C-squares
Encyclopedia
C-squares is a system of geocode
s (actually a type of global grid
) that provides a basis for simple spatial indexing of geographic features or data. It was devised by Tony Rees of CSIRO Marine and Atmospheric Research
(then "CSIRO Marine Research") in 2001-2, and described in the literature in 2003. The notation system of c-squares incorporates a compact encoding of latitude
and longitude
coordinates into a machine- and human-readable
c-squares code, which can then be used either for spatial search or display via a suitable mapping application. The c-squares codes also provide an application- and vendor-independent, interoperable notation system for any gridded data whose units of organization correspond with steps of the c-squares hierarchy (e.g. 5-, 1-, 0.5 degree cells, etc.).
catalogues, in place of (or in addition to) conventional bounding rectangle
representations. The method is also useful as a generic, interoperable notation for gridded data (see above), for example a variety of datasets that describe environmental characteristics of global half-degree cells (see AquaMaps site). C-squares can also simply be used for mapping (example: CSIRO Marine and Atmospheric Research's "CAAB" application), although the most value is obtained when the system is used for spatial search as well (e.g. OBIS database, CMAR's "MarLIN" metadatabase, etc.).
into smaller units (each an individual "c-square") of 5°x5°, 1°x1°, 0.5°x0.5°, 0.1°x0.1°, etc., using an alternating base 2, base 5 linear division, as fine as may be required. Each cell of the resulting subdivision is allocated a unique alphanumeric identifier (c-squares code), such that the position of an object or objects on the surface of the Globe
can be represented by a set of one or more such codes that define the cell(s) within which the object occurs. Storing these codes as text identifiers, for example in a database
, repository of spatial metadata
, searchable text file or web page, then offers the functionality for a simple, text-based spatial search, without the requirement for any more complex geographic information system
(GIS). Once stored (or if desired, generated on-the-fly using a c-squares encoder), a code or set of codes can also be rendered on a map by a utility (for example, the web-accessible c-squares mapper) that incorporates the relevant decoding routines.
The actual assignment of the individual cell identifiers to vector objects whose position is expressed in latitude, longitude coordinates follows rules described in reference (1) and the c-squares website and can be automated via simple routines, and the reverse is also possible (decoding) in a straightforward manner. In addition, since the codes are hierarchical and interleaved (each "cycle" containing identifiers for both longitude and latitude, at progressively finer levels of resolution), only the relevant "leading" portion of a (for example) high resolution code need be interrogated to match a lower resolution spatial query.
Conceptually, the c-squares encoding method belongs to a class of algorithms which can be considered derivations of the Z-order
principle.
, UK, occupies (for example) portions of four 0.5°x0.5° cells:
In c-squares notation these are cells 7500:110:3, 7500:110:1, 1500:110:3 and 1500:110:1 (at 0.5°x0.5° resolution). Alternatively at 1°x1° they are portions of two cells, 7500:110 and 1500:110; at 5°x5° resolution, portions of two cells 7500:1 and 1500:1; and at 10°x10° resolution, portions of 2 cells 7500 and 1500 (equivalent to the same identifiers as in WMO squares
).
To visualize the position of these squares on a map, the current syntax to address an installation of the "c-squares mapper" is (e.g.):
http://www.obis.org.au/cgi-bin/cs_map.pl?csq=7500:110:3|7500:110:1|1500:110:3|1500:110:1.
In a system that uses c-squares codes as units of spatial indexing, a text-based search on any of these square identifiers will retrieve data associated with the relevant square. If a wildcard search is supported (for example suppose that the wildcard character is a percent sign), a search on "7500%" will retrieve all data items in that ten degree square, a search on "7500:1%" will retrieve all data items in that five degree square, etc.
The asterisk character "*" has a special (reserved) meaning in c-squares notation, being a "compact" notation indicating that all finer cells within a higher level cell are included, to the level of resolution indicated by the number of asterisks. In the example above, "7500:*" would indicate that all 4 five-degree cells within parent ten-degree cell "7500" are filled, "7500:***" would indicate that all 100 one-degree cells within parent ten-degree cell "7500" are filled, etc. This approach enables the filling of contiguous blocks of cells with an economy of characters in many cases (a form of data compression
), that is useful for efficient storage and transfer of c-squares codes as required.
; FishBase
; AquaMaps
; and a variety of web-accessible applications at CSIRO Marine and Atmospheric Research
. For a full list, see the link Sample c-squares enabled systems on the c-squares website.
Geocode
GEOCODE is a standardized all-natural number representation format specification for geospatial coordinate measurements that provide details of the exact location of geospatial point at, below, or above the surface of the earth at a specified moment of time.Geocode is patented under US Patents...
s (actually a type of global grid
Grid (spatial index)
In the context of a spatial index, a grid is a regular tessellation of a manifold or 2-D surface that divides it into a series of contiguous cells, which can then be assigned unique identifiers and used for spatial indexing purposes...
