Accounting for the influence of the Earth’s atmosphere on the accuracy of distance measurements by electronic total stations along horizontal traces

Various types of laser rangefinders and electronic total stations are currently widely used to measure distances with electromagnetic waves of the optical range along surface traces. One of the key factors limiting the accuracy of such measurements is the difference between the propagation speed of an optical signal in the spatially heterogeneous Earth’s atmosphere and the speed of light in vacuum. Methods for accounting for this influence, being actively developed at present, involve correcting the results of distance measurements by introducing a correction to the refractive index of air averaged along the measured trace. At the same time, in geodetic practice, when measuring distances with electronic total stations, the empirical approach is widely applied: when the correction is determined only from meteorological parameters at the point of the device. This paper discusses the conditions for applying the empirical approach using simplified analytical models of atmospheric heterogeneity. The analysis concludes that the systematic error caused by relying solely on local atmospheric data is directly related to the air temperature gradient and the length of the measured trace. Based on the derived relations, limiting distances are determined, within which the simplified method provides accuracy comparable to the specifications of the instrument. Numerical examples for the Trimble 3305DR total station confirm that it is possible to preliminarily assess the feasibility of the empirical approach before field measurements. The proposed methodology provides scientifically grounded criteria for selecting an appropriate correction method depending on observation conditions. Not only can it be used to improve geodetic practice, but also to extend the potential of electronic total stations in high-precision distance measurements.