tony rees: the c-squares nested global grid

Nested Grids: the c-squares global grid and its notation

Tony Rees – CSIRO Marine and Atmospheric Research, Australia

September 2011

Tony Rees: C-squares nested grid notation

Rationale for c-squares and this talk

• C-squares aims to provide a hierarchical, globally applicable system of geocodes representing discrete areas on the ground at a range of scales, including commonly used 1×1 and 0.5×0.5 degree squares, useful for:

• spatial indexing and data aggregation

• rapid data search

• representation of complex areas (as strings of relevant c-squares)

• simple/rapid web mapping (using the CMAR-developed c-squares mapper web utility)

• The codes are parseable to easily extract location information for any desired scale down to the finest resolution represented

• Moving location data into and out of the system (encoding and decoding) i.e. from/to lat-lon coordinates in decimal degrees is intended to be very logical, and can be accomplished by trivial amounts of code.

Rationale for this talk:• Introduce the domain within which c-squares operates

• Walk through the c-squares notation

• Look briefly at some real-world applications presently using c-squares.


Starting point for hierarchical subdivision

• Decimal degrees of lat, lon are preferred international data and metadata interchange format (in WGS84)

• 10 deg. squares are most logical starting point for recursive subdivision (other available options, e.g. 6×4 deg. squares, less useable)

• Three notations have been proposed / used for global 10 deg. squares, of these the “WMO Square” notation is the most tractable, e.g. see the following from oceanteacher.org:

• (See also e.g. Wikipedia for further information)


WMO Squares: global quadrants


7817 7816 7815 7814 7813 7812 7811 7810 7809 7808 7807 7806 7805 7804 7803 7802 7801 7800 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817

7717 7716 7715 7714 7713 7712 7711 7710 7709 7708 7707 7706 7705 7704 7803 7702 7701 7700 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717

7617 7616 7615 7614 7613 7612 7611 7610 7609 7608 7607 7606 7605 7604 7803 7602 7601 7600 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617

7517 7516 7515 7514 7513 7512 7511 7510 7509 7508 7507 7506 7505 7504 7803 7502 7501 7500 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517

7417 7416 7415 7414 7413 7412 7411 7410 7409 7408 7407 7406 7405 7404 7803 7402 7401 7400 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417

7317 7316 7315 7314 7313 7312 7311 7310 7309 7308 7307 7306 7305 7304 7803 7302 7301 7300 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317

7217 7216 7215 7214 7213 7212 7211 7210 7209 7208 7207 7206 7205 7204 7803 7202 7201 7200 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217

7117 7116 7115 7114 7113 7112 7111 7110 7109 7108 7107 7106 7105 7104 7803 7102 7101 7100 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117

7017 7016 7015 7014 7013 7012 7011 7010 7009 7008 7007 7006 7005 7004 7803 7002 7001 7000 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017

5017 5016 5015 5014 5013 5012 5011 5010 5009 5008 5007 5006 5005 5004 5003 5002 5001 5000 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017

5117 5116 5115 5114 5113 5112 5111 5110 5109 5108 5107 5106 5105 5104 5103 5102 5101 5100 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117

5217 5216 5215 5214 5213 5212 5211 5210 5209 5208 5207 5206 5205 5204 5203 5202 5201 5200 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217

5317 5316 5315 5314 5313 5312 5311 5310 5309 5308 5307 5306 5305 5304 5303 5302 5301 5300 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317

5417 5416 5415 5414 5413 5412 5411 5410 5409 5408 5407 5406 5405 5404 5403 5402 5401 5400 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417

5517 5516 5515 5514 5513 5512 5511 5510 5509 5508 5507 5506 5505 5504 5503 5502 5501 5500 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517

5617 5616 5615 5614 5613 5612 5611 5610 5609 5608 5607 5606 5605 5604 5603 5602 5601 5600 3600 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617

5717 5716 5715 5714 5713 5712 5711 5710 5709 5708 5707 5706 5705 5704 5703 5702 5701 5700 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713 3714 3715 3716 3717

5817 5816 5815 5814 5813 5812 5811 5810 5809 5808 5807 5806 5805 5804 5803 5802 5801 5800 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817

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

(7---)

NE

(1---)

SE

(3---)

SW

(5---)

Global quadrants numbered 1, 3, 5, 7 anticlockwise from NE


WMO Squares: ten degree squares


7817 7816 7815 7814 7813 7812 7811 7810 7809 7808 7807 7806 7805 7804 7803 7802 7801 7800 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817

7717 7716 7715 7714 7713 7712 7711 7710 7709 7708 7707 7706 7705 7704 7803 7702 7701 7700 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717

7617 7616 7615 7614 7613 7612 7611 7610 7609 7608 7607 7606 7605 7604 7803 7602 7601 7600 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617

7517 7516 7515 7514 7513 7512 7511 7510 7509 7508 7507 7506 7505 7504 7803 7502 7501 7500 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517

7417 7416 7415 7414 7413 7412 7411 7410 7409 7408 7407 7406 7405 7404 7803 7402 7401 7400 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417

7317 7316 7315 7314 7313 7312 7311 7310 7309 7308 7307 7306 7305 7304 7803 7302 7301 7300 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317

