Datums, Coordinates, &
Projections
UNCLASSIFIED
National Geospatial Intelligence College
Lesson Objectives
• Modeling the earth
• Horizontal Datums:
Traditionally Derived Regional Horizontal Datums
– Satellite Derived: World Geodetic System 1984
• Vertical Datums and the Earth Gravitational
Model
• Coordinate Systems:
– Geographic (Lat\Lon)
– Universe Transverse Mercator (UTM)
– Military Grid Reference System (MGRS)
• NGA’s Primary Map Projections
• Datum Transformation & Coordinate Conversion
UNCLASSIFIED
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Geospatial
Foundation Theory
The World Geodetic System,
Coordinate Systems, & Projections
Geographic: 38° 41' 08.73" N 077° 08’ 08.37" W
Cartesian: X= 1,109,928m Y= -4,860,097m Z= 3,965,162m
UTM: 18 314251mE 4284069mN
MGRS: 18S UH 14258406
UNCLASSIFIED
National Geospatial Intelligence College
Learning Objective
• Discuss the difference between traditionally
derived and satellite derived datums
• Understand the components of datums
• Know why datum mismatch is important to you
• Describe the ellipsoid, geoid and topographic
surface and how they affect datums
• Identify the difference between Geodetic, UTM
and MGRS coordinate systems
• Understand the principles of projections
• Describe the process of datum transformation
and coordinate conversion
UNCLASSIFIED
National Geospatial Intelligence College
Foundation Data
Foundation Data
UNCLASSIFIED
UNCLASSIFIED
National Geospatial Intelligence College
Digital Point Positioning
Data Base (DPPDB)
Digital Nautical Chart (DNC)
Foundation Data
Controlled Image Base 5
meter (CIB5)
Foundation Data
Foundation Feature Data
(FFD)
• Navigation Safety
• Gravity
• Magnetics
Digital Terrain Elevation
Data Level 2 (DTED2)
UNCLASSIFIED
UNCLASSIFIED
National Geospatial Intelligence College
What is Location?
Relative: Closeness of
estimated position to
another position.
Absolute:
Closeness of
estimated position to “true”
location.
Z
Y
UNCLASSIFIED
{
{
X
National Geospatial Intelligence College
What is Location?
Consider
Location only makes sense when compared to some
frame of reference.
Relative - “Bldg 215 is to the left of the post office”
Absolute - “38° 41’ 20” N, 77 ° 08’ 09” W”
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National Geospatial Intelligence College
What is Location?
The Relative Approach
Building 215
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Post Office
What is Location?
The Absolute Approach?
N
Greenwich, UK
Equator
Prime Meridian
Still Relative Positioning!!!
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National Geospatial Intelligence College
What is Location?
The Absolute Approach?
38° 41’ 20” N,
77 ° 08’ 09” W
N
Greenwich, UK
Equator
Prime Meridian
Now It’s Absolute
Positioning!!!
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National Geospatial Intelligence College
Modeling the Earth
• 4th Century
1670 A.D.
B.C.
-
– The Earth assumed to
be
perfectly
round;
hence, a sphere
– In
250
B.C.,
Eratosthenes was the
first to approximate
Earth’s
circumference
at 46,250 km (he was
off by only 15%)
– Sphere is not accurate
due to flattening at the
poles due to rotation
UNCLASSIFIED
r = radius
of the Earth
National Geospatial Intelligence College
Modeling the Earth
Is there a perfect Earth model?
UNCLASSIFIED
National Geospatial Intelligence College
Modeling the Earth
The Ellipsoid/Spheroid is a better approximation
of the Earth’s shape
N
Equatorial Axis (Semi-Major Axis): a
Polar Axis (Semi-Minor)
Semi-Minor Axis: b
a
b
S
Rotation about the polar axis result is the 3-dimensional
Ellipsoid of Revolution or Oblate
 x2   y2   z2 
Spheroid
+
+
=1
 a 2   a 2   b2 
     
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National Geospatial Intelligence College
Modeling the Earth
• Oblateness (or polar
flattening) specified by
ratio:
f
(
a − b)
=
a
• In 1670, Newton predicted the ratio to be 1/300
• Current, satellite derived values are closer to
1/298
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National Geospatial Intelligence College
Satellite Observations
• The
European
Remote
Sensing
Satellite,
ERS-1,
captures the earth’s shape
without water and clouds from
780 km.
