| Aberration | The apparent displacement of a celestial object’s position due to the finite speed of light combined with Earth’s orbital motion. The sun appears slightly displaced from its true geometric position, requiring a correction of approximately 20 arcseconds in longitude. |
| Air Mass | The ratio of the path length of sunlight through Earth’s atmosphere to the path length at zenith (sun directly overhead). Air mass equals 1 at zenith and increases with solar zenith angle, reaching ~38 at the horizon. Higher air mass means more atmospheric absorption and scattering. |
| Angle of Incidence | The angle between the sun’s rays and the perpendicular (normal) to a surface. When the sun is directly facing a surface, the angle of incidence is 0° and maximum irradiance is received. As the angle increases, the irradiance on the surface decreases proportionally to cos(θ). For tracking systems, the goal is to minimize angle of incidence to maximize energy capture. |
| Astronomical Unit (AU) | The mean distance from Earth to the Sun, approximately 149.6 million kilometers (93 million miles). Used as a standard unit for measuring distances within the solar system. Earth’s distance from the Sun varies from ~0.983 AU at perihelion to ~1.017 AU at aphelion due to its elliptical orbit. |
| Atmospheric Attenuation | The reduction in solar radiation intensity as it passes through Earth’s atmosphere, caused by absorption (by gases like ozone, water vapor, and CO₂) and scattering (by molecules and aerosols). Attenuation increases with air mass—at higher zenith angles, sunlight travels through more atmosphere and experiences greater losses. |
| Azimuth | The horizontal angle measured clockwise from north (0° = North, 90° = East, 180° = South, 270° = West). For the sun (solar azimuth), this is the compass direction to the sun’s position projected onto the horizon. For a surface (surface azimuth), this is the compass direction the surface faces—the horizontal projection of the outward normal vector. |
| Clearness Index | The ratio of measured global horizontal irradiance (GHI) to extraterrestrial horizontal irradiance, quantifying atmospheric transmittance. Values range from 0 (complete overcast) to ~0.8 (very clear sky). Used in diffuse-direct decomposition models. |
| Column Depth | The total amount of an atmospheric constituent (such as ozone or water vapor) contained in a vertical column of atmosphere, expressed as the equivalent thickness the substance would have if compressed to standard conditions. For ozone, column depth is typically ~0.3 cm; for water vapor (called precipitable water), typical values range from 0.5 to 5 cm. Column depth is multiplied by air mass to obtain the slant column along the sun’s path. |
| Closure Equation | The fundamental relationship between horizontal irradiance components: GHI = DNI × cos(θz) + DHI, where θz is the solar zenith angle. This equation states that global horizontal irradiance equals the horizontal projection of direct normal irradiance plus diffuse horizontal irradiance. Used for quality control validation and to calculate missing irradiance components. |
| Day Angle | The angular position of Earth in its orbit, measured in radians from the start of the year. Ranges from 0 to 2π over the course of a year and is used in calculating extraterrestrial irradiance and the equation of time. |
| Declination | The angular distance of a celestial object north or south of the celestial equator, analogous to latitude on Earth. Solar declination ranges from +23.45° (summer solstice) to −23.45° (winter solstice) and determines the sun’s path across the sky at different times of year. |
| Decomposition | The process of separating global horizontal irradiance (GHI) into its direct (DNI) and diffuse (DHI) components using empirical models. Common decomposition models include Erbs, Reindl, and DIRINT. These models use the clearness index and other parameters to estimate the fraction of irradiance that is direct vs. diffuse based on atmospheric conditions. |
| DHI (Diffuse Horizontal Irradiance) | Solar radiation received on a horizontal surface from the sky dome after scattering by atmospheric constituents (molecules, aerosols, clouds), excluding the direct beam component from the sun’s disk. DHI represents the “soft” light that arrives from all directions of the sky. Typical clear-sky values range from 50–150 W/m², increasing under partly cloudy conditions. |
| DNI (Direct Normal Irradiance) | Solar radiation received on a surface held perpendicular (normal) to the sun’s rays, representing only the direct beam component from the sun’s disk. DNI is the highest-intensity component under clear skies (typically 800–1000 W/m²) and is the primary driver of energy production for tracking systems. DNI drops to zero under overcast conditions. |
