Angstrom-Prescott A-B Coefficient Solver
Fit measured Angstrom–Prescott sunshine/solar fraction coefficients and predict supplied sunshine fraction, exposing calibration-range extrapolation; no universal local coefficients or sunshine forecast.
Description
The Ångström–Prescott relation links sunshine fraction to a solar-energy fraction using a fitted line.
The Ångström–Prescott relation links sunshine fraction to a solar-energy fraction using a fitted line. Local measurements determine its coefficients instead of assuming a universal calibration.1, 2
Fit measured Angstrom–Prescott sunshine/solar fraction coefficients and predict supplied sunshine fraction, exposing calibration-range extrapolation; no universal local coefficients or sunshine forecast.
When to use Angstrom-Prescott A-B Coefficient Solver
Use this tool to fit measured Angstrom–Prescott sunshine/solar fraction coefficients and predict supplied sunshine fraction, exposing calibration-range extrapolation; no universal local coefficients or sunshine forecast.
Prepare the climate observations and independently chosen model parameters. Confirm units, daily coverage, chronological order and the intended seasonal window.
How to use Angstrom-Prescott A-B Coefficient Solver 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 observedSunshineFractions, observedSolarEnergyFractions, predictionSunshineFraction using the field table and calculation rules, then run the tool.
- Read angstromPrescottA, angstromPrescottB, predictedSolarEnergyFraction, predictionOutsideCalibrationRange. 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 |
|---|---|---|---|
| observedSunshineFractions | Observed sunshine fractions | list of number | Required |
| observedSolarEnergyFractions | Observed solar energy fractions | list of number | Required |
| predictionSunshineFraction | Prediction sunshine fraction | number | Required |
Enter aligned observed sunshine and solar-energy fractions from zero to one, and a prediction sunshine fraction in the same range. Fit at least two observations with varying sunshine fraction by ordinary least squares. Return intercept a, slope b and predicted fraction; the prediction itself must remain between zero and one. A requested fraction outside observed sunshine coverage is flagged as extrapolation.
The least-squares fit needs at least two aligned observations and a varying independent variable. Where R² is returned, the helper assigns 1 for a constant dependent variable.
solarFraction = a + b × sunshineFraction Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| angstromPrescottA | Angstrom prescott a | number |
| angstromPrescottB | Angstrom prescott b | number |
| predictedSolarEnergyFraction | Predicted solar energy fraction | number |
| predictionOutsideCalibrationRange | Prediction outside calibration range | boolean |
{
"input": {
"observedSunshineFractions": [
0,
1
],
"observedSolarEnergyFractions": [
0.2,
0.7
],
"predictionSunshineFraction": 0.5
},
"output": {
"angstromPrescottA": 0.19999999999999998,
"angstromPrescottB": 0.49999999999999994,
"predictedSolarEnergyFraction": 0.44999999999999996,
"predictionOutsideCalibrationRange": false
}
}Limitations and assumptions
The tool does not predict sunshine, select reference radiation or certify fitted coefficients. The fit can have either slope sign if the data imply it. Extrapolation is allowed only when its calculated fraction remains within the valid fraction range.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Clear Sky Transmissivity Estimate: Estimate observed clear-sky bulk transmissivity from paired integrated surface/extraterrestrial energies; observations must be independently identified clear-sky, not assumed clear from station elevation. 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
- Clear Sky Transmissivity Estimate
Estimate observed clear-sky bulk transmissivity from paired integrated surface/extraterrestrial energies; observations must be independently identified clear-sky, not assumed clear from station elevation.
- 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.