• This image shows the true
undulating shape of the Earth
and image looks more like a
sloppily peeled potato, not a
smoothly shaped ellipse.
• Satellite geodesy has enabled
geodesists to determine the
earth’s geocentric center to
w/in +/- 10 cm.
UNCLASSIFIED
A worldwide horizontal datum requires
an accurate
estimation of the earth’s center
National Geospatial Intelligence College
Horizontal Datum
DEFINITION
Horizontal Datum - A base reference for a
coordinate system. It includes the position and
orientation of an initial point of origin and an
ellipsoid that models the surface of the earth in
the region of interest.
North American Datum 1927 (NAD27)
US Geological Center: Meades Ranch - Kansas
Clarke Ellipsoid (1866)
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National Geospatial Intelligence College
Components of
Datums
The Ellipsoid
b
a
WGS-84 Ellipsoid
Semi-major Axis: a = 6371837 m
Semi-minor Axis: b = 6356752.3142
Flattening Ratio: f=(a-b)/a =
1/298.257223563
Rotate Ellipse in 3
Dimensions:
f
The ellipsoid is a mathematical model for the shape of
the planet.
It gives cartographers a smooth
mathematical surface to put a coordinate system on.
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National Geospatial Intelligence College
Traditional Horizontal
Datums
Limitations to the Traditional Approach
NAD 27
ED 50
(Clarke Ellipsoid )
(International Ellipsoid)
• Many nations established their own datum
- Standards and procedures vary widely
• Coordinates from different datums are completely incompatible
- Relative to Initial Point of Datum
- Will vary as a function of Ellipsoid parameters
UNCLASSIFIED
National Geospatial Intelligence College
Horizontal Datums
Regional vs. Global Approach
• Global replaces regional datums with a common, accurate
standard
• One system for maps of the entire planet
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National Geospatial Intelligence College
Horizontal Datums
World Geodetic System 1984 (WGS-84)
• Formal DoD Earth reference frame
• An Earth Centered Earth Fixed
(ECEF) Cartesian coordinate system
w/the origin fixed to +/- 10 cm.
• Defined by ellipsoid parameters,
angular velocity, and gravitational
constant
• Includes
gravity
model:
Earth
Gravity Model 96
Prime
Meridian
Semi-major axis (a): 6,378,137.0m
Flattening ( f ): 1/298.257223563
Rotational velocity (ω): 7292115.0 x 10-11 rad/sec
Gravitational Constant (GM): 3986004.418 x 108m3/s2
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National Geospatial Intelligence College
What is the Problem for
DoD?
World Geodetic System 1984--The DoD Standard
• WGS 84 is used on almost all new NGA-produced
GI&S products (all digital)
• There are still hundreds of legacy local datums in
use throughout the world on existing products
> 30 Datums with > 5 Ellipsoids used by NGA
> 150 Datums with > 25 Ellipsoids used by others
• It would take NGA years and lots of DoD money to
update the entire existing product line
• NGA
can
transform
Datums
and
convert
coordinates between WGS 84 and over 200 local
datums
UNCLASSIFIED
National Geospatial Intelligence College
Where is the Datum
Problem?
Most widely used local Datum/Ellipsoid pairs
North American Datum
Clarke 1866
European
Datum
International
WGS Datum
Tokyo Datum
Bessel
South American Datum
International
UNCLASSIFIED
Arc Datum
Clarke 1880
National Geospatial Intelligence College
Impact of Datum
Mismatch
Map dated 1989 - WGS-84
Map dated 1957 - NAD-27
15S WC438306
15S WN438304
31
31
41
42
43
30
30
29
29
UNCLASSIFIED
National Geospatial Intelligence College
WGS-84 vs. Traditional
Datums
Coordinate Shifts From
Local Datums to WGS 84
Location
Datum
(US)
18Q VT 81170149 NAD27
(Japan)
52S BS 84457638 TOKYO
(Europe)
29°18’12.7”N
ED-50
47°46”57.9”E
(Africa)
01°18’18.4”S
ARC-50
15°46’56.6”E
UNCLASSIFIED
National Geospatial Intelligence College
Shift
201meters
754 meters
176 meters
296 meters
Datum Shifts
97:44:25.19 West Longitude (WGS-84)
Horizontal Benchmark Texas Capital Dome
Arc 1950
+
European Datum 1950
+
WGS-72
++
+
30:16:28.82 North Latitude (WGS-84)
NAD 27
+
Australian Geodetic System 1984
500 meters
+
Ordnance Survey 1936
1000 meters
Modeled from Peter H. Dana 9/1/94
UNCLASSIFIED
Tokyo
National Geospatial Intelligence College
Lessons Learned
Collateral Damage?
