Nested Grids - CSIRO Marine and Atmospheric Research

Tony Rees
–

C
-
squares Oct 2007









1

Nested Grids: the c
-
squares global grid


Tony Rees

CSIRO Marine and Atmospheric Research, Hobart


Tony.Rees@csiro.au


for: PEMS Workshop on Nested Grids, 21 October 2007

version: final

-

with update, September 2009

Tony Rees
–

C
-
squares Oct 2007









2

The Big Challenge:

Integrating distributed and heterogeneous spatial data
resources to advance science and societal goals

Opening the “Data Closet”

(With thanks to K. Stocks et al. / SDSC for the image and concept!)

Tony Rees
–

C
-
squares Oct 2007









3

One solution: rasterised data on a common grid

–
Grids come in different flavours…

•
Geodesic, global “equal area”

(e.g. triangular, hexagonal, other)

•
Lat / lon, “equal angle”

e.g. 1º x 1º grids, etc. (in unprojected, =
“geographic” projection)

•
Local projected “equal area” grids

e.g. 100 km grids, etc.

–
Typically regional / national scale, do not integrate globally;

do not cope well with longitudinal shifts

–
Areas of interest are sometimes outside the grid (e.g. offshore islands,
high seas, etc.)

–
This project (PEMS) has identified a requirement for a large
scale “Grid System 1” lat / lon based grid, meshing with local,
projected “System 2” grids for finer scale data

–
C
-
squares is an example global scale, lat / lon based grid that
may be of interest for this project’s needs for Grid System 1.

Tony Rees
–

C
-
squares Oct 2007









4

The c
-
squares global grid

–
C
-
squares: acronym for
“Concise Spatial Query and Representation
System” (or: CSIRO squares ??)

–
Developed at CMAR in 2001
-
2, published in scientific literature in 2003*

–
Cover entire world surface, not just the sea (despite choice of journal for
initial publication)

–
Based on pre
-
existing, established “WMO square” notation, for global 10º x
10º squares

–
C
-
squares notation subdivides WMO squares into a nested grid using
alternate base 2, base 5 division, giving the sequence

10º x 10º > 5º x 5º > 1º x 1º > 0.5º x 0.5º > 0.1º x 0.1º, etc.




*
Rees, Tony. 2003. "C
-
squares", a new

spatial indexing system and its applicability

to the description of oceanographic datasets.

Oceanography

16 (1), pp. 11
-
19.

Tony Rees
–

C
-
squares Oct 2007









5

WMO 10
-
degree squares

(starting point for c
-
squares recursive subdivision)

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30
°

N


60
°

N


90
°

N


0
°


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°

S


60
°

S


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°

S


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°

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°

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°

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°

W


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°

W


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°

W


0
°


30
°

E


60
°

E


90
°

E


120
°

E


150
°

E


180
°

E


NW

(7xxx)


NE

(1xxx)


SE

(3xxx)


SW

(5xxx)

Tony Rees
–

C
-
squares Oct 2007









6

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30
°

N


60
°

N


90
°

N


0
°


30
°

S


60
°

S


90
°

S


180
°

W


150
°

W


120
°

W


90
°

W


60
°

W


30
°

W


0
°


30
°

E


60
°

E


90
°

E


120
°

E


150
°

E


180
°

E


NW

(7xxx)


NE

(1xxx)


SE

(3xxx)


SW

(5xxx)

*

you are

here!

WMO 10
-
degree squares

(starting point for c
-
squares recursive subdivision)

Tony Rees
–

C
-
squares Oct 2007









7

The c
-
squares global grid
–

cont’d

–
Each grid cell identifier (= c
-
squares code) “knows” the identity of its
parent, grandparent, etc.

–
Aggregated search can be done by interrogating only the required
leading chars. of the code, e.g.:

•

10º c
-
square code (~1000 km):

3414

(= WMO square code)

•

5º c
-
square code (~500 km):

3414:2

•

1º c
-
square code (~100 km:

3414:227

•

0.5º c
-
square code (~50 km):

3414:227:3

•

0.1º c
-
square code (~10 km):

3414:227:383

(etc.)

