Aim.To investigate the possibilities of applying non-simultaneous reciprocal trigonometrical levelling over water surfaces while partially taking into account vertical refraction. Methodology. Experimental investigations of vertical refraction over water surfaces during day time on a plain and hilly terrains in summer. Non-simultaneous reciprocal observations were made over different water surfaces with the use of an automated electronic tachymeter. For comparing the results, the elevations between the points of observation were determined by the method of geometric levelling. Results. Average integral quantities of vertical refraction have been computed. It has been revealed that either stable or unstable stratification of the terrestrial atmospheric layer can set in over the water surfaces.

Aims. The investigations of the transmission of elevations over water surfaces remain topical, so the first aim is to develop the technique of increasing the accuracy of the trigonometric instead of geometrical one. The second aim is to investigate the methods of trigonometric which can be used for the transmission of elevations over water surfaces with the use of modern devices. Methodology. Simultaneous and non-simultaneous reciprocal observations over different water surfaces have been carried out. The results of the trigonometric leveling carried out by different methods have been processed. Results. On the territories of training geodetic site in Berezhany city (Ternopil region) and urban settlement Shatsk (Volyn' region) the activities directed to the creation of elevation geodetic base have taken place, including the investigations of the accuracy of trigonometric leveling during the transmission of elevation over the water surfaces. Vertical tie-in of geodetic datum has been done by the III class geometrical leveling. For determining heights on the investigated points, linear and angular measurements have been made with the use of automated tachymeters TPS 1201R Leica and TC 2003 Leica. According to the results of the observations on the geodetic site in urban settlement Shatsk, the comparison of the elevations obtained by the geometric leveling and trigonometric leveling by the methods "from inside", "across the point", "refraction basis" and non-simultaneous reciprocal leveling has been conducted. Balancing of the analytical network by a method of least squares has been done. According to the results obtained in Berezhany, the coefficients of vertical refraction along different directions have been computed and the comparison of elevations obtained from the III class geometric leveling and from the trigonometric leveling done by the method "from inside" have been conducted. The investigations of the accuracy of different methods of trigonometric leveling compared to III class geometric leveling have shown that they both generally meet the accuracy requirements of leveling on the flat grounds. Since the rough terrain has its peculiarities, some additional measured characteristics of the propagation of the axis of sight over different surfaces should be taken into account, for example, fluctuations of zenith distances determining atmosphere stratification or measured elevations. Scientific novelty. The application of non-simultaneous reciprocal trigonometric leveling over the water surfaces instead the III class geometric leveling on the paths under 1 km in length. Practical applicability. The possibility of replacing the cost-based geometric leveling with the trigonometric leveling without accuracy losses during the transmission of elevations over the water surfaces is shown.