Local Datum
Target
WGS 84
UNCLASSIFIED
• Strike
aircraft
missed
targets by 300m w/INS set
to local datum & targets
derived from WGS-84
• Navigational systems set on
a different datum than the
chart can quickly ground
naval vessels
National Geospatial Intelligence College
Datums Matter
Actual Position
Datum shift applied
GPS Position
No datum shift applied
UNCLASSIFIED
“GPS IS VITAL TO, BUT ALSO LIMITED IN SUPPORT
OF, MILITARY TACTICAL NAVIGATION. ITS
RELIABILITY DEPENDS ON THE USERS'
UNDERSTANDING OF CHARTS, NAVIGATION, AND
THE OPERATION AND LIMITATIONS OF THE GPS
EQUIPMENT USED. LACKING THIS BASIC
UNDERSTANDING CAN CONTRIBUTE TO SEVERE
MISHAPS.”
- NAVSAFECEN
201909ZCollege
OCT 00
National
Geospatial
Intelligence
Vertical Datum
• Traditional surveys are referenced to Mean Sea Level
(MSL), which is commonly referred to as the Geoid.
– The geoid is a closed surface of constant gravity
potential approximated by MSL & the theoretical
extension of MSL through land areas.
• GPS surveys are referenced to the Ellipsoid.
UNCLASSIFIED
National Geospatial Intelligence College
Vertical Datum
Earth Modeling Terminology
Topographic Surface
Geoid
Physical
Model
Land
Ocean
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National Geospatial Intelligence College
Ellipsoid
Geometric
Model
Vertical Datum
“The relationship between the reference ellipsoid, the
geoid, & the physical surface of the Earth.”
Earth’s
Physical Surface
Geoid
h
Geoid
Separation
(- N)
H
Geoid
Ellipsoid
Geoid
Separation
(+ N)
Geodetic height (h), geoid separation (N), and elevation (H)
are depicted above and related by: h ~ H + N
H (orthometric height) is measured traditionally
N is modeled using Earth Geoid Model 96 or 180
UNCLASSIFIED
National Geospatial Intelligence College
Vertical Datum
Modern Methods
• Use of GPS to help determine geometric
relationships between given points
• Use of satellite radar to measure sea level
directly; helps determine geoid shape
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U.S. Geoid Heights
(GEOID96)
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National Geospatial Intelligence College
WGS-2000?
No, Better Geoid Models
• WGS-84 will not change to WGS-20XX
• Estimates of Geoidal Separation (deviation of
the vertical) will improve
• Earth Gravitational Model 1996 (EGM 96)
Separation accurate to +/- 50 cm-1 meter
(globally)
Local deviations can be up to several
meters
• Earth Gravitational Model 180-180
Separation accurate to +/- 2-3 meters
(globally)
Local deviations can be up to 20 meters
• Many NGA & DoD systems still use EGM 180
National Geospatial
Intelligence College
(e.g. Production
Equipment,
GPS receivers)
UNCLASSIFIED
Coordinate Systems
A datum defines
the initial point
and reference
surface
UNCLASSIFIED
A coordinate system
determines how locations
are referenced from the
datum
National Geospatial Intelligence College
Which Coordinate
Should Be Used?
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
UNCLASSIFIED
National Geospatial Intelligence College
Coordinate Systems
Cartesian Coordinates:
X= 1,109,928m Y= - 4,860,097m Z= 3,965,162m
Geographic:
DD 38°.684N, 077°.150W
DM 38° 41.145'N, 077° 08.135’W
DMS 38° 41' 08.73"N, 077° 08’ 08.37"W
UTM:
18 314,251mE 4,284,069mN
MGRS:
18S UH 1425 8406 (New)
18S UT 1421 8385 (Old)
UNCLASSIFIED
National Geospatial Intelligence College
Coordinate Systems
Cartesian Coordinate System
Three dimensional right hand coordinate system with an
origin at the center of the earth and the X axis oriented
at at the Prime Meridian and the Z at the North Pole
– X Axis Coordinate Distance from the Y-Z
Z
(X,Y,Z)
plane measured parallel to the X-Axis;
positive from90º W Long to 90º E Long
– Y Axis Coordinate Perpendicular distance
from the plane of the prime meridian;
Y
positive in the eastern hemisphere
90°E
and negative in the western.