(this is the nested set of squares that includes the point at lat
-
42.82, lon 147.38,
in decimal degrees)

•
Search for character string “3414” (ten degree square), with wildcard
appended, will return any of these nested data items

•
Same available at other levels of the hierarchy as applicable (i.e.,
search on any parent code can easily be configured to return all of its
children as well, if desired)

Tony Rees
–

C
-
squares Oct 2007









8

10
-
, 5
-

degree c
-
squares in the Australian region

3314

Tony Rees
–

C
-
squares Oct 2007









9

10
-
, 5
-

degree c
-
squares in the Australian region

3314

1

2

3

4

Tony Rees
–

C
-
squares Oct 2007









10

Recursive subdivision principle (in the SE global quadrant)

-

for 10
-
> 1, 1
-
> 0.1, 0.1
-
> 0.01 degree squares, etc.

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144

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1


2


3


4

Tony Rees
–

C
-
squares Oct 2007









11

3314:100


3314:1


3314





3314:499


Tony Rees
–

C
-
squares Oct 2007









12

Points of interest

–
C
-
squares notation for 10º squares is identical to that for
WMO 10º squares (i.e., no transformation required)

–
1º and 0.5º squares are popular data aggregation sizes at
regional scales

–
0.5º squares are equivalent to 1:100,000 Australian
mapsheets (with global, cf. locally applicable, numbering
system)

–
0.1º squares and finer are useful for data holdings at sub
-
regional / local scales

–
No direct support for 2.5º, 2º, or 0.25º squares in this
system, or degrees / mins / secs notation (except 30 min, =
0.5 degrees)

Tony Rees
–

C
-
squares Oct 2007









13

Who uses what? (Google search hits
–

October 2007…)

•
“10 degree squares” OR “ten degree squares”
:



193

•
“5 degree squares” OR “five degree squares”
:



563

•
“2.5 degree squares” OR “two point five degree squares”:


4

•
“2 degree squares” OR “two degree squares”:



135

•
“1 degree squares” OR “one degree squares”
:



1,660

•
“0.5 degree squares” OR “half degree squares”

(30 min)
:


1,060

•
“0.25 degree squares” OR “quarter degree squares” (15 min):


17,300 *

•
“10 minute squares” OR “ten minute squares”:



249

•
“0.1 degree squares” OR “tenth degree squares”

(6 min)
:


575

•
“5 minute squares” OR “five minute squares”:



47

•
“3 minute squares” OR “three minute squares”
:



1

•
“1 minute squares” OR “one minute squares”:



51

•
“0.01 degree squares” OR “hundredth degree squares”

(0.6 min)
:

1


* NB: (1) “quarter degree squares” are a common standard in use in Africa for wildlife surveys, which
accounts for many / most of these hits


(2) Of the above, c
-
squares directly supports the resolutions shown in
bold + underline
, indirectly
could support others (by aggregation / approximate matching??)

Tony Rees
–

C
-
squares Oct 2007









14

D/M/S vs. decimal degrees…

•
What fine scale grids (e.g. sub 1
-
degree) are in use locally /
internationally
–

e.g.:

–
30 minute = 0.5 degree (~50 km)

–
5 minute = 0.0833 degree (~10 km)

–
1 minute = 0.0167 degree (~2 km)

–
30 second = 0.00833 degree (~1 km)

–
9 second = 0.0025 degree (~250m)

–
2 second = 0.00055 degree (~50m)

–
1 second = 0.000278 degree (~25m)

•
Is there a requirement / preference to maintain similar (deg / min /
sec) resolutions in the selected system? (cf. c
-
squares is based on
decimal degrees and half steps)

•
Does this preclude (or encourage) the use of c
-
squares for
resolutions e.g. 0.5 degrees and above?

