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Photosynthetically Active Radiation: Measurement and Modeling



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Photosynthetically Active Radiation:
Measurement and Modeling
Department of Geosciences and Geography,
University of Helsinki, Helsinki, Finland
Tartu Observatory, To
˜ravere, Tartumaa, Estonia
INRA, UMR Environnement Me
´en et
´lisation des Agro-Hydrosyste
`mes, EMMAH,
Avignon, France
Article Outline
Deﬁnition of the Subject
Techniques for Measuring PAR
PAR in Various Environments
PAR in Vegetation Canopies
Future Directions
Photosynthetically active radiation (PAR) The part
of electromagnetic radiation that can be used as the
source of energy for photosynthesis by green plants,
measured as PAR irradiance or PPFD.
PAR waveband Spectral region for electromagnetic
radiation deﬁned by the wavelength limits of
400–700 nm.
PAR irradiance Radiant ﬂux density, or the radiative
energy received by unit surface area in unit time,
carried by photons in the PAR waveband.
Photosynthetic photon ﬂux density (PPFD) The
number of photons with wavelengths in the PAR
waveband passing through unit surface area in unit
time; synonymous to PAR quantum ﬂux.
Photosynthetic action spectrum The spectral
dependence of photosynthetic productivity per
unit absorbed energy, usually plotted in relative
IPAR Intercepted PAR, or the amount of incident PAR
not directly transmitted to the ground by
a vegetation canopy.
APAR Absorbed PAR, the amount of incident PAR
absorbed by a vegetation canopy.
fIPAR The fraction of incident PAR not directly trans-
mitted to the ground by a vegetation canopy.
fAPAR The fraction of incident PAR absorbed by
a vegetation canopy.
Global PAR The sum of diffuse and direct PAR: total
PAR falling on a horizontal surface.
Ideal PAR energy sensor PAR sensor with output
proportional to PAR irradiance.
Ideal PAR quantum sensor PAR sensor with output
proportional to PPFD.
Spectral error Broadband radiation measurement
errors arising from the deviation of the predicted
radiation spectrum from the actual one.
Radiative transfer theory (RTT) The mathematical
framework for describing the radiation ﬁeld in an
absorbing, scattering, and emitting medium based
on radiation beams traveling in straight lines.
Definition of the Subject
In the broad sense, photosynthetically active radiation
(PAR) is the part of electromagnetic radiation that can
be used as the source of energy for photosynthesis by
green plants. Technically, it is deﬁned as radiation in
the spectral range from 400 to 700 nm [1,2]. It is
expressed either in terms of photosynthetic photon
ﬂux density (PPFD, mmol photons m
), since
photosynthesis is a quantum process, or in terms of
photosynthetic radiant ﬂux density (PAR irradiance,
), more suitable for energy balance studies.
A fundamental term in the quantiﬁcation of light
used by plants in the photosynthesis process is the
fraction of absorbed photosynthetically active radia-
tion (fAPAR) calculated as the ratio of absorbed to
total incident PAR in a vegetation canopy. This variable
is widely used in vegetation functioning models at
a range of spatial scales from the plant to the globe as
an indicator of the amount of energy available for
photosynthesis [3].
Defining PAR
Photosynthetically active radiation (PAR) is commonly
deﬁned as electromagnetic radiation in the waveband
7902 PPhotosynthetically Active Radiation: Measurement and Modeling
between 400 and 700 nm, or 0.400–0.700 mm[1,2,
4,5]. The modern deﬁnition of PAR arises from the
understanding that the measurement system should be
based on a single, generalized spectral response curve
based on measured data and usable with sufﬁcient
accuracy for all practical purposes [6]. This response
curve is commonly known as the action spectrum of
photosynthetic radiation and is deﬁned as the photo-
synthetic productivity (measured as CO
uptake or
production of O
) of a leaf plotted against the wave-
length lof the incident spectral irradiance I
In addition to the action spectrum, the efﬁciency of
photosynthesis is often presented as quantum yield:
photosynthetic productivity divided by the amount of
absorbed photons. Both quantities are plotted in rela-
tive units in Fig. 1: the maximum value of the action
spectrum and the relative spectral quantum yield are
normalized to unity. The action spectrum and relative
spectral quantum yield differ (1) in the units used to
measure radiation (amount of photons or amount of
radiative energy), and (2) whether the incident or
absorbed radiation ﬂux is used. Radiation units for
monochromatic radiation can be easily converted: the
number of photons with wavelength land the
corresponding spectral irradiance I
are connected via
the Planck law (see section “Quantifying PAR”).
