Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling

G. E. Valov; O. V. Vshivkova

doi:10.30533/GiA-2025-057

VAK Russia 1.6.22 UDC 528.024.4 CSCSTI 36.16

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FIELD TESTING OF ALGORITHM FOR REFRACTION COEFFICIENT DETERMINING FROM GRADIENT GEODETIC MEASUREMENTS FOR UNILATERAL TRIGONOMETRIC LEVELLING Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling

АА Аа

Published in Izvestia Vuzov. Geodesy and Aerophotosurveying · Volume 69, Issue 6 · Pages 8–24 · Rubric: Geodesy

DOI: https://doi.org/10.30533/GiA-2025-057

Received: 18.04.2025 Accepted: 19.12.2025 Published: 26.12.2025 Language of publication: RUS

Authors

G. E. Valov

O. V. Vshivkova

G. E. Valov

Moscow State University of Geodesy and Cartography Moscow

Schmidt Institute of Physics of the Earth, Russian Academy of Sciences Russian Federation

O. V. Vshivkova

Moscow State University of Geodesy and Cartography Moscow

ABSTRACT

The article presents a field testing of an algorithm for refraction coefficient determining from gradient geodetic measurements for unilateral trigonometric levelling. The algorithm developed by the authors is based on solving by the Monte Carlo method a system of nonlinear equations describing the vertical refraction angle changing in the working air layer. The authors performed analysis of the factors of vertical refraction formation, which to be taken into account in the production of gradient (at several levels) geodetic measurements. It is noted that the successful implementation of the developed algorithm is possible under the condition of unidirectional changes in the vertical atmosphere profile, i. e. in the absence of layers with different atmospheric stratification character. At the stage of preparing field observations, first of all methodological approaches for the production of gradient geodetic measurements were developed. These approaches are based on the analysis of the factors of vertical refraction formation which to be taken into account. Besides a procedure for angular measurements at several levels was proposed. The proposed procedure ensures the efficiency and accuracy, which are necessary to obtain the initial data for the refraction coefficient determining. The performed field observations and the further analysis of the obtained results proved the possibility of using the trend of changes in the increment of the refraction angle with height as an objective criterion for detecting atmospheric stratification change in the working air layer. The accuracy evaluation of the elevation differences corrected for the refraction influence using the algorithm developed by the authors showed that the results obtained met the requirements of geometric levelling of class IV.

KEYWORDS

trigonometric levelling, refraction coefficient, gradient geodetic measurements, atmospheric stratification

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Valov G. E., Vshivkova O. V. Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling // Izvestia Vuzov. Geodesy and Aerophotosurveying. 2026. no. 6. pp. 8-24. DOI: https://doi.org/10.30533/GiA-2025-057. (Date of access 22.09.2026).

MLA

G. E. Valov, Vshivkova O. V.. "Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling." Izvestia Vuzov. Geodesy and Aerophotosurveying 69.6 (2026): 8-24. DOI: https://doi.org/10.30533/GiA-2025-057.

APA

Valov G. E., Vshivkova O. V. (2026). Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling. Izvestia Vuzov. Geodesy and Aerophotosurveying, 69(6), 8-24. https://doi.org/10.30533/GiA-2025-057

Chicago

G. E. Valov, Vshivkova O. V.. "Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling." Izvestia Vuzov. Geodesy and Aerophotosurveying 69, no. 6 (2026): 8-24. https://doi.org/10.30533/GiA-2025-057.

WIKI

{{cite journal | author = Valov G. E., Vshivkova O. V. | title = Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling | journal = Izvestia Vuzov. Geodesy and Aerophotosurveying | year = 2026 | volume = 69 | issue = 6 | pages = 8-24 | doi = 10.30533/GiA-2025-057 }}

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FIELD TESTING OF ALGORITHM FOR REFRACTION COEFFICIENT DETERMINING FROM GRADIENT GEODETIC MEASUREMENTS FOR UNILATERAL TRIGONOMETRIC LEVELLING Field Testing of Algorithm for Refraction Coefficient Determining from Gradient Geodetic Measurements for Unilateral Trigonometric Levelling

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