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A solar azimuth formula that renders circumstantial treatment unnecessary without compromising mathematical rigor: Mathematical setup, application and extension of a formula based on the subsolar point and atan2 function

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  • Zhang, Taiping
  • Stackhouse, Paul W.
  • Macpherson, Bradley
  • Mikovitz, J. Colleen

Abstract

A conceptually and mathematically concise formula for computing the solar azimuth angle has been used by a subgroup of scientists, but for lack of documentation and publication, it has not been well circulated. This paper introduces this formula which is based on the idea of a unit vector, S, originating from the observer’s location and pointing toward the center of the Sun. The vector is completely determined by the coordinates of the subsolar point and of the observer. The x- and y-components of the vector determine the solar azimuth angle, and their use along with the function atan2, which is available in a number of programming/scripting languages, including Fortran and Python, renders any circumstantial treatment absolutely unnecessary. The z-component of the vector, at the same time, determines the solar zenith angle. The use of the unit vector also facilitates a figure that can be used as a full 3D graphic depiction of the daily and annual cycles of the Sun’s position for any given location, and this figure can be called “wreath of analemmas”.

Suggested Citation

  • Zhang, Taiping & Stackhouse, Paul W. & Macpherson, Bradley & Mikovitz, J. Colleen, 2021. "A solar azimuth formula that renders circumstantial treatment unnecessary without compromising mathematical rigor: Mathematical setup, application and extension of a formula based on the subsolar poin," Renewable Energy, Elsevier, vol. 172(C), pages 1333-1340.
    • Handle: RePEc:eee:renene:v:172:y:2021:i:c:p:1333-1340
    DOI: 10.1016/j.renene.2021.03.047
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    References listed on IDEAS

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    1. Sproul, Alistair B., 2007. "Derivation of the solar geometric relationships using vector analysis," Renewable Energy, Elsevier, vol. 32(7), pages 1187-1205.
    2. Soulayman, S., 2018. "Comments on solar azimuth angle," Renewable Energy, Elsevier, vol. 123(C), pages 294-300.
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    1. João R. B. Paiva & Alana S. Magalhães & Pedro H. F. Moraes & Júnio S. Bulhões & Wesley P. Calixto, 2021. "Stability Metric Based on Sensitivity Analysis Applied to Electrical Repowering System," Energies, MDPI, vol. 14(22), pages 1-21, November.

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