Purpose. The purpose of this work is obtaining connections between the Baltic and European height systems based on the I class leveling between the Ukrainian and Polish control points of the base vertical networks and construction of the quasigeoid surface on the border area. Method. Full integration of the hight system of Ukraine into the European vertical reference system (EVRS) consists of two stages: modernization of the height network of Ukraine through its integration into the United European leveling network UELN; construction and use as a regional vertical date the model of high-precision quasigeoid, which will be consistent with the European geoid EGG2015. The analysis of methods of high-precision leveling in Ukraine and Poland, and also the analysis of methods of construction of quasigeoid models in these countries is performed. Results. For integrating the Ukrainian hight system into the UELN/EVRS2000 system, the Ukrainian side performed I class geometric leveling along two lines: Lviv - Shehyni - Przemysl and Kovel - Yagodyn - Chelm with total length of 196 km. The root mean square systematic error on both lines of leveling was s<0.01 mm/km. In turn, the mean square random error along the line Lviv - Shehyni - Przemysl is h=0.29 mm/km, and along the line Kovel - Yagodyn - Chelm is h=0.27 mm/km. For double control on the cross-border part, the Polish side performed high-precision leveling with a length of 33 km. The differences between the Ukrainian and Polish leveling in all sections are within the tolerance. The analysis of influence of geodynamic phenomena on control of high-precision leveling is carried out. GNSS-leveling was performed on all fundamental and ground benchmarks, as well as horizontal marks. These measurements were used to build a quasigeoid model for the border area of Ukraine. The MSE of the obtained quasigeoid model is about 2 cm, which corresponds to the accuracy of the input information. Scientific novelty and practical significance. The connection of the Ukrainian and European height systems will ensure Ukraine’s integration into the European economic system, participation in international research of global ecological and geodynamic processes, study of the Earth’s shape and gravitational field and mapping of Ukraine using navigational and remote-sensing satellite technologies. Calculation of a high-precision model of a quasigeoid on the Ukraine area in relation to the European height system, agreed with the European geoid EGG2015, will allow to obtain gravity-dependent heights using modern satellite technologies.
1. Chernyaga, P. G., Yanchuk, A. Y., & Ishutina, A. S. (2010). The calculation of geometrical levelling accu¬racy on geodynamic polygons. Geodynamics, 1(9), 10-21.
https://doi.org/10.23939/jgd2010.01.010
2. Denker H. (2015). A new European gravimetric (quasi)geoid EGG2015. Poster presented at XXVI General Assembly of the International Union of Geodesy and Geophysics (IUGG), Earth and Environmental Sciences for Future Generations, 22 June - 02 July 2015, Prague, Czech Republic.
3. Dzhuman, B. (2018). Modeling of the regional gravitational field using first and second derivative of spherical functions. Geodesy, cartography and aerial photography, 88, 5-12
https://doi.org/10.23939/istcgcap2017.02.005
4. Instructions for calculating leveling. M. publishing house "Nedra", 1971, p. 102. (in Russian).
5. Instructions for leveling I, II, III and IV classes, Moscow, publishing house "Nedra", 1966. (in Russian).
6. Knudsen, P. (1987). Estimation and modelling of the local empirical covariance function using gravity and satellite altimeter data. Bulletin géodésique 61(2), 145-160. doi:10.1007/BF02521264
https://doi.org/10.1007/BF02521264
7. Marchenko, О. N., Kucher, O. V., & Renkevych, O. V. (2007). The results of the construction of quasi-geoid for the region of Ukraine (UQG-2006). Bulletin of Geodesy and Cartography. 2, 3-13. (in Ukrainian).
8. Marchenko, O. N., Kucher, O. V., & Marchenko, D. O. (2013). The results of the clarification of the quasi-geoid UQG2012 for the territory of Ukraine. Bulletin of Geodesy and Cartography, 3(84), 3-10. (in Ukrainian).
9. Marchenko, A. N., & Dzhuman, B. B. (2015). Regional quasigeoid determination: an application to arctic gravity project. Geodynamics, 1(18), 7-17.
https://doi.org/10.23939/jgd2015.02.007
10. Marchenko, A., & Lopushanskyi, A. (2018). Change in the zonal harmonic coefficient C20, Earth's polar flattening, and dynamical ellipticity from SLR data. Geodynamics. (2 (25)), 5-14.
https://doi.org/10.23939/jgd2018.02.005
11. Melnik, S. (2014). Matching of altitude systems in Ukraine. The journal of cartography. 10, 28-37. (in Ukrainian). file:///C:/Users/AB68~1/AppData/Local/ Temp/ktvsh_2014_10_6-4.pdf
12. Mordvinov, I. S., Pakshin, M. Yu., Lyaska, I. I., Zayats, O. S., Petrov, S. L., & Tretyak, K. R. (2018). Moni¬toring of vertical movements on Miningand Che¬mical Plant "Polimineral" area based on processing results of interferometric satellite radar images and tilt measurements. Modern achievements of geodetic science and production. I (35), 70-75. (in Ukrainian).
