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This section covers the fundamental astronomical calculations required for solar energy prediction. These models calculate the solar irradiance at the top of the atmosphere and the sun’s apparent position from the point of vue of the observer, forming the foundation for all subsequent irradiance and energy production models.

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Models in This Section

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Extraterrestrial Irradiance

Calculates the solar irradiance at the top of the atmosphere using the Spencer equation for Earth-Sun distance correction. This represents the maximum possible solar energy available before atmospheric attenuation.

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Solar Position Algorithm

Calculates the sun’s apparent position ( and angles) using the NREL Solar Position Algorithm (SPA). Includes corrections for , , and atmospheric .

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Sunrise and Sunset Determination

Determines daily sunrise and sunset times for the site location. Used for timestamp adjustment, handles the edge cases of polar regions where the sun may not rise or set for multiple days.

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Air Mass

Calculates the relative path length of solar radiation through the atmosphere ( or AM). Two model options: Bird-Hulstrom and Kasten-Sandia. Both include pressure correction for site elevation.

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Calculation Sequence

  1. Extraterrestrial Irradiance → Top-of-atmosphere DNI
  2. Solar Position → Apparent sun zenith and azimuth angles
  3. Sunrise/Sunset → Day boundaries for timestamp adjustment
  4. Air Mass → Atmospheric path length (depends on zenith angle)
These outputs feed into models, tracking algorithms, diffuse-direct , and spectral corrections.