1. Geographic Datums Y X Z
The National Imagery and Mapping Agency (NIMA) and the Defense Mapping School
Reviewed by:____________ Date:_________
Objective: Given an overview of the National Imagery and Mapping Agency and the Defense Mapping School, the student will understand the mission issues associated with Datums, Map Projections and Coordinates.
Time: 1.5 hours
Training Aids and Devices: Computer, Projector/LCD Panel, Screen, Pointer, Map Examples and a PracticalExercise.
Student Material and Equipment: Mapping Charting & Geodesy for the Warrior Notes.
Special Requirements: None
Text References: Elements of Cartography by Robinson, Geodesy for the Layman, DMA TM ; DMA TR ; TEC-SR-7; 8

2. Lesson Outline Defining Location Horizontal Datums Gravity
Vertical Datums 2

3. 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”

4. What is Location?
The Relative Approach
Building 215
Post Office

5. What is Location? The Absolute Approach N Greenwich, UK Equator
Prime Meridian

6. Horizontal Datum Defined:
Horizontal Datum - A base reference for a coordinate system. It includes the position of an initial point of origin and the orientation of an ellipsoid that models the surface of the earth in the region of interest. Z
Prime Meridian Y X 3

7. This simplified mathematical surface is an ellipsoid.
Why do we need an ellipsoid?
European Remote Sensing satellite, ERS-1 from 780Km
This image depicts the earth’s shape without water and clouds. It looks like a sloppily peeled potato, not a smoothly shaped ellipsoid.
Calculation of geographic position on this irregular surface is very complex. A simpler model is needed.
This simplified mathematical surface is an ellipsoid.

8. Ellipsoid Semi-major Axis: a = 6371837 m
Rotate Ellipse in 3
Dimensions: b a
The reason we use an ellipsoid and not a perfect sphere is because the Earth spins, it bulges out a little bit at the equator. Geodesists (who study the shape of the earth) and Physicists have argued over just how much "bulge" there really is for centuries.
Since the actual Earth is irregularly shaped, you can come up with a number of different values for a, b, and f, depending on where you measure them. In any case, the ellipsoid is just a math model for the shape of the planet. Its purpose is to give cartographers a smooth mathematical surface to design coordinate systems.
Semi-major Axis: a = m
Semi-minor Axis: b =
Flattening Ratio: f=(a-b)/a = 1/ 14

9. 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
The traditional approach we've talked about so far produces local or regional datums.
About 140 different datums in use throughout the world - all of which end up producing completely incompatible coordinates.
Some of these datums use initial points that are in areas of severe deflection of the vertical.
Some used ellipsoid parameters that were calculated from sets of poorly surveyed measurements.
And using relative computations to come up with coordinates won't work if you can't see any known points from your area. This would be the case for islands in the middle of the ocean, for example Hawaii.
But where this really comes into play for the military is primarily:
- Targeting: visual vs precision
- Search and Rescue
- Combined and Joint Operations 22

10. Traditional Approach Initial Point
Astronomic positions are measured by observing stars
Variations in the Earth's gravity field complicate this procedure
local level plane 18

11. Traditional Approach Control Network
A method of surveying for extending horizontal control by establishing and chain of triangles which starts at A and B as a baseline. Basically, by using surveying techniques such as trilateration, triangulation, and transverse you carefully construct a horizontal network relative to point A. This is a crude diagram of what a survey network might look like. The positions of points A and B are already known. The surveyor then makes measurements of angles and distances between A, B, C, and D using trig. He thus determines the relative difference in position between the known points and the unknown ones. He plugs these differences into equations (that include the size and flatness of the Earth) to determine the actual positions of the new points. In other words, most surveys don't really measure the positions of anything, just the relative range and bearing between things. So ellipsoid parameters are used for determining the Lat/Lon of everything. B D
Purpose of the control network is the orientation of the coordinate system 19