– Z Axis Coordinate Perpendicular distance
from the plane of the equator;
X
positive in the northern Hemisphere
Prime
negative in the southern
0º Long Meridian
UNCLASSIFIED
National Geospatial Intelligence College
Geographic Coordinates
• Rules of thumb for latitude
–
–
–
–
–
1º latitude
1’ latitude
1” latitude
.1” latitude
. 01”latitude
≅ 60 nautical miles
≅ 1 nautical mile
≅ 30 meters
≅ 3 meters
≅ 30 centimeters
• Don’t forget longitude converges
• Don’t forget the base 60 conversion
– 60 minutes per degree
– 60 seconds per minute
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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
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Universal Tranverse
The UTM graticule coverage
Mercator
Each belt is 6O in longitude wide
84o N
0 meters
10,000,000m
Equator
80o S
180o
1
UNCLASSIFIED
0o
180o
30
60
National Geospatial Intelligence College
UTM Grid
Central
Meridian
2 3 4
7 8
6
5 6 7
5
82 3 4 5 6 7 82 3 4
16o
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
300,000
200,000
100,000
0o
2 3 4
5 6 7
8
o
174
2 3 4 5 6 7 8
o
0o
7 8
6
5
2 3 4
o
Zone 2 168 Zone 3 162 Zone 4
03 508,256mE 0,567,359mN
UNCLASSIFIED
National Geospatial Intelligence College
156o
Military Grid Reference
System (MGRS)
• Subdivides the UTM into 6°X 8°
zones numbered 1-60 west to east
and c-x from south to north
• Each 6°X 8° area is divided into
100,000m squares
• Each square gets a two-letter
designator
• A level of detail is achieved by
moving so many meters east and
north within the zone (i.e. 8 digit
coordinate)
UNCLASSIFIED
National Geospatial Intelligence College
MGRS-Old vs. MGRS-New
• There are two different MGRS ID schemes: MGRSOld and MGRS-New
– A 10 letter shift exists in the 100,000 squares
causing a 1000km (600 nM) northing shift
– MGRS-Old is based on 3 local Ellipsoids
Bessel; Clark 1866; Clark 1880
– MGRS-New is based on 8 Ellipsoids
GRS80; International; WGS84; WGS72; Australian
National; Everest; South American 1969 (GRS67);
Clark 1866 (UTM Zones 47-50)
UNCLASSIFIED
National Geospatial Intelligence College
Coordinate Complexity
Operational Examples
• Operation Deliberate Force
– Air Force pilot passed “Degrees and Decimal
Minutes”
– Navy pilot expected “Degrees Minutes Seconds”
• Combined and Joint Exercises
– SEAL Team drop off at Lake Towada Training
Area
– NATO Bombing Range Exercise
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National Geospatial Intelligence College
Important Questions
(Precise Targeting)
• Know the source of your coordinates:
– Is it accurate enough for precise targeting?
– Are coordinates coming from paper map or
chart (i.e., an improper source)?
– Are the shooter / weapon, target locator, and
target coordinates on the same datum?
– Does everyone involved understand the
coordinate system(s) being used?
• Avoid friendly fire and mission
failure!!!
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National Geospatial Intelligence College
Map Projections
• pro•jec’tion n. The
result of causing (light or an
image) to fall upon a surface or the distortion of the truth...
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Map & Chart Projections
Projections are attempts to portray the surface of the earth
on a flat surface. Some distortions of conformality (shapes
& angles), distance, direction, scale, and area always result
from the process.
3
2
1
#
#
Three map
projections
2 - Albers Equal-Area (Conterminous U.S.)
of the US centered
3 - Transverse Mercator
on Wichita, KS
National Geospatial Intelligence College
1 - Unprojected Lat/Lon
UNCLASSIFIED
“Round Earth, Flat Map”
This much Earth surface...
projection
plane
…must fit on this amount of map surface!