7217 7216 7215 7214 7213 7212 7211 7210 7209 7208 7207 7206 7205 7204 7803 7202 7201 7200 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217

7117 7116 7115 7114 7113 7112 7111 7110 7109 7108 7107 7106 7105 7104 7803 7102 7101 7100 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117

7017 7016 7015 7014 7013 7012 7011 7010 7009 7008 7007 7006 7005 7004 7803 7002 7001 7000 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017

5017 5016 5015 5014 5013 5012 5011 5010 5009 5008 5007 5006 5005 5004 5003 5002 5001 5000 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017

5117 5116 5115 5114 5113 5112 5111 5110 5109 5108 5107 5106 5105 5104 5103 5102 5101 5100 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117

5217 5216 5215 5214 5213 5212 5211 5210 5209 5208 5207 5206 5205 5204 5203 5202 5201 5200 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217

5317 5316 5315 5314 5313 5312 5311 5310 5309 5308 5307 5306 5305 5304 5303 5302 5301 5300 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317

5417 5416 5415 5414 5413 5412 5411 5410 5409 5408 5407 5406 5405 5404 5403 5402 5401 5400 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417

5517 5516 5515 5514 5513 5512 5511 5510 5509 5508 5507 5506 5505 5504 5503 5502 5501 5500 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517

5617 5616 5615 5614 5613 5612 5611 5610 5609 5608 5607 5606 5605 5604 5603 5602 5601 5600 3600 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617

5717 5716 5715 5714 5713 5712 5711 5710 5709 5708 5707 5706 5705 5704 5703 5702 5701 5700 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713 3714 3715 3716 3717

5817 5816 5815 5814 5813 5812 5811 5810 5809 5808 5807 5806 5805 5804 5803 5802 5801 5800 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817

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

(7yxx)

NE

(1yxx)

SE

(3yxx)

SW

(5yxx)

Then: y = tens of latitude N / S 0–8 xx = tens of longitude W / E 00–17


WMO Squares: ten degree squares


7817 7816 7815 7814 7813 7812 7811 7810 7809 7808 7807 7806 7805 7804 7803 7802 7801 7800 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817

7717 7716 7715 7714 7713 7712 7711 7710 7709 7708 7707 7706 7705 7704 7803 7702 7701 7700 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717

7617 7616 7615 7614 7613 7612 7611 7610 7609 7608 7607 7606 7605 7604 7803 7602 7601 7600 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617

7517 7516 7515 7514 7513 7512 7511 7510 7509 7508 7507 7506 7505 7504 7803 7502 7501 7500 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517

7417 7416 7415 7414 7413 7412 7411 7410 7409 7408 7407 7406 7405 7404 7803 7402 7401 7400 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417

7317 7316 7315 7314 7313 7312 7311 7310 7309 7308 7307 7306 7305 7304 7803 7302 7301 7300 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317

7217 7216 7215 7214 7213 7212 7211 7210 7209 7208 7207 7206 7205 7204 7803 7202 7201 7200 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217

7117 7116 7115 7114 7113 7112 7111 7110 7109 7108 7107 7106 7105 7104 7803 7102 7101 7100 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117

7017 7016 7015 7014 7013 7012 7011 7010 7009 7008 7007 7006 7005 7004 7803 7002 7001 7000 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017

5017 5016 5015 5014 5013 5012 5011 5010 5009 5008 5007 5006 5005 5004 5003 5002 5001 5000 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017

5117 5116 5115 5114 5113 5112 5111 5110 5109 5108 5107 5106 5105 5104 5103 5102 5101 5100 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117

5217 5216 5215 5214 5213 5212 5211 5210 5209 5208 5207 5206 5205 5204 5203 5202 5201 5200 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217

5317 5316 5315 5314 5313 5312 5311 5310 5309 5308 5307 5306 5305 5304 5303 5302 5301 5300 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317

5417 5416 5415 5414 5413 5412 5411 5410 5409 5408 5407 5406 5405 5404 5403 5402 5401 5400 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417

5517 5516 5515 5514 5513 5512 5511 5510 5509 5508 5507 5506 5505 5504 5503 5502 5501 5500 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517

5617 5616 5615 5614 5613 5612 5611 5610 5609 5608 5607 5606 5605 5604 5603 5602 5601 5600 3600 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617

5717 5716 5715 5714 5713 5712 5711 5710 5709 5708 5707 5706 5705 5704 5703 5702 5701 5700 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713 3714 3715 3716 3717

5817 5816 5815 5814 5813 5812 5811 5810 5809 5808 5807 5806 5805 5804 5803 5802 5801 5800 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817

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

(7yxx)

NE

(1yxx)

SE

(3yxx)

SW

(5yxx)

Example: Canberra (SE global quadrant, lat. 35.27603 S, 149.13435 E) is in square 3314 (simple to encode/decode once the principle is known;next digits “5” and “9” will be used in c-squares notation for 1 deg. square, and so on)


Other 10 deg. squares in the Australian + NZ region of interest


“C-squares” hierarchical subdivision of 10 degree WMO squares

• No previous established method for hierarchical(recursive) subdivision of WMO or other10 degree squares