12. NAD27 Example Traditional Approach in North America circa 1927
In 1879 the first official datum in the US was adopted it was called the New England Datum based on numerous surveys taken along the east coast. It was based on the Clarke Ellipsoid of It eventually, grew into the North American Datum of The arbitrary point used for the North American Datum of 1927 (NAD 27) was a marker on Meades Ranch in Kansas, presumably because it was right in the center of the continent, and because the "flatness" of the area would minimize problems stemming from deflection of the vertical and geoid undulation. Something like 250,000 survey stations throughout the continent are defined by positions computed relative to Meades Ranch, using the a and b that were available at the time from the Clarke 1866 ellipsoid.
Meades Ranch - Kansas
Clarke Ellipsoid (1866) 20

13. Traditional Horizontal Datums
Limitations to the Traditional Approach
Here's where the fun begins. Practically every country in the world has gone out and created their own system at some time in the last few hundred years. All of these individual systems produce completely incompatible coordinates. In this example (highly exaggerated for visual effect), we can see that the Europeans who use the European Datum of 1950 (ED 50) (Potsdam) have created a system which models their area of the world just fine, but does not agree with the model that fits North America. Their ellipsoid is bigger and flatter than ours, and their initial point is outside of a university in Potsdam. As long as all maps and surveys in an area use the same system, there is no problem. But any weapon with a global range will now have a tough time figuring out which system to use in which area. Notice that we don't agree on the location of the center of the Earth.
NAD 27
ED 50
(Clarke Ellipsoid )
(International Ellipsoid) 21

14. Traditional Horizontal Datums
Example (circa 1960): How well can we hit Minsk, USSR with a missile from Kansas?
Minsk (Pulkovo, 1942)
N 53° 52' 57.78" E 028° 01' 58.00"
Minsk (NAD-27)
N 53° 53' 02.76" E 028° 01' 43.06”
 Latitude = ~ 5”,  Longitude = ~15”
Around 313 meters of error

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

16. DoD’s Satellite Derived Horizontal Datum
NIMA’s World Geodetic System 1984
WGS - 84 is an Earth Centered Earth Fixed Cartesian coordinate system with it’s origin fixed to +/- 10 cm. An ellipsoid is placed on top of the axis to create a geodetic foundation for the various coordinate systems. Z
Prime Meridian X Y
WGS 84 11

17. What is the Problem for DoD?
World Geodetic System The DoD Standard
WGS 84 is used on almost all new NIMA-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 NIMA
> 150 Datums with > 25 Ellipsoids used by others
It would take NIMA years and lots of DoD money to update the entire existing product line
You can transform Datums and convert coordinates between WGS 84 and over 200 local datums
WGS 84 was recently enhanced to the point that NIMA can now define coordinates to better than 25 cm of accuracy worldwide (this requires complex GPS surveys and computations, and can only be done by NIMA surveyors). All the new products we make are based on WGS 84, except for a few products intended for combined operations where the other countries insist (often for monetary reasons) on using old local datum maps.
In the mean time, it's possible that troops will still have to use local datum products. NIMA has the ability to transform coordinates between WGS 84 and about 137 local datums. As time goes on, those transformations are continually refined and updated. Sometimes, multiple transformations will be made for different sections of old local datums to try and account for the errors made in the original local datum surveys. All of these transformations can be found in the latest version of NIMA TR (the WGS 84 manual).
The services are far more interested in having NIMA make maps of areas that aren't covered now by any products, instead of going back to update the old maps on the shelves. For this reason, it could be 20 or more years before all NIMA products are switched to WGS 84. 28

18. Where is the Datum Problem?
Most widely used local Datum/Ellipsoid pairs
North American Datum
Clarke 1866
South American Datum
International
Arc Datum
Clarke 1880
European
Datum
WGS72 Datum
Tokyo Datum
Bessel

