Geodetic Surveying Made Plain

Jerry McGray
Most GPS users in the surveying community would agree, I believe, with the notion that the accuracy and precision of GPS is a settled issue. We would probably also agree that problems nonetheless still arise, and that those problems usually have at their core some sort of human blunder. I am referring here to such complaints as “My GPS coordinates don’t fit his GPS coordinates” or “My RTK unit is giving me a WGS 84 error, saying I’m not where I think I am.” Or even “Our street design survey does not fit the city’s GIS.”

While all of these are symptoms of coordinate system mismatches and can be caused by various things, there is one error source that, in my experience, greatly overshadows all the others. That is the common practice of applying a surface adjustment factor to State Plane (by definition, grid) Coordinates in order to make measurements on the earth’s surface match up with those coordinates. For me, surface adjustment factors are the 900 lb gorilla.

While there are more sophisticated techniques to transform a grid coordinate network to one compatible with surface measurements, the application of a surface adjustment factor is a simple, easily reproducible method. The factor is derived mathematically from two components: a coordinate’s position in its State Plane zone and the point’s height above the ellipsoid. They are usually expressed in their native forms, which would be divided into the State Plane values, but sometimes the reciprocal of the native form is used; in reciprocal form they are of course multiplied by the coordinate values.

But they can be deceptive because typical surface adjustment factors like .99996 or 1.00007 are so close to unity. After all, 128 divided by .99996 is still 128. Multiplying 31.26 by 1.00009 still gives 31.26. But when the other factor is one of those inch-and-a-half numbers we call State Plane Coordinates, it is a different story. For instance, 3,700,000.000 (a typical value for northing meters in Texas) becomes 3,700,148.006 when divided by .99996. One hundred forty eight (148) meters—that is more than 485 feet! When we do the same thing to the easting, the resulting coordinate pair is even further from its native State Plane location.

Two things happen to a set of coordinates when a surface adjustment factor is applied. The one we want to happen is that the amount a coordinate increases varies with the value of the coordinate. So if a factor is applied to two points, they will end up stretched a little farther apart after the factoring than before, when they were represented by the grid values. That is the desired result. But the second effect is definitely not desired. That effect is that the entire group of coordinate pairs are picked up and plopped down several hundred feet from their original locations. Witness the 148 meter example above. We wanted the slight stretching; what we got was both slight stretching and gross plopping.

“So what?” one may ask. “They still accomplish their intended purpose, don’t they? What do I care what the actual values are.” That is correct. And if we are careful to include the metadata when we communicate the coordinate values, everything is fine. But if somebody mistakes the coordinates for grid values, trouble can ensue.

A 900 Lb Example

Suppose, for illustration, that a county wishes to set up a county-wide GIS. Suppose further that the county engineering department has divided the county into quadrants for surface adjustment to facilitate road construction. (By the way, unless the county were very small in area, four surface adjustment factors would probably be too few to effectively handle surface-grid distortion. But, it’s plenty for our example, since we’re making it all up anyway.) Say the four factors are .99991, .99994, .99998 and .99911. We can grasp intuitively that each of the quadrants would suffer a different amount of plopping. They would enjoy different amounts of stretching, too, but that part is not a problem. The difference resulting from the stretching part wouldn’t be enough to affect GIS accuracy. But if the GIS department unknowingly uses the coordinate values that have been surface-adjusted, the four quadrants would not be in the correct relationship to one another, by perhaps hundreds of feet. That unhappy truth is in addition to the fact that none of them would be in their proper places with relation to the rest of the world, as plotted on a quad sheet.

GIS professionals are of course aware of this situation and would use the original grid coordinates, as they should. But one can see in that example the complications that the introduction of surface-adjustment coordinates can cause. Here’s another scenario that could easily befall a surveyor: suppose a client asks a surveyor to determine the latitude and longitude of a radio tower on the client’s property. The surveyor knows that a major thoroughfare in front of the property was recently widened. He also knows not only that there is a pair of construction control monuments nearby but also the engineering firm who designed the improvement. So he calls that engineer and asks for the monuments’ coordinates. Their values are sufficiently huge to qualify as State Plane values. He ties the tower in question to the monuments’ coordinates. Then he uses a computer program like CORPSCON to convert the supposedly State Plane Coordinates to geographic coordinates and delivers the lat/long values to his client. When those coordinates get to the federal agency, which originally asked for them, they are scaled on an ordinary USGS quad. But lo and behold, they plot on the wrong side of the street!

I’m sure readers are way ahead of me by now; the reason they don’t plot correctly is that the engineer who did the design was working in surface-adjusted values. As far as he was concerned, those were the only coordinates for those monuments. But they were not the true State Plane Coordinates for which a transformation to lat/long would have been valid. Such chaos is all in a day’s work for a 900 lb gorilla.

There is yet another problem. It can be easily illustrated that there is no reason to carry these factors out beyond five decimal places. We’ll perform that demonstration another time. For now, let’s just look at what happens if the first geodetic surveyor on a project unknowingly creates a factor carried out further, like .9999390123. This happens all the time. The bad thing is, when somebody has used such a factor, any subsequent work that needs to coincide with that earlier system must also carry it out that far. No rounding off allowed...none. In the long factor above, .99994 would have been appropriate. It would have worked just as well and been much easier to deal with. But try this: take a nice big state plane coordinate and divide it first by .99994, then by .9999390123. Still using our old 3,700,000, it looks like the results differ by three or four meters. That won’t do, of course. These things are so volatile and wield such leverage, they must be entered exactly and handled with great care. Gorillas make unpleasant enemies.

What can we do to head off these problems? More than anything, communicate. Any coordinate information transmitted to others, and internally as well, should clearly show any surface adjustment information. Any plat or other document that reflects coordinate values that resemble State Plane Coordinates should display all the metadata. That should include not only the surface adjustment information, but datum (like NAD83) and other information, like either (86) to indicate non-HARN or (9x) to indicate HARN values. Another good practice for publishing information on control monuments is to show all the values for a point. For example, a control data sheet might show the original NAD83 (or other datum) geographic coordinates (lat/long), the State Plane Coordinates and the surface-adjusted version, along with the factor, of course. Following those guidelines will help keep the 900 lb gorilla safely in his cage.

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