells formed from faces of the five (5) Platonic solids (tetrahedron-triangle, cube-quadrilateral, octahedron-triangles, dodecahedron-pentagons, icosahedron-triangles) all satisfy the requirements for simple cells. Larger numbers of faces and therefore cells at the top of the hierarchy of tessellations, increases the uniformity of the cell shape. The truncated icosahedron, with thirty-two (32) faces is often used for DGGSs. It produces mostly hexagons augmented by twelve (12) pentagons in each tessellation. Each cell shape has its own advantages and disadvantages [2] and it is usually desirable for each refined discrete global grid to have a majority of cells with the same shape [8],[9]. Triangular, quadrilateral and hexagonal cells are common choices used in DGGSs on the surface of the Earth. These shapes provide regular tiling of the plane [8], which can be mapped to a curved surface such as a spherical or ellipsoidal Earth surface model.
The cell structures in each successive level of cell refinement are constrained by the properties of the initial tessellation, but do not necessarily have the same geometry as the initial tessellation. Simple two-dimensional cells have the following properties:
edges meet only at the vertices;
exactly two edges meet at each vertex;
exactly the same number of edges and vertices; and,
enclose a region which always has a measurable area.
Each EA_Cell shall be referenced at its centroid. This is because the centroid is the only location that provides a representative point that behaves consistently with shape and is invariant under orientation. The representative point for an EA_Cell shall lie on the surface of the cell. For curved surfaces, the “centre of gravity” computed in three-dimensions cannot actually lie on the surface (see 6.4.4.8). If, however, the “centre of gravity” is computed using distances computed along geodesic arcs on the curved surface, then the centroid is constrained to lie on the surface. This is a centroid calculated as the “geodesic centre of surface area” of an EA_Cell.
The centroid enables a dual representation of a DGGS tessellation as both two-dimensional areal cell grids and as point-based lattices of cell reference locations.
This document defines an EAERS based on a hierarchy of equal area tessellations. Cells of equal area provide global grids with spatial units that (at multiple resolutions) have an equal probability of contributing to an analysis. Equal area cells also help to minimize the confounding effects of area variations in spatial analyses where the curved surface of the earth is the fundamental reference frame.
In an EAERS the unit of measure is a unit of area, not length as in a cartesian XYZ coordinate system or angle as in an ellipsoidal coordinate system. For angular measures the degree is defined as one 360th integer fraction of a full circle, and by analogy the areal unit of measure of a DGGS coordinate reference system is an integer fraction of the surface area of the chosen ellipsoidal surface model for the earth. For DGGSs the integer fraction is the number of cells in the initial discrete global grid. Continuing the angular analogy with minutes being 1/60th of a degree and seconds being 1/60th of a minute, for DGGSs, recursive use of the refinement ratio generates a sequence of smaller areal units, one for each refined discrete global grid.
Standard units of measure are defined through a reference measure with defined precision. The meter unit of length has been redefined a number of times as technology has improved. For example:
From 1793: 1/10 000 000 of the meridian through Paris between the North Pole and the Equator (+/- ~10-4 m); and
From 1983: The length of the path travelled by light in a vacuum in 1/299 792 458th of a second (+/- 10-10 m).
To address the need for transparency of the precision in its units of area, this document uses the concept of a specified error budget. The error budget takes into account all sources of variation that are relevant to the particular DGGS, its derivation, and its expected use. For most day to day uses, most of these sources contribute errors that are significantly smaller than the precision required of the DGGS. However, as technology pushes the limits of available precision, use-cases demand combining data from highly disparate sources, and users push their expectations, it becomes increasingly important to know when limits of use are reached.
The sources considered for inclusion in the error budget can include:
spatial variation: whether the available precision of each source of error is uniform or variable across the DGGS’s domain;
datum: precision of the underlying measurements for the datum;
static datum: precision of the assertion that the coordinates are static both on the tectonic plate the datum is tied to, and away from the static plate;
earth model: differences between the chosen ellipsoidal or spherical earth model and the real earth’s surface. Spheres lead to faster and more precise computations for the tessellations but have a less precise fit to the real earth’s surface.
While implementation issues are beyond the scope of this document, the following sources may contribute to increases in error budgets for an implementation:
spherical maths: exact solutions are available for solving the required mathematics on the surface of a sphere;
ellipsoidal maths: solving the required mathematics on the surface of an ellipsoid requires the use of iterative numerical methods which result in approximate solutions with an uncertainty determined by both the method and the number of iterations used to perform the computation;
data-type precision: most will probably use 64-bit double precision for location, anything less will have a significant impact on the error budget;
cell edge type: geodesics, small circles, small ellipses, and projected lines each have different solutions with different consequences for their precision and performance. At finer resolutions it may be possible to implement a simpler edge type and still stay within the implementation error budget;
error propagation: the choice of strategy for implementing the sequence of tessellations.
The error budget puts a limit on the number of iterations in the sequence of refined discrete global grids. This is acknowledged in the requirements.
DGGSs may validly comprise more than one cell geometry. This most typically arises for systems based on truncated polyhedra such as the cuboctahedron — with both square and triangular faces, and the truncated icosahedron — with pentagonal and hexagonal faces. In these situations, equal area is interpreted to mean that all of the cells of a particular geometry are equal area, and that the ratio of the areas of the two geometries is preserved through the tessellations. For example, in the truncated icosahedron used by ISEA the ratio of pentagonal to hexagonal areas within a tessellation level is always 5/6.