) that provides a basis for simple spatial indexing of geographic features or data. It was devised by Tony Rees of CSIRO Marine and Atmospheric Research
CSIRO Marine and Atmospheric Research
CSIRO Marine and Atmospheric Research is one of the currently c.20 Research Divisions of the Commonwealth Scientific and Industrial Research Organisation, Australia's largest government-supported research agency.-About CMAR:...
(then "CSIRO Marine Research") in 2001-2, and described in the literature in 2003. The notation system of c-squares incorporates a compact encoding of latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
coordinates into a machine- and human-readable
Human-readable
A human-readable medium or human-readable format is a representation of data or information that can be naturally read by humans.In computing, human-readable data is often encoded as ASCII or Unicode text, rather than presented in a binary representation...
c-squares code, which can then be used either for spatial search or display via a suitable mapping application. The c-squares codes also provide an application- and vendor-independent, interoperable notation system for any gridded data whose units of organization correspond with steps of the c-squares hierarchy (e.g. 5-, 1-, 0.5 degree cells, etc.).
Rationale
According to the initial system description, c-squares was devised as an improved (more precise) method for expressing dataset geographic extents in searchable metadataGeospatial metadata
Geospatial metadata is a type of metadata that is applicable to objects that have an explicit or implicit geographic extent, in other words, are associated with some position on the surface of the Globe...
catalogues, in place of (or in addition to) conventional bounding rectangle
Minimum bounding rectangle
The minimum bounding rectangle , also known as bounding box or envelope, is an expression of the maximum extents of a 2-dimensional object within its 2-D coordinate system, in other words min, max, min, max...
representations. The method is also useful as a generic, interoperable notation for gridded data (see above), for example a variety of datasets that describe environmental characteristics of global half-degree cells (see AquaMaps site). C-squares can also simply be used for mapping (example: CSIRO Marine and Atmospheric Research's "CAAB" application), although the most value is obtained when the system is used for spatial search as well (e.g. OBIS database, CMAR's "MarLIN" metadatabase, etc.).
Description
C-squares provides a hierarchical nomenclature for dividing 10°x10° World Meteorological Organization (WMO) squaresWorld Meteorological Organization squares
World Meteorological Organization squares or WMO squares is a system of geocodes that divides a chart of the world with latitude-longitude gridlines into grid cells of 10° latitude by 10° longitude, each with a unique, 4-digit numeric identifier...
into smaller units (each an individual "c-square") of 5°x5°, 1°x1°, 0.5°x0.5°, 0.1°x0.1°, etc., using an alternating base 2, base 5 linear division, as fine as may be required. Each cell of the resulting subdivision is allocated a unique alphanumeric identifier (c-squares code), such that the position of an object or objects on the surface of the Globe
Globe
A globe is a three-dimensional scale model of Earth or other spheroid celestial body such as a planet, star, or moon...
can be represented by a set of one or more such codes that define the cell(s) within which the object occurs. Storing these codes as text identifiers, for example in a database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
, repository of spatial metadata
Geospatial metadata
Geospatial metadata is a type of metadata that is applicable to objects that have an explicit or implicit geographic extent, in other words, are associated with some position on the surface of the Globe...
, searchable text file or web page, then offers the functionality for a simple, text-based spatial search, without the requirement for any more complex geographic information system
Geographic Information System
A geographic information system, geographical information science, or geospatial information studies is a system designed to capture, store, manipulate, analyze, manage, and present all types of geographically referenced data...
(GIS). Once stored (or if desired, generated on-the-fly using a c-squares encoder), a code or set of codes can also be rendered on a map by a utility (for example, the web-accessible c-squares mapper) that incorporates the relevant decoding routines.
The actual assignment of the individual cell identifiers to vector objects whose position is expressed in latitude, longitude coordinates follows rules described in reference (1) and the c-squares website and can be automated via simple routines, and the reverse is also possible (decoding) in a straightforward manner. In addition, since the codes are hierarchical and interleaved (each "cycle" containing identifiers for both longitude and latitude, at progressively finer levels of resolution), only the relevant "leading" portion of a (for example) high resolution code need be interrogated to match a lower resolution spatial query.
Conceptually, the c-squares encoding method belongs to a class of algorithms which can be considered derivations of the Z-order
Z-order (curve)
In mathematical analysis and computer science, Z-order, Morton order, or Morton code is a space-filling curve which maps multidimensional data to one dimension while preserving locality of the data points. It was introduced in 1966 by G. M. Morton...
principle.
