# How Things Work: Parts Per Million (PPM)

Professional Surveyor Magazine -

February 2004

Surveyors often have to deal with the concepts of parts per million. While most of the world, and indeed even scientists in this country use this expression frequently, it sometimes befuddles surveyors. They are not even sure how to classify this concept. This article is written to shed some light for all surveyors, particularly those who use total stations and GPS. Many of the instrumentation and software used in these areas require an understanding of the PPM concept to use them properly.

Parts per million can be used to express the likely error in a measurement as in an instrument specification e.g., 2mm + 3ppm for an EDM, or as a resulting error in a measurement or a survey, based on a comparison with another measurement, or a value taken as definite, or even the mean of a group of measurements of the same quantity. Note that as "parts per million" it has nothing that ties it only to EDM measurements. We mention this here because surveyors often refer to "PPM" as the system or process of compensating for errors in a distance measurement with EDM that are caused by fluctuations in the speed of light by the temperature, pressure, and water vapor content of the atmosphere through which the light passes.

A part per million simply means a fraction of 1/1,000,000

So an error or variance or uncertainty of 20 PPM is 20/1,000,000 = 1/50,000

An error of 50 parts per million is 50/1,000,000 = 1/20,000

And an error of 100 parts per million is 100/1,000,000 = 1/10,000

Surveyors are used to expressing this same error as a representative fraction, that is, a fraction with 1 always in the numerator. It should now be obvious that any representative fraction (or precision value) can be converted to a PPM value, and any PPM value converted to a representative fraction. This means that there is equivalence between these terms and the difference is simply a way of expressing the deviation differently, in the same way that one person might express a distance in feet and another in meters.

Any representative fraction can be converted to PPM, it just involves dividing the denominator into a million to determine the PPM value. So a representative fraction of 1: 6,600 converts to 152 PPM. This is obtained by 1/000,000/66,0000 =1 51,51.

When you see the PPM expression used, one way of gaining familiarity with it is to immediately convert it to a representative fraction. And when the surveyor calculates a representative fraction, converting it to PPM aids in familiarity.

PPM is not simply a way of being different; it is a superior way of evaluating errors individually and combining them. For example, it may be determined that with an EDM, a 1ºC change in temperature causes a change in the EDM reading of 1 PPM. If the temperature goes up, the impact on the reading is to make the measured value longer than the true value. So subtracting 1 PPM could make a correction for this effect. It can also be determined that an atmospheric pressure change of 0.1 inch of mercury approximately will cause an error in the EDM reading of 1 PPM. If the pressure increases by 0.1 inch of mercury, the impact on the distance reading is to make the value shorter. Thus with PPM, if both conditions exist at the same time, it is easy to determine that the net effect is zero.

A crucial impact of understanding PPM is to better evaluate and analyze your own surveys. Many times, surveyors will report outstanding precisions or representative fractions for their surveys. Perhaps a number such as 1:100,000 will be reported. This corresponds to 10 PPM and unless the surveyor has taken pains to remove all systematic errors from the traverse, it is more likely a measurement of precision than accuracy. The question in the back of the surveyor's mind is "what is the survey's accuracy?" If no attention was paid to the temperature and pressure effects on the EDM, and the temperature was 10ºC higher (an effect of +10 PPM), and the pressure was 1 inch of mercury lower (an effect of +10 PPM) than for the EDM's standard temperature and pressure, an estimate of accuracy degradation can be made. Simply sum the PPM values, which in this case results in 20 PPM or 1:50,000. So even though the precision calculation shows a 1:100,000 figure, the accuracy of the survey is at best 1:50,000.

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