Tony Rees
–

C
-
squares Oct 2007









15

Use cases for c
-
squares, of possible interest to this project

–
Hierarchical spatial search

•
Example shown: OBIS (Ocean Biogeographic information System), USA

–
C
-
squares as spatial metadata, and associated spatial search
(also: mapping)

•
Example shown: MarLIN (Marine Laboratories Information Network),
CSIRO, Australia

–
C
-
squares as grid cell identifiers, for data storage, rapid access,
and mapping of outputs

•
Example shown: AquaMaps project (Germany + Philippines)

–
Variable resolution encoding within the same dataset (or data item)

•
Example shown: CSIRO (CMAR) satellite data index

–
Using c
-
squares for Antarctic / Southern Ocean / Polar data

•
Examples shown: CMAR satellite data index; online polygon fill algorithm (on
c
-
squares website)

Tony Rees
–

C
-
squares Oct 2007









16

Hierarchical spatial search: OBIS example


http://www.iobis.org/

Tony Rees
–

C
-
squares Oct 2007









17

OBIS, USA: Hierarchical spatial search (for species with records in selected area)

Tony Rees
–

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-
squares Oct 2007









18

OBIS, USA: Hierarchical spatial search (for species with records in selected area)

Tony Rees
–

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-
squares Oct 2007









19

C
-
squares as spatial metadata: MarLIN
example


http://www.cmar.csiro.au/marlin/

Tony Rees
–

C
-
squares Oct 2007









20

C
-
squares as spatial metadata (list of square IDs = “dataset footprint”)

Tony Rees
–

C
-
squares Oct 2007









21

C
-
squares as spatial metadata (list of square IDs = “dataset footprint”)

Tony Rees
–

C
-
squares Oct 2007









22

C
-
squares as spatial metadata (list of square IDs = “dataset footprint”)

Tony Rees
–

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-
squares Oct 2007









23

C
-
squares as spatial metadata (list of square IDs = “dataset footprint”)

Tony Rees
–

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-
squares Oct 2007









24

C
-
squares as spatial metadata (list of square IDs = “dataset footprint”)

(A)

(B)

…search for matching square (=tile) ID (A) is much more precise than
search by bounding box using “overlapping rectangles” test (B)

[far fewer false positives]
–

presuming tile size is well matched to
the data and / or intended query scale (may be an optimization
issue here)

Tony Rees
–

C
-
squares Oct 2007









25

C
-
squares as grid cell identifiers: AquaMaps
example


http://www.aquamaps.org/

Tony Rees
–

C
-
squares Oct 2007









26

C
-
squares as grid cell identifiers: example from the AquaMaps project

“Half degree cell authority file” (HCAF)
–

covers the world in 259,200 database rows

Tony Rees
–

C
-
squares Oct 2007









27

(Looks familiar?)

(from PEMS presentation, SSC2007)

Tony Rees
–

C
-
squares Oct 2007









28

C
-
squares as grid cell identifiers: example from the AquaMaps project

“Half degree cell authority file” (HCAF)
–

covers the world in 259,200 database rows

Tony Rees
–

C
-
squares Oct 2007









29

C
-
squares as grid cell identifiers: example from the AquaMaps project

1.0

0.5

0

28

29

30

31

32

1.0

0.5

0

7

8

9

10

11

1.0

0.5

0

10

20

30

40

50

1.0

0.5

0

A

B

Temperature

Substrate type

Salinity

Depth

Modelled fish
-
habitat
relationships (SI’s)

Temperature SI map

Depth SI map

Salinity SI map

Substrate SI map







HSI =

1/4

Low
suitability

High suitability

Unsuitable

Medium

Habitat suitability
index map

Digital environmental maps
recoded with the SI’s

Tony Rees
–

C
-
squares Oct 2007









30

C
-
squares as grid cell identifiers: example from the AquaMaps project

Sample map output (produced by the c
-
squares mapper)

NB with multiple maps, can then query individual cells for species richness, etc. etc.

Tony Rees
–

C
-
squares Oct 2007









31

Variable resolution encoding using c
-
squares: Satellite Data Index example


http://www.marine.csiro.au/remotesensing/csq
-
chooser.htm

Tony Rees
–

C
-
squares Oct 2007









32

Variable resolution encoding: example from the CMAR satellite data index

Special notation available, e.g.

3414



= ten degree square only (data may be anywhere within it);










3414:***:*

= all of the 0.5 degree squares within ten degree square 3414.

Tony Rees
–

C
-
squares Oct 2007









33

Antarctic data
–

special case or not?