13. Moritz, H. (1976). Integral formulas and Collocation. Man. Geod. 1, 1-40.
14. Petrov S. L. Monitoring of vertical displacement of technogenic-loaded territories by geodetic methods: tesis … PhD. Lviv, 2018. 156 p.
15. Sacher, M., Ihde, J., & Svensson, R. (2006, June). Status of UELN and steps on the way to EVRS 2007. In Report on the Symposium of the IAG Subcommission for Europe (EUREF), Riga (pp. 14-17).
16. Sacher, M., Ihde, J., & Liebsch, G. (2007, June). Status of EVRS2007. In Presentation at the Symp. of the IAG Sub-commission for Europe (EUREF) (Vol. 42, pp. 53-57).
17. Sánchez, L., & Sideris, M. G. (2017). Vertical datum unification for the international height reference system (IHRS). Geophysical Journal International, 209(2), 570-586.
https://doi.org/10.1093/gji/ggx025
18. Sansò, F., Reguzzoni, M., & Barzaghi, R. (2019). Geodetic heights. Springer International Publishing.
https://doi.org/10.1007/978-3-030-10454-2
19. Savchyn, I., & Vaskovets, S. (2018). Local geodynamics of the territory of Dniester pumped storage power plant. Acta Geodyn. Geomater, 15(1), 189.
https://doi.org/10.13168/AGG.2018.0002
20. Savchyn, I., & Pronyshyn, R. (2020). Differentiation of recent local geodynamic and seismic processes of technogenic-loaded territories based on the example of Dnister Hydro Power Complex (Ukraine). Geodesy and Geodynamics, 11(5), 391-400.
https://doi.org/10.1016/j.geog.2020.06.001
21. Szelachowska, M., & Krynski, J. (2014). GDQM-PL13-the new gravimetric quasigeoid model for Poland. Geoinformation Issues, 6(1), 5-19.
22. Tretyak, K., & Turuk, D. (2003). Estimation of accuracy of state leveling network of 2 class of Ukraine. Geodesy, cartography and aerial photography, 63, 9-16. (in Ukrainian).
23. Tretyak, K. R., Maksimchuk, V. Y., Kutas, R. I., Rokityansky, I. I., Gnilko, A. N., Kendzera, A. V., & Tereshin, A. V. (2015). Modern geodynamics and geophysical fields of the Carpathians and adjacent territories. Lviv: Publishing House of Lviv Polytechnic (in Ukrainian
24. Tretyak, K. R., & Vovk, A. I. (2016). Differentation of the rotational movements of the european continents earth crust. Acta Geodynamica et Geomaterialia, 13(1), 181.
https://doi.org/10.13168/AGG.2015.0046
25. Tretyak, K. & Vovk, A. I. (2014). Results of determination of horizontal deformations of the crust of Europe according to GNSS-observations and their connection with tectonic structure. Geodynamics. 1 (16), 21-33.
https://doi.org/10.23939/jgd2014.01.021
26. Tretyak, K., & Romanyuk, V. (2014). Investigation of the relationship between modern vertical displa¬cements of the earth's crust and seismic activity in Europe. Geodynamics. 1, 7-20.
https://doi.org/10.23939/jgd2014.01.007
27. Tretyak, K., & Romaniuk, V. (2018). The research on the interrelation between seismic activity and mo¬dern vertical movements of the european permanent gnss-stations. Acta Geodynamics et Geomaterial, 15(2), 143-164.
https://doi.org/10.13168/AGG.2018.0010
28. Trimble DiNi Digital Level User Guide, 2017, p. 145.
29. Tscherning C. C, & Rapp R. H (1974) Closed covariance expressions for gravity anomalies, geoid undu¬lations, and deflections of the vertical implied by anomaly degree variance models. Report Depart¬ment of Geodetic Science, no. 208, The Ohio State University, Columbus, Ohio, USA
30. Vovk, A. I. (2016). Spatio-temporal differentiation of horizontal crust movements in Europe, according GNSS measurements: tesis … PhD. Lviv, 153 p. (in Ukrainian).
31. Vovk, A. (2015). Analysis of horizontal movements of the earth's crust of Central Europe determined by GNSS-measurements. Modern achievements of geodetic science and production. II (30), 28-31. (in Ukrainian).
32. Zablotskyi F. D., Dzhuman, B., & Brusak, I. (2021). On the accuracy of (quasi) geoid models with respect to the UELN/EVRS2000 height system. Modern achievements of geodetic science and production. № І(41), 29-36. (in Ukrainian).
https://doi.org/10.33841/1819-1339-1-41-29-36
33. Zayats, О., Navodych, M., Petrov, S., & Tretyak, K. (2017). Precise tilt measurements for monitoring of mine fields at Stebnyk potassium deposit area. Geodynamics. 2 (23), 25-33.