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System concept and development by: Tony Rees Divisional Data Centre

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c-squares - a new method for representing, querying, displaying and exchanging dataset spatial extents. System concept and development by: Tony Rees Divisional Data Centre CSIRO Marine Research, Australia. some example Metadatabases (Data Directories). + many others -- 100 < 1000?.

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c-squares - a new method for representing, querying, displaying and exchanging dataset spatial extents

System concept and development by:

Tony Rees

Divisional Data Centre

CSIRO Marine Research, Australia

some example Metadatabases (Data Directories)

+ many others -- 100 < 1000? ...

  • Typical features: include searchability by
    • text
    • keywords
    • spatial and time constraints
  • This presentation - focus onspatial searching
--------- data

----- data bounding rectangle (MBR)

--------- search rectangle

current “base level” representation of spatial data coverage in metadata is by bounding box (minimum bounding rectangle, MBR)

  • concept introduced in 1994 (FGDC)
  • used for spatial searching, 1995 onwards
  • still the primary tool for metadata spatial searches
SRTM 8-449 catch data

Catch records - Hoplostethus atlanticus

How well do MBR’s represent spatial data?

(examples from our own metadata system)

MBR actual data locations

Franklin 02/1999 hydrology data

alternatives to MBR’s for representation of data spatial extents ...
  • bounding polygons
  • multiple bounding rectangles
  • defined regions - countries, administrative areas, bio- or geo-regions …
  • circles (centre point + radius)
  • pre-defined path + distance (e.g. along a contour, coastline, satellite path)
  • actual point locations held in the metadata record
  • grid-based system
global grid systems already available ...
  • International Map of the World (IMW) rectangles (6 x 4 degrees)
  • Marsden Squares (10 x 10 degrees)
  • Maidenhead Squares (2 x 1 degree)
  • WMO (World Meteorological Organisation) Squares (10 x 10 degrees)
  • others ?
  • -- WMO squares eventually chosen for ease of subdivision (base 10) and simple relationship between WMO numbers and lat/long values


WMO 10-degree squares notation (part)

(Available via the web in NODC, 1998:World Ocean Database 1998 Documentation)

The “c-squares”



Concise Spatial Query and Representation System

same using 0.5 x 0.5 degree c-squares

data “footprint” using 1 x 1 degree c-squares

“c-squares” principle

data “footprint” using bounding rectangle

actual ship’s track - “Franklin” voyage 10/87

“c-squares” numbering system
  • each square is numbered according to a globally applicable system based on recursive divisions of WMO (World Meteorological organisation) 10-degree squares, e.g.:
  • 10 degree square: 3414 (= WMO number)
  • 5 degree square: 3414:2
  • 1 degree square: 3414:227
  • 0.5 degree square: 3414:227:4
  • 0.1 degree square: 3414:227:466
  • (etc.)
  • strings of codes represent an individual dataset extent, e.g.
  • 3013:497|3111:468|3111:478|3111:479|3111:488|3111:489|3111:499|3112:122|3112:123|
  • 3112:131|3112:132|3112:134|3112:141|3112:142|3112:143|3112:217|3112:218|3112:219|
  • 3112:226|3112:235|3112:350|3112:351|3112:352|3112:353|3112:360|3112:361|3112:362|
  • 3112:363|3112:370|3112:371|3112:380|3112:381|3112:390|3113:100|3113:101|3113:102|
  • 3113:103|3113:104|3113:205|3113:206|3113:207|3113:216|3113:217|3113:228|3113:238|
  • 3113:239
  • encodes the extent
  • shown in the example:
0.5- and 0.1- degree squares

Codes have straightforward relationship with lats/longs, mapsheets, etc. ...