The following requirements apply:
Table 73 — Elements of Equal-Area Cell::EA_BoundaryData
Table 74 — Elements of Equal-Area Cell::EA_Cell
Table 75 — Elements of Equal-Area Cell::EA_Zone
Table 76 — Elements of Equal-Area Cell::EA_BoundaryType
Table 73 — Elements of Equal-Area Cell::EA_BoundaryData
Curve data for the permitted boundary types. greatCircle and greatEllipse boundary types use the same data types as smallCircle and smallEllipse respectively. | |||||||
Table 74 — Elements of Equal-Area Cell::EA_Cell
Table 75 — Elements of Equal-Area Cell::EA_Zone
Table 76 — Elements of Equal-Area Cell::EA_BoundaryType
This annex specifies Abstract test suites for the conformance categories in this document. The requirement tests associated with each conformance category are listed in Table A.1–Table A.3. Tests identifiers below are relative to http://www.opengis.net/spec/dggs/2.0/
The requirement tests that apply to each conformance category in the Common Spatio-temporal Classes package are listed in Table A.1
Table A.1 — Conformance classes for Common Spatio-temporal Classes package
Conformance class | Requirement tests |
Temporal geometry and topology | Annex A.1, Requirement test A.1 |
Temporal reference systems using period identifiers | Annex A.1, Requirement test A.4 |
Spatial zone geometry and topology | Annex A.1, Requirement test A.2 |
Spatial reference systems using zonal identifiers | Annex A.1, Requirement test A.3, & Annex A.1, Requirement test A.5 |
Spatio-temporal zone geometry and topology | Annex A.1, Requirement test A.1, & Annex A.1, Requirement test A.2 |
Spatio-temporal reference systems using zonal identifiers | Annex A.1, Requirement test A.3, Annex A.1, Requirement test A.4, & Annex A.1, Requirement test A.5 |
Requirement test A.1: Common Spatio-temporal Classes — Temporal — Geometry | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 7.2.1.2, Requirement 1: http://www.opengis.net/spec/DGGS/2.0/req/cc/temporal/geometry |
Reference subclause | |
Test purpose |
To verify the common classes for temporal geometry and topology conform to the data model in Figure 3 and Figure 4, and defining tables in Table 5–Table 16. |
Test method |
Requirement test A.2: Common Spatio-temporal Classes — Zone — Geometry | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 7.2.2.2, Requirement 2: http://www.opengis.net/spec/DGGS/2.0/req/cc/zone/geometry |
Reference subclause | |
Test purpose |
To verify the common classes for zonal geometry and topology conform to the data model in Figure 5 and defining tables in Table 17–Table 22. |
Test method |
Requirement test A.3: Common Spatio-temporal Classes — Spatial — Location | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 7.3.1.2, Requirement 3: http://www.opengis.net/spec/DGGS/2.0/req/cc/spatial/location |
Reference subclause | |
Test purpose |
To verify the common classes for spatial location conform to the data model in Figure 6 and defining tables in Table 23. |
Test method |
Requirement test A.4: Common Spatio-temporal Classes — Temporal — Reference system using period identifiers | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 7.3.2.2, Requirement 4: http://www.opengis.net/spec/DGGS/2.0/req/cc/temporal/rsupi |
Reference subclause | |
Test purpose |
To verify the common classes for reference systems using period identifiers conform to the data model in Figure 6 and defining tables in Table 24–Table 27. |
Test method |
Requirement test A.5: Common Spatio-temporal Classes — Zone — Reference system using zonal identifiers | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 7.3.3.2, Requirement 5: http://www.opengis.net/spec/DGGS/2.0/req/cc/zone/rsuzi |
Reference subclause | |
Test purpose |
To verify the common classes for reference systems using zonal identifiers conform to the data model in Figure 8–Figure 12 and defining tables in Table 28–Table 39. |
Test method |
The requirement tests that apply to each conformance category in the DGGS Core package are listed in Table A.2
Table A.2 — Conformance classes for DGGS Core package
Conformance class | Requirement tests |
Spatial DGGS Core | Annex A.1, Requirement test A.2, Annex A.1, Requirement test A.3, Annex A.1, Requirement test A.5, and all Core requirements in Annex A.2.1, Requirement test A.6–Annex A.2.2, Requirement test A.19. |
Spatio-temporal DGGS Core | Annex A.1, Requirement test A.1, Annex A.1, Requirement test A.2, Annex A.1, Requirement test A.3, Annex A.1, Requirement test A.4, Annex A.1, Requirement test A.5, and all Core requirement tests in Annex A.2.1, Requirement test A.6–Annex A.2.2, Requirement test A.19. |
Requirement test A.6: Core — Reference system — Harmonized model | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.2, Requirement 6: http://www.opengis.net/spec/DGGS/2.0/req/core/rs/harmonized_model |
Reference subclause | |
Test purpose |
To verify that all DGGS RS classes comply with classes in the DGGS Core RS data model in Figure 13 and definitions in Table 40–Table 46. |
Test method |
Requirement test A.7: Core — Reference system — CRS | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.2, Requirement 7: http://www.opengis.net/spec/DGGS/2.0/req/core/rs/crs |
Reference subclause | |
Test purpose |
To verify that the DGGS RS defines a CRS and complies with coordinate epoch requirements as specified for MD_ReferenceSystem. |
Test method |
Requirement test A.8: Core — Reference system — Global Domain | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.3, Requirement 8: http://www.opengis.net/spec/DGGS/2.0/req/core/rs/global_domain |
Reference subclause | |
Test purpose |
To verify a DGGS RS specifies a global domain, and its spatial, temporal and topological dimensionality. |
Test method |
Requirement test A.9: Core — Reference system — Global Domain — Complete | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.3, Requirement 9: http://www.opengis.net/spec/DGGS/2.0/req/core/rs/global_domain/complete |
Reference subclause | |
Test purpose |
To verify reference system domain completeness, with the level zero discrete global grid covering the entire global domain. |
Test method |
Requirement test A.10: Core — Reference system — Global Domain — Unique | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.3, Requirement 10: http://www.opengis.net/spec/DGGS/2.0/req/core/rs/global_domain/unique |
Reference subclause | |
Test purpose |
To verify reference system domain uniqueness, with every location in the domain of the DGGS located in exactly one cell of the level zero discrete global grid. |
Test method |
Requirement test A.11: Core — Reference system — Cell — Simple | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.4.1, Requirement 11: http://www.opengis.net/spec/DGGS/2.0/req/core/cell/simple |
Reference subclause | |
Test purpose |
To verify that all the cells of a DGGS specification have shapes that are simple geometry, where the geometry of the cell: does not self-intersect; is topologically the same as the equivalent shape of a circle with the cell’s dimensionality; and encloses a region that is measurable in the cell’s metric. |
Test method |
Requirement test A.12: Core — Reference system — Cell — Direct position | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.4.2, Requirement 12: http://www.opengis.net/spec/DGGS/2.0/req/core/cell/direct_position |
Reference subclause | |
Test purpose |
To verify that all zones in each discrete global grid are assigned a direct position that is within the zone’s boundary. |
Test method |
Requirement test A.13: Core — Reference system — Cell — Address | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.4.3, Requirement 13: http://www.opengis.net/spec/DGGS/2.0/req/core/cell/address |
Reference subclause | |
Test purpose |
To verify that all zones in all discrete global grids have a globally unique zonal identifier (or cell index) that provides a spatio-temporal reference. |
Test method |
Requirement test A.14: Core — Reference system — Discrete global grid | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.5, Requirement 14: http://www.opengis.net/spec/DGGS/2.0/req/core/rs/discrete_global_grid |
Reference subclause | |
Test purpose |
To verify that a DGGS RS defines discrete global grids as aggregations of all the cells at the same level in the hierarchy. |
Test method |
Requirement test A.15: Core — Reference system — Discrete global grid — Sequence | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.2.5, Requirement 15: http://www.opengis.net/spec/DGGS/2.0/req/core/rs/discrete_global_grid/sequence |
Reference subclause | |
Test purpose |
To verify a DGGS RS orders its discrete global grids in a sequence of increasing refinement level. |
