Growing Degree Days Single Sinusoid Method
Integrate ideal single-sinusoid daily temperature excess between caller lower and horizontal upper cutoffs analytically; differs from arithmetic daily-mean GDD and is not a development-event forecast.
Description
Single-sine growing degree days approximate the daily temperature cycle with a sine curve between observed minimum and maximum.
Single-sine growing degree days approximate the daily temperature cycle with a sine curve between observed minimum and maximum. A lower threshold starts heat accumulation and an upper horizontal cutoff limits the contribution at high temperatures.1
Integrate ideal single-sinusoid daily temperature excess between caller lower and horizontal upper cutoffs analytically; differs from arithmetic daily-mean GDD and is not a development-event forecast.
When to use Growing Degree Days Single Sinusoid Method
Use this tool to integrate ideal single-sinusoid daily temperature excess between caller lower and horizontal upper cutoffs analytically; differs from arithmetic daily-mean GDD and is not a development-event forecast.
Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
How to use Growing Degree Days Single Sinusoid Method and understand its results
- Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
- Enter dailyMinimumTemperaturesC, dailyMaximumTemperaturesC, lowerDevelopmentThresholdC, upperHorizontalThresholdC using the field table and calculation rules, then run the tool.
- Read singleSineDegreeDays, accumulatedSingleSineDegreeDays. 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 |
|---|---|---|---|
| dailyMinimumTemperaturesC | Daily minimum temperatures c | list of number | Required |
| dailyMaximumTemperaturesC | Daily maximum temperatures c | list of number | Required |
| lowerDevelopmentThresholdC | Lower development threshold c | number | Required |
| upperHorizontalThresholdC | Upper horizontal threshold c | number | Required |
Enter aligned nonempty daily minimum and maximum temperatures in °C, with each maximum at least its minimum, and finite lower and upper thresholds with lower below upper. The tool analytically integrates each positive part of the daily sine curve and subtracts the upper-threshold integral from the lower-threshold integral. Entirely cool days contribute zero; entirely above-upper days contribute upper minus lower. Constant-temperature days use their clipped excess directly. Results include daily °C·days and their sum.
Paired lists must be nonempty and have equal lengths.
daily GDD = mean_sine max(T − lower, 0) − mean_sine max(T − upper, 0) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| singleSineDegreeDays | Single sine degree days | list of number |
| accumulatedSingleSineDegreeDays | Accumulated single sine degree days | number |
{
"input": {
"dailyMinimumTemperaturesC": [
0
],
"dailyMaximumTemperaturesC": [
20
],
"lowerDevelopmentThresholdC": 10,
"upperHorizontalThresholdC": 20
},
"output": {
"singleSineDegreeDays": [
3.183098861837907
],
"accumulatedSingleSineDegreeDays": 3.183098861837907
}
}Limitations and assumptions
The sine curve is an approximation rather than hourly temperature data. This is a horizontal upper cutoff, not a vertical cutoff or a simple average-temperature method. Thresholds and biological response relationships must be chosen separately; the total is not a phenology forecast on its own.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. 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.
Alternative or Complementary methods
Use Winkler Index GDD Region Classifier: Resolve an already supplied seasonal GDD into caller Winkler-region policy bands, using lower-inclusive boundaries; no duplicate GDD accumulation, mutable region constants or crop recommendation. For a complementary task, use Huglin Heliothermal Index: Calculate Huglin mean/maximum heliothermal contributions over caller supplied season with caller latitude/daylength coefficient and base; no implicit hemisphere calendar or grape suitability classification.
References
Similar or alternative tools
- Winkler Index GDD Region Classifier
Resolve an already supplied seasonal GDD into caller Winkler-region policy bands, using lower-inclusive boundaries; no duplicate GDD accumulation, mutable region constants or crop recommendation.
- Huglin Heliothermal Index
Calculate Huglin mean/maximum heliothermal contributions over caller supplied season with caller latitude/daylength coefficient and base; no implicit hemisphere calendar or grape suitability classification.