| Ecliptic | The plane of Earth’s orbit around the Sun, or equivalently, the apparent annual path of the Sun across the celestial sphere. The ecliptic is inclined at approximately 23.44° to the celestial equator (Earth’s equatorial plane projected onto the sky). This tilt causes the seasons. |
| Ecliptic Coordinates | A celestial coordinate system based on the ecliptic plane as the fundamental reference. Positions are specified by ecliptic longitude (measured eastward from the vernal equinox along the ecliptic, 0°–360°) and ecliptic latitude (angular distance north or south of the ecliptic, ±90°). Used in planetary and solar position calculations. |
| Ecliptic Reference Frame | A coordinate system with the ecliptic (Earth’s orbital plane) as its fundamental plane. The x-axis points toward the vernal equinox, and the z-axis is perpendicular to the ecliptic. Used for describing planetary positions and as an intermediate step in solar position calculations. See also: Ecliptic Coordinates. |
| Elevation (Solar) | The angular height of the sun above the horizon, measured in degrees. Also called solar altitude. Ranges from 0° (horizon) to 90° (directly overhead). Related to zenith angle by: elevation = 90° − zenith. |
| Ephemeris Time | A historical uniform time scale based on the motion of celestial bodies, independent of Earth’s variable rotation. Ephemeris Time was replaced by Terrestrial Time (TT) in 1984, though the two are continuous and equivalent for practical purposes. Used in astronomical calculations where precise orbital mechanics are needed. Differs from Universal Time by ΔT. |
| Equatorial Coordinates | A celestial coordinate system based on Earth’s equatorial plane projected onto the celestial sphere. Positions are specified by right ascension (measured eastward from the vernal equinox along the celestial equator, 0h–24h or 0°–360°) and declination (angular distance north or south of the equator, ±90°). Used for specifying positions as seen from Earth. |
| Equatorial Reference Frame | A coordinate system with Earth’s equatorial plane as its fundamental plane. The x-axis points toward the vernal equinox, and the z-axis points toward the celestial north pole. Used for describing celestial positions as seen from Earth and for calculating hour angles. See also: Equatorial Coordinates. |
| Equinox | The moment when the Sun crosses the celestial equator, making day and night approximately equal length worldwide. The vernal (spring) equinox occurs around March 20 when the Sun moves northward; the autumnal equinox occurs around September 22 when it moves southward. The equinox points also serve as reference points for celestial coordinate systems. |
| Equation of Time | The difference between apparent solar time (based on the actual Sun’s position) and mean solar time (based on a hypothetical Sun moving at constant rate). The equation of time varies from approximately −14 to +16 minutes throughout the year due to two effects: (1) Earth’s elliptical orbit causes varying orbital speed per Kepler’s second law, and (2) Earth’s axial tilt causes the Sun’s east-west motion projected onto the celestial equator to vary seasonally. PlantPredict uses a second-order Fourier series approximation following Spencer (1971). |
| Fractional Year Angle | The angular position in the annual cycle, ranging from 0 to 2π radians over the course of a year. Computed as γ = (2π/365.24)(n − 1 + t/24), where n is the day of year and t is the hour of day. Used in Fourier series approximations for seasonal solar variations such as the equation of time and extraterrestrial irradiance. Also called the day angle. |
| GAST (Greenwich Apparent Sidereal Time) | The hour angle of the true vernal equinox at the Greenwich meridian. GAST measures Earth’s rotational position relative to the stars, accounting for nutation. It is computed from Greenwich Mean Sidereal Time (GMST) plus the equation of the equinoxes (Δψ cos ε). Used to calculate the local hour angle of celestial objects. |
| Geocentric | Measured from Earth’s center, treating the planet as a point mass. Geocentric coordinates do not account for the observer’s position on Earth’s surface, making them suitable for astronomical calculations where parallax effects are negligible. |
| GHI (Global Horizontal Irradiance) | Total solar radiation received on a horizontal surface from the entire sky hemisphere, including direct beam, diffuse sky radiation, and ground-reflected radiation. GHI is the most commonly measured irradiance component and equals DNI × cos(θz) + DHI, where θz is the solar zenith angle. Typical peak values are 900–1100 W/m² at solar noon under clear skies. |