Test method |
Requirement test A.16: Core — Functions — Quantization | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.3.2, Requirement 16: http://www.opengis.net/spec/DGGS/2.0/req/core/functions/quantization |
Reference subclause | |
Test purpose |
To verify that a DGGS specification has operations to assign data from external sources to cells that conform to the data model in Figure 14 and definitions in Table 47–Table 51. |
Test method |
Requirement test A.17: Core — Functions — Query — ZoneQuery | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.3.4, Requirement 17: http://www.opengis.net/spec/DGGS/2.0/req/core/functions/query/zonequery |
Reference subclause | |
Test purpose |
To verify that a DGGS specification implements query operations that conform to the data model in Figure 16 and definitions in Table 52–Table 54, across its entire domain. |
Test method |
Requirement test A.18: Core — Functions — Interoperation — Query | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.3.5.4, Requirement 18: http://www.opengis.net/spec/DGGS/2.0/req/core/functions/interoperation/query |
Reference subclause | |
Test purpose |
To verify that a DGGS specification implements operations to read, interpret and execute external data queries that conform to the data model Figure 17 and Figure 18 and definitions in Table 55–Table 59. |
Test method |
Requirement test A.19: Core — Functions — Interoperation — Broadcast | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 8.3.5.6, Requirement 19: http://www.opengis.net/spec/DGGS/2.0/req/core/functions/interoperation/broadcast |
Reference subclause | |
Test purpose |
To verify that a DGGS specification implements operations to translate data results from interoperation queries to standard data formats and broadcast the reformatted result set that conform to the data model in Figure 17, Figure 19, Table 55, and definitions in Table 60…Table 62_. |
Test method |
The requirement tests that apply to each conformance category in the Equal-Area Earth DGGS package are listed in Table A.3
Table A.3 — Categories of conformance for Equal-Area Earth DGGS package
Conformance class | Requirement tests |
Equal-Area Earth DGGS | Annex A.1, Requirement test A.2, Annex A.1, Requirement test A.3, & Annex A.1, Requirement test A.5, and all Core requirement tests in Annex A.2.1, Requirement test A.6–Annex A.2.2, Requirement test A.19, and all EAERS requirement tests in Annex A.3, Requirement test A.20–Annex A.3, Requirement test A.29. |
Requirement test A.20: Equal area — Earth reference system — Harmonized model | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.2, Requirement 20: http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/harmonized_model |
Reference subclause | |
Test purpose |
To verify an EAERS specification complies with the data model in Figure 20, Figure 21 and Figure 22 and definitions in Table 63–Table 76 |
Test method |
Requirement test A.21: Equal area — Earth reference system — Global domain | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.3, Requirement 21: http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/global_domain |
Reference subclause | |
Test purpose |
To verify the domain of an EAERS is the whole surface of the reference frame’s earth model and the DGG_ReferenceSystem cellEqualSized is specified as a DGGS_Grids constraint. |
Test method |
Requirement test A.22: Equal area — Earth reference system — Tessellation — Initial | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.4.2, Requirement 22 : http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/tessellation/initial |
Reference subclause | |
Test purpose |
To verify that an EAERS specification has an initial tessellation comprising equal area cells produced by mapping the faces of a base unit polyhedron to a surface model of the Earth. |
Test method |
Requirement test A.23: Equal area — Earth reference system — Tessellation — Sequence | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.4.3, Requirement 23 : http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/tessellation/sequence |
Reference subclause | |
Test purpose |
To verify an EAERS defines tessellation operations that generate a sequence of discrete global grids with progressively smaller cells. |
Test method |
Requirement test A.24: Equal area — Earth reference system — Tessellation — Sequence — Max | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.4.3, Requirement 24 : http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/tessellation/sequence/max |
Reference subclause | |
Test purpose |
To verify that an EAERS specifies a limit in its sequence of discrete global grids that ensures the error budget for EA_Cell area cannot be exceeded. |
Test method |
Requirement test A.25: Equal area — Earth reference system — Tessellation — Global area preservation | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.4.4, Requirement 25 : http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/tessellation/global_area_preservation |
Reference subclause | |
Test purpose |
To verify for EA_Cells in each successive discrete global grid, that domain completeness and location uniqueness are preserved, with total area of those EA_Cells the same as the initial global grid and no overlapping DGGS cells. |
Test method |
Requirement test A.26: Equal area — Earth reference system — Cell — Simple — 2D polygon | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.5.1, Requirement 26: http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/cell/simple/2d_polygon |
Reference subclause | |
Test purpose |
To verify that all of the cells of an EAERS specification have shapes that are simple polygons on the surface model of the Earth where: edges only meet at vertices; exactly two edges meet at each vertex; the number of edges and vertices are the same; and the region enclosed always has a measurable area. |
Test method |
Requirement test A.27: Equal area — Earth reference system — Cell — Direct position — Centroid | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.5.2, Requirement 27: http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/cell/direct_position/centroid |
Reference subclause | |
Test purpose |
To verify that the cells defined by an EAERS are referenced at the centroid of each cell. This test requires verification that the attribute EA_Zone(centroid) returns a direct position on the surface of the cell. |
Test method |
Requirement test A.28: Equal area — Earth reference system — Cell — Equal area — Error budget | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.5.3, Requirement 28: http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/cell/equal_area/error_budget |
Reference subclause | |
Test purpose |
To verify that an EAERS specification defines error budget(s) of 1% or less that represents the maximum ratio of a cell’s area to the theoretical cell area computed from the number of cells and the surface area of the Earth model. |
Test method |
Requirement test A.29: Equal area — Earth reference system — Cell — Equal area | |
---|---|
Abbreviation | |
Type | |
Requirement |
Clause 9.1.5.3, Requirement 29: http://www.opengis.net/spec/DGGS/2.0/req/ea/ers/cell/equal_area |
Reference subclause | |
Test purpose |
To verify that the cells in each discrete global grid, and of each cell geometry in a DGGS specification have equal area within the specified error budget. |
Test method |
Inspect documentation of the EAERS specification, and for each discrete global grid, compare the area of each cell defined by its geometry with the average area of all cells of the same geometry (triangle, quadrangle, pentagon, or hexagon). |
All Discrete Global Grid Systems (DGGS) are structured for information as distinct from conventional coordinate reference systems originally designed for navigation. For a grid based global spatial information system to operate effectively as an analytical system it should be constructed using cells that represent the surface of the Earth in a uniform way. This ensures that, at each resolution, all cells have the same probability of contributing to an analysis. An Equal Area DGGS is a spatial reference system that uses a hierarchy of equal area tessellations to partition the surface of the Earth into grid cells or their analogous lattice points. In this way, information recorded about phenomena at a location can be easily referenced to the explicit area of the associated cell, integrated with other cell values, and provides statistically valid summaries based on any chosen selection of cells. With equal area partitioning, spatial analysis can be replicated consistently anywhere on the Earth independent of resolution or scale.
