C-squares (acronym for the Concise Spatial QUery And REpresentation System) is a system of spatially unique, location-based identifiers (geocodes) for areas on the surface of the earth, represented as cells from a latitude- and longitude-based Discrete Global Grid at a hierarchical set of resolution steps, obtained by progressively subdividing 10×10 degree World Meteorological Organization squares; the term "c-square" is also available for use to designate any component cell of the grid. Individual cell identifiers incorporate literal values of latitude and longitude in an interleaved notation (producing grid resolutions of 10, 1, 0.1 degrees, etc.), together with additional digits that support intermediate grid resolutions of 5, 0.5, 0.05 degrees, etc.
The system was initially designed to represent data "footprints" or spatial extents in a more flexible manner than a standard minimum bounding rectangle, and to support "lightweight", text-based spatial querying; it can also provide a set of identifiers for grid cells used for assembly, storage and analysis of spatially organised data, in a unified notation that transcends national or jurisdictional boundaries. Dataset extents expressed in c-squares notation can be visualised using a web-based utility, the c-squares mapper, an online instance of which is currently provided by CSIRO Oceans and Atmosphere in Australia. C-squares codes and associated published software are free to use and the software is released under version 2 of the GNU General Public License (GPL), a licence of the Free Software Foundation.
History
The c-squares method was developed by Tony Rees at CSIRO Oceans and Atmosphere in Australia (then "CSIRO Marine Research") in 2001–2, initially as a method for spatial indexing, rapid query, and compact storage and visualization of dataset spatial "footprints" in an agency-specific metadata directory (data catalogue);CSIRO Marine Research, 2002: About C-Squares. it was first publicly announced at the 2002 "EOGEO" Technical Workshop held at Ispra, Italy in May 2002.Rees, Tony (2002): "C-squares–a new metadata element for improved spatial querying and representation of spatial dataset coverage in metadata records" [abstract]. Proceedings of EOGEO Technical Workshop May 2002, Ispra, Italy. Archived copy available via the Internet Archive (accessed 24 October 2020) A more complete description was published in the scientific literature in 2003, together with a web-accessible mapping utility entitled the "c-squares mapper" for visualisation of data extents expressed in the c-squares notation. Since that time, a number of projects and international collaborations have employed c-squares to support spatial indexing and/or map production, including FishBase (to map stored data points for any species), the Ocean Biogeographic Information System (OBIS),Tony Rees and Phoebe Zhang, 2007. "Evolving concepts in the architecture and functionality of OBIS, the Ocean Biogeographic Information System". in Vanden Berghe, E. et al. (ed.) Proceedings of Ocean Biodiversity Informatics: an international conference on marine biodiversity data management Hamburg, Germany, 29 November-1 December 2004. IOC Workshop Report, 202, VLIZ Special Publication 37: pp. 167-176. AquaMaps, data analysis to support the designation of marine biogeographic realms, for multi-national fisheries data collation by the Scientific, Technical and Economic Committee for Fisheries (STECF) of the European Commission,Willy Vanhee, Arina Motova & Antonella Zanzi (eds) (2018). Scientific, Technical and Economic Committee for Fisheries - 59th Plenary Meeting Report (PLEN-18-03). Publications Office of the European Union, Luxembourg, 95 pp. , and for data reporting by ICES.ICES, 2011. Report of the Study Group on VMS data, its storage, access and tools for analysis (SGVMS), 7–9 September 2011, Hamburg, Germany. ICES CM 2011/SSGSUE:07. 27 pp. Available online at http://www.ices.dk/sites/pub/Publication%20Reports/Expert%20Group%20Report/SSGSUE/2011/SGVMS11.pdfInternational Council for the Exploration of the Sea (2019) ICES Technical Guidelines: 16.3.3.3 Spatial distribution of fishing effort and physical disturbance of benthic habitats by mobile bottom trawl fishing gear using VMS. doi: 10.17895/ices.advice.4683 1 Available at https://www.ices.dk/sites/pub/Publication%20Reports/Guidelines%20and%20Policies/16.03.03.03_Guidelines_Vessel_Monitoring_Systems_Data.pdf For its application in displaying and modelling global biodiversity data, c-squares was one of four components cited in the award of the Ebbe Nielsen Prize to Rees by the Global Biodiversity Information Facility (GBIF) in 2014.gbif.org, News, 13 July 2014: CSIRO’s Tony Rees named 2014 Ebbe Nielsen Prize winner The concept of representing dataset "footprints" as cells of spatial data of this nature and alignment was stated to have been inspired by the data addressing method in the U.S. National Oceanographic Data Center (NODC) "World Ocean Database" product,U.S. National Oceanographic Data Centre, 1998: "World Ocean Database 1998: Documentation and Quality Control, Version 1.2." Appendix 10A: World Meteorological Organization (WMO) Squares for the Atlantic and Indian Oceans; Appendix 10B: World Meteorological Organization (WMO) Squares for the Pacific Ocean. which uses 10 degree World Meteorological Organization squares (the starting point for c-squares hierarchical subdivision) for organising its data content, and the set of 1:100,000 topographic maps issued by the national mapping agency for Australia (coverage and index here); each map covers a 0.5 degree square and, with its associated mapsheet labels, can notionally be used as a unit of spatial identification. The method has been discussed further in texts on georeferencing, including those by Hill, 2006Hill, Linda (2006). Georeferencing: The Geographic Associations of Information. MIT Press, Cambridge, Mass. and London, England, 260 pp. and Guo et al., 2020.Huadong Guo, Michael F. Goodchild & Alessandro Annoni (eds.) (2020). Manual of Digital Earth. Springer, Singapore, 852 pp.
