Isnít One Datum Enough?

I often ask attendees at my seminar: How did the surveyors perform their calculations in 1927? Did they whip out their HP-999? Boot up their Pentium notebook computer? The most frequent response is "Slide Rule?" Not quite; a slide rule only generates about 3 digits of precision. Do you remember a thing called logarithms? Thatís right: pencil, paper, and thick book of logarithm tables. Sounds boring; but thatís how it was done.

How did they measure distances? A thing called a chain; an elaborate form of measuring tape. Measurements were adjusted for sag in the chain and expansion/contraction of the chain due to temperature.

Of course the point of all this is that with modern technology, measurements and calculations, the heart of any surveying project, can be performed much more accurately with much greater precision than ever before. This new technology also produced scenarios such that which follows:

A surveyor carefully measures and calculates from "known point" A to the new point to be determined. The surveyor then measures and calculates from the new point to known point B. When he/she gets to point B, the surveyed results are compared to the published location assigned to "known point" B; and a significant discrepancy is observed. The surveyor swears, then cusses, and then dutifully adjusts all of his/her very precise measurements to distribute the observed error among all measured points. This is required by standard surveying practice. Surveyors knew that their measurements were much better than this, and that the error being introduced into their measurements was due to the "ancient" datum; not their work. Surveyors take great pride in the precision of their work, and were not happy campers.

When an existing datumís accuracy is inconsistent with the precision of the surveying practices currently in use, its time to think about a new datum. Thus, in the late 1980ís, the North American Datum of 1927 gave way to the North American Datum of 1983. The 250,000 (or so) "known points" are still in the same physical location, but they have new numbers assigned to them. Surveyors no longer need to downgrade high precision measurements to accommodate a (relatively) imprecise datum.

How much of difference is there? The differences can be significant. When reworking one datum to produce a new datum (as described last month), several issues come into play. One is the ellipsoid in use. NAD27 was based on the Clarke 1866 ellipsoid. By the 1980ís a more accurate ellipsoid had been established with the assistance of satellites and other sophisticated technology. (More about ellipsoids in a future issue of the Casual Cartographer.) Thus the switch from NAD27 to NAD83 also includes the switch from the Clarke 1866 ellipsoid to the GRS1980 ellipsoid. This has lead to some substantial differences way beyond what one would expect. That is, if the only difference between NAD27 and NAD83 was limited to very small differences in measurements, one would expect the difference between the two datums to be rather small. However, since a change in ellipsoids was also included, the shift from NAD27 to NAD83 is as large as 100 meters (325 feet) in portions of California.

The rework of NAD27 to produce NAD83 also included the checking of all calculations used to produce the "known points" of NAD27. Differences between NAD27 and NAD83, therefore, also include a random factor due to the correction of calculation error. Because of this, analytical formulas are inadequate to compute the difference between NAD27 and NAD83 in a precise fashion. Thus, the conversion process is based on a region by region basis. For example, for the lower 48 states, a 15 by 15 minute grid was established with the shift in latitude and longitude very carefully calculated for each point in the grid. Two dimensional interpolation between the grid points provides conversions accurate to 15 centimeters RMS. In practice most points are correctly calculated to within 2 or 3 centimeters. These grids are published in the form of .LAS and .LOS files. The .LAS grid file contain the latitude shift values, while the .LOS grid file contains the longitude shift values.

The grids for Hawaii were developed using a 1.5 minute grid cell; those for Alaska use a 7.5 minute grid cell. Thus, the grid file associated with these geographic regions are significantly larger than the conterminous 48 states even though less real estate is actually covered. The Canadian National Transformation uses the same technique, but uses a more sophisticated grid file format. A single data file is used since both latitude and longitude shift values are contained in a single grid. Also, the file format supports multiple grids, and the grid density varies from 5 minutes to as little as 30 seconds.

In the early half of this century, the traditional measure and calculate techniques of surveying were limited to accessible land masses. Crossing the oceans, for example, was not possible. Thus, around the world there are literally hundreds of datums as surveyors in all parts of the world needed a datum to which their work could be referenced. Some are old, some are new. Some address a geographic area defined by political boundaries, some defined by geographic boundaries. In any case, the datum has been an evolving thing; gradually evolving to reflect the latest and greatest in geodetic measuring techniques.

Using satellites, bouncing laser beams off the moon, and a whole raft of other high tech stuff which I canít even spell (much less understand), the US military defined a world wide datum upon which its Global Positioning System (GPS) is based. WGS84 is valid, accurate, and useful world wide. Will WGS84 preclude the need for anymore new datums in the future? Not likely. However, it may be safe to say that the differences between WGS84 and any future datum will be substantially less than what has been experienced in the past.

The grid technique of converting from one datum to another described above is, perhaps, the best of the several techniques used to convert from one datum to the next. Other techniques are commonly used when less information is available, or the amount of real estate involved is limited. These techniques will be described next issue.