| Heliocentric | Measured from the center of the Sun. Heliocentric coordinates describe Earth’s position in its orbit around the Sun, used as an intermediate step in calculating the Sun’s apparent position as seen from Earth. |
| Julian Calendar | A calendar system introduced by Julius Caesar in 46 BC, using a 365.25-day year with leap years every 4 years. In astronomy, “Julian” refers to the Julian Day Number—a continuous count of days since January 1, 4713 BC—which provides a uniform time reference independent of calendar systems. Julian Day 2451545.0 corresponds to January 1, 2000, 12:00 TT (the J2000.0 epoch). |
| Local Hour Angle | The angular distance of a celestial object (typically the Sun) from the observer’s local meridian, measured westward in degrees or hours. An hour angle of 0° means the object is on the meridian (local noon for the Sun); positive values indicate the object has passed the meridian (afternoon). Computed as H = GAST + observer’s longitude − right ascension. |
| Local Solar Time | A time scale based on the Sun’s actual position relative to the observer’s meridian. Solar noon (12:00 local solar time) occurs when the Sun crosses the local meridian. Local solar time differs from clock time due to the observer’s position within their time zone and the equation of time (which accounts for Earth’s elliptical orbit and axial tilt). |
| Local Standard Time | Clock time for a given time zone, defined as a fixed offset from Coordinated Universal Time (UTC). For example, US Eastern Standard Time is UTC−5. Local standard time differs from local solar time due to the observer’s longitude within the time zone and the equation of time. To convert from local solar time to local standard time, apply the equation of time correction and adjust for the difference between the observer’s longitude and the time zone’s central meridian. |
| Normalized Path Length | The ratio of the actual path length that sunlight travels through the atmosphere to the path length at zenith (sun directly overhead). This is equivalent to air mass. A normalized path length of 1 means the sun is overhead; values increase with zenith angle, reaching ~38 at the horizon. Used in transmittance calculations where the amount of absorbing or scattering material encountered is proportional to path length. |
| Nutation | Short-period oscillations in Earth’s rotational axis caused by gravitational torques from the Sun and Moon. Nutation causes periodic variations of up to ±17 arcseconds in longitude and ±9 arcseconds in obliquity, with the primary period being 18.6 years. |
| Obliquity | The angle between Earth’s rotational axis and the perpendicular to its orbital plane (the ecliptic), currently approximately 23.44°. Obliquity determines the severity of seasons and varies slowly over time due to gravitational perturbations. |
| Orbital Plane | The flat, two-dimensional surface in which a celestial body travels around another. Earth’s orbital plane around the Sun defines the ecliptic. Other planets have orbital planes inclined at various angles to Earth’s, causing gravitational perturbations that affect Earth’s position. |
| Parallax | The apparent displacement of a celestial object’s position due to the observer’s location on Earth’s surface rather than at Earth’s center. Solar parallax causes the sun’s position to shift by up to ~8.8 arcseconds depending on the observer’s latitude, longitude, and altitude. PlantPredict applies a parallax correction to convert geocentric coordinates to topocentric coordinates. |
| Radius Vector | The distance from the center of the Sun to the center of Earth, measured in astronomical units (AU). Varies from ~0.983 AU (perihelion, early January) to ~1.017 AU (aphelion, early July) due to Earth’s elliptical orbit. |
| Rayleigh Scattering | Elastic scattering of light by particles much smaller than the wavelength (such as air molecules N₂ and O₂). The molecule’s electron cloud oscillates in response to the electromagnetic wave and re-radiates at the same frequency. Rayleigh scattering is symmetric—equal amounts scatter forward and backward—and is wavelength-dependent (∝ λ⁻⁴), scattering blue light more than red. This causes the blue color of the sky and contributes to diffuse irradiance in clear-sky models. |
| Refraction | The bending of light as it passes through Earth’s atmosphere, caused by the decrease in air density with altitude. Atmospheric refraction makes the sun appear higher than its true geometric position, with the effect increasing at lower elevations. At the horizon, refraction displaces the sun by approximately 0.57°. PlantPredict applies a refraction correction to the calculated zenith angle based on temperature and pressure. |
| Right Ascension | The angular distance of a celestial object measured eastward along the celestial equator from the vernal equinox, analogous to longitude on Earth. Typically expressed in hours, minutes, and seconds (0h to 24h) or degrees (0° to 360°). |
