*Image above: The author performs deformation monitoring on a Colorado reservoir with a Leica TS15.*

## Pt. 1: Ellipsoids, Datums, and Realizations

Land surveying is one of the oldest professions to exist throughout the world. Evidence of its use can be found dating as far back as 2700 BC when the Great Pyramid of Giza was constructed.

The difficulty of obtaining accurate measurements pertaining to our work has always involved elaborate mathematics and calculations. Although technology has advanced immensely in our favor over the years, we are still faced with the great burden of truly understanding our profession and any new technologies that come along with it.

The development of robotic total stations and Global Navigation Satellite System (GNSS) equipment has completely changed how the surveying profession is practiced today. It seems that, if you own a private practice, you absolutely need to have this new technology to compete in current markets. However, simply owning this equipment is not enough to get you up to speed; you need to have a firm understanding of how the equipment works and what it is actually doing for you.

One of the most important things to understand when it comes to using survey-grade GNSS equipment is the difference among the many datums, reference ellipsoids, and coordinate systems. If you do not understand what these systems actually mean, the results of your work are destined to be flawed and inaccurate at some point in your career.

Just as important as you understanding these systems is that anyone working for you understand them, as well. I hope that after reading this article you will have further developed your understanding of GNSS positioning tools as they relate to land surveying and are more prepared to educate your employees or colleagues.

### WGS84

Quite a few reference ellipsoids have been created throughout history. The main ones in this article series are the Clarke 1886 ellipsoid, the Geodetic Reference System of 1980 (GRS80) ellipsoid, and the World Geodetic System of 1984 (WGS84) ellipsoid. All of these reference ellipsoids are simply a mathematical representation of the Earth defined by a particular center point, semi-major axis, semi-minor axis, and flattening calculation that accurately represents the north and south poles.

The WGS84 ellipsoid is the reference ellipsoid that the entire United States GPS constellation is based upon today. In 1987 the WGS84 ellipsoid was published by United States Department of Defense, Defense Mapping Agency (DMA) using a mathematical position thought to be the exact center of the Earth, calculated by a multitude of different measurements taken on the Earth’s surface—and then mathematically calculating a smooth elliptical surface around it.

The shape of an ellipsoid was chosen to represent the Earth instead of a true sphere because the Earth is not actually a true sphere at all; planet Earth is “squashed” at the north and south poles.

After the original creation of the WGS84 ellipsoid, our technology and ability to make more accurate measurements increased dramatically with the use of satellites. These advancements allowed us to calculate a new and more accurate mathematical position representing the center of the Earth.

These new center points were calculated multiple times throughout the years. The WGS84 ellipsoid, being based upon and calculated from the center point, changed along with it. This means that previously known positions upon the original ellipsoid would have to change, as well.

### Realizations

Since the original development of WGS84, there have been five additional realizations (or shifts) to the WGS84 ellipsoid. These realizations are known as WGS84 (G730), (G873), (G1150), (G1674), and (G1762). The numbers represent the age of the global positioning system measured in weeks, meaning that G730 was developed in the 730th week after the creation of the GPS.

The WGS84 realization that we use today is WGS84 (G1762). The total horizontal shift of the defined center from the original WGS84 ellipsoid and the current one is approximately 2.2 meters.

All of our GPS work today is referenced to the WGS84 ellipsoid, and, in turn, that is what the global coordinate values known as latitudes and longitudes (lats and longs) assigned to positions we observe on the surface of the Earth are actually representing, a position on the reference ellipsoid (not the Earth’s surface).

It is the equipment that we use, i.e. data collectors, that apply calculations in split seconds to take the measured position on the Earth’s surface and translate them to lats and longs on the ellipsoid.

Something I find interesting and that needs to be understood is that GPS positioning tools produce only Earth-centered, Earth-fixed (ECEF) coordinates (X, Y, Z). The latitudes, longitudes, northings, and eastings that we are familiar with are all calculated from the ECEF values by our equipment based upon our settings and selected datums.

As if having the WGS84 ellipsoid realizations isn’t confusing enough, we also must pay attention to our local (national for the purpose of this article) datums and their realizations.

As mentioned earlier, the WGS84 ellipsoid is a global representation of the Earth, and therefore the coordinates derived from it are global (geodetic) coordinates. A datum is a local representation of the Earth that is developed for specific regions, and the coordinates derived from it are known as local coordinates.