The system name "c-squares" was chosen because it can be represented as an acronym (for "concise spatial query and representation system") and also because it signals that this method belongs to a notional group of similarly named, latitude-longitude gridded subdivisions of the Globe that includes World Meteorological Organization Squares and Marsden squares, and contrasts with other tessellations of the Globe that use different shaped basic units such as rectangles, triangles, diamonds, and hexagons (for examples refer e.g. Sahr et al., 2003). It is also intended that any individual component cell of the grid can be referred to as a "c-square" (no initial capitalization required).
Rationale
Spatial data are inherently (at least) 2-dimensional; without additional indexing, a numeric range query in 2 dimensions (e.g. x and y, or latitude and longitude) is required to retrieve data items within a particular area. Such queries are computationally expensive so it can be beneficial to pre-process (index) the data in some manner that reduces the inherent dimensionality from two to one dimension, for example as labelled cells of a grid. The grid labels can then be indexed by standard, one dimensional methods for rapid search and retrieval,Rigaux, P., Scholl, M., and Voisard, A. 2002. Spatial Databases - with application to GIS. Morgan Kaufmann, San Francisco, 410pp. and/or searched by simple alphanumeric text searches. C-squares is an example of such a grid where the cell identifiers are designed to be human- as well as machine-readable, and to be concordant with recognizable and commonly intervals of latitude and longitude.
Additional areas where a grid-based approach to spatial indexing can be beneficial can be for the representation of data "footprints" in support of spatial search, data binning to reduce complex and potentially voluminous data into "blocks" which then can be more easily compared and summarised, and the potential for a hierarchical approach wherein finer resolutions of the grid are nested into coarser ones, with a shared notation (common identifiers for the larger portions of the relevant grid cells). A jurisdiction-independent, (global) grid such as c-squares can also be used to integrate data across national boundaries, in contrast to (for example) the national grids of various countries such as those of the United Kingdom, Ireland, etc., which are not the same in their approach and may have differences or gaps where such grids overlap, or fail to meet (for example in marine regions around two areas).
A potential disadvantage of "equal angle" grids (the class that includes c-squares), which are based on standardised units of latitude and longitude, is that the length of the "sides" and the shape (and area) of the grid cells is not constant on the ground (the height remains approximately constant but the width varies with latitude), and some particular effects are noticeable at the poles, where the cells become 3- rather than 4-sided in practice (refer illustration). These disadvantages can be offset by the advantages that data transformation in and out of grid notation can be accomplished by relatively straightforward steps, the results are congruent with conventional maps that show intervals of latitude and longitude, and the concepts of (for example) "1-degree squares" and "0.5 degree squares" may have familiarity and meaning to human users, in a way that non-square, purely mathematically derived shapes and sizes (based upon some form of spherical trigonometry) may not.
The c-squares global grid notation
Initial 10 degree squares 10-degree c-squares are specified as being identical to equivalent World Meteteorological Organization (WMO) square codes, refer illustration at right. These squares are aligned with 10-degree subdivisions of the global latitude–longitude grid, which for c-squares use is specified as employing the WGS84 datum. WMO (10 degree) squares are encoded with four digits, in the series 1xxx, 3xxx, 5xxx and 7xxx. The leading digit indicates the "global quadrant" with 1 for north-east (latitude and longitude are both positive), 3 for south-east (latitude is negative and longitude positive), 5 for south-west (latitude and longitude are both negative) and 7 for north-west (latitude is positive and longitude negative). The next digit, 0 through 8, corresponds to the tens of latitude degrees either north or south; while the remaining 2 digits, 00 through 17, correspond to the tens of longitude degrees either east or west (by specification, 0 is treated as positive). Thus the 10 degree cell with its lower left corner at 0,0 (latitude,longitude) is encoded 1000, and acts as a bin to contain all spatial data between 0 and 10 degrees north (actually, 0 and 9.999...) and 0 and 9.999... degrees east; the 10 degree cell with its lower left corner at 80 N, 170 E is encoded 1817, and acts as a bin to contain all spatial data between 80 and 90 degrees north and 170 and 179.999... degrees east.
Subsequent recursive subdivision C-squares extends the initial WMO 10×10 square notation via a recursive series of "cycles", each 3 digits long (the final one may be 1 digit), separated by the colon character, the number of characters (and cycles) indicating the resolution encoded, as per these examples: 1000 ... 10×10 degree square (up to 1000×1000 km nominal) 1000:1 ... 5×5 degree square (up to 500×500 km nominal) 1000:100 ... 1×1 degree square (up to 100×100 km nominal) 1000:100:1 ... 0.5×0.5 degree square (up to 50×50 km nominal) 1000:100:100 ... 0.1×0.1 degree square (up to 10×10 km nominal) 1000:100:100:1 ... 0.05×0.05 degree square (up to 5×5 km nominal) (etc.)