Vol. XV, No. 1
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Spring, 2002

Measuring with Precision and Accuracy

Total stations have become the standards to which other surveying instruments are compared. Using them in the field permits contemporary archaeologists to achieve a level of precision that their forebears could not have imagined. Measurements are routinely made and recorded to the tenth or hundredth of a millimeter. Those measurements are then transported into CAD or GIS systems and become part of the data from field work. A given object, wall corner, or survey location is then forever said to be at a point in space defined to an extraordinary level of precision -- one that is absolutely meaningless.

Such precision is meaningless is two senses. First, the precision is meaningless because it provides useless information. To know that a block has been measured as 1.234 m. long is one thing; to claim that the length is 1.23432 m. is something quite different. Assuming for the moment that the measurement is accurate -- an assumption to which we will return momentarily -- having the dimension of a stone to such precision is simply not useful. It provides no real information, only the appearance of scientific precision.

Even if such a measurement were of a building stone in a structure like the Parthenon, one that required incredible precision of the builders, would anyone really argue that the difference between thinking that a block is 1.234 long and thinking that it is 1.23432 long can change our understanding of anything about the block, much less the building in which it has been used? Using the more precise measurement suggests that the building was constructed to incredibly tight tolerances, which it was, but it also suggests that the precise dimensions were planned, which is not the case. Using such a measurement also suggests that the ancients could have measured so precisely themselves, which is also not the case. In sum, sub-mm. precision is unnecessary to show tight building tolerances and misleading if it indicates either precise planning of block dimensions or precise measurement by the ancients.

In the cases of buildings constructed of concrete or with mortar, not to mention mud-brick, such precision is not just useless; it is ludicrous. If mortar is involved, even precision to the nearest mm. was never necessary; with concrete and mud brick, the original surfaces are so long gone that it is impossible to know what has actually been measured, much less what such a precise measurement would imply.

Second, that level of precision is meaningless because it is the result of a process that has so many opportunities for error -- in many instances error that propagates -- that the precise numbers must be seen as inaccurate.1Such numbers are almost always more precise than the technology really can produce accurately. If the measurements are rounded to a more reasonable level of precision, they will be less precise, and they will be accurate; otherwise they will remain precise but they will be inaccurate. (That distinction between accuracy and precision is not well-respected by English usage. An accurate measurement is simply a correct one, regardless of precision. A precise one is made to tighter tolerances, regardless of accuracy. Thus, a block 1.23632 m. long may be measured as 1.24 m., 1.236 m., 1.2363 m., or 1.23632 m. long, and all those measurements will be accurate, though different as to precision. The measurements 1.23 m., 1.235 m., 1.2364 m., and 1.23633 m. are all inaccurate, though different as to precision.)

Depending upon the procedures used with a total station, accurate measurements may be made to looser or tighter tolerances. The more experienced the surveyor and the better the instrument, the tighter the tolerances possible. Of course, producing measurements to tighter tolerances requires more careful and controlled survey procedures, not simply more experienced personnel or better equipment.

What level of precision is meaningful, and how should surveyors accurately measure to that level of precision? Those seem to be the real questions about surveying that archaeologists should be asking themselves as projects enter the planning phases.

The first question should really be this: What level of precision is meaningful for this project? To determine the answer, one must consider the nature of the remains (cut stone as on the Acropolis in Athens, Roman concrete building cores as at Pompeii, mud-brick wall stubs as at Gordion) and what level of precision suits those remains and the project aims. As it is pointless to seek sub-mm. precision for a mud-brick wall, it is irresponsible to measure the blocks of the Erechtheum only to the nearest cm., regardless of the measuring system used -- unless the project is to survey the building footprints of all Acropolis structures, in which case, what is the appropriate level of precision?

Precision need not be the same for all aspects of a project. For instance, the internal parts of a well-preserved and highly-decorated structure may be measured very carefully while its exterior is measured with lower precision. Although any measurements involving interior and exterior will have only the precision of the least precise data point, those that involve the interior alone will be more precise -- and presumably there will be benefits from that precision.

The second question -- truly second, coming after the decisions about appropriate precision have been made -- is simply about how to satisfy the surveying needs of the project. It will then be necessary to consult surveyors to be sure of the procedures. For instance, higher levels of precision will require more painstaking selection of instrument locations and more careful laying out of the entire survey frame. Following up to be sure the procedures are followed then falls to the site architect or the project director.

When the necessary decisions about precision have been made and the survey procedures established, a system for dealing with survey data must be established. Before survey data points are entered into CAD or GIS systems, all points should be rounded as necessary to supply the appropriate level of precision. The process, of course, should be documented. However, there should also be a permanent record of the original survey data, prior to rounding, so that any processes can be repeated or new technologies applied, starting with the actual field data.

The crucial issue here -- as is often the case with the new technologies -- is to remember that the needs of the work should determine the use of the survey technology. The capabilities of the technology should not determine the nature of the work. This is the case today because the capabilities of current technologies now exceed the needs of the discipline. When that was not the case, when archaeologists needed more survey precision than could normally be provided, it was indeed necessary to let the technology of the day determine some field methods. That time has passed.

This issue of survey precision is similar to the issue of "data density" discussed in a previous issue of the Newsletter, Harrison Eiteljorg, II, "Using CAD on an Archaeological Site," Fall, 1999, Vol XII, No. 2 (http://csanet.org/newsletter/fall99/nlf9905.html). Archaeological requirements, not technological possibilities, must be the determinants of data precision and data density. These important decisions about working procedures are the ones that require the most careful consideration, the ones that must be made long before the first shovel enters the earth. They should not be left to the technicians to decide.

1. For instance, CSA's total station produces results that can be expected to be within a mm. of the surveyed point so long as measurements are taken from reasonably close range. If a number of points are surveyed from a given starting point, all should be accurate to the nearest mm. If the instrument must be moved for surveying more points, however, its new position can only be determined to the nearest mm.; as a result, new points surveyed from the second instrument location will have slightly less precision than those taken from the original point because the starting point is very slightly less precisely known.

If points used to help locate the instrument when it is moved again have been surveyed from the secondary location, the next instrument location, determined with the aid of those points, may yield slightly more loss of precision. This process can continue, with steadily decaying levels of precision, unless the survey procedure is very carefully controlled. Return to body of text.

For other Newsletter articles concerning the applications of CAD modeling in archaeology and architectural history, consult the Subject index.

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