Scale Factor Examples
a
b
c
a: 1.00198 c: 1.00000
UNCLASSIFIED
d
e
a
b
c
d
e
a: 1.00015
c: 0.9996
e: 1.00015
b: 1.0000
d: 1.0000
National Geospatial Intelligence College
e: 1.00198
Spatial Attribute
Preservation
•
•
•
•
“Choosing the right projection is crucial for
achieving the map’s objective.”
Azimuthal - preservation of direction from
one point to all other points.
Conformal - preservation of shape for small
areas. Angles are preserved.
Equal Area - preservation of area. Area of
all features on the map have the same
relative proportions and size as they do on
the globe.
Equidistant - preservation of distance.
Scale stays the same across the entire map
National Geospatial Intelligence College
sheet.
UNCLASSIFIED
Mercator Projection
• Good for ocean
navigation
• Parallels of latitude
are not equidistant
but longitude are
• Great Circle: Shortest
Distance
• Rhumb Line:
Line of Constant
Bearing (also called a
loxodrome)
UNCLASSIFIED
National Geospatial Intelligence College
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 and change tangency, you create
the UTM projection.
UNCLASSIFIED
National Geospatial Intelligence College
Equal ARC Standard
Projection
• Problem:
Problem How to make raster data square and
seamless over large area?
• ARC Projection shrinks lower latitude pixels
and stretches higher latitude pixels to square
data
• Problems printing small scale charts (JNC/GNC)
• Must re-project ARC data to get around
problem
Original
Chart to be
scanned
12%
Scanning Stretch
Process
Digital Chart in
ARC
projection
Up to 12%
Shrink
UNCLASSIFIED
National Geospatial Intelligence College
Lambert Conformal
Conic Projection
• Shape is preserved
• Great Circles are near
straight lines
• Rhumb Line is curved
• Used for small scale
products with large EastWest expanses
• Common NGA projection
for:
JNC, GNC, ONC
(Aerial Navigation Charts)
UNCLASSIFIED
National Geospatial Intelligence College
Standard DoD Projections
• All U.S. military maps are based on projections
with conformal characteristics:
– Maps at scales of 1:500,000 & larger for areas between
80o south and 84o north are based on the Transverse
Mercator Projection
– Maps at 1:1,000,000 scale between 80o south and 84o
north are based on the Lambert Conformal Conic
Projection
– Maps at 1:1,000,000 scale & larger of the polar regions
are based on the Polar Stereographic Projection
– General maps at scales smaller than 1:1,000,000 are
based on projections individually selected to conform
w/the intended use of the map.
UNCLASSIFIED
National Geospatial Intelligence College
Coordinate Conversion &
Datum Transformation
•
•
•
•
References: NGA TR8350.2, TEC-SR-7, DMA TM 8358.1
Convert from Grid to Geographic Coordinates
Convert from Geographic to Cartesian Coordinates
Apply Datum Transformation
3 Parameter (∆X, ∆Y, ∆Z, and a & f of Ellipsoid)
7 Parameter (∆X ε, ∆Y ψ, ∆Z ω, ∆S, a & F of Ellipsoid)
* For most uses 3 parameter shifts are
acceptable
• Compute New Geographic Coordinates
• Compute New UTM, MGRS etc. Coordinates
• Error in transformation propagates to final coordinates
UNCLASSIFIED
National Geospatial Intelligence College
Geographic Translator
(GEOTRANS)
• Converts coordinates among a
variety of coordinate systems,
projections, and datums.
wide
map
– 11 different coordinate systems and map
projections
– Over 200 different datums
– Choose between Ellipsoid and MSL height
– Program can receive coordinates from a text
file, convert them, and output results in
another file.
UNCLASSIFIED
National Geospatial Intelligence College
GEOTRANS Processes
UNCLASSIFIED
National Geospatial Intelligence College
GEOTRANS Setup
UNCLASSIFIED
National Geospatial Intelligence College
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
UNCLASSIFIED
Questions?
National Geospatial Intelligence College
Summary
• Horizontal & Vertical Datums
– Satellite derived vs. traditional datums
• Coordinates
– Geographic, GEOREF
– UTM, MGRS
• Projections
Mercator, Lambert, UTM, ARC
• Datum Transformation and Coordinate
Conversion
UNCLASSIFIED
National Geospatial Intelligence College