An Error Modeling Framework for the Sun Azimuth Obtained at a Location with the Hour Angle Method

Tarig A. Ali

Department of Civil Engineering, American University of Sharjah, Sharjah, United Arab Emirates..

DOI: 10.4236/pos.2012.32004                

Abstract

Sun observations provide a robust way for determining the geodetic or true azimuth at a location. Azimuth is generally defined as the angle in the plane measured from the meridian’s north (or south) to the location of the line of interest. It is common to use the north azimuth; also referred to as “azimuth”, especially in civilian surveying applications. The astronomic meridian is obtained through astronomic observations of the Sun or North Star (Polaris) and it is important since it provides one instance of the geodetic or true meridian. There are two methods for determining the sun azimuth; the first is known as the hour angle method and the other is called the altitude method. The hour angle method requires the determination of accurate time while altitude method requires accurate vertical angle. The hour angle method is more popular because it is more accurate, can be performed at any time of day and is applicable to the sun, Polaris and other stars. In this article, an error modeling framework for the errors result in the process of determining the sun azimuth using the hour angle method; namely random errors, is presented. A Gauss-Markov model is used to represent the errors in the true azimuth estimation process. Six sets of sun observation for azimuth data; three with telescope direct and three reverse, including horizontal circle’s readings and time were collected and used in order to estimate the true azimuth of a line in a study area in central Orlando, Florida, United States.

Keywords

True Azimuth; Astronomic Meridian; Hour Angle

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. Wolf and C. Ghilani, “Elementary Surveying: An In- troduction to Geomatics,” 10th Edition, Prentice Hall, Up- per Saddle River, 2002.
[2]	J. McCormack, “Surveying,” 5th Edition, John Wiley and Sons, New York, 2004.
[3]	E. Mikhail and G. Gracie, “Analysis and Adjustment of Survey Measurements,” Van Nostrand Reinhold, New York, 1982.
[4]	R. Buckner, “Astronomic and Grid Azimuth,” Landmark Enterprises, Rancho Cordova, 1984.
[5]	J. Mackie, “The Elements of Astronomy for Surveyors,” Charles Griffin House, 1985.
[6]	R. Elgin, R., D. Knowles and J. Senne, “Celestial Obser- vation Handbook and Ephemeris,” Lietz Co., Overland Park, 2000.
[7]	C. Ghilani and P. Wolf, “Adjustment Computations: Spa- tial Data Analysis,” 4th Edition, John Wiley and Sons, New York, 2006.