GRID SYSTEMS
Size and Shape of the earth:
Approximate sphere - about 20
km wider at equator than poles.
Circumference = 40,000 km
(25,000 miles).
The Graticule, consisting of
meridians and parallels forms a
natural Geographic Grid. The grid
has a natural basis - the equator
and poles of the earth.
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Any point on the
surface of the earth
can be located in
terms of its latitude
and longitude
(angles measured
from the equator and
Prime Meridian).
Passes through
Greenwich, England.
Point P for example
is at 30o north, 20o
west.
Latitude varies from
0o to 90o north or
south.
Longitude varies
from from 0o to 180o
east or west.
Figure courtesy of Anthony P. Kirvan, and NCGIA Core Curriculum in
GIScience.
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Degrees, Minutes, and Seconds
•Angular measurement must be used to specify location on the earth's
surface. A circle has 360 degrees, 60 minutes per degree, and 60 seconds
per minute. Example: 45° 33' 22" (45 degrees, 33 minutes, 22 seconds).
• At the equator 1 degree of longitude = 40,000 km/360 = 111 km. 1
minute = 111 km/60 = 1.85 km. 1 second = 1.85 km/60 = 30 m. Note: 1'
latitude at the equator = 1 nautical mile; 1 knot = 1 nautical mile per
hour.
• Meridians converge, therefore at 60o latitude, 1 degree of longitude =
55.5 km.
•There are 3,600 seconds per degree (60 x 60).
•It is sometimes necessary to convert this conventional angular
measurement into decimal degrees (e.g. often used in GIS’s). E.g. 45° 33'
22“ = 45° 2,002“ = 45° 2,002/3,600 = 45.55°.
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By convention,
latitude is given
before longitude. E.g.
the corner of the map
is:
33o 15’ N
97o 07’ 30” W
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Plane-coordinate Grid Systems.
Problems with the Geographic Grid (Latitude and Longitude):
1. Curved lines on many projections.
2. Lines not equidistantly-spaced.
3. Scale variations.
A practical grid system should Have:
1. Straight lines.
2. Lines intersect at right angles.
3. Lines equally-spaced.
4. Grid squares have equal area.
Two examples are:
Universal Transverse Mercator Grid System
State Plane Grid System
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Universal Transverse Mercator Grid System (UTM)
A transverse cylindrical projection is used:
A narrow strip, 6o of
longitude wide, astride
the central meridian
has very little distortion.
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By moving the cylinder around the globe, 60 strips can be created:
these are UTM grid zones, numbered 1-60.
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For example, grid zone 14 is centered on
99o west and runs through Texas. This
zone covers 96o to 102o west. A 1-km grid
is superimposed onto this map. The grid
lines are numbered by their distance north
from the equator and east from an
imaginary base line which is arbitrarily
located 500 km west of the central
meridian (so the central meridian
becomes the 500,000 m east grid line).
Any point within the grid zone can be
fixed by these two distances (a northing
and an easting).
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The UTM reference:
Zone 14: 621161 m E, 3349894 m N
is a unique location within grid zone 14, accurate to the nearest
meter. The grid zone number must be specified because this same
reference occurs in all grid zones.
When working on a map of a small area in the U.S. such as Denton,
UTM grid references are usually given to the nearest hundred
meters (i.e. the nearest 1/10 of a grid square; so 621161 m E would
become 621200 m E). Also by convention, the zone number, the
first digit in the easting, the first two digits in the northing and the
two zeros (10’s and 1’s of meters) can be dropped. The example
above would then become:
212499 …. This is a 6-digit UTM grid reference.
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For example, this
point is 674100 m
east and 3680300 m
north in grid zone 14.
It’s 6 digit UTM
reference is: 741803
UTM grid tick
Note: to find the original
UTM reference, you can
put the “missing’
numbers back, so
741803 becomes 674100
m east and 3680300 m
north
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Plane-coordinate grid references like UTM references can be used to calculate
distances between points because they are based on measured distances. For
example, the UTM references 123456 and 333777 would have an easting separation
of 33300 -12300 m = 21000 m = 21 km; and a northing separation of 77700 – 45600
m = 32100 m = 32.1 km. By Pythagoras theorem, the straight line distance between
these points would be: sqrt 212 + 32.12 = sqrt 1471.41 = 38.36 km.
333777
38.36 km
123456
32.1 km
21 km
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State Plane Grid System:
In the United States, the State Plane System was developed in the
1930s and was based on the North American Datum 1927
(NAD27). This is similar to the UTM system. Older NAD-27
coordinates are in feet. Newer NAD-83 coordinates are usually in
meters (can be in feet too). State plane systems were developed in
order to provide local reference systems that were tied to a national
datum (NAD-27, NAD-83). Larger states are divided into several
zones. Lambert Conformal Conic projections are commonly used
for rectangular zones with a larger east-west than north-south
extent.
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Texas has 5
NAD-83
State Plane
zones.
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Each zone has an origin with a false easting and northing to
ensure positive coordinates.
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Some examples of State Plane Coordinates in Austin:
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State Plane coordinates
are also shown on
USGS maps (although
there are only a few tick
marks)
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Who uses the State Plane
System? Many local
governments do. North
Central Texas Council of
Governments (NCTCOG
- www.dfwinfo.com) map
data is usually in State
Plane Coordinates.
Example metadata is
shown here for a map of
city boundaries.
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