19. Impact of Datum Mismatch
Map dated WGS-84
Map dated 1957 NAD-27
15S WC4330
15S WN4430

20. Datum Shifts

21. WGS-84 vs. Traditional Datums
Coordinate Shifts From Local Datums to WGS 84
Location
Datum
Shift
(US)
18Q VT
NAD27
201meters
(Japan)
52S BS
TOKYO
754 meters
So how big is the difference between datums? The numbers here show the linear shift between WGS 84 ellipsoid and 4 local datums. The coordinates were used in the region where the the datum was predominate. Some combinations can be up to kilometer in shift. We already know about NAD 27 and ED 50. Decades ago, the Japanese created a local datum, and initialized it at a point in Tokyo without doing any of the statistical analysis of multiple stations the way we did for NAD 27. Japan, Korea, & Vietnam, are still using maps based on this "unusual" model. The average coordinate shift between the Tokyo datum and WGS 84 is 755 meters in Korea, and can be even worse in some areas. 29
18’12.7”N
(Europe)
176 meters 47
46”57.9”E
ED-50 01
18’18.4”S
(Africa) 15
46’56.6”E
ARC-50
296 meters 34

22. WGS-20XX? WGS-84 will not change to WGS-20XX
Estimates of Geoid Separation (deviation of the vertical) will improve
Earth Gravitational Model Separation accurate to +/- 2-3 meters (globally) Local deviations can be up to 20 meters
Earth Gravitational Model 1996 (EGM 96) Separation accurate to +/- 50 cm-1 meter (globally) Local deviations can be up to several meters

23. Mean sea level is the most common vertical datum.
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.

24. Chart Datum
Marine Navigation charts use variations of low tide instead of mean sea level for referencing depth.
A: Ships are expensive. Users like to add tides to soundings.
Q: Why?

25. Geoid
A Gravitational Surface of Equal Potential, which Approximates Mean Sea Level.

26. Shape of the Geoid
The Geoid is an undulating surface, not smooth and regular, due to density variations inside the earth.
Density Variations

27. Shape of the Geoid

28. Instrument Measurement
Problem
Measuring from Geoid
Calculating on Ellipsoid
Ellipsoidal Surface
Geopotential Surface
Instrument centered on plumb line
Error
Topographic Surface

29. Defining the Vertical Position
Geoid - Ellipsoid Separation
Defining the Vertical Position h - -
Orthometric Height (Height above Mean Sea Level)
Geodetic Height
(Height above Ellipsoid) H - N
Geoid Separation { { H h { N
Here's another diagram of explanations. The reason the equation is only approximate is that the various measurements are all measured along lines normal to different surfaces (geodetic height is measured normal to the ellipsoid, while Orthometric height is measured normal to the geoid). Since GPS receivers use geodetic height internally, NIMA recommends that weapons developers work with h whenever possible - for consistency's sake. That way, we never need to bother ourselves with elevations subject to gravity measurements. Unfortunately, anything that uses inertial measurements will be pulled around by all of those gravity variations, so Inertial Navigation Systems (INS) will always have to contain a gravity model.
Further understanding the Geoid/Ellipsoid relationship will define a better vertical datum.
Geoid
Topo Surface
Ellipsoid
H is measured traditionally h is approximately = N+H N is modeled using Earth Geoid Model 96 or 180 32

30. World Geoid Separation

31. Model Accuracy
Earth Gravitational Model Separation accurate to +/- 2-3 meters (globally) Local deviations can be up to 20 meters
Earth Gravitational Model 1996 (EGM 96) Separation accurate to +/- 50 cm-1 meter (globally) Local deviations can be up to several meters
Many NIMA & DoD systems still use EGM (e.g. Production Equipment, GPS receivers)

32. Review
Horizontal and Vertical Datums provide a frame of reference in which to calculate locations
A datum definition requires an initial point location, orientation, and an ellipsoid
WGS-84 is the datum of choice for NIMA products
WGS-84 is an earth centered Cartesian system using a globally fitted ellipsoid
Gravity affects horizontal and vertical instrument measurements
Datum mismatches can cause serious operational errors

33. 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
It is critically important to know the intended use of your product and be aware of the potential error involved. As we can see each product has a specific use.
Questions? 36