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.
Description
Extraterrestrial radiation is the solar energy available above the atmosphere before cloud and atmospheric attenuation.
Extraterrestrial radiation is the solar energy available above the atmosphere before cloud and atmospheric attenuation. Daily geometry depends on latitude, solar declination and Earth–Sun distance, including polar day and night.1, 2
Integrate geometric daily extraterrestrial solar radiation from independently supplied declination/distance correction, handling polar day/night without apparent sunrise/refraction or cloud attenuation.
When to use Extraterrestrial Radiation Daily
Use this tool to integrate geometric daily extraterrestrial solar radiation from independently supplied declination/distance correction, handling polar day/night without apparent sunrise/refraction or cloud attenuation.
Prepare the climate observations and independently chosen model parameters. Confirm units, daily coverage, chronological order and the intended seasonal window.
How to use Extraterrestrial Radiation Daily 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 latitudeDegrees, solarDeclinationRadians, inverseRelativeDistanceSquared, solarConstantMjPerM2Minute using the field table and calculation rules, then run the tool.
- Read extraterrestrialDailyRadiationMjPerM2, geometricSunsetHourAngleRadians. 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 |
|---|---|---|---|
| latitudeDegrees | Latitude degrees | number | Required |
| solarDeclinationRadians | Solar declination radians | number | Required |
| inverseRelativeDistanceSquared | Inverse relative distance squared | number | Required |
| solarConstantMjPerM2Minute | Solar constant mj per m2 minute | number | Required |
Enter latitude within ±90°, declination within ±π/2 radians, positive inverse relative distance squared and a positive solar constant in MJ/m²/minute. The tool obtains the geometric sunset hour angle from the clipped solar geometry, using π for polar day and zero for polar night. It evaluates the daily integral and clips negative roundoff to zero. Outputs are MJ/m²/day and radians.
Ra = (1440/π)Gsc dr[ω sinφ sinδ + cosφ cosδ sinω] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| extraterrestrialDailyRadiationMjPerM2 | Extraterrestrial daily radiation mj per m2 | number |
| geometricSunsetHourAngleRadians | Geometric sunset hour angle radians | number |
{
"input": {
"latitudeDegrees": 0,
"solarDeclinationRadians": 0,
"inverseRelativeDistanceSquared": 1,
"solarConstantMjPerM2Minute": 0.082
},
"output": {
"extraterrestrialDailyRadiationMjPerM2": 37.586031360582005,
"geometricSunsetHourAngleRadians": 1.5707963267948966
}
}Limitations and assumptions
These are geometric top-of-atmosphere quantities. Refraction, terrain, cloud, aerosols and surface albedo are excluded. Supply compatible declination and distance correction for the intended date.
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 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.
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.
- 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.