1400:458(1-degree square with origin at

45 ºN, 008 ºE)

additional degrees E [00+8] =8

additional degrees N [40+5] = 45

5-degree quadrant, i.e. 3 4

1 2

tens of degrees E (i.e., 00)

tens of degrees N (i.e., 40)

global sector (1=NE, 3=SE, 5=SW, 7=NW)




110 km




“quad tree” -type approach used where numerous adjacent squares are occupied

squares can be “bulked” - example: 3212:*** instead of specifying every 1-degree square within 10 degree square 3212.

This leads to corresponding data reduction, e.g. Australia (at 1-degree resolution) can be described in 343 squares rather than 800:

Example database-level implementation of c-squares for metadata records(e.g. at 1 degree resolution)


Spatial queries using c-squares
  • c-squares spatial queries simply test whether a text string representing the search box (ideally one or several c-squares) is matched anywhere in the c-squares string …
  • example: - search square 3113:2 will match any c-squares string which includes 3113:2 within it, e.g.:
  • 3112:363|3112:370|3112:371|3112:380|3112:381|3112:390|3113:100|3113:101|3113:102|
  • 3113:103|3113:104|3113:205|3113:206|3113:207|3113:216|3113:217|3113:228|3113:238|
  • 3113:239
  • hierarchical naming system for c-squares means that finer resolution squares are automatically picked up in any “coarser resolution” search
Viewing the full metadata record produces ...

with clickable link to show dataset extent using c-squares:


Base maps for displayed data can be changed at will by the user, e.g.:

(numerous other maps available, sample only shown)

Process invoked for web mapping

c-squares strings can be sent directly to the CMR c-squares mapper (accessible via the web), e.g. from OBIS (Ocean Biogeographic Information System, USA):

c-squares strings are suitable for inclusion as a new metadata element alongside “bounding box”, for example ...

Franklin Voyage FR 10/87 CTD Data

CSIRO Marine Research

(etc. etc.)







… would permit interoperability with both enabled and non-enabled systems

Summary - strengths and weaknesses of c-squares
  • Strengths ...
  • “c-squares” is a concise and flexible method of encoding simple to moderately complex forms
  • automated or manual code entry (and maintenance) is straightforward
  • spatial searching is simple text string matching operation (no GIS involved)
  • “c-squares mapper” utility available via simple web call
  • can be used as adjunct to bounding coordinates searches
  • Weaknesses …
  • some other numbering systems in use (Marsden Squares, Maidenhead Locators) - needs willingness to standardise on a single system for interoperability
  • c-squares are not a fixed multiple of kilometres, miles, etc.
  • strings can become quite long for large, complex regions (e.g. “Pacific Ocean”) - need to be able to incorporate data reduction using “bulk” method
other comments ...
  • “c-squares” notation is language-independent - can be equally useful in English, French, Italian, Japanese … also discipline-independent
  • downwards-scalability of the c-squares notation means that it can be applied to any size region (e.g. local level)
  • equally applicable to both terrestrial and marine data
  • uses established standards for nomenclature, basis already available via the web (e.g. NODC site)
c-squares current and future status...
  • Implemented already in CMR’s “MarLIN” metadata system and “CAAB” taxon dictionary
  • concept is available for implementation in any other agencies’ metadata systems without cost or technology overhead
  • potential to to be recognised as a formal metadata element by relevant user communities / national bodies
  • current CMR c-squares mapper is already accessible for general use
  • c-squares website constructed as a focal point for all c-squares related materials - including:
    • initial c-squares specification
    • connection information to the c-squares mapper
    • sample PL/SQL code (to convert lat/long pairs to c-squares)
    • on-line lat/long - to - c-square converter
    • example c-squares-enabled metadata records, and more
Acknowledgements …
  • Miroslaw Ryba and other CMR staff for assistance with constructing the c-squares mapper and general feedback
  • “Blue Pages” Marine and Coastal Data Directory (MCDD) for the notation for subdividing WMO squares
  • Martin Dix (CSIRO Atmospheric Research) and NOAA “Globe” Project for base maps as used in the mapper (used by permission)

Questions, comments?


(NB: handout available at this meeting)

My email: [email protected]