Photosynthetically active radiation

Yield photon flux

There are two common measures of photosynthetically active radiation: photosynthetic photon flux (PPF) and yield photon flux (YPF). PPF values all photons from 400 to 700 nm equally, while YPF weights photons in the range from 360 to 760 nm based on a plant's photosynthetic response.

PAR as described with PPF does not distinguish between different wavelengths between 400 and 700 nm, and assumes that wavelengths outside this range have zero photosynthetic action. If the exact spectrum of the light is known, the photosynthetic photon flux density (PPFD) values in μmol⋅s⁻¹⋅m⁻²) can be modified by applying different weighting factors to different wavelengths. This results in a quantity called the yield photon flux (YPF). The red curve in the graph shows that photons around 610 nm (orange-red) have the highest amount of photosynthesis per photon. However, because short-wavelength photons carry more energy per photon, the maximum amount of photosynthesis per incident unit of energy is at a longer wavelength, around 650 nm (deep red).

It has been noted that there is considerable misunderstanding over the effect of light quality on plant growth. Many manufacturers claim significantly increased plant growth due to light quality (high YPF). The YPF curve indicates that orange and red photons between 600 and 630 nm can result in 20 to 30% more photosynthesis than blue or cyan photons between 400 and 540 nm. But the YPF curve was developed from short-term measurements made on single leaves in low light. More recent longer-term studies with whole plants in higher light indicate that light quality may have a smaller effect on plant growth rate than light quantity. Blue light, while not delivering as many photons per joule, encourages leaf growth and affects other outcomes.

The conversion between energy-based PAR and photon-based PAR depends on the spectrum of the light source (see Photosynthetic efficiency). The following table shows the conversion factors from watts for black-body spectra that are truncated to the range 400–700 nm. It also shows the luminous efficacy for these light sources and the fraction of a real black-body radiator that is emitted as PAR.

For example, a light source of 1000 lm at a color temperature of 5800 K would emit approximately 1000/265 = 3.8 W of PAR, which is equivalent to 3.8 × 4.56 = 17.3 μmol/s. For a black-body light source at 5800 K, such as the sun is approximately, a fraction 0.368 of its total emitted radiation is emitted as PAR. For artificial light sources, that usually do not have a black-body spectrum, these conversion factors are only approximate.

The quantities in the table are calculated as

${\displaystyle {\eta }_v(T)=\frac{{\int }_{{\lambda }_1}^{{\lambda }_2}B(\lambda ,T)683[\mathrm{l}\mathrm{m}/\mathrm{W}]y(\lambda )d\lambda }{{\int }_{{\lambda }_1}^{{\lambda }_2}B(\lambda ,T)d\lambda },}$

${\displaystyle {\eta }_{\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}}(T)=\frac{{\int }_{{\lambda }_1}^{{\lambda }_2}B(\lambda ,T)\frac{\lambda }{hc{N}_{\text{A}}}d\lambda }{{\int }_{{\lambda }_1}^{{\lambda }_2}B(\lambda ,T)d\lambda },}$

${\displaystyle {\eta }_{\mathrm{P}\mathrm{A}\mathrm{R}}(T)=\frac{{\int }_{{\lambda }_1}^{{\lambda }_2}B(\lambda ,T)d\lambda }{{\int }_0^{\mathrm{\infty }}B(\lambda ,T)d\lambda },}$

where ${\displaystyle B(\lambda ,T)}$ is the black-body spectrum according to Planck's law, ${\displaystyle y}$ is the standard luminosity function, ${\displaystyle {\lambda }_1,{\lambda }_2}$ represent the wavelength range (400–700 nm) of PAR, and ${\displaystyle N_{\text{A}}}$ is the Avogadro constant.

Second law PAR efficiency

Besides the amount of radiation reaching a plant in the PAR region of the spectrum, it is also important to consider the quality of such radiation. Radiation reaching a plant contains entropy as well as energy, and combining those two concepts the exergy can be determined. This sort of analysis is known as exergy analysis or second law analysis, and the exergy represents a measure of the useful work, i.e., the useful part of radiation which can be transformed into other forms of energy.