Equal Area Earth DGGS reference systems are polyhedral reference systems on the surface of a base unit polyhedron’s circumscribed ellipsoid. The base unit polyhedron’s location and orientation is defined in Earth Centered (EC) coordinates. The initial equal area tessellation of the chosen ellipsoidal Earth model is constructed by scaling a unit polyhedron of defined orientation until its vertices all touch the ellipsoid and connecting adjoining vertices with arcs selected from the set of permitted arcs, the simplest of which are geodesic, small circle or small ellipse arcs. Appropriate differential scaling is applied to the unit polyhedron to ensure an equal area initial tessellation. For the simple case of regular polyhedra and geodesic (i.e. great circle) arcs on its circumscribed spheroid, the scaling is uniform. Figure B.1 illustrates their simplest form using a regular spherical polyhedron with a spheroidal circumscribing ellipsoid and geodesic arcs. Small circle arcs are typically used to construct arcs along lines of latitude for both ellipsoids and spheroids. Both small circle and small ellipse arcs are formed from the intersection of a defined plane with the ellipsoid, and in that sense they can be considered equivalent to the “straight” lines of two-dimensional cell boundaries. More complex forms of straight line, such as arcs that project to a straight line in an equal area projection are also allowed.
Figure B.1 — Regular polyhedra (top) and their corresponding initial equal area tessellation (bottom)
Table B.1
a) tetrahedron | b) cube | c) octahedron | d) icosahedron | e) dodecahedron |
NOTE Based on Figure 2 in [1] |
There is a gap between conventional coordinate reference systems and the reference system needed to define DGGSs. This document fills the gap in existing ISO standard reference systems and establishes requirements for globally interoperable equal-area cell- or lattice-based information frameworks.
Existing spatial CRS (e.g. ECEF [Earth Centered Earth Fixed], WGS 84 or Web Mercator) build grids from projected Cartesian or ellipsoidal coordinate axes. Rectangular planar grids are typically formed by establishing a set of regular ticks on a pair of linear axes with grids cells being formed by the intersection of straight lines drawn normal to the ticks on each axis. Analogous construction techniques can be used to create triangular or hexagonal grids. The properties of grids built this way arise from the premise of planar geometry and not the curved geometry of the surface of a sphere or ellipsoid. While these properties hold true at local scales, in curved geometries they increasingly fail at progressively larger regions of interest (see Figure B.2). Take for example the assumption that a grid cell’s geometric properties are independent of its size or resolution, which is implicit in constructing sets of planar aligned (or ‘nested’) 10 m, 30 m and 90 m grids. As shown in Figure B.3, a 90 m square cell formed from nine 30 m square child cells has the following properties:
It is also square;
Its edges are three times the edge length of its 30 m child cells, which in turn all are three times the edge length of their 10 m child cells;
Its interior angles are all right angles and identical to the interior angles of all of the child cells;
Its edges follow the shortest linear path between neighbouring cell vertices; and,
The angles or bearings from centroid to centroid between cells are preserved irrespective of the direction of travel.
Figure B.2 — Comparison of a grid (in this case radial) represented on both (a) curved and (b) planar surfaces.
Note |
With increasing distance away from the point P there is an increasing deviation between the two representations of the grid [Based on Figure 15 in [2]; and Figure 3 in [44]]. |
Note |
The red and yellow cells have identical geometry, and in each case the geometry is also shared with all other cells of the same size. |
On a curved surface, however, this is never the case. Yet we often make the same assumption; that all cells are geometrically identical in, for example, a country- or continental-wide mosaic comprising many satellite images. Consequently, under this paradigm assumption, choosing a fixed cell size for a global grid whose cells represent equal areas and seamlessly fit the earth’s surface is problematic. When this is required, conventional spatial standards enforce latitude-longitude axes to be used and these grids are therefore described in these spherical coordinates. But the cells of these types of (equal-angular) grids do not have the same properties of planar grids. Figure B.4 shows a similar consideration to that of Figure B.3, only the grids are constructed using spherical instead of planar Cartesian coordinates. In this scenario, the largest (parent) cell does not necessarily have the same shape or internal angles as the child cells. Also, its edges do not follow the shortest linear path from corner to corner. Bearing directions between cell centroids, however, are preserved in both planar and curved geometry spaces.
Table B.2
a) Square grid with nested child cells on a portion of a sphere (projected from the planar grid shown in Figure B.3) |
b) Latitude-longitude (equal angular) grid, the red cell is 90o x 90o and has nine 30o x 30o child cells (the central child cell is shown in yellow) |
In an attempt to address this dichotomy, conventional spatial standards therefore support either small. local, well-behaved planar grids or global grids that preserve bearings and angular lengths, and do not preserve area, but not both at the same time. This document fills this gap by providing a formal specification for area preserving reference systems based on the surface model of the Earth that respect the accuracy and precision of spatial data at all scales from local to global. These systems use a hierarchical tessellation of the entire Earth to produce equal-area grids. Figure B.5 shows two examples. We anticipate that future extensions of the specifications in this document will support higher dimensions, such as the volume of the Earth and its atmosphere, and the Earth through time.
Table B.3
The language and foundations of current geospatial standards are deeply rooted in planar thinking, so while this document leverages as much as it can from existing standards, it also introduces new concepts that are subtly and yet fundamentally, different from those described by the standards that it draws from. These subtle differences challenge our thinking. As a consequence, this document is an evolution of both existing raster processing practice and past usage of discrete global grids.
As a specification for an area preserving earth reference system, this document defines more than just grids and lattices. The underlying geometry of the cells and the topological relationships between neighbouring cells can be used to define GUIDs for the cells across all resolution.
Earlier, we noted that planar grids are formed from the pairs of axes each with regular ticks corresponding to the cell dimension, facilitating a simple topological referencing schema for each cell (usually via a matrix style index for each cell along the axes of the grid, i.e. rows and columns for a two-dimensional grid). With DGGSs, we introduce a more sophisticated set of cell referencing schemas, such as space filling curves which traverse all of the cells in a manner that is functionally equivalent to the axes. As shown in Figure B.6, cell indices are assigned to cells along the path of the space filling curve. These indices, together with the geometry of the space filling curve, carry the metrics of the curved surface and the topological relationships between neighbouring cells. The cell indices are explicitly treated as GUIDs.
Note |
Labels of 4×4 square cells. (after [Based on Figure 25 in[2]]) |
The mathematical properties of integers and real numbers on axis pairs in a plane are known implicitly and are therefore not part of any ISO document concerning planar grids. The theoretical basis on which the separate disciplines for space filling curves, GUIDs, grids, spatial topology and discrete global grids are also well founded. However, their roles in DGGSs are not implicitly understood. This document therefore defines these roles and relationships explicitly. This is a necessary departure from previous DGGS work that is needed to ensure a robust spatial reference frame standard. A brief history of DGGSs is provided in Annex C for reference.
Conventional coordinate reference systems address the globe with a continuous field of points suitable for repeatable navigation and analytical geometry. While this continuous field is represented on a computer in a digitized and discrete fashion by tuples of fixed-precision floating point values, it is a non-trivial exercise to relate point observations spatially referenced in this way to areal features on the surface of the Earth. In contrast, a DGGS is designed to be an information grid, not a navigation grid. DGGS provide a fixed areal based geospatial reference frame for the persistent location of measured Earth observations, feature interpretations, and modelled predictions. DGGS address the entire planet by partitioning it into a discrete hierarchical tessellation of progressively finer resolution cells. The geometry and location of the cell is the principle aspect of a DGGS. Data integration, decomposition, and aggregation is optimized in the DGGS’s hierarchical structure and can be exploited for efficient multi-source data processing, storage, discovery, transmission, visualization, computation, analysis, and modeling.
