Q: I have a two-part question. I have a total station setting for curvature and refraction correction. To turn it on, I have to select from one of two constants to be used in the correction. Which one should I be using? The second part of my question comes from noticing that my surveying textbook (Moffit & Bossler) uses only one constant for the curvature and refraction correction. Why the difference?
A: The two constants arise from different estimates of the average refraction of the Earth's atmosphere as it pertains to a line of sight taken with surveying instruments. Even though it is called the "curvature and refraction" correction, most equations assume the same (average) amount of curvature even though the Earth is an oblate spheroid. The estimates of this refraction vary from country to country and from research report to research report, so your manufacturer is probably attempting to cater to customs in different countries or other regional differences.
As it turns out, if you are using your total station for trigonometric leveling, these differences create very small, virtually imperceptible differences in the final result of a difference in elevation in most surveying situations. Where the results are different, the horizontal distance will have to be so large that the error from other sources will add more uncertainty than the discrepancy caused by incorrect selection of the constant. Users should be aware that the refraction of the atmosphere varies with density, and thus barometric pressure and temperature of the air. When doing trigonometric leveling over long distances or great differences in elevation, keep in mind that the effects of elevation on pressure and temperature are such that one end of the line or both ends will have refraction that is somewhat different from the "average" value used in the equation. Experts will tell you that changes in refraction become greater and practically unpredictable, sometimes even reversing in direction, when the line of sight passes within a few feet of the Earth's surface as well.
When doing trigonometric leveling or differential leveling, it is preferable to perform what is known as reciprocal leveling to improve the accuracy of the survey. This involves setting up the instrument at one end of the line and then at the other, determining the difference in elevation at each end and then averaging the result. A further refinement is to do simultaneous reciprocal leveling, where two instruments are used to simultaneously observe the difference in elevation from each end of the line, and then to eliminate systematic errors in the instruments, the observations are repeated with the instrument stations swapped.
Q: I've noticed that the only inputs for the parts per million (PPM) correction on my total station are temperature and pressure of the atmosphere. I've heard that some instruments also have an input for relative humidity. How come?
A: It is correct that the overall effect of the atmosphere on the speed and path of electromagnetic radiation (which includes visible and infrared light and microwaves) is determined by the temperature, pressure and relative humidity of the air, theoretically measured at an infinite number of points along the measured line and then averaged. However, for visible light (current red laser) EDM as well as invisible light (infrared) EDM, examination of the equations for calculating the index of refraction of the atmosphere will show that the impact of relative humidity is relatively small, usually less than one-half of a part in a million. Many manufacturers, therefore, ignore the impact of relative humidity, probably reasoning that even if the line measured was 20,000 ft long, the resulting error due to ignoring the impact of relative humidity is only on the order of 0.01 ft and is probably much smaller than errors entering into the measurement from other sources.
You didn't say what type of equipment uses the relative humidity correction. It used to be that some EDMs used microwaves to measure distances. In this case, because of the longer wavelengths (between 1 mm and 30 cm), inspection of those same equations for determining the index of refraction of the air will show a much higher impact on the overall measurement. In fact, in the days of microwave distance measurement, it was well understood that the relative humidity had to be carefully measured and, in spite of that, could account for the largest component of the error sources from the atmosphere. This was partly due to the fact that relative humidity was measured using what was referred to as a sling psychrometer, which consisted of two thermometers, one with a wet bulb and the other dry. This package was swung through the air for a sufficiently long period to be assured that the temperature of the wet bulb had stabilized. Because the bulb was wet, evaporation had a cooling effect. The relative humidity was determined by using an equation or graph that used the dry bulb temperature as one input and the difference between the dry bulb and wet bulb temperatures as the other. Errors of even 1Â°C in measuring this difference would induce a 1 PPM error in the measurement, and could be much higher at higher dry bulb temperatures.
You may be aware that GPS satellites broadcast on microwave frequencies. There-fore, the effect of relative humidity on the ranges (distances from antenna to satellite) is potentially large and should be considered. This requires sophisticated observations of relative humidity throughout the path of the microwaves through the atmosphere, something that the average surveyor is not able to easily do. This has resulted in much research and development of sophisticated models for estimating the impact of relative humidity on the GPS signal.