Photosynthetic Photon Flux Density (PPFD) - Concepts
Lighting for plants is different from lighting for humans. Light energy for humans is measured in lumens, with light falling onto a surface measured as illuminance with units of lux (lumens per square meter) or footcandles (lumens per square foot). Light energy for plants, on the other hand, is measured as photosynthetic active radiation (PAR), with light falling onto a surface measured as photosynthetic photon flux density (PPFD) with units of μmol/s-m2.
| Light for Humans | Light for Plants | |
| Radiant power, 400-700 nm | Lumens | Photosynthetic Active Radiation (PAR) |
| Light falling onto a surface | Illuminance | Photosynthetic Photon Flux Density (PPFD) |
| Units | Lux, Footcandles | Micromoles per second per sq.meter (μmol/s-m2) |
The spectrum to which plants are most sensitive varies with the species, but for most plants the spectrum is very similar to the visual spectrum to which humans are sensitive, approximately 400-700 nm. This is the range that stimulates photosynthesis. Any photons within this spectrum that are absorbed by the plant will contribute to photosynthesis. However, not all wavelengths have an equal likelihood of being absorbed, as determined by the various plant pigments that might be present. As with human vision, plants are more likely to respond to (absorb) light in some wavelengths than others.
General Notes:
In AGi32, PPFD is selected as the calculation type rather than as a light source characteristic. (See Procedures tab for specifics.)
AGi32 assumes that all sources contributing to the calculation grid have the same PPFD Factor, as selected in the PPFD Conversion Factors dialog.
PPFD can only be calculated with the Full Radiosity calculation method.
PPFD is not available as a Statistical Area metric, but it is available in the Schedules, Isolines, and Highlight Values commands.
The mathematical basis for the calculation of PPFD:
If the spectral power distribution (SPD) of a light source is known across the relevant wavelengths (400-700 nm), then the amount of photosynthetic energy available to plants can be determined. Based on its SPD, a light source will have a conversion factor that can be used to translate luminous flux density (illuminance) received by the plant into photosynthetic photon flux density (PPFD), in μmol/s-m2.
One watt of radiant power at 555 nm is by definition equal to 683 lumens. Given the CIE 1931 luminous efficiency function V(λ), we can calculate the spectral radiant flux Φ(λ) for plants in watts per nanometer for each lumen as:
Φ(λ)/lumen = [Wrel(λ)] / [683 * Σ(400-700) [V(λ) Wrel(λ) Δλ]]
where Wrel(λ) is the relative spectral power distribution and V(λ) is the luminous efficiency function at wavelength λ.
With this, the photosynthetic photon flux (PPF) per nanometer in micromoles per second per nanometer can be calculated:
PPF /nm = (10-3) * [λ Φ(λ)] / (Nahc),
where:
Na = Avogadro's constant, 6.022 x1023
h = Planck's constant (6.626 x 10-34 joule-seconds)
c = speed of light, 2.998 x 108 m/s
λ = wavelength in meters.
Summing over the range of 400-700 nm yields the photosynthetic photon flux (PPF) per lumen for the given light source:
PPF » 8.359 * 10-3 * Σ(400-700) [λ Φ(λ) Δλ]
Given an illuminance value (lux or footcandles), we can similarly calculate the photosynthetic photon flux density (PPFD) in micromoles per second per square meter (μmol/s-m2) for the given light source.
SPD graphs are relatively easy to come by, but finding the same information in tabular form, needed for the above equations, is more difficult. One source is CIE 15:4, Colorimetry (2004). Adding digitized data from one LED manufacturer's white LED SPD curves, we can arrive at the following table of PPFD Conversion Factors, for converting illuminance in kilolux to PPFD in μmol/s-m2:
|
Light Source |
Conversion Factor |
|
CIE A (incandescent, 2856K) |
20.3 |
|
CIE 5000K daylight (D50) |
18.1 |
|
CIE 5500K daylight (D55) |
18.1 |
|
CIE 6500K daylight (D65) |
18.3 |
|
CIE 7500K daylight (D75) |
18.6 |
|
CIE HP1 (standard HPS, 1959K) |
11.7 |
|
CIE HP2 (color-enhanced HPS, 2506K) |
19.3 |
|
CIE HP3 (metal halide, 3144K) |
14.4 |
|
CIE HP4 (metal halide, 4002K) |
15.0 |
|
CIE HP5 (metal halide, 4039K) |
16.3 |
|
2700K white light LED (Philips Luxeon Rebel LXW9-PW27) |
18.1 |
|
3000K white light LED (Philips Luxeon Rebel LXW9-PW30) |
17.1 |
|
3500K white light LED (Philips Luxeon Rebel LXW7-PW35) |
14.6 |
|
4000K white light LED (Philips Luxeon Rebel LXW8-PW40) |
14.3 |
|
5000K white light LED (Philips Luxeon Rebel LXW8-PW50) |
14.6 |
These Conversion Factors are available in the PPFD Factors dialog in AGi32.
Note: The PPFD Factors dialog uses one daylight value, called "Average Daylight." In the real world, daylight CCTs vary from 4500K in the mid-morning and mid-afternoon to 7500K from skylight only on a clear day and 6000K on an overcast day (www.ephotozine.com/article/guide-to-colour-temperature-4804). An average value of 18.3 is therefore appropriate as an average for greenhouse applications.
Click on the Procedures tab at the top of this topic for information on how to calculate PPFD in AGi32.
Acknowledgment: Thank you to Ian Ashdown, Lighting Analysts' Chief Scientist, for the formulas and resulting conversion table.