•
AAD, satellite imagery, oceanographic data
–

much data
from region between Australia and Antarctica, as well as on
landmass itself and adjacent waters

•
Definite integration benefits if on a common grid / spatial
query interface, e.g. OBIS example, others… (no fixed
boundary in the ocean / natural world)

•
C
-
squares covers polar regions as well as rest of world (just
have to decide which square to allocate actual pole to!)
–

uses more squares, but otherwise no intrinsic problem

•
Example from CMAR satellite data index (uses 0.5 degree
squares):

Tony Rees
–

C
-
squares Oct 2007









34

Tony Rees
–

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-
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35

Tony Rees
–

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-
squares Oct 2007









36

Tony Rees
–

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-
squares Oct 2007









37

(what just happened here?)

fragment of the spatial index…

–
We clicked on square with bounds

(lat)
-
65
–

-
70, (lon) 130
–

135 … = c
-
square 3613:3 (user never sees this, but
system generates it for the search)

–
System searches for unique scenes with
prefix “3613:3” in the spatial index, does a
join on other table[s] to satisfy any other
criteria

–
Generates list of 473 matching targets in
(in this case) <2 seconds

–
Spatial partitioning used in this system, to
optimise search and index rebuild speeds
(single table split into 100 smaller ones);
“duplicate” single large one retained to
quickly retrieve all squares associated
with a particular scene (for mapping)

Tony Rees
–

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-
squares Oct 2007









38

Tony Rees
–

C
-
squares Oct 2007









39

Tony Rees
–

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-
squares Oct 2007









40

Tony Rees
–

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-
squares Oct 2007









41

Tony Rees
–

C
-
squares Oct 2007









42

–
Polygons encoded to c
-
squares can include a pole without
problem: e.g. on
-
line polygon
-
fill algorithm on c
-
squares
web site:


http://www.cmar.csiro.au/csquares/converter.htm


Tony Rees
–

C
-
squares Oct 2007









43

Tony Rees
–

C
-
squares Oct 2007









44

Successful filled polygon conversion

c
-
square code:

3606:104|3606:114|3606:124|3606:134|3606:143|3606:144|3606:2**|3606:353|
3606:354|3606:363|3606:364|3606:372|3606:373|3606:374|3606:382|3606:383|
3606:384|3606:391|3606:392|3606:393|3606:394|3606:4**|3607:1**|3607:205|
3607:215|3607:225|3607:235|3607:245|3607:246|3607:3**|3607:455|3607:456|
3607:465|3607:466|3607:475|3607:476|3607:477|3607:485|3607:486|3607:487|
3607:495|3607:496|3607:497|3607:498|3705:239|3705:248|3705:249|3705:384|
3705:392|3705:393|3705:394|3705:457|3705:458|3705:459|3705:466|3705:467|
3705:468|3705:469|3705:475|3705:476|3705:477|3705:478|3705:479|3705:485|
3705:486|3705:487|3705:488|3705:489|3705:495|3705:496|3705:497|3705:498|
3705:499|3706:101|3706:102|3706:103|3706:104|3706:110|3706:111|3706:112|
3706:113|3706:114|3706:120|3706:121|3706:122|3706:123|3706:124|3706:130|
3706:131|3706:132|3706:133|3706:134|3706:140|3706:141|3706:142|3706:143|
3706:144|3706:2**|3706:3**|3706:4**|3707:1**|3707:205|3707:206|3707:207|
3707:208|3707:215|3707:216|3707:217|3707:218|3707:219|3707:225|3707:226|
3707:227|3707:228|3707:229|3707:235|3707:236|3707:237|3707:238|3707:239|
3707:245|3707:246|3707:247|3707:248|3707:249|3707:3**|3707:4**| (etc.)

Tony Rees
–

C
-
squares Oct 2007









45

Successful filled polygon conversion

c
-
square code:

