1. Map Projection & Coordinate
Systems (review)
Ellipsoids and Datums
●
Map Projections
●
Coordinate Systems
●
Philippine Coordinate System
●

2. Ojibwe (Native American) ca. 1820, drawn on birch bark (which accounts for its shape), shows the
migration legend of the Ojibwe, from the creation of their people to their home .
Sketch maps on home ranges. Map
was made by Chris (middle schooler),
who rode bus #71.
Earth’s shape. Without water and clouds, it looks like a
sloppily peeled potato. European Remote Sensing
satellite, ERS­1 from 780 Km.

3. The equatorial radius of the earth
3,443.609 – Airy (1830)
3,443.931 – Austrian Nat'l­South Am. (1969)
3,443.957 – Clark 1866
3,443.980 – Clark (1850)
3,443.939 – Geodetic Reference System (1980)
3,444.054 – International (1924)
3,443.917 – World Geodetic System (1972)
Defense Mapping Agency, Hydrographic Center, American Practical Navigator (1977),
Map Projections – A working Manual (1987)

4. The equatorial radius of the earth
3,443.609 – Airy (1830)
3,443.931 – Austrian Nat'l­South Am. (1969)
3,443.957 – Clark 1866
3,443.980 – Clark (1850)
3,443.939 – Geodetic Reference System (1980)
3,444.054 – International (1924)
3,443.917 – World Geodetic System (1972)
Defense Mapping Agency, Hydrographic Center, American Practical Navigator (1977),
Map Projections – A working Manual (1987)

5. • How well can we hit Minsk, USSR with a missile
from Kansas (circa 1960)?
Minsk (Pulkovo, 1942)
N 53° 52' 57.78quot; E 028° 01' 58.00quot;
Minsk (NAD­27)
N 53° 53' 02.76quot; E 028° 01' 43.06”
∆ Latitude = ~ 5”, ∆ Longitude = ~15”
Around 313 meters of error

6. These Coordinates Refer
to the Same Bridge!
a) 37° 53.423’ N, 126° 43.990’ E, h = 23 m
b) 37° 53.423’ N, 126° 43.990’ E, H = 0 m
c) 37° 53’ 25.4” N, 126° 43’ 59.4” E, h = 23 m
d) 37° 53’ 25.4” N, 126° 43’ 59.4” E, H = 0 m
e) 37.89038° N, 126.73316° E, h = 23 m
f) 37.89038° N, 126.73316° E, H = 0 m
g) Zone 52, 300669 m E, 4196075 m N, h = 23 m
h) Zone 52, 300669 m E, 4196075 m N, H = 0 m
i) 52S CG 00668 96075, h = 23 m
j) 52S CG 00668 96075, H = 0 m
k) ­3014326.6 m, 4039148.7 m, 3895863.0 m
l) 37° 53.260’ N, 126° 44.116’ E, h ≅ H = 0 m
m) 37° 53’ 15.6” N, 126° 44’ 6.9” E, h ≅ H = 0 m
n) 37.88767° N, 126.73526° E, h ≅ H = 0 m
o) Zone 52, 300872 m E, 4195348 m N, h ≅ H = 0 m
p) 52S CS 00870 95350, h ≅ H = 0 m
q) ­3014213.2 m, 4038687.9 m, 3895223.3 m

7. Simplified Representation:
Geoid
Ellipsoid
Projection on
Planar map with
developable surface
coordinate system

8. Shape of the Earth
Approximated by a mathematical model
●
represented by an ellipsoid (also called
spheroid)
A number of cartographic ellipsoids has been
●
designed for certain portions of the Earth's
surface
Ellipsoids are usually sufficient for horizontal
●
positioning; however, the geoid has to be used
for exact elevation calculations

9. Ellipsoid
Rotate Ellipse in 3
b
Dimensions:
a
Semi­major Axis: a = 6371837 m
Semi­minor Axis: b = 6356752.3142
Flattening Ratio: f=(a­b)/a = 1/298.257223563