Absorbed radiative energy (or, equivalently, the num-
ber of photons) for each wavelength can be obtained
from incident energy by multiplying it by the leaf
spectral absorptance.
The shape of photosynthetic action spectrum is
almost universal [1,7]. Small variations are due to
between-species differences (e.g., differences in the
blue and ultraviolet spectral regions have been noted
for arboreous and herbaceous plants [7]), differences in
development phase, place of growth, water supply,
mineral nutrition, incident irradiance, and other
locally varying conditions. This is due to all plants
containing the same photochemical apparatus based
on the same radiation-absorbing pigments like chloro-
phyll-A, chlorophyll-B, and carotenoids. These pig-
ments also govern the leaf spectral absorption in the
PAR waveband. Only at blue wavelengths,
a considerable absorption by non-photosynthetic pig-
ments can be observed [7].
The photosynthetic action spectrum does not
decrease to zero at the limits of the PAR waveband
since the change in photosynthetic potential at 400
and 700 nm is fast but not abrupt. Thus, to exactly
measure the true photosynthetic potential of incident
radiation, one would need to calculate the incident
photon ﬂux density weighed by the relative photosyn-
thetic action spectrum for all wavelengths where the
action spectrum is not zero, between 360 and 760 nm.
The quantity thus obtained is known as the yield pho-
ton ﬂux (YPF) [8].
However, to simplify calculations and measure-
ments, the limits of the PAR waveband have been set
to 400 and 700 nm by convention, ignoring the relatively
small photosynthetic contribution of photons with
wavelengths below 400 nm or above 700 nm. Addition-
ally, the true action spectrum and the spectral compo-
sition of incident radiation are generally not used,
except for most detailed calculations. Instead, an inte-
gral value known as PPFD (section “Quantifying PAR”)
Wavelength λ (nm)
Leaf absorptance, relative quantum yield
relative action spectrum
Mean relative
quantum yield
Leaf absorption
Mean relative
action spectrum
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 1
The mean spectral absorption of green leaves (average of
measurements in Estonia for common local broad-leaf
tree species in 2006) together with the action spectrum of
PAR and the relative spectral quantum yield of
photosynthesis for field-grown plants (Tables IV and VI
in [1])
7903PPhotosynthetically Active Radiation: Measurement and Modeling
is applied (both as a measured value and a theoretical
driving force behind photosynthesis in mathematical
models) as an adequate descriptor of the photosynthe-
sis-inducing capability of incident radiation under
most illumination conditions [2]. The small improve-
ment achievable by using the detailed curve in Fig. 1
does not outweigh the increase in technical and com-
putational complexities.
The radiation incident on a plant canopy arrives as
direct and diffuse ﬂuxes. The direct ﬂux is formed by
photons having passed through the atmosphere
unscattered, whereas the diffuse ﬂux consists of pho-
tons scattered by air molecules, aerosol particles, or
clouds. As the two ﬂuxes penetrate a vegetation canopy,
photons hitting the leaves and other plant elements are
intercepted, that is, removed from the incident ﬂuxes.
This photon ﬂux hitting plant elements is known as the
intercepted PAR ﬂux and denoted with IPAR. Only the
intercepted fraction of radiation, or IPAR, constitutes
a potential energy source for photosynthesis. However,
not all of this potential is realized: a fraction of radia-
tion is always reﬂected or transmitted by the
intercepting element. After being transmitted or
reﬂected, photons may eventually escape the vegetation
canopy without any contribution to photosynthesis.
Only photons actually absorbed by the canopy con-
stitute the absorbed PAR (APAR) ﬂux and may be used
for photosynthesis. It usually holds that APAR <IPAR
and a constant coefﬁcient, APAR = 0.85 IPAR, has been
proposed for radiation use efﬁciency calculations [9]
based on the work presented in [10]. Both IPAR and
APAR are often expressed in relative units as fractional
IPAR (fIPAR) and fractional APAR (fAPAR), respec-
tively, by dividing the relevant quantity by the incident
PAR ﬂux. These fractional quantities are expressed as
numbers between 0 (no interception or no absorption)
and 1 (total interception or total absorption). More
details on calculating and measuring APAR, fAPAR,
and fIPAR are given in section “PAR in Vegetation
Quantifying PAR
The radiometric quantity for measuring the amount of
radiation falling on unit area of a surface (e.g., plant
leaf) is irradiance, also known as radiant ﬂux density.