The concept of using polyhedra to model the surface of the Earth is by no means new. In 1509 Lucia Pacioli published “De Devina Proportione” [11] a treatise, illustrated by Leonardo Da Vinci, exploring the mathematical characteristics of the “golden ratio” (also referred to as the “divine proportion”) which included a consideration of the properties of the five platonic solids circumscribed within the sphere and the eminent role of the “golden ratio” in the construction of two of them (the icosahedron and dodecahedron). It is likely that his time studying with Pacioli influenced Da Vinci’s later thinking regarding spherical geometry; evidenced in 1515 by his derivation of the octahedral analysis of the volume of a sphere with various forms of segmentation [12]. This work is suggested to have led to the development of the Reuleaux triangular formulation of the world map (or mappamundi), attributed to Da Vinci [13], and can be considered a precursor to differential calculus, formally developed by Newton and Leibniz nearly two centuries later.
In the 1940’s, a similar approach was used by R. Buckminster Fuller in the development of the Dymaxion map of the world [14], a physical model of the Earth mapped onto the planar faces of a polyhedron (first presented as a cuboctahedron [15] and then later as an icosahedron [16]). The aim of the Dymaxion map was to depict the spherical world as a flat surface with true scale, true direction and correct configuration, all at the same time. Although a physical model of the Earth, and not strictly a DGGS, it inspired later researchers to produce digital Earth models, which in turn has led to the development of DGGS.
Formal development of DGGS began in the 1950s with the promising value of global analysis coinciding with the increased use of geographic information systems and the availability of global mapping data and positioning systems. Perhaps the first published instance of formalized discrete global grids with application to numerical analysis was described by Vestine et. al. [17] in 1955, where they define and use an equal-area grid based on the mapping of a spherical icosahedron onto the surface of the Earth as a framework to conduct areal based integral and spherical-harmonic analyses of the geomagnetic field. This grid was later used (and re-described) by Sadourny et. al. [18] in 1968 to model equations of atmospheric motion without distortion across the entire globe. Another style of discrete global grid, and perhaps the first application of hierarchical indexing schemas as an analytic cell referencing tool was implemented by Geoffrey Dutton in 1984 [19],[20],[21] at the Laboratory for Computer Graphics and Spatial Analysis at Harvard Graduate School of Design. Dutton’s first global grid was designed for assembling and managing global terrain data on a triangular global grid. His global GEM [19],[20],[21],[22] started with a cuboctahedron connected into a rhombic dodecahedron (which is its dual polyhedron where the vertices of one corresponds to the centre of the faces of the other) and recursively divided the initial 12 triangular faces into refinements of 9 partially nested equilateral triangles. Dutton refined GEM to use only an octahedral basis in the QTM DGGS [19],[20],[21],[23]. QTM is a fourfold hierarchical decomposition of facets of an octahedron into triangles whose edges follow small circles. Elevations were assigned to the centroids of child triangles and to the vertices that coincided with them. Waldo Tobler and Zi-tan Chen [24] imagined the primary purpose for a formal discrete global grid standard would be information exchange and storage. Tobler argued that as a generalized information medium “coverage must be uniform and that every element of area must have an equal probability of entering the system. This suggests that the world should be partitioned into chunks of equal size” [24]. Tobler’s global grid started with a cube as a base unit polyhedron and divided into rectilinear quad-trees to create successive subdivisions with unlimited resolution. Dennis White, Scott Overton, and Jon Kimerling, driven by a need for a statistically valid sampling to integrate aquatic and terrestrial monitoring for the US-EPA, designed a global grid in 1989 using closely packed hexagonal cells that started with a truncated icosahedron as the base unit polyhedron [25].
There have been numerous methods proposed for achieving a tessellation of the Earth, each with different distortion characteristics [26]. These tessellations can be organized into a limited set of categories that describe a hierarchical taxonomy of global grids Figure C.1, [26],[27]. Only two groups of classes of global grid achieve an equal area solution [26]: those based on equal area mapping of a base unit polyhedron (such as the ISEA projection [28]) and those based on direct surface tessellations using small circle subdivision (e.g. References [29],[30]).
Figure C.1 — Global Grid Taxonomy (Based on Figure 4 in [2]).
Key |
Table C.1
A | Direct surface tessellations | B | Projected polyhedron tessellations |
---|---|---|---|
A-1 | voronoi — Hipparchus geo-positioning [31] | B-1* | equal area — single projection [24],[36] |
A-2 | polyhedral — great circle boundary [32] | B-2* | equal area — multiple projection [28],[38],[39] |
A-3* | polyhedral — small circle boundary [29],[30],[21] | B-3 | non-equal area — single projection [37] |
A-4 | quadrilateral —” constant” area [33] | B-4 | non-equal area — multiple projection [40],[41] |
A-5† | quadrilateral — equal angle [34],[35],[45],[46] | ||
NOTE Tessellations marked in the key as suitable for use with this document are: |
There are many possible DGGS, each with their own advantages and disadvantages. Criteria for a discrete global grid are well developed by both Michael F. Goodchild [7] and Jon Kimerling [26], the foremost requirements being a tessellation of cells that exhaustively cover the globe with each cell having an equal area, and a centroid representing a single point. The points and cells of the various resolution grids which constitute the grid system form a hierarchy which displays a high degree of regularity [42]. Choices for an appropriate tessellation include properties of shape, adjacency, connectivity, orientation, self-similarity, decomposability, and packing properties. Cell choices are generally taken from the three shapes that uniformly tile a plane — rectilinear, triangular, and hexagonal cells.
While it is possible to map any polyhedral solid to the surface of the earth, the Platonic solids (tetrahedron, cube, octahedron, dodecahedron and icosahedron; see Figure B.1) are the only polyhedral solids that perfectly partition the surface of a sphere into regular, equal area cells [43]. As a result, the Platonic solids are used in the construction of most equal area DGGS, often via a mapping of the polyhedral faces to the surface model of the Earth (some examples are shown in Figure C.2). This method of mapping the faces of a base unit polyhedron to the surface model of the Earth creates a coordinate reference system that is based on a curved geometric framework. GIS and image analysis packages that assume flat earth geometries need to adapt to support this new construct, which more closely represents the Earth.
Figure C.2 — Examples of DGGS based on the mapping of the faces of Platonic solids to the surface model of the Earth
Note |
Table C.2
Any tessellation of the Earth does not necessarily produce a DGGS. Single resolution computational grids are not sufficient to constitute a DGGS. Spatial data structures used to organize map tiles or optimize rapid spatial search cannot be considered to qualify as a DGGS in and of themselves. Although DGGS often utilize hierarchical indices to identify a cell, the primary feature of the DGGS is the cell geometry, not the optimization of a spatial query. Further, DGGS have data independent geometry — their geometry is not formed to optimize a balanced search like R-Trees or maximal spacing of data as generated by Voronoi diagrams.