3606:104|3606:114|3606:124|3606:134|3606:143|3606:144|3606:2**|3606:353|
3606:354|3606:363|3606:364|3606:372|3606:373|3606:374|3606:382|3606:383|
3606:384|3606:391|3606:392|3606:393|3606:394|3606:4**|3607:1**|3607:205|
3607:215|3607:225|3607:235|3607:245|3607:246|3607:3**|3607:455|3607:456|
3607:465|3607:466|3607:475|3607:476|3607:477|3607:485|3607:486|3607:487|
3607:495|3607:496|3607:497|3607:498|3705:239|3705:248|3705:249|3705:384|
3705:392|3705:393|3705:394|3705:457|3705:458|3705:459|3705:466|3705:467|
3705:468|3705:469|3705:475|3705:476|3705:477|3705:478|3705:479|3705:485|
3705:486|3705:487|3705:488|3705:489|3705:495|3705:496|3705:497|3705:498|
3705:499|3706:101|3706:102|3706:103|3706:104|3706:110|3706:111|3706:112|
3706:113|3706:114|3706:120|3706:121|3706:122|3706:123|3706:124|3706:130|
3706:131|3706:132|3706:133|3706:134|3706:140|3706:141|3706:142|3706:143|
3706:144|3706:2**|3706:3**|3706:4**|3707:1**|3707:205|3707:206|3707:207|
3707:208|3707:215|3707:216|3707:217|3707:218|3707:219|3707:225|3707:226|
3707:227|3707:228|3707:229|3707:235|3707:236|3707:237|3707:238|3707:239|
3707:245|3707:246|3707:247|3707:248|3707:249|3707:3**|3707:4**| (etc.)

Tony Rees
–

C
-
squares Oct 2007









46

Successful filled polygon conversion

c
-
square code:

3606:104|3606:114|3606:124|3606:134|3606:143|3606:144|3606:2**|3606:353|
3606:354|3606:363|3606:364|3606:372|3606:373|3606:374|3606:382|3606:383|
3606:384|3606:391|3606:392|3606:393|3606:394|3606:4**|3607:1**|3607:205|
3607:215|3607:225|3607:235|3607:245|3607:246|3607:3**|3607:455|3607:456|
3607:465|3607:466|3607:475|3607:476|3607:477|3607:485|3607:486|3607:487|
3607:495|3607:496|3607:497|3607:498|3705:239|3705:248|3705:249|3705:384|
3705:392|3705:393|3705:394|3705:457|3705:458|3705:459|3705:466|3705:467|
3705:468|3705:469|3705:475|3705:476|3705:477|3705:478|3705:479|3705:485|
3705:486|3705:487|3705:488|3705:489|3705:495|3705:496|3705:497|3705:498|
3705:499|3706:101|3706:102|3706:103|3706:104|3706:110|3706:111|3706:112|
3706:113|3706:114|3706:120|3706:121|3706:122|3706:123|3706:124|3706:130|
3706:131|3706:132|3706:133|3706:134|3706:140|3706:141|3706:142|3706:143|
3706:144|3706:2**|3706:3**|3706:4**|3707:1**|3707:205|3707:206|3707:207|
3707:208|3707:215|3707:216|3707:217|3707:218|3707:219|3707:225|3707:226|
3707:227|3707:228|3707:229|3707:235|3707:236|3707:237|3707:238|3707:239|
3707:245|3707:246|3707:247|3707:248|3707:249|3707:3**|3707:4**| (etc.)

Tony Rees
–

C
-
squares Oct 2007









47

–
Note, (1) C
-
squares (and the polygon fill algorithm) copes with
the polar case with no intrinsic problem

–
(2) automatic, multi
-
resolution data compression incorporated
into the encoding algorithms on the c
-
squares web site (can be
disabled if desired)

–
(3) relevant decompression stage incorporated into the c
-
squares mapper, also can be disabled as required (e.g. for
demo purposes i.e. these slides)


…Of course, can do much of this (in principle) with any type of
grid structure / nomenclature for grid cells, however, c
-
squares
compatible datasets are in general use at sub
-
national,
national, and international scale, e.g.:


Tony Rees
–

C
-
squares Oct 2007









48

Museum Victoria Bioinformatics search interface (0.5 degree squares,
regional)

Tony Rees
–

C
-
squares Oct 2007









49

AquaMaps, also similar CMAR data (0.5 degree squares,
national + global)

Tony Rees
–

C
-
squares Oct 2007









50

Vertebrate census data, e.g. birds (1 degree squares, national)

Tony Rees
–

C
-
squares Oct 2007









51

BRS fisheries / associated data (0.5 degree squares, national)

Tony Rees
–

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-
squares Oct 2007









52

AFMA data (0.1 degree / 6 minute squares,
sub
-
national)

Tony Rees
–

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-
squares Oct 2007









53

Selected bibliography / reference materials

Rees, T. 2002.
C
-
squares
–

a new method for representing, querying, displaying and
exchanging dataset spatial extents
. Abstract and presentation at EOGEO Technical
Workshop, May 2002, accessible via
http://www.cmar.csiro.au/csquares/eogeo2002
-
rees.ppt

Rees, T. 2003. "C
-
squares", a new spatial indexing system and its applicability to the
description of oceanographic datasets.
Oceanography

16 (1), 11
-
19.

