Inversion method of atmospheric refraction coefficient based on trigonometric leveling network

Deformation measurements are repeatable. Therefore, they are often performed with the same equipment, methods, and geometric conditions in different epochs. However, although the measuring environment might be the same in different epochs, it sometimes changes significantly. Of all environmental parameters (atmospheric pressure, temperature, etc.), the atmospheric refraction coefficient is the most significant. Because it is unstable and changeable, measurement accuracy is affected. To solve this issue, an inversion method of the atmospheric refraction coefficient based on a trigonometric leveling network is proposed. This method is based on a mathematical model of the atmospheric refraction coefficient with weighted values, which are determined according to the difference between direct and reversed elevations. Therefore, the weighted average height of the closure errors of all triangles are considered. By iterative calculation, the atmospheric refraction coefficient is estimated. The estimated atmospheric refraction coefficient is applied successfully to the adjustment and analysis of the external control network of a dam. In this aspect, one does not need to solve the atmospheric refraction coefficient for each station and edge. Moreover, one of the most suitable atmospheric refraction coefficients for the whole trigonometric leveling network can be provided from the relevant conditions. The approach provides the advantages of flexibility and practicality, effectively weakening the influence of the atmospheric refraction coefficient on measurement accuracy in the trigonometric leveling network. Furthermore, it provides a theoretical basis for further engineering applications.