The SI (International System of Units) unit for
irradiance is watts per square meter (W m
): thus,
electromagnetic radiation is described in terms of the
energy it carries. Generally, the term “irradiance” is
used to denote the energy carried by photons regardless
of their wavelength. When dealing with photons in the
PAR waveband, the term “PAR irradiance” should be
used to denote the irradiance contributed by photons
with wavelengths between 400 and 700 nm:
IPAR ¼Z700
where I
is spectral irradiance.
PAR measurement in plant sciences has aimed at
quantitatively describing radiation as the driving force
behind photosynthesis. The intensity of photosynthesis
is better predicted by the number of absorbed photons
than by the radiant energy received by a leaf [2,6]. This
is illustrated by the ﬂatter, more rectangular shape of
the quantum yield curve in Fig. 1 compared with that
of the action spectrum. For this reason, PAR is often
measured as a ﬂux of photons, the quanta of electro-
magnetic radiation. As we are dealing with the PAR
waveband, the particle ﬂux is most commonly termed
“photosynthetic photon ﬂux density” or PPFD. Math-
ematically, PPFD is deﬁned as the number of photons
with wavelengths in the PAR waveband crossing a small
surface element in unit time divided by the area of the
There is no ofﬁcial SI unit for photon ﬂux or PPFD.
A unit deﬁned after the famous physicist, Einstein, is
used to designate one mole or Avogadro’s number
= 6.022 10
) of photons. To describe the
PPFD under natural illumination conditions,
a suitable unit is thus mEm
(microeinsteins per
square meter per second). In modern practice, how-
ever, mmol m
(micromoles of photons per square
meter per second) is the most extensively used unit for
PPFD. The increased popularity of micromoles com-
pared with microeinsteins is explained by the common
requirement of scientiﬁc publishers to use SI units
whenever possible. The base unit for amount of sub-
stance of the international system of units is the mole.
Although the (micro) einstein is based on the mole, it is
not on the list of SI-derived units. At the same time,
mmol m
is a combination of SI units and thus
explicitly compatible with it. Use of mmol m
7904 PPhotosynthetically Active Radiation: Measurement and Modeling
measuring PAR is also suggested by the International
Commission on Illumination [5].
For a monochromatic beam of radiation, the ﬂux of
photons is proportional to the ﬂux of energy. The
coefﬁcient of proportionality results from Planck
law: the energy of a photon is related to its
wavelength las E = hc/l, where his the Planck constant
(6.34 10
J s) and cis the speed of light in vacuum
(c= 3.00 10
). Thus, we may write the math-
ematical deﬁnition of PPFD as
QPAR ¼Z700
and deﬁne the broadband conversion factor
400 IllðÞldl
400 IllðÞdl:ð3Þ
For a waveband such as that of PAR containing
many wavelengths, the conversion factor Q
depends on the actual spectral composition of radia-
tion, that is, on irradiance conditions [11]. The tech-
nical aspects of the problem are further discussed in
section “Calibration and Spectral Corrections, and
experimental values for PPFD to irradiance conversion
are given in section “PAR Below the Atmosphere”.
There have been several attempts to deﬁne PAR in
the history of photosynthesis research. Currently, there is
very little ambiguity in the term PAR with regard to the
wavelength interval. However, other intervals have also
been used [1214], most notably the interval between
380 and 710 nm (e.g., in the Soviet Union, [15]). Thus,
historical PAR measurement data may not be compat-
ible with modern data sets despite similar measure-
ment units: careful evaluation and recalibration is
required when dealing with long time series.
PAR waveband coincides almost exactly with the
visible part of the solar spectrum. The similarity of
the wavelength ranges of PAR and visible light may be
useful in solving scientiﬁc problems. For example, the
directional distribution of diffuse sky brightness has
been parametrized for different sky conditions [16]
and using the high correlation between PAR and visible
light, these distributions may be useful in modeling
directional distribution of incident PAR. Similarly, an
expression such as “availability of light” is reasonable in
everyday use. In scientiﬁc literature, however, the less
ambiguous term “radiation” should always be pre-
ferred to “light.” Ambiguity may emerge as the science
of visible light, photometry, has long traditions in
quantitative measurements: a standardized luminosity
function is used to describe the brightness of radiation
as perceived by the human eye. The luminosity func-
tion is analogous to the action spectrum of PAR in
deﬁning the response of a biological system (the aver-
age human eye) to incident radiation. Photometric
units have a strong user base with a wide ﬁeld of
applications. The modern unit for measuring visible
light incident on a surface (illuminance), lux, was
widely used in photosynthesis research half a century
ago. However, despite the similarity of the luminosity
function and the action spectrum, human vision is not
related to the photobiology of photosynthesis, and the
use of photometric units and terminology in treatment
of PAR is strongly discouraged.