10. Ellipsoids in various countries
Ellipsoid Name Region of use
Airy 1858 Great Britain
Airy modified Ireland
Australian National Australia
Bessel 1841 Austria, Chile, Croatia, Czech Rep., Germany, Greece
Indonesia, Netherlands, Slovakia, Sweden, Switzerland
Bessel modified Norway
Clark 1880 Africa, France
Clarke 1866 North America, Philippines
Everest 1830 Afghanistan, Myanmar, India, Pakistan, Thailand,
other countries in southern Asia
GRS 1980 North America, worldwide
Hayford (Int'l) 1909 Beguim, Finland, italy, all countire using ED50 system
New International 1967 many other countires
Krassovsky 1938 Albania, Poland, Romania, Russia and neighboring countires
WGS 1984 North America, worldwide
WGS 1972 NASA satellite

11. Traditional Horizontal Datums
The Traditional Approach
• Many nations established their own regional datum
– Used various national standards and procedures
– Different time frames
– Calculated ellipsoids that fit well locally
• Established initial point location and orientation with
astronomic observations
Result:
Inconsistent Datums

12. Traditional Horizontal Datums
Limitations to the Traditional Approach
NAD 27 ED 50
(Clarke Ellipsoid ) (International Ellipsoid)

13. Horizontal Datums
Regional vs. Global Approach
• Global replaces regional datums with a common,
accurate standard
• One system for maps of the entire planet

14. DoD’s Satellite Derived
Horizontal Datum
NIMA's World Geodetic System 1984
WGS ­ 84 is an Earth
Z
Centred Earth Fixed
Prime
An ellipsoid is placed Meridian
on top of the axis to
Y
create a geodetic
foundation for the various
coordinate systems.
X
WGS 84

15. Vertical Datums
Like horizontal measurements, elevation
only has meaning when referenced to some
start point.
MSL Elevation
High Tide
Mean Sea Level
Low Tide
Mean sea level is the most common vertical datum.

16. A datum defines the A coordinate system determines
initial point and reference how locations are referenced from
surface the datum

17. Map projection
To transform a curved Earth surface into a
●
plane
Direct projection of a spherical object to a plane
●
cannot be performed without distortion

18. The surface of the Earth tears when you
peel and flatten it. Peel a globe and you
will get globe gores.
Most map projections stretch and distort
the earth to fill in the tears. The Mercator
projection preserves angles, and
so shapes in limited areas, but it greatly
distorts sizes. Look at the size of Greenland
on the globe compared to the Mercator.

19. Different projections are designed to
minimize the distortion and preserve certain
properties:
conformal ­ preserves angles (shapes for small
●
areas), used for navigation and most national
grids systems
equidistant ­ preserves certain relative
●
distances, used for measurement of length
equivalent ­ preserve area, used for
●
measurement of areas

20. Geometry of a developable surface
cylindrical
conic
transforms
uses the
the spherical
tangent or
surface to
secant cone
a tangent or
secant cylinder
azimuthal
use a tangent
or secant plane
(flat sheet)

21. Coordinate System
Accurately identify a
Observer’s ●
Z Meridian
location on the Earth
Defined by its origin
●
Latitude
(prime meridian, datum),
Prime
coordinate axes (x, y, z)
Meridian Y
and untis (angle:
degree, gon, radiant;
Longitude
length: meter, feet)
X

22. Coordinate systems commonly
used in GIS
geographic (global) coordinate system (latitude­
●
longitude)
planar (cartesian) georeferenced coordinate
●
system (easting, northing, elevation) which
includes projection from an allipsoid to a plane,
with origin and axes tied to the Earth surface
planar (cartesian) non­georeferenced coordinate
●
system, such as image coordinate system with
origin and axes defined arbitrarily (e.g. image
corner) without defining its position on the Earth.