One way to understand the important difference between a DGGS and a conventional spatial reference system is to consider that a DGGS provides a digital framework for geospatial information. Geospatial information is essentially a signal, that is a variable (e.g. measurement of phenomena), which changes subject to another independent variable (e.g. spatial location, time, some physical interaction etc.). Conventional geospatial data are analogue signals, as they reference to a continuous space: geographic coordinates on an ellipsoidal datum. Even the discrete pixels of a satellite Earth observation image reference this continuous analogue model of Earth. However, these pixels do not observe precisely the same locational area for successive observations. Spatial reference by geographic identifier is described in ISO 19112. DGGS provide this globally in a structured form which is analogous to the ellipsoidal coordinate system described in ISO 19111, but is based on discrete cells rather than continuous point locations (e.g. Reference [46]).
Sampling and quantization are necessary for a signal to be considered digital. As the name implies, the DGGS provides the regular discrete intervals or cell partitioning to which location information (e.g. signal values) are sampled. A well-designed quantization strategy is also an important component of a DGGS which should maintain the fidelity of the original information in the values assigned to each cell. The discrete data values can be sampled from any geospatial data source, regardless of the original spatial reference, scale, format, type, frequency or time. A DGGS is a discrete “digital” model of the Earth.
As each cell in a DGGS is fixed in location, and the location provides an explicit area representation, basic geospatial enquiries, such as “Where is it?”, “What is here?”, and “How has it changed?”, are simplified into set theory operations. As any data values referenced to a particular DGGS are, by the nature of the grid, aligned, the high costs of integrating data in traditional systems are dramatically reduced.
A DGGS can even be designed for lossless encoding of vector geometry such that cells, and their integer addressing, predictably converge to the real number coordinate pairs of each observation with each successive refinement: an essential property of a conventional coordinate system.
DGGS are designed to eliminate requirements for complex data fusion processes. Reducing the reliance on an intermediary integrator or analyst is a key requirement for distributed participatory digital-Earth information systems. “[Digital-Earth] “can clearly benefit from developments in discrete global grid, which can provide the georeferencing, the indexing, and the discretization needed for geospatial data sets. They have properties, in particular hierarchical structure, uniqueness, explicit representation of spatial resolution, and consistency, that make them superior to any single alternative. [7].
A DGGS provides a uniform environment to integrate, aggregate and visualize both vector/point cloud geometries and raster-based geospatial data sources in much the same way that information within a computer graphics pipeline becomes the pixels on a computer screen. Efficiencies are gained through implementing the Dimensionally Extended nine-Intersection Model (DE-9IM) set of fundamental spatial operations [3]–[5],[6] directly on the DGGS cell structure. This allows for higher order analytics (via bindings to external analytic libraries) to be created on the DGGS structure itself, independent of the data sources.
This document builds on the spatio-temporal definitions in ISO 19111:2019 to achieve a broader integration of spatio-temporal concepts. In addressing alignment with ISO 19108:2002, the reader is directed to the discussion in ISO 19111:2019, Annex D as a starting point which is adopted in full in this document.
Time can be represented as an ordered, one dimensional geometry with topology. The only significant difference between one-dimensional spatial and one-dimensional temporal is the importance of direction, and the topological relationships that explicitly address direction. ISO 19107:2019 and ISO 19108:2002 define terms for geometric and topological primitives and their complexes that are functionally equivalent but different in structure. To achieve spatio-temporal uniformity this document aligns its definitions with ISO 19107:2019. When compared with equivalent terms in ISO 19108:2002 this primarily results in differences in class inheritance rather than in underlying meaning. Comparing ISO 19108:2002 terms to this document’s terms, while putting the structural differences aside:
TM_GeometricPrimitive and TM_TopologicalPrimitive map to this document’s TemporalGeometricPrimitive, TemporalTopologicalPrimitive respectively;
TM_TopologicalComplex maps to this document’s TemporalTopologicalComplex;
this document introduces TemporalGeometricComplex and TemporalGeometricCollection;
the super classes of TM_Primitive, TM_Complex and TM_Object are not implemented and instead this document introduces TemporalGeometry and TemporalTopology;
TM_Instant and TM_Period map to this document’s Instant and Interval respectively;
TM_Node and TM_Edge map to this document’s NodeT and EdgeT respectively;
TM_Duration, and its subclasses TM_PeriodLength and TM_IntervalLength map to this document’s Duration, which encompasses any valid unit on a TemporalCS (ISO 19111:2019); and
TM_RelativePosition maps to this document’s RelativePosition, which is defined to reflect modern usage by SDWIG and OGC as defined in OWL-time.
ISO 19108:2002 includes the concepts of a named Ordinal Era, and Ordinal reference systems which address the needs of geological time. While the topology of Ordinal Era are known, their extent is in general ill-defined. To achieve spatio-temporal uniformity this document aligns itself with ISO 19112:2019. Named Periods are introduced as the temporal equivalent of named Locations ISO 19112:2019). Periods have well-defined extents as well as well-defined topology. Comparing the terms of ISO 19108:2002 with this document’s terms, while acknowledging this difference:
TM_OrdinalEra maps to both Period and PeriodClass in this document depending on context; and
TM_OrdinalReferenceSystems maps to TemporalReferenceSystemUsingPeriodIdentifers in this document.
Topic 21 v1.0 has only one conformance class — Equal Area Earth DGGS, Topic 21 v2.0 extends the 2D surface only data model to a potentially 3D+T data model by establishing Common Spatio-temporal Classes, and a dimension agnostic DGGS Core Reference system and dimensionally agnostic Functions for Quantisation, Query, and Interoperability. The conformance for Equal Area Earth DGGS is addressed in terms of conformance to the DGGS Core Functions for the 2D Earth surface and conformance to the Equal Area Earth Reference systems class built on the DGGS Core Reference system.
Requirements in Topic 21 v1.0 are addressed in a number of different ways in Topic 21 v2.0:
1:1 with a DGGS Core Requirement,
1:1 with an Equal Area Earth DGGS Reference system Requirement,
many:1 where multiple requirements have been consolidated into a single all inclusive requirement,
1:many for example where conformance to the data model was addressed as a single requirement
in v1.0 but this is now specifically incorporated into other requirements, and
0:1 with a new requirement, either in the Core or in the Equal Area Earth DGGS Reference system.
Even if the correspondence is 1:1, a new number has been assigned in v2.0 since the underlying data model is substantially different, or the definitions of terms used in the requirement have been rephrased, or the scope of the test has been broadened, for instance to include relevant parts of the data model. Requirements introduced in v2.0 appear with their number in brackets in the following list, grouped with other related requirements, and requirements that are only a partial match have their requirement number in italics.