The spectral distribution of the exergy of radiation is defined as:

${\displaystyle E{x}_{\lambda }=L_{\lambda }(T)-L_{\lambda }(T_0)-T_0[S_{\lambda }(T)-S_{\lambda }(T_0)]}$

One of the advantages of working with the exergy is that it depends not only on the temperature of the emitter (the Sun), ${\displaystyle T}$, but also on the temperature of the receiving body (the plant), ${\displaystyle T_0}$, i.e., it includes the fact that the plant is emitting radiation. Naming ${\displaystyle x=\frac{hc}{\lambda kT}}$ and ${\displaystyle y=\frac{hc}{\lambda k{T}_0}}$, the exergy emissive power of radiation in a region is determined as:

${\displaystyle {\int }_0^{{\lambda }_i}Ex(\lambda ,T)d\lambda ={\mathrm{\Im }}_{E{x}_{0\to {\lambda }_i}}=\frac{15}{{\pi }^4}\sigma \{T^3[(T-T_0)x^3{\mathrm{L}\mathrm{i}}_1(e^{-x})+(3T-4T_0)x^2{\mathrm{L}\mathrm{i}}_2(e^{-x})}$

${\displaystyle +(6T-8T_0)x{\mathrm{L}\mathrm{i}}_3(e^{-x})+(6T-8T_0){\mathrm{L}\mathrm{i}}_4(e^{-x})]}$

${\displaystyle +T_0^4\left[y^2{\mathrm{L}\mathrm{i}}_2(e^{-y})+2y{\mathrm{L}\mathrm{i}}_3(e^{-y})+2{\mathrm{L}\mathrm{i}}_4(e^{-y})\right]\}}$

Where ${\displaystyle {\mathrm{L}\mathrm{i}}_s(z)}$ is a special function called the polylogarithm. By definition, the exergy obtained by the receiving body is always lower than the energy radiated by the emitting blackbody, as a consequence of the entropy content in radiation. Thus, as a consequence of the entropy content, not all the radiation reaching the Earth's surface is "useful" to produce work. Therefore, the efficiency of a process involving radiation should be measured against its exergy, not its energy.

Using the expression above, the optimal efficiency or second law efficiency for the conversion of radiation to work in the PAR region (from ${\displaystyle {\lambda }_1=}$ 400 nm to ${\displaystyle {\lambda }_2=}$ 700 nm), for a blackbody at ${\displaystyle T}$ = 5800 K and an organism at ${\displaystyle T_0}$ = 300 K is determined as:

${\displaystyle {\eta }_{\text{PAR}}^{ex}(T)=\frac{{\int }_{{\lambda }_1}^{{\lambda }_2}Ex(\lambda ,T)d\lambda }{{\int }_0^{\mathrm{\infty }}L(\lambda ,T)d\lambda }=0.337563}$

about 8.3% lower than the value considered until now, as a direct consequence of the fact that the organisms which are using solar radiation are also emitting radiation as a consequence of their own temperature. Therefore, the conversion factor of the organism will be different depending on its temperature, and the exergy concept is more suitable than the energy one.

Measurement

PAR is normally measured with a PAR meter, which measures the amount of light in the 400-700 nanometer range that plants use for photosynthesis. There are several commercial varieties as well as a multi-channel spectral sensors based version that has lower-costs, and was released as open hardware.

Researchers at Utah State University compared measurements for PPF and YPF using different types of equipment. They measured the PPF and YPF of seven common radiation sources with a spectroradiometer, then compared with measurements from six quantum sensors designed to measure PPF, and three quantum sensors designed to measure YPF.

They found that the PPF and YPF sensors were the least accurate for narrow-band sources (narrow spectrum of light) and most accurate for broad-band sources (fuller spectra of light). They found that PPF sensors were significantly more accurate under metal halide, low-pressure sodium and high-pressure sodium lamps than YPF sensors (>9% difference). Both YPF and PPF sensors were very inaccurate (>18% error) when used to measure light from red-light-emitting diodes.

Similar measurement

Photobiologically Active Radiation (PBAR)

Photobiologically Active Radiation (PBAR) is a range of light energy beyond and including PAR. Photobiological Photon Flux (PBF) is the metric used to measure PBAR.