Fundamentals of Radiation Transfer Theory
The physical laws and concepts used in describing the
complex interactions of electromagnetic waves with
matter can be readily applied to describe the processes
related to PAR. However, trying to follow this path
would ultimately lead to tracking every wave or particle
using quantum electrodynamics. While accurate laws
are used, for example, to describe the scattering of
radiation (including PAR) by molecules, aerosols, and
cloud particles in the atmosphere, it is impractical to
apply the fundamental theory to plants, vegetation
canopies, or the whole planet. The common formula-
tion used for accurate computations of PAR, called the
radiative transfer theory (RTT), is a simpliﬁcation
based on ray optics: radiation is described in terms of
photon bundles traveling in straight lines with inﬁnite
In principle, RTT is a mathematical formulation of
the law of conservation of radiative energy. Using given
sources of radiation and the absorptive, scattering, and
emissive properties of the medium, it predicts the
detailed angular and spatial distribution of radiation.
RTT describes radiation in terms of the energy it
carries. However, since it is deﬁned for monochromatic
radiation, the particle and energy ﬂows are propor-
tional. RTT is a special case of the more general transfer
theory dealing with particles (e.g., neutrons or
7905PPhotosynthetically Active Radiation: Measurement and Modeling
electrons) in a scattering, absorbing, and generating
Radiative transfer theory is exactly applicable to
monochromatic radiation (i.e., radiation consisting of
a single wavelength). Solutions for the entire PAR
waveband may be obtained by dividing the waveband
into narrow spectral intervals, solving the radiative
transfer equation for each wavelength, and then adding
the contributions of the wavelength intervals. Thus,
RTT deals with spectral radiance as the most detailed
descriptor of the radiation ﬁeld. (Spectral) radiance
OÞ, sometimes erroneously termed radiation inten-
sity, is deﬁned as the radiative energy arriving from
a given direction crossing a small (imaginary) surface
element per unit solid angle per unit surface area. The
SI unit of radiance is W m
(Watts per square
meter per steradian). Evidently, Rð~
OÞis a function of
the direction ~
and thus describes the angular distri-
bution of the radiation ﬁeld. When dealing with the
spectral characteristics of radiation, spectral radiance,
or radiance per unit wavelength interval, is used. Sim-
ilarly, when describing PAR, the PAR radiance RPARð~
is used, or radiance carried by photons with wave-
lengths in the PAR waveband. The mathematical for-
mulation of the theory does not depend on the
wavelength interval and is the same for Rð~
OÞ. Similarly, the units of PAR radiance are
those of the radiance Rð~
Integrating radiance over the hemisphere
(corresponding to a solid angle of 2p) using cosine as
the weighing function yields irradiance:
cos d
where d
Ois the angle between the directions ~
O0. Irradiance Iequals the amount of radiative energy
carried through a unit area of the surface. A similar
equation may be written to relate the PAR radiance
and the PAR irradiance I
.FromEq. 4,itis
evident that the irradiance I
is a function of
a directional variable ~
Odescribing the normal of the
surface: for any given surface, the amount of radiative
energy it receives depends on its orientation. Com-
monly, irradiance is measured on a horizontal surface.
When measuring downward-directed ﬂux arriving
from the upper hemisphere (i.e., incident ﬂux), ~
points downward; when measuring reﬂected radiation,
Opoints upward.
Radiation ﬂux, or the amount of radiation crossing
a surface in unit time, is calculated by dividing the
surface into small surface elements, ﬁnding the ﬂux
density (i.e., irradiance) for each element, and ﬁnally
adding the contributions of the surface elements. In
mathematical terms, the summation is performed as an
integration. In this way, a quantitative measure of radi-
ation ﬂow can be obtained through any (possibly imag-
inary) surface regardless of its shape and orientation.