Table E.1 — Requirements crosswalk from Topic 21 v1.0 to v2.0
Table E.2 — Requirements crosswalk from Topic 21 v2.0 to v1.0
Table F.1
[1] Mahdavi-Amiri, A., Samavati, F. F., Peterson, P., 2015, “Categorization and conversions for indexing methods of discrete global grid systems”, ISPRS International Journal of Geo-Information, 4(1), pp 320–336. https://dx.doi.org/10.3390/ijgi4010320DOI:10.3390/ijgi4010320
[2] Mahdavi-Amiri, A., Alderson, T., & Samavati, F., 2015, “A Survey of Digital Earth Representation and Visualization”, Computers & Graphics, Elsevier Ltd., pp. 95–117. https://dx.doi.org/10.11575/PRISM/30985DOI:10.11575/PRISM/30985
[3] Clementini, E., Di Felice, P., van Oosterom, P., 1993. “A small set of formal topological relationships suitable for end-user interaction”. In Abel, David; Ooi, Beng Chin. Advances in Spatial Databases: Third International Symposium, SSD ’93 Singapore, June 23–25, 1993 Proceedings. Lecture Notes in Computer Science. 692/1993. Springer. pp 277–295. https://dx.doi.org/10.1007/3-540-56869-7_16DOI:10.1007/3-540-56869-7_16.
[4] Clementini, E., Sharma, J., Egenhofer, M. J., 1994, “Modelling topological spatial relations: Strategies for query processing”. Computers & Graphics 18 (6), pp 815–822. https://dx.doi.org/10.1016/0097-8493(94)90007-8DOI:10.1016/0097-8493(94)90007-8.
[5] Clementini, E., and Di Felice P. A., 1996, “A Model for Representing Topological Relationships between Complex Geometric Features in Spatial Databases.” Information Sciences, 90(1), pp 121–136. http://dx.doi.org/10.1016/0020-0255(95)00289-8DOI:10.1016/0020-0255(95)00289-8
[6] Egenhofer, M.J.; Herring, J.R., 1990, “A Mathematical Framework for the Definition of Topological Relationships”. Fourth International Symposium on Spatial Data Handling Zürich, Switzerland, pp 803–813.
[7] Goodchild, M. F., 2000, “Discrete global grids for digital earth”, International Conference on Discrete Global Grids. Santa Barbara.
[8] Peterson, P. R., 2017, “Discrete Global Grid Systems.” In The International Encyclopedia of Geography, edited by Douglas Richardson. Malden, Oxford: John Wiley and Sons, Ltd. DOI:10.1002/9781118786352.wbieg1050
[9] Sahr, K., White, D., Kimerling, A. J., 2003, “Geodesic discrete global grid systems”, Cartography and Geographic Information Science, 30 (2), pp 121–134. https://dx.doi.org/10.1559/152304003100011090DOI:10.1559/152304003100011090
[10] Postel, J., 1981, “RFC 791: Internet protocol”, Darpa Internet Protocol Specification (September 1981).
[11] Pacioli, L., 1509, “De Davina Proportione” (Illustrated by Leonardo Da Vinci), Venice.
[12] da Vinci, L, 1514, “Manuscript E, 24v-25r (1513-14)”. Pen and ink on paper, 150 x 99 mm. Bibliothéque de l’Institut de France, Paris.
[13] da Vinci, L, 1478–1518, “Codex Atlanticus”. Pen and ink on paper, 61 x 44 cm. (collated by Pompeo Leoni). Biblioteca Ambrosiana, Milan, Italy.
[14] “Life Presents R. Buckminster Fuller’s Dymaxion World”. Life, 1 March 1943, pp 41–45
[15] Fuller, R. B., 1946, Cartography. U.S. Patent 2,393,676.
[16] Fuller, R. B. and Sadao, S., 1954, “Dymaxion Airocean World: The Raleigh Edition of Fuller Projection”. Student Publications of the School of Design, North Carolina State College, Raleigh, North Carolina, USA.
[17] Vestine, E. H. Sibley, W. L. Kern, J. W. and Carlstedt,J. L. “Integral and Spherical-Harmonic Analyses of the Geomagnetic Field for 1955.0, Part 2,” Journal of Geomagnetism and Geoelectricity, vol. 15, No. 2, Aug. 1963, pp. 73–89.
[18] Sadourny, R.; Arakawa, A.; Mintz, Y. (1968). “Integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere”. Monthly Weather Review 96 (6): 351–356.
[19] Dutton, G., 1989, “Modelling location uncertainty via hierarchical tessellation”. In: Accuracy of Spatial Databases, Goodchild, M. and Gopal, S. (eds.), London: Taylor & Francis, pp 125–140.
[20] Dutton, G., 1999, “A hierarchical coordinate system for geoprocessing and cartography”. Lecture Notes in Earth Science 79. Berlin: Springer-Verlag. XIX + 231 pp. 97 figs. 12 plates, 16 tabs. ISSN 0930-0317, ISBN 3-540-64980-8.
[21] Dutton, G., 1984, “Part 4: Mathematical, Algorithmic and Data Structure Issues: Geodesic Modelling Of Planetary Relief”, Cartographica: The International Journal for Geographic Information and Geovisualization, 21(2–3), pp 188–207. https://dx.doi.org/10.3138/R613-191U-7255-082NDOI:10.3138/R613-191U-7255-082N
[22] Dutton, G., 1996, “Encoding and handling geospatial data with hierarchical triangular meshes”, In Proceeding of 7th International symposium on spatial data handling, 43, Netherlands: Talyor & Francis. DOI:10.1.1.461.5603
[23] Dutton, G., 1999, “Scale, Sinuosity, and Point Selection in Digital Line Generalization”, Cartography and Geographic Information Science, 26(1), pp 33–54. https://doi.org/10.1559/152304099782424929DOI:10.1559/152304099782424929
[24] Tobler, W., & Chen, Z.-t., 1986, “A Quadtree for Global Information Storage”, Geographical Analysis, 18(4), pp 360–371. https://dx.doi.org/10.1111/j.1538-4632.1986.tb00108.xDOI:10.1111/j.1538-4632.1986.tb00108.x
[25] White, D., Kimerling, J., & Overton, W. S., 1992, “Cartographic and geometric components of a global sampling design for environmental monitoring”, Cartography and Geographic Information Systems, 19(1), pp 5–22. https://dx.doi.org/10.1559/152304092783786636DOI:10.1559/152304092783786636
[26] Kimerling, A. J., Sahr, K., White, D., & Song, L., 1999, “Comparing Geometrical Properties of Global Grids”, Cartography and Geographic Information Systems vol. 26, no. 4, pp 271–88. https://dx.doi.org/10.1559/152304099782294186DOI:10.1559/152304099782294186
[27] Dutton, G., 1994, “Geographical grid models for environmental monitoring and analysis across the globe (panel session)”. In: Proceedings of GIS/US’94 Conference, Phoenix, Arizona.
