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## Theoretical and numerical aspects of the geodetic method for determining the atmospheric refraction coefficient using simultaneous and mutual zenith observations

Tsoulis, Dimitrios; Petrović, Svetozar; Kilian, Nicole
Theoretical and numerical aspects of the geodetic method for determining the atmospheric refraction coefficient using simultaneous and mutual zenith observations // Journal of Surveying Engineering - ASCE, 134 (2008), 1; 3-12 (međunarodna recenzija, članak, znanstveni)

Naslov
Theoretical and numerical aspects of the geodetic method for determining the atmospheric refraction coefficient using simultaneous and mutual zenith observations

Autori
Tsoulis, Dimitrios ; Petrović, Svetozar ; Kilian, Nicole

Izvornik
Journal of Surveying Engineering - ASCE (0733-9453) 134 (2008), 1; 3-12

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
numerical analysis; geodetic surveys; simulation; refraction

Sažetak
The estimation of the atmospheric refraction coefficient by conducting simultaneous and mutual zenith observations is a well-known geodetic procedure. The respective mathematical model is based on certain assumptions regarding the actual path followed by the optical ray while propagating in the atmosphere (spherical symmetric model). Starting from this model an approximate solution can be derived, which is generally accepted in the literature on the subject. The present paper examines the mathematical model of this geodetic technique in a rigorous manner, which results in an exact solution for the computation of the atmospheric refraction coefficient or equivalent for the zenith angle correction that is due to the effect of the atmospheric refraction. As the direct computation of the exact solution is rather complicated, an iterative way of computing the same quantity is derived, which can be realized easily on any pocket calculator. In order to assess the derived formulas we investigate the applicability of the exact, the convergence rate of the iterative and the errors introduced by the approximate formulas, by conducting a representative series of synthetic numerical experiments. The overall discussion aims to provide a helpful insight into the geometric and theoretical features of this traditional geodetic method. To practitioners that attempt to apply the standard correction formulas to zenith observations in order to compensate the effect of atmospheric refraction in the frame of typical surveying applications, such as trigonometric leveling, the paper also points out possible numerical errors introduced by the traditional approximate formulas.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Geologija, Geodezija

Projekt / tema
007-0071588-1593 - Kartografija Jadrana (Miljenko Lapaine, )

Ustanove
Geodetski fakultet, Zagreb

Profili:

Svetozar Petrović (autor)

#### Citiraj ovu publikaciju

Tsoulis, Dimitrios; Petrović, Svetozar; Kilian, Nicole
Theoretical and numerical aspects of the geodetic method for determining the atmospheric refraction coefficient using simultaneous and mutual zenith observations // Journal of Surveying Engineering - ASCE, 134 (2008), 1; 3-12 (međunarodna recenzija, članak, znanstveni)
Tsoulis, D., Petrović, S. & Kilian, N. (2008) Theoretical and numerical aspects of the geodetic method for determining the atmospheric refraction coefficient using simultaneous and mutual zenith observations. Journal of Surveying Engineering - ASCE, 134 (1), 3-12.
@article{article, year = {2008}, pages = {3-12}, keywords = {numerical analysis, geodetic surveys, simulation, refraction}, journal = {Journal of Surveying Engineering - ASCE}, volume = {134}, number = {1}, issn = {0733-9453}, title = {Theoretical and numerical aspects of the geodetic method for determining the atmospheric refraction coefficient using simultaneous and mutual zenith observations}, keyword = {numerical analysis, geodetic surveys, simulation, refraction} }

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• Scopus
• Academic Search Premier