American Journal of Civil Engineering and Architecture
ISSN (Print): 2328-398X ISSN (Online): 2328-3998 Website: Editor-in-chief: Dr. Mohammad Arif Kamal
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American Journal of Civil Engineering and Architecture. 2023, 11(2), 38-44
DOI: 10.12691/ajcea-11-2-2
Open AccessArticle

Improved Model of Refracted Horizontal Angle: Dependency on Zenith Angle

Mansoor Sabzali1, and Lloyd Pilgrim1

1Department of Civil, Surveying and Environmental Engineering, University of Newcastle, Callaghan, New South Wales, Australia

Pub. Date: April 26, 2023

Cite this paper:
Mansoor Sabzali and Lloyd Pilgrim. Improved Model of Refracted Horizontal Angle: Dependency on Zenith Angle. American Journal of Civil Engineering and Architecture. 2023; 11(2):38-44. doi: 10.12691/ajcea-11-2-2


Refraction is always a major problem for the near-ground geodetic measurements. Thus far, there have been numerous studies showing the influences of atmosphere on the refracted ray leading to the variation in the distance and direction measurements. The refraction is projected into two non-correlated components on horizontal and vertical planes called horizontal and vertical refraction, respectively. Both impact the measurements in their corresponding directions. It is noted that, in terms of magnitude, the refracted zenith angle, in vertical plane, has always been assumed to be far larger than refracted horizontal angles (i.e., refracted horizontal angle is imagined to be minor or negligible). There are considerable productive understandings of vertical refraction influencing the vertical/zenith direction in the literatures. However, the limitation in determination of the horizontal (side or lateral) refraction is still a debatable issue. The research aimed to reveal the broader comprehension of the horizontally refracted ray affecting horizontal angle measurements. The presented model embraces the relationship between the zenith angle and refracted horizontal angle, which could be the desirable technique to computation of refracted horizontal angle at each zenith angle (i.e., ideally, it can be employed in the case of terrestrial laser scanning due to the change of zenith angle for every individual measured point). Thus, the dependency between vertical and horizontal refraction will be obvious.

dependency horizontal refraction influence of atmosphere vertical refraction

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[1]  Brys. H., and Justyniak. N., “Mathematical-physical model of horizontal refraction in measuring alignment of elongated engineering objects,” Geomatics, Landmanangement and Landscape, pp. No. 1, 25-32, 2016.
[2]  Sabzali. M., and Pilgrim. L., “Updated Atmospheric Modelling of Refracted Zenith Angle Using Vertical Temperature Gradient for Refraction Coefficient,” Journal of Geosciences and Geomatics, 11(1), pp. 11-20. 2023.
[3]  Sabzali. M., and Jazirian. I., “Improvement the modelling of atmospheric effects for electronic distance measurement (EDM): Analysis of air temperature, atmospheric pressure and relative humidity of air,” Geodesy and Cartography, 2022.
[4]  Reuger. J. M., Electronic Distance Measurements (3rd Edition), Springer-Verlag, 1990.
[5]  Bajtala. M., Sokol. S., and Cernota. P., “Estimation of a Horizontal Refraction in Geodetic Network,” Journal of the polish Mineral Engineering Society, 2016.
[6]  Bomford. B. G., Geodesy, Oxford, 1962.
[7]  Johnston. A., “Lateral Refraction in Tunnels,” Survey Review, pp. 31:242, 201-220, 1991.
[8]  Innocenti. C., and Corsontini. A., “Refractive index gradient of the atmosphere at Near Ground Levels,” Journal of Modern Optics, pp. 52: 5, 671-689, 2005.
[9]  Redovniković. L., Alisic. I., and Luketic. A., “Infleunce of Lateral Refraction on Measured Horizontal Directions,” Survey Review, pp. 45:331, 285-295, 2013.
[10]  Labriji. H., Herscovici-Schiller. O., and Cassaing. F., “Computation of the Lateral Shift due to the Atmsopheric Refraction,” Astronomy and Astrophysics, pp. 662, A61, 2022.
[11]  Wallner. E. P., “Minimizing atmospheric dispersion effects in compensated imaging,” Journal of the Optical Society of America, pp. 407-409, 1977.
[12]  Wallner. E. P., “The effects of atmospheric dispersion on compensated imaging,” in Proc. SPIE 0075, Imaging Through the Atmosphere, 1976.
[13]  “International Association of Geodesy [IAG],” in IAG Resolutions at the XXIIth General Assembly, Birmingham, 1999.