• DOI:10.1016/J.RENENE.2021.03.047
• Corpus ID: 233631040

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

@article{Zhang2021ASA,
  title={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},
  author={Taiping Zhang and Paul W. Stackhouse and Bradley D. Mark Macpherson and J. C. Mikovitz},
  journal={Renewable Energy},
  year={2021}
}

• Taiping Zhang, P. Stackhouse, +1 author J. Mikovitz
• Published 15 March 2021
• Computer Science
• Renewable Energy

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”.