[28] Snyder, J. P., 1992, “An equal-area map projection for polyhedral globes”. Cartographica, 29(1), pp.10–21.
[29] Song, L., 1997, “Small circle subdivision method for development of global sampling grid”, Unpublished Masters Thesis, Oregon State University, 176pp.
[30] Song, L., Kimerling, A. J., and Sahr, K., 2002, “Developing an Equal Area Global Grid by Small Circle Subdivision”. In M. Goodchild and A. J. Kimerling (Eds.), Discrete Global Grids: A Web Book
[31] Lukatela, H., 1987, “Hipparchus geopositioning model: An overview”, In: Proceedings of Auto Carto 8 Symposium, Baltimore, Maryland. pp 87–96.
[32] Fekete, G., Treinish, L., 1990, “Sphere quadtree: A new data structure to support the visualization of spherically distributed data”. SPIE: Extracting Meaning from complex data: Processing, display, interaction. 1259, pp 242–253.
[33] Bjorke, J. T., Grytten, J. K., Haeger, M., Nilsen, S., 2003, “A Global Grid Model Based on ‘Constant Area’ Quadrilaterals”, ScanGIS, 3, pp 238–250. DOI: 10.1.1.105.2253
[34] Amante, C. and Eakins, B. W., 2009, “ETOPO1 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis”, NOAA Technical Memorandum NESDIS NGDC-24, 19 pp.
[35] Rees, T., 2002, “‘C-Squares’ — a new metadata element for improved spatial querying and representation of spatial dataset coverage in metadata records”, in EOGEO 2002 Proceedings, Ispra, Italy.
[36] Loveland, T. R., Merchant, J. W., Ohlen, D., O., Brown, J. F., 1991, “Development of a land-cover characteristics database for the conterminous U.S.”. Photogrammetric Engineering and Remote Sensing, 57(11), pp 1453–1463
[37] Snyder J. P., 1993, “Flattening the Earth: Two Thousand Years of Map Projections”, pp5–8. ISBN 0-226-76747-7)
[38] Gibb, R.G., 2016, “The rHEALPix Discrete Global Grid System”, Proceedings of the 9th Symposium of the International Society for Digital Earth (ISDE), Halifax, Nova Scotia, Canada. IOP Conf. Ser.: Earth Env. Sci., 34, 012012. DOI:10.1088/1755-1315/34/1/012012
[39] Ma, T., Zhou, C., Xie, Y., Qin, B., Ou, Y., 2009, “A discrete square global grid system based on the parallels plane projection”. International Journal of Geographical Information Science. 23(10), pp 1297–1313. https://doi.org/10.1080/13658810802344150DOI:10.1080/13658810802344150
[40] Fisher, I., 1943, “A World Map on a Regular Icosahedron by Gnomonic Projection”, Geographical Review, 33(4), pp 605–619, https://www.jstor.org/stable/209914DOI:10.2307/209914
[41] Fuller, R. B., 1982, “Synergetics”, New York.
[42] Clarke, K. C., 2000, “Criteria and Measures for the Comparison of Global Geocoding Systems”, International Conference on Discrete Global Grids. Santa Barbara: University of California, Santa Barbara.
[43] Fitzpatrick, R., 2008. Euclid’s Elements of Geometry. Richard Fitzpatrick. ISBN 978-0-6151-7984-1
[44] Schmidt, R., Grimm, C., Wyvill, B., 2006, Interactive decal compositing with discrete exponential maps, ACM Transactions on Graphics, 25 (3), pp 605–613.
[45] Cheng, C., Tong, X., Chen, B., Zhai, W., 2016, “A Subdivision Method to Unify the Existing Latitude and Longitude Grids”, ISPRS International Journal of Geo-Information, 5(9), 161, DOI:10.3390/ijgi5090161
[46] Li, S., Cheng, C., Chen, B., Meng, M., 2016, “Integration and management of massive remote-sensing data based on GeoSOT subdivision model”, J. Appl. Remote Sens. 10(3), 034003, DOI:10.1117/1.JRS.10.034003
[47] Allen, J. F., 1983, “Maintaining Knowledge about Temporal Intervals”, Communications of the ACM, vol. 26 pp. 832–843
[48] ISO/IEC: ISO/IEC 2382:2015, Information technology — Vocabulary. International Organization for Standardization and International Electrotechnical Commission, Geneva (2015). https://www.iso.org/standard/63598.html
[49] ISO: ISO 8601-1:2019, Date and time — Representations for information interchange — Part 1: Basic rules. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/70907.html
[50] ISO: ISO 19101-1:2014, Geographic information — Reference model — Part 1: Fundamentals. International Organization for Standardization, Geneva (2014). https://www.iso.org/standard/59164.html
[51] ISO: ISO 19103:2015, Geographic information — Conceptual schema language. International Organization for Standardization, Geneva (2015). https://www.iso.org/standard/56734.html
[52] ISO: ISO 19107:2019, Geographic information — Spatial schema. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/66175.html
[53] ISO: ISO 19108:2002, Geographic information — Temporal schema. International Organization for Standardization, Geneva (2002). https://www.iso.org/standard/26013.html
[54] ISO: ISO 19111:2019, Geographic information — Referencing by coordinates. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/74039.html
[55] ISO: ISO 19112:2019, Geographic information — Spatial referencing by geographic identifiers. International Organization for Standardization, Geneva (2019). https://www.iso.org/standard/70742.html
[56] ISO: ISO 19115-1:2014, Geographic information — Metadata — Part 1: Fundamentals. International Organization for Standardization, Geneva (2014). https://www.iso.org/standard/53798.html
[57] ISO: ISO 19117:2012, Geographic information — Portrayal. International Organization for Standardization, Geneva (2012). https://www.iso.org/standard/46226.html
[58] ISO: ISO 19123:2005, Geographic information — Schema for coverage geometry and functions. International Organization for Standardization, Geneva (2005). https://www.iso.org/standard/40121.html
[59] ISO: ISO 19156:2011, Geographic information — Observations and measurements. International Organization for Standardization, Geneva (2011). https://www.iso.org/standard/32574.html
[60] Arliss Whiteside: OGC 05-042r2, OpenGIS Web services architecture description. Open Geospatial Consortium (2005). https://portal.ogc.org/files/?artifact_id=13140
[61] Arliss Whiteside Jim Greenwood : OGC 06-121r9, OGC Web Service Common Implementation Specification. Open Geospatial Consortium (2010). https://portal.ogc.org/files/?artifact_id=38867
[62] Simon Cox, Chris Little: OGC 16-071r3, Time Ontology in OWL. Open Geospatial Consortium (2020). https://www.w3.org/TR/2020/CR-owl-time-20200326/
[63] Peter Baumann: OGC 17-089r1, OGC Web Coverage Service (WCS) 2.1 Interface Standard — Core. Open Geospatial Consortium (2018). http://docs.opengeospatial.org/is/17-089r1/17-089r1.html