### NAD27

There are two major datums for the contiguous United States that are the focus of this section; however, literally hundreds of datums exist throughout the world. The first datum I discuss was developed by the United States Coast and Geodetic Survey (now known as National Geodetic Survey, or NGS) and is called the North American Datum of 1927 (NAD27).

It is important to note that NAD27 was created based upon the Clarke 1866 ellipsoid. The ellipsoid was “attached to the surface of the Earth” in a way that was intended to best-fit the Earth’s surface over North America as well as possible. That means that the center point of this ellipsoid was not intended to match the true center point of Earth at all, and therefore this was not a geocentric datum with relation to how it was oriented. There is a difference of approximately 236 meters between the center point of GRS80 and the center point of Clarke 1866.

The point of origin for the NAD27 datum is a monument known as Meades Ranch located in Tipton, Kansas. This point was chosen because it was well known that, as good a fit as it was, the Clarke 1866 ellipsoid was not a perfect fit for the surface of the Earth in the contiguous United States, and the only way to appropriately distribute the anticipated distortion somewhat equally was to have the origin be as close as possible to the approximate geographic center point of the United States.

The orientation of this datum was then set by calculating the azimuth and distance from Meades Ranch to another point within the U.S. Coast and Geodetic Survey control network that is known as station Waldo. After this azimuth and distance had been calculated, the NAD27 officially had its orientation and basis of bearing. Surveyors were then able to calculate local coordinates to any other point in the country based upon this line and therefore based upon NAD27.

Although this datum is very old and there have been more accurate developments, many important surveys were conducted using it, and it remains relevant and important to future work we may be asked to do.

### NAD83

The next major North American datum developed was NAD83(1986). This datum is defined with respect to the GRS80 ellipsoid, which was adopted as the international standard by the International Union of Geodesy and Geophysics in 1979. This was the first national reference system to have the origin of coordinates as close to Earth’s geocenter as the technology would allow.

It is important to note that the GRS80 ellipsoid and the WGS84 ellipsoid are extremely similar but do have a slight difference in their mathematical calculations, which effects the flattening.

There are a lot of people out there who will tell you that these ellipsoids are basically the same and there is not really a difference between coordinate values because of it. That is incorrect. The ellipsoids themselves are virtually identical, yes. In fact, calculating distances and azimuths between two points based on one ellipsoid will yield the same answer within about one-tenth of a millimeter as calculating the same two points being based upon the other ellipsoid.

However, the geocentric origin (center-point of the models representing the true center of the actual Earth) are different by approximately 2 meters. Therefore, their orientations are not the same at all and will yield different coordinate values for the same physical monuments on the Earth’s surface. Inversing a coordinate value for a particular point from one ellipsoid model to that of another point based upon the other ellipsoid model will not result in a true answer.

### Realizations

Okay, back to datums. It is highly important that you pay attention to any information inside of parenthesis that are attached to datum names at all times [i.e. NAD83(2011)]. The parenthetical information is telling you that the datum used for a particular project is, in fact, a realization of the datum itself.

What is a realization? To put it into the simplest terms that I can: As time goes on, our measurement capabilities become more and more accurate.

A datum is based upon known coordinates of physical points or locations on the Earth’s surface. When our measurements become more accurate, we come to the “realization” that many of our known coordinates for these physical points are actually incorrect.

Once we realize that there are quite a few differences throughout our control networks, we create a datum realization to reflect the true coordinate values of these points based upon our new measurements. This creates a shift between the original datum and its new realization. A few of the other NAD83 realizations include NAD83(HARN), NAD83(2007NSRS), and NAD83(2011). NAD83(2011) is the latest NAD83 realization to date.

As stated earlier, our equipment is simply calculating longitudes, latitudes, northings, and eastings based upon ECEF coordinates that are derived from the satellite measurements to our receivers. If you do not have the correct parameters keyed into your equipment, the calculations will be incorrect, and you will be creating erroneous data.

If you are not extremely careful while performing GPS survey work, I guarantee that eventually, you will end up with a sizable amount of error in your work.

References

- NOAA.NGS.gov – Official National Geodetic Survey Website
- GPS for Land Surveyors 4th Edition – Jan Van Sickle (I Highly recommend purchasing)
- https://www.youtube.com/channel/UCG69vYuN1Q61fWKiXffzo9A/videos – Dave Doyle (NGS Chief Geodetic Surveyor, Retired