When measuring PAR ﬂux for estimating photosynthe-
sis (in either quantum or energy units), the surface
should be that of a plant leaf. To ﬁnd PPFD on an
arbitrarily inclined leaf surface, the angular distribu-
tion of the radiation ﬁeld quantiﬁed by the radiance
OÞhas to be known. However, it is impractical, if
not impossible, to measure the angular variation of
radiance for each point inside a complex vegetation
canopy. Under natural conditions, PAR arrives from
the upper hemisphere only and to estimate the energy
received, intercepted, and absorbed by a canopy, it is
sufﬁcient to measure ﬂuxes on horizontal surfaces. This
is in good accordance with the common practice of
using the terms “irradiance” or “PPFD”: unless speci-
ﬁed otherwise, ﬂuxes are measured using a horizontal
(and leveled) sensor. However, for the sake of clarity, it
is advisable to always specify the directionality of the
radiation receiving surface when describing ﬂux
Techniques for Measuring PAR
Sensors Used for PAR Measurements
The actual sensors used to measure PAR vary in con-
struction and the principle behind the radiation-to-
voltage conversion. Two broad classes may be deﬁned,
corresponding roughly to instruments for measuring
the two quantities deﬁned in the previous section,
PPFD and PAR irradiance. Accordingly, two ideal
PAR sensors may be deﬁned: the ideal PAR quantum
sensor, designed to measure PPFD, and the ideal PAR
energy sensor, to measure PAR irradiance. The deﬁni-
tion of an ideal sensor is not based on its construction
quality or working principle, but on its spectral
response function e(l). This function, similar to the
7906 PPhotosynthetically Active Radiation: Measurement and Modeling
photosynthetic action spectrum, describes the output
of the instrument when illuminated by a
monochromatic radiation source with wavelength l.
To obtain the response of the sensor to any natural
radiation source, the spectral response function has to
be integrated over the spectral sensor’s sensitivity
MPAR ¼Zlmax
where M
is the sensor reading, l
and l
the spectral interval where the sensitivity function is
nonzero, and I
is the spectral irradiance. The sensor
reading M
is usually obtained in electric units: volt-
age or current produced by the sensor. While M
not directly usable for characterization of the radiation
ﬁeld, it is assumed to be proportional to the radiomet-
ric quantity of interest. The coefﬁcient of proportion-
ality, or calibration coefﬁcient, is discussed in the next
The spectral sensitivity function for an ideal PAR
energy sensor is constant with wavelength, e
(l) = const
inside the PAR waveband. The ideal PAR quantum
sensor measures the number of incident photons inde-
pendent of their wavelengths. To achieve this, Planck’s
law prescribes that the spectral sensitivity function of
an ideal PAR quantum sensor has to be proportional to
wavelength, e
(l)l, in the spectral interval of
400–700 nm. Outside the PAR waveband, e
The spectral sensitivity functions of the two ideal sen-
sors are presented in Fig. 2 together with the response
functions of two commercially available sensors.
Real PAR quantum sensors are usually photovoltaic
sensors based on the photoelectric effect. Use of the
photoelectric effect makes the response to the number
of photons, regardless of their wavelengths, almost
linear. This also makes PAR quantum sensors very
responsive: they respond to changes in PPFD almost
instantly and the upper limit on temporal sampling
frequency is determined by the timescale of natural
PAR changes, not the technical capabilities of the
Common photovoltaic sensors are, in principle,
photodiodes working in photo-galvanic regime.
A complete hemispheric ﬁeld of view is achieved by
placing a diffuser, a carefully shaped piece of diffusely
transparent material, in front of the receiving element
(the diode). The spectrally nonselective nature of the
diffuser material in the PAR waveband makes the
receiving surface look white. A suitable ﬁlter blocks
out wavelengths outside the PAR region. Choice of
the ﬁlter, along with the physical design of the instru-
ment, brings the spectral response curve closer to that
of an ideal sensor. The most widely used quantum
sensor is the LI-190SA by LI-COR, Inc. [17,18]
which consists of a silicon photodiode covered by
a visible band-pass interference ﬁlter and a colored
glass ﬁlter. Since its introduction, use of quantum sen-
sors to measure PAR has been expanding rapidly
[1924]. Currently, PAR sensors with silicon photodi-
odes are manufactured by several companies
(e.g., PARLite by Kipp and Zonen, E90 Quantum sen-
sor of Jauntering International Corp, SAT-LANTIC
PAR sensor for underwater measurements) and form
the most commonly used PAR sensor class.