Rees, T. 2004.
Use of c
-
squares spatial indexing and mapping in the 2004 release of
OBIS, the Ocean Biogeographic Information System
. Abstract and presentation at
EOGEO Technical Workshop, July 2004, accessible via
http://www.cmar.csiro.au/csquares/eogeo04
-
rees.ppt

Rees, T. and Smith, G. 2004.
Application of c
-
squares spatial indexing to an archive of
remotely sensed data
. Abstract and presentation at EOGEO Technical Workshop, July
2004, accessible via
http://www.cmar.csiro.au/csquares/eogeo04
-
reessmith.ppt

Kaschner, K., J. S. Ready, E. Agbayani, J. Rius, K. Kesner
-
Reyes, P. D. Eastwood, A. B.
South, S. O. Kullander, T. Rees, C. H. Close, R. Watson, D. Pauly, and R. Froese.
2007.
AquaMaps
.
Abstract and presentation at Ocean Biodiversity Informatics 2007,
accessible via
http://www.cmar.csiro.au/datacentre/presentations/
OBI
-
2007
-
Kaschner.ppt


C
-
squares resources on the web:

•
C
-
squares home page:
http://www.cmar.csiro.au/csquares/

•
C
-
squares on SourceForge:
http://csquares.sourceforge.net/

.

Tony Rees
–

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-
squares Oct 2007









54

http://www.cmar.csiro.au/csquares/

Tony Rees
–

C
-
squares Oct 2007









55

http://www.cmar.csiro.au/csquares/

Tony Rees
–

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-
squares Oct 2007









56

Update September 2009

•
(1) C
-
squares functionality is currently being added to the IMOS (and
AODCJF/BlueNet) Metadata Search and Entry Tool
–

MEST

–
IMOS MEST is part of the GeoNetwork Open Source Development Community
(origin with FAO in Italy)
–

currently installed base in >20 countries worldwide;
Australian developments will be fed back into the GeoNetwork trunk for anyone to
use

•
(2)
IHO (International Hydrographic Office) is considering a recommendation
from their technical committee to use c
-
squares for spatial indexing of
hydrographic charts from all nations; proposal made at Montreal, May 2009,
to be progressed at Sydney, October 2009

•
(3) C
-
squares is still providing backbone of all the spatial searches and
mapping for OBIS (USA); 3 attempts to introduce more sophisticated GIS
front ends have so far failed to deliver desired outcomes, c
-
squares is still
mission critical for them…

•
(4) AquaMaps
–

another bulk c
-
squares user
–

is engaged with Google
Oceans to provide prototype “what lives here” functionality on
mouseover/click, for waters anywhere in the world.

Tony Rees
–

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-
squares Oct 2007









57

Conclusions

•
C
-
squares may be a good fit with PEMS data store needs for “Grid System 1” (but may
need to think further about finer scale, D/M/S grid requirements)

•
System has global coverage / interoperability, has been real
-
world tested for 5+ years,
Antarctic / polar data not a problem (or features crossing the date line)

•
Some supporting infrastructure already in place, e.g.:

–
Tools i.e. encoders (lat/lon to c
-
squares), decoders, validators

–
C
-
squares mappers (x 4 worldwide at present time)

… possibly useful starting point for further development to suit project needs

•
Supports efficient, variable
-
resolution (quadtree
-
like) encoding for large regions if
required, no impact on search performance (actually, it gets faster!)

•
Database, platform, & vendor independent system; transparent & simple / rapid
operation (no “black boxes”); open source repository for code, suits multi
-
developer
model

•
Potential for ongoing interaction with local development “team” at CMAR as needed.