| Sidereal Time | Time measured relative to the fixed stars rather than the Sun. A sidereal day is ~4 minutes shorter than a solar day because Earth advances in its orbit. Local sidereal time is used to calculate the local hour angle of celestial objects. |
| Slant Column | The total amount of an atmospheric constituent (such as ozone or water vapor) along the actual slant path from the sun to the observer, as opposed to the vertical column. Calculated as the product of column depth and air mass (normalized path length): slant column = column depth × AM. For example, with ozone column depth of 0.3 cm and air mass of 2, the ozone slant column is 0.6 cm. |
| Spectral Effects | Changes in the solar spectrum as sunlight passes through the atmosphere, affecting PV module performance. At higher air mass (lower sun angles), the atmosphere absorbs more blue light and transmits relatively more red/infrared light. Different PV cell technologies respond differently to these spectral changes—modules with narrow spectral response (e.g., CdTe) are more affected than those with broad response (e.g., crystalline silicon). PlantPredict uses spectral shift models to account for these effects. |
| Terrestrial Time (TT) | A uniform time scale based on celestial mechanics, independent of Earth’s variable rotation. TT replaced Ephemeris Time in 1984 and is used for astronomical ephemerides and orbital calculations. TT runs at a constant rate defined by atomic clocks, differing from Universal Time by ΔT (67 seconds in PlantPredict). In the SPA algorithm, TT is used to compute planetary positions while UT is used for Earth rotation. |
| Topocentric | Measured from a specific point on Earth’s surface, as opposed to geocentric (from Earth’s center). Topocentric coordinates account for the observer’s actual position including latitude, longitude, and elevation. |
| Transposition | The process of converting horizontal irradiance components (GHI, DNI, DHI) to plane-of-array (POA) irradiance on a tilted surface. Transposition models calculate beam, sky diffuse, and ground-reflected irradiance contributions based on surface orientation, solar position, and view factors. Common transposition models include Hay-Davies and Perez. |
| Transmittance | The fraction of solar radiation that passes through the atmosphere to reach the Earth’s surface. In clear-sky models, transmittance decreases with air mass as sunlight travels through more atmosphere. The DISC model decomposes transmittance into clear-sky transmittance (Knc, the theoretical maximum under clear conditions) minus a transmittance reduction (ΔKn, accounting for clouds, aerosols, and turbidity), yielding actual transmittance (Kn). DNI is then calculated as transmittance times extraterrestrial irradiance. |
| Turbidity | A measure of the cloudiness or haziness of the atmosphere caused by aerosols, water vapor, dust, and other suspended particles that scatter and absorb sunlight. Higher turbidity reduces direct normal irradiance and increases diffuse irradiance. In decomposition models, turbidity effects are captured indirectly through the clearness index and transmittance reduction factors. Unlike clouds, which cause rapid fluctuations in irradiance, turbidity typically produces steady attenuation—a distinction exploited by the DIRINT model’s temporal stability parameter. |
| Universal Time (UT) | A time standard based on Earth’s rotation, closely approximating mean solar time at the Prime Meridian. UT1 is determined by astronomical observations and varies slightly due to irregularities in Earth’s rotation. UTC (Coordinated Universal Time) is kept within 0.9 seconds of UT1 through leap seconds. |
| Vernal Equinox | The point on the celestial sphere where the Sun crosses the celestial equator moving from south to north, occurring around March 20. Also called the “First Point of Aries,” it serves as the zero point for measuring right ascension and ecliptic longitude. The position of the vernal equinox slowly shifts due to precession (~50 arcseconds/year) and oscillates due to nutation. |
| VSOP87 | Variations Séculaires des Orbites Planétaires (Secular Variations of Planetary Orbits), a high-precision planetary theory developed by Bretagnon and Francou (1988). VSOP87 provides polynomial and periodic series for computing the heliocentric positions of planets. The NREL Solar Position Algorithm uses VSOP87 to calculate Earth’s heliocentric longitude, latitude, and radius vector. |
| Zenith Angle | The angle between the local vertical (zenith) and the line of sight to the sun, measured in degrees. A zenith angle of 0° means the sun is directly overhead; 90° means it is at the horizon. Related to solar elevation by: zenith angle = 90° − elevation. |