Recently, GaAsP photodiodes have become avail-
able for use in PAR sensors (e.g., QSP-2100 by
Ideal PAR energy sensor Ideal PAR quantum sensor
LI-190SA PARLite
Wavelength λ (nm)
Relative spectral sensitivity
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 2
The relative spectral sensitivity functions (normalized so
that the maximum value of each curve equals unity) of two
ideal sensors for measuring PAR irradiance (Ideal PAR
energy sensor) and PPFD (Ideal PAR quantum sensor)
together with the curves for two real sensors (LI-COR
LI-190SA and Kipp and Zonen PARLite)
7907PPhotosynthetically Active Radiation: Measurement and Modeling
Biospherical Instruments Inc., JYP 1000 by SDEC
France). These sensors are inexpensive because the
spectral sensitivity curve of a GaAsP photodiode is
close to that of an ideal PAR quantum sensor. Wave-
lengths below 400 nm may be cut off by choosing a
suitable material for the diffuser (usually polyacrylite),
and special correction ﬁlters are not needed [25].
The second broad class of PAR sensors, PAR energy
sensors, includes mostly thermoelectric instruments.
These instruments are designed to measure PAR irra-
diance with a constant sensitivity function using
a black receiving surface which is heated by incident
radiation. Using a calibration coefﬁcient, the tempera-
ture reading of the receiving surface is converted into
irradiance. The receiving surface is covered by a glass
ﬁlter to block photons with wavelengths outside the
PAR waveband. Compared with quantum sensors,
thermoelectric instruments are technically more com-
plicated and expensive. However, such instruments can
be constructed with the same bodies as standard short-
wave solar radiation measurement devices,
pyranometers and pyrheliometers, making the mea-
surements robust and repeatable. The ﬁrst hemispheric
measurements of global, diffuse, and reﬂected PAR
were made using pyranometers covered with hemi-
spherical glass ﬁlters [14,2633] and measurements
of direct solar PAR with pyrheliometers covered with
ﬂat glass ﬁlters [3436]. A thermoelectric device for
measuring submarine PAR was also constructed from
a thermopile coated with Parsons’ black lacquer and
covered by a glass ﬁlter [37]. Compared to quantum
receivers, thermoelectric instruments exhibit large
inertia: changes in the temperature of the receiving
surface follow the changes in irradiance after
a substantial time delay. The time constant (the time
it takes for the output signal to decrease by e2:72
times after incident radiation is completely blocked) of
common thermoelectric instruments is about 10 s.
Although such timescales are reasonable when measur-
ing incident PAR in the open (affected mainly by solar
elevation and atmospheric transmission), variations in
radiation ﬂuxes inside a plant canopy happen on much
shorter timescales.
An interesting novel idea is to use light emitting
diodes (LEDs) in photo-galvanic regime as radiation
sensors. A combination of blue and red LEDs provides
an acceptable approximation of the PAR spectral curve.
An inexpensive sensor consisting of blue SiC and red
GaP or AlGaAs LEDs exhibited good correlation with
the LI-COR LI-190SA quantum sensor when measur-
ing global PAR [38].
The most complete way to describe radiation in the
PAR waveband is to measure its spectral composition.
Unfortunately, the instruments for spectral radiation
measurements, spectroradiometers (more commonly
called just spectrometers), have been expensive and
not well suited for ﬁeld measurement or long-time
automatic monitoring. In recent years, developments
in affordable photodiode array technology have made
the construction of spectroradiometers with few or no
moving parts possible. These lightweight ﬁeld instru-
ments typically measure radiation between 350 and
1,050 nm with a sampling interval of a few nanometers.
