# Solar azimuth angle

The solar azimuth angle is the azimuth angle of the sun .    It qui olefins in the direction the sun is, whereas the solar zenith angle gold icts complementary angle Solar elevation olefins how high the sun is. There are several conventions for the solar azimuth, however it is traditionally defined as the angle between a vertical line and a vertical line. This convention states the angle is positive if the line is east of south and negative if it is west of south.  For example, due east would be 90 ° and due west would be -90 °. Another convention is the reverse; it also has the origin at the south, but measures angles clockwise, so that it is due east positive and positive. 

However, despite tradition, the most widely accepted convention for analyzing solar irradiation , eg for solar energy applications, is clockwise from north, so is east 90 °, south is 180 ° and west is 270 °. This is the definition used by NREL in their solar position calculators  and is also the convention used in the formulas presented here. Note however Landsat photos and other USGS products, while also defining azimuthal angles relative to north, take counterclockwise angles as negative. 

## Formulas

Note: Both of these formulas assume the north-clockwise convention . The solar azimuth angle can be calculated to a good approximation with the following formula, but it should be interpreted with care because the inverse sine, ie x = sin -1 (y) or x = arcsin (y), has multiple solutions, only one of which will be correct.

{\ displaystyle \, \ sin \ phi _ {\ mathrm {s}} = {\ frac {- \ sin \ cos \ delta} {\ sin \ theta _ {\ mathrm {s}}}}}

The following formulas can also be used to approximate the azimuth angle, but these formulas use a cosine, so the azimuth angle as shown by a calculator will be positive, and should be interpreted as the angle between zero and 180 degrees when the hour angle , h , is negative (morning) and the angle between 180 and 360 degrees when the hour angle, h , is positive (afternoon). These two formulas are equivalent if you assume the ” solar elevation angle ” approximation formula.   

{\ displaystyle \, \ cos \ phi _ {\ mathrm {s}} = {\ frac {\ sin \ delta \ cos \ Phi – \ cos \ cos \ delta \ sin \ Phi} {\ sin \ theta _ { \ mathrm {s}}}}}
{\ displaystyle \, \ cos \ phi _ {\ mathrm {s}} = {\ frac {\ sin \ delta – \ cos \ theta _ {\ mathrm {s}} \ sin \ Phi} {\ sin \ theta _ {\ mathrm {s}} \ cos \ Phi}}}

The formulas use the following terminology:

• {\ displaystyle \, \ phi _ {\ mathrm {s}}} is the solar azimuth angle
• {\ displaystyle \, \ theta _ {\ mathrm {s}}}is the solar zenith angle
• {\ displaystyle \, h}is the hour angle , in the local solar time
• {\ displaystyle \, \ delta}is the current sun declination
• {\ displaystyle \, \ Phi}is the local latitude

• Equation of time
• Horizontal coordinate system
• Hour angle
• Position of the Sun
• Solar time
• Solar tracker
• Sun path
• Sunrise
• Sunset
• Zenith

## References

1. ^ Jump up to:b Sukhatme, SP (2008). Solar Energy: Principles of Thermal Collection and Storage (3rd ed.). Tata McGraw-Hill Education. p. 84. ISBN  0070260648 .
2. ^ Jump up to:c Seinfeld, John H .; Pandis, Spyros N. (2006). Atmospheric Chemistry and Physics, from Air Pollution to Climate Change (2nd ed.). Wiley. p. 130. ISBN  978-0-471-72018-8 .
3. ^ Jump up to:c Duffie, John A .; Beckman, William A. (2013). Solar Engineering of Thermal Processes (4th ed.). Wiley. pp. 13, 15, 20. ISBN  978-0-470-87366-3 .
4. ^ Jump up to:b Reda, I., Andreas, A. (2004). “Solar Position Algorithm for Solar Radiation Applications” . Solar Energy . Elsevier. 76 (5): 577-589. Bibcode : 2004SoEn … 76..577R . ISSN  0038-092X . doi : 10.1016 / j.solener.2003.12.003 .
5. Jump up^ https://lta.cr.usgs.gov/landsat_dictionary.html#sun_azimuthLandsat Data Dictionary 