Example c-squares codes
LondonLondon
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
, UK, occupies (for example) portions of four 0.5°x0.5° cells:
- -0.5°W to 0°W, 51.5°N to 52.0°N
- -0.5°W to 0°W, 51.0°N to 51.5°N
- 0°E to 0.5°E, 51.5°N to 52.0°N
- 0°E to 0.5°E, 51.0°N to 51.5°N
In c-squares notation these are cells 7500:110:3, 7500:110:1, 1500:110:3 and 1500:110:1 (at 0.5°x0.5° resolution). Alternatively at 1°x1° they are portions of two cells, 7500:110 and 1500:110; at 5°x5° resolution, portions of two cells 7500:1 and 1500:1; and at 10°x10° resolution, portions of 2 cells 7500 and 1500 (equivalent to the same identifiers as in WMO squares
World Meteorological Organization squares
World Meteorological Organization squares or WMO squares is a system of geocodes that divides a chart of the world with latitude-longitude gridlines into grid cells of 10° latitude by 10° longitude, each with a unique, 4-digit numeric identifier...
).
To visualize the position of these squares on a map, the current syntax to address an installation of the "c-squares mapper" is (e.g.):
http://www.obis.org.au/cgi-bin/cs_map.pl?csq=7500:110:3|7500:110:1|1500:110:3|1500:110:1.
In a system that uses c-squares codes as units of spatial indexing, a text-based search on any of these square identifiers will retrieve data associated with the relevant square. If a wildcard search is supported (for example suppose that the wildcard character is a percent sign), a search on "7500%" will retrieve all data items in that ten degree square, a search on "7500:1%" will retrieve all data items in that five degree square, etc.
The asterisk character "*" has a special (reserved) meaning in c-squares notation, being a "compact" notation indicating that all finer cells within a higher level cell are included, to the level of resolution indicated by the number of asterisks. In the example above, "7500:*" would indicate that all 4 five-degree cells within parent ten-degree cell "7500" are filled, "7500:***" would indicate that all 100 one-degree cells within parent ten-degree cell "7500" are filled, etc. This approach enables the filling of contiguous blocks of cells with an economy of characters in many cases (a form of data compression
Data compression
In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....
), that is useful for efficient storage and transfer of c-squares codes as required.
Sample c-squares enabled systems
C-squares spatial indexing, search, and/or mapping routines are currently incorporated into OBIS, the Ocean Biogeographic Information SystemOcean Biogeographic Information System
The Ocean Biogeographic Information System is a web-based access point to information about the distribution and abundance of living species in the ocean.-History:...
; FishBase
FishBase
FishBase is a comprehensive database of information about fish species . It is the largest and most extensively accessed online database on adult finfish on the web...
; AquaMaps
AquaMaps
AquaMaps is a collaborative project with the aim of producing computer-generated predicted global distribution maps for marine species on a 0.5 x 0.5 degree grid of the oceans based on data available through online species databases such as FishBase and SeaLifeBase and species occurrence records...
; and a variety of web-accessible applications at CSIRO Marine and Atmospheric Research
CSIRO Marine and Atmospheric Research
CSIRO Marine and Atmospheric Research is one of the currently c.20 Research Divisions of the Commonwealth Scientific and Industrial Research Organisation, Australia's largest government-supported research agency.-About CMAR:...
. For a full list, see the link Sample c-squares enabled systems on the c-squares website.
See also
- World Meteorological Organization squaresWorld Meteorological Organization squaresWorld Meteorological Organization squares or WMO squares is a system of geocodes that divides a chart of the world with latitude-longitude gridlines into grid cells of 10° latitude by 10° longitude, each with a unique, 4-digit numeric identifier...
- Grid (spatial index)Grid (spatial index)In the context of a spatial index, a grid is a regular tessellation of a manifold or 2-D surface that divides it into a series of contiguous cells, which can then be assigned unique identifiers and used for spatial indexing purposes...
- GeocodeGeocodeGEOCODE is a standardized all-natural number representation format specification for geospatial coordinate measurements that provide details of the exact location of geospatial point at, below, or above the surface of the earth at a specified moment of time.Geocode is patented under US Patents...
- Minimum bounding rectangleMinimum bounding rectangleThe minimum bounding rectangle , also known as bounding box or envelope, is an expression of the maximum extents of a 2-dimensional object within its 2-D coordinate system, in other words min, max, min, max...
- Geospatial metadataGeospatial metadataGeospatial metadata is a type of metadata that is applicable to objects that have an explicit or implicit geographic extent, in other words, are associated with some position on the surface of the Globe...
- Ocean Biogeographic Information SystemOcean Biogeographic Information SystemThe Ocean Biogeographic Information System is a web-based access point to information about the distribution and abundance of living species in the ocean.-History:...
- AquaMapsAquaMapsAquaMaps is a collaborative project with the aim of producing computer-generated predicted global distribution maps for marine species on a 0.5 x 0.5 degree grid of the oceans based on data available through online species databases such as FishBase and SeaLifeBase and species occurrence records...
- FishBaseFishBaseFishBase is a comprehensive database of information about fish species . It is the largest and most extensively accessed online database on adult finfish on the web...
- CSIRO Marine and Atmospheric ResearchCSIRO Marine and Atmospheric ResearchCSIRO Marine and Atmospheric Research is one of the currently c.20 Research Divisions of the Commonwealth Scientific and Industrial Research Organisation, Australia's largest government-supported research agency.-About CMAR:...