23. Geographic coordinate system:
latitude­longitude
Most common for glaoal data coverage
●
Meridians are the longitude lines connecting the
●
north and south poles (0­180 degrees east from
the prime meridian and 0­180 degrees west)
0 degrees longitude is the prime meridian and
●
1980 degrees longitude is the international date
line

24. Geographic coordinate system:
latitude­longitude
Parallels are the latitude lines which form a
●
around the Earth parallel with the equator (0­90
degrees north and 0­90 degrees south of the
equator)
Decimal values ­ W and S as negative
●
numbers, N and E as positive (­1.167 deg, 38.0
deg)
Sexasgesimal ­ always use positive number
●
together with N, S, E, W (1:10:00W, 38:00:00N)

25. N
Greenwich, UK
Longitude
Equator
Prime Meridian
Latitude

26. Universal Transverse Mercator
•Projecting the sphere onto a cylinder
tangent to a central meridian.
•Distortion of scale, distance, direction
and area increase away from the central
meridian.
•If you rotate the cylinder every 6º of
longitude you create the UTM projection.
•This projection is used on map scales of
1:500,000 and larger
(TPCs, JOGs, and TLMs).

27. UTM Coordinates
• Flat Grid extending from 84N to 80S
• Each zone is numbered Eastward starting at
177°W (6° wide from 180°W to 174°W)
• Coordinates are read east then north
• Many map products from
foreign countries use UTMs
• Most often used on large
scale maps and charts e.g.
TLM, JOGs, TPCs

28. Universal Transverse Mercator
The UTM graticule coverage
Each belt is 6O in longitude wide
84o N
0 meters N
Equator 10,000,000m N
80o S
180o
180o 0o
1 30 60

29. Universal Transverse Mercator Grid
Central
Meridian 2 3 16o
7 8
4 5
5 6
6 7 8 4
2 3 4 5 6 7 8 2 3
1,700,000
1,600,000
1,500,000
1,400,000
1,300,000
1,200,000
1,100,000
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
0 o
300,000
0o
200,000
100,000
2 3 4
7 8
5 6
4 5 6
7 8
174o 156o
2 3
2 3 4 5 6 7 8
Zone 2 168o Zone 3 162o Zone 4
03 508,256mE 0,567,359mN

30. Sample Coordinates
ECEF Cartesian Coordinates:
X= 1,109,928m Y= ­4,860,097m Z= 3,965,162m
Geographic:
38°.684N, 077°.150W
38° 41.145' N, 077° 08.135’ W
38° 41' 08.73quot; N, 077° 08’ 08.37quot; W
GEOREF: GJNJ5141
UTM:
18 314,251mE 4,284,069mN
MGRS:
18S UH 1425 8406 (New)
18S UT 1421 8385 (Old)

31. Luzon Datum of 1911
Origin near San Andres Point on Marinduque
●
island
Ellipsoid of reference is the Clarke 1866
●
Controlled by 98 measure baselines, 52
●
observed azimuths, 49 latitude and longitude
stations
Philippine topographic maps uses the Luzon
●
1911 datum

32. Philippine Transverse Mercator
Divided into 4 zones
●
False easting at the Central Meridian of 500 km
●
Scale Factor at Origin = 0.9995
●
False Northing Latitude of Origin = 04:00:00
●
Central Meridian of Zones II, III, IV = 121
●
degrees, 123 degrees, 125 degrees

33. Philippine Reference System of
1992 (PRS92)
Determination of seven (70 Bursa­Wolf
●
transformation parameters detween Luzon
Datum of 1911 and WGS 84
So far no accuracy statesments were published
●
It is still the original Luzon Datum of 1911 with
●
published transformation parameters frpm
WGS84 datum

35. Datums, Projections, &
Coordinates Review
• Know What Datums Exist in AOR
• Always Pass Datum w/Coordinate
• Understand Map Projection Used for Your
Products
• Understand Coordinate System in Use
• Know Resources to Transform Datums
and Convert Coordinates
Questions?

36. References
Neteler, M. & Mitasova, H. 2004. Open source GIS: a
GRASS GIS approach, 2nd edition. The Netherlands:
Kluwer Academic Publishers
Burrough, P. A. & McDonnel R.A. 1998. Principles of
Geographical Information System. New York, USA:
Oxford University Press
Dent, B. 1990. Cartography Thematic Map Design, 2nd
Edition. USA: Wm. C. Brown Publishers
Datum and Grids. Navigator of the Navy. link:
https://www.navigator.navy.mil/navigator/coordinates.p
pt

37. License of this Document
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Emmanuel P. Sambale. November, 2006
http://esambale.wikispaces.com