• C-squares notation developed to fill this need,late 2001

• Has been in use since that time without problem,also written descriptions available in 2 publishedsources (“Oceanography” article 2003; L. Hill “Georeferencing” textbook, 2006), plus Wikipedia

• Supported by available utilities including global + regionalc-squares mapper, online and offline encoders/decoders, plus more (refer www.cmar.csiro.au/csquares)

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


The c-squares hierarchical notation

• For decimal degrees, could simply nest recursively at /10 intervals, however in practice intermediate resolutions often useful – e.g. 0.5 deg. global grids used by AquaMaps, others

• C-squares therefore nests at alternating /2 then /5 intervals: produces grid compatible with decimal degrees, but also serves needs of users for intermediate resolution steps

• Notation examples:

• 3314 10×10 deg. square (~1000 km nominal)• 3314:1 5×5 deg. square (~500 km nominal)• 3314:100 1×1 deg. square (~100 km nominal)• 3314:100:1 0.5×0.5 deg. square (~50 km nominal)• 3314:100:100 0.1×0.1 deg. square (~10 km nominal) (etc.)

• Note, this is a true nested notation – every child cell explicitly references its parent, can do coarser <> finer searches as required over codes without any transform needed (alternative would be non-interleaved codes e.g. British system, which does not support this feature)

• Leading digit of each “triple” indicates “intermediate quadrant”, as follows:


C-squares nested subdivisions (e.g. in SE global quadrant):

Intermediate quadrant notation (based on absolute values irrespective of positive or negative): 1: low lat, low lon 2: low lat, high lon 3: high lat, low lon 4: high lat, high lon


C-squares nested subdivisions (e.g. in SE global quadrant):

Continuing “Canberra” example , lat. 35 S, 149 E:5 deg. square will be 3314:41 deg. square will be 3314:459 (etc.)


• Result: ~simple, logical system for encoding / decoding; encoders can be written very easily (examples in 5+ languages already available), decoding even by mental arithmetic

• Note, actual bounds of squares are technically adjacent, not congruent

• Square 1000 extends northwards from 0 to 9.999… (not 0 to 10) for encoding purposes (data located at lat. 10.0 is into the next square) – however is rendered as 0 to 10 for display

• A few special cases to handle:

• zero lat, lon is positive, not negative (-0 does not exist for encoding purposes)

• 90 N/S treated as 89.999… (no next available square)

• 180 E/W treated as 179.999… (same) – also, could make executive decision to deprecate one of these if preferred

C-squares encoding / decoding


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


C-squares in practice – e.g. in CMAR “MarLIN” metadata system



adds these elements:



adds these elements:

…can even Google “3414:371:2” to retrieve this dataset description (plus spatially overlapping ones)


Sample c-squares enabled systems (as at Sep 2011)

AquaMaps marine species modelled distribution

OBIS point data recordsCMAR project survey sites

CMAR satellite data footprint


Some stats

GLOBAL:

• Global 1 deg. squares (100 km nominal): 64,800

• Global 0.5 deg. squares (50 km nominal): 259,200

• Global 0.1 deg. squares (10 km nominal): 6.48 million

Austr. continental area (e.g. for an array of 5 x 4 10 deg. squares):

• 1 deg. squares (100 km nominal): 2,000

• 0.5 deg. squares (50 km nominal): 8,000



• 0.01 deg. squares (1 km nominal): 20 million

• 0.005 deg. squares (500 m nominal): 80 million


In conclusion…

• C-squares offers a scalable, easy-to-use indexing system for lat-lon based grid cells across the Australian region, also completely compatible with global data needs

• C-squares hierarchical codes can be searched at a range of scales via substring comparisons, also can be truncated as needed to coarsen resolutions if required

• C-squares has no real-world competitors as a coding system compatible with decimal degrees; systems employing c-squares have been in continuous production use in Australia and elsewhere for almost 10 years with zero problems.

Contact UsPhone: 1300 363 400 or +61 3 9545 2176

Email: [email protected] Web: www.csiro.au

Thank you


image courtesy Tisham Dhar, CMAR VIZ project


Supplementary slides


British National Grid indexing

• Initial letter (H, J, N, O, S, T) indicates 500km square. Theoretically, the system extends far over the Atlantic Ocean and well into Western Europe with square AA near Iceland and square ZZ in northern Italy, however the normal area mapped is shown on the diagram.

• For the second letter, each 500 km square is subdivided into 25 squares of 100 by 100 km, each with a letter code from A to Z (omitting I) starting with A in the north-west corner to Z in the south-east corner.

• Within each square, eastings and northings from the origin (south west corner) of the square are given numerically. For example, NH0325 means a 1 km square whose south-west corner is 3 km east and 25 km north from the south-west corner of square NH. A location can be indicated to varying resolutions numerically, usually from two digits in each coordinate (for a 1 km square) through to five (for a 1 m square); in each case the first half of the digits is for the first coordinate and the second half for the other.


Equal area satellite data swath requires more grid squares as it approaches the poles – but system can handle this

tony rees: the c-squares nested global grid

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