Declination Angle Day-of-Year
Evaluate named approximate FAO ordinal-day solar declination, not NOAA date/location sunrise calculation, sidereal astrometry or a geodesy operation.
Description
Solar declination is the Sun's angular position north or south of Earth's equatorial plane.
Solar declination is the Sun's angular position north or south of Earth's equatorial plane. A day-of-year approximation provides the seasonal angle needed by simple radiation geometry.1, 2
Evaluate named approximate FAO ordinal-day solar declination, not NOAA date/location sunrise calculation, sidereal astrometry or a geodesy operation.
When to use Declination Angle Day-of-Year
Use this tool to evaluate named approximate FAO ordinal-day solar declination, not NOAA date/location sunrise calculation, sidereal astrometry or a geodesy operation.
Prepare the climate observations and independently chosen model parameters. Confirm units, daily coverage, chronological order and the intended seasonal window.
How to use Declination Angle Day-of-Year and understand its results
- Prepare the climate observations and independently chosen model parameters. Confirm units, daily coverage, chronological order and the intended seasonal window.
- Enter dayOfYear, daysInYear using the field table and calculation rules, then run the tool.
- Read faoSolarDeclinationRadians, faoSolarDeclinationDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| dayOfYear | Day of year | integer | Required |
| daysInYear | Days in year | integer | Required |
Supply a positive integer day within a 365- or 366-day year. The tool evaluates the named approximate seasonal equation and returns declination in radians and degrees. The input ordinal starts at one rather than zero.
δ = 0.409 sin(2π dayOfYear/daysInYear − 1.39) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| faoSolarDeclinationRadians | Fao solar declination radians | number |
| faoSolarDeclinationDegrees | Fao solar declination degrees | number |
{
"input": {
"dayOfYear": 81,
"daysInYear": 365
},
"output": {
"faoSolarDeclinationRadians": 0.0017794355959882655,
"faoSolarDeclinationDegrees": 0.1019541495654739
}
}Limitations and assumptions
This is an approximate FAO seasonal relation, not a precise ephemeris, sunrise calculation or location-dependent observation. Time of day, refraction and topography are not modeled.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Solar Constant Adjustment Eccentricity Factor: Evaluate FAO seasonal inverse relative Earth–Sun distance squared correction on a caller valid ordinal day/year length; not true orbital elements or a sunlight/irradiance forecast. For a complementary task, use Extraterrestrial Radiation Daily: Integrate geometric daily extraterrestrial solar radiation from independently supplied declination/distance correction, handling polar day/night without apparent sunrise/refraction or cloud attenuation.
Further background: Meteorological data and solar radiation equations.
References
Similar or alternative tools
- Solar Constant Adjustment Eccentricity Factor
Evaluate FAO seasonal inverse relative Earth–Sun distance squared correction on a caller valid ordinal day/year length; not true orbital elements or a sunlight/irradiance forecast.
- Extraterrestrial Radiation Daily
Integrate geometric daily extraterrestrial solar radiation from independently supplied declination/distance correction, handling polar day/night without apparent sunrise/refraction or cloud attenuation.