Practical formulas for the refraction coefficient

Abstract

Knowledge of the actual refraction coefficient is essential in leveling surveys and precise electromagnetic distance measurement reduction. The most common method followed by the surveyor for its determination is based on the use of simultaneous reciprocal zenith observations. The commonly used formula is only an approximation valid for approximately horizontal sightings, whereas the exact geometric solution turns out to be very complicated so that an iterative computation procedure is suggested instead. In the present paper, the goal is to derive a compact formula from the complete solution that is easy to implement and retains the necessary accuracy for horizontal and slanted sightings. In addition, the paper will also focus on the common situation for the surveyor where isolated observations have to be done and no partially compensating procedures—e.g., leap-frog or middle point—are possible. If temperature vertical profiles are unknown then the refraction coefficient cannot be reliably determined. Some surveyors may customarily use then an average value, e.g., k 5 0:13, perhaps being unaware of the risks involved in such simplistic assumption. In the present paper, it is also a goal to present a useful and simple formula for approximately estimating the refraction coefficient in terms of easily accessible parameters to correct the bulk of the refraction effect in single observations, always bearing in mind that determination of the refraction coefficient by means of a model may turn out to be somewhat inaccurate, but still better than the blind use of a universal k.