However, judging from the relatively small number of
published results, the simplicity, robustness, and low
price of quantum sensors outweigh the increased
amount of data and the higher price tag produced by
a spectroradiometer. In many common applications in
agriculture, horticulture, or monitoring of photosyn-
thetic productivity, monitoring of the amount of avail-
able PAR, rather than its spectral composition, is
sufﬁcient. Nevertheless, advances in technology indi-
cate that in the decades to come, radiometry will be
shifting from broadband sensors toward spectral
Most sensors described above are intended to mea-
sure global PAR: they have been designed to integrate
the radiation arriving from all directions in
a hemisphere and output radiation ﬂux density. Such
sensors are also called cosine receivers after the
weighing function used in the mathematical formula-
tion of the integration formula (Eq. 4). Thus, the ﬁeld
of view (FOV) of a cosine receiver is 2p, the solid angle
corresponding to a hemisphere. Sometimes, the FOVof
an instrument is restricted to receive photons coming
from a single direction, for example, the sun. Alterna-
tively, to measure only diffuse sky radiation, sensors
may be equipped with a shadow band blocking the
diurnal path of the sun in the sky, or a tracking shade
disc (i.e., a small disc mounted on an arm activated by
a mechanical device used to keep scientiﬁc instruments
directed toward the sun). To measure the direct solar
7908 PPhotosynthetically Active Radiation: Measurement and Modeling
component of PAR, that is, the ﬂux density of PAR not
scattered by the atmosphere, a pyrheliometer may be
equipped with glass ﬁlters; alternatively, a common
hemispheric PAR sensor may be ﬁtted with a view-
limiting tube analogous to that of a pyrheliometer
[39]. Unfortunately, no PAR quantum sensors specially
designed to measure direct radiation are commercially
available. A narrow FOV is also used to study the
directional properties of radiation ﬁeld: directional
reﬂectance or directional distribution of incident
radiation [40,41]. Additionally, instruments to mea-
sure radiation arriving from all directions
(corresponding to a solid angle of 4p) have been
designed. Such instruments measure a quantity called
radiation ﬂuence rate and they are more commonly
used in aquatic environments (see section “Description
of PAR in Water”).
To quantify the enormous variability of the radia-
tion ﬁeld inside and below a plant canopy, single sen-
sors do not sufﬁce. Elaborate systems can be combined
with consumer equipment to obtain the best results.
The measurement systems used in plant canopies are
brieﬂy discussed in section “Instruments for Measuring
fAPAR. Although only a few of these devices include
the PAR sensors described above, the implicit physical
principles of radiometry in these instruments, and thus
also the inherent limitations and potential errors, are
exactly the same.
Calibration and Spectral Corrections
Direct comparison of two PAR sensors is not a simple
task. The reading of a PAR sensor can be predicted
from the reading of another sensor if the spectral sen-
sitivity functions of both sensors are known as well as
the spectral composition of incident radiation.
Although most producers of PAR sensors provide the
spectral response functions for their instruments,
the spectral composition of incident radiation is gen-
erally unknown: the relatively stable spectral composi-
tion of extraterrestrial solar PAR is heavily altered when
passing through the atmosphere. Inside a plant canopy,
the spectral composition of PAR is further distorted by
the removal of photons at blue and red wavelengths,
where the absorptance of plant leaves is the highest.
Thus, care must be taken when comparing the
numerical outputs of different sensors in radiation
absorption measurements as well as during calibration.
To calibrate a PAR sensor, one needs to measure its
output in a controlled experimental situation (e.g.,
using a calibration lamp) where the value of the mea-
sured quantity is known. A calibration coefﬁcient is the
ratio of the actual value of the measurable quantity
(e.g., I
) to the instrument reading (M
400 Il;LAMP lðÞdl
lmin elðÞIlLAMP lðÞdl:ð6Þ
Two calibration coefﬁcients are usually provided for
PAR sensors: one to convert the sensor’s reading into
energy units (W m
) deﬁned by Eq. 6 and one for
quantum units (mmol m
). The coefﬁcient for
quantum units is deﬁned similarly to that for energy
units, m
Most manufacturers calibrate the sensors in labo-
ratory using standard lamps, which is indicated by
using the subscript LAMP for the spectral irradiance
in Eq. 6,I
. Thus, the manufacturers can control
(within a given measurement uncertainty of a few per-
cent determined by the calibration of the lamp) both
the energy content and the spectral composition of
incident radiation. If the spectral sensitivity of the
actual sensor being calibrated deviates from that of
the perfect sensor, as it invariably does, the calibration
coefﬁcient depends on the spectral composition of
incident radiation. Therefore, the laboratory-derived
calibration is only directly valid for irradiation by
a calibration lamp and does not hold exactly under
ﬁeld conditions.
The errors arising from the mismatch of the
predicted and actual ﬁeld conditions are usually called
spectral errors. Spectral errors depend on the spectral
sensitivity of the sensor, the spectral composition of
incident irradiance, and the spectral composition of
radiation used to calibrate the sensor. Mathematically,
the spectral error in PAR irradiance measurements can
be written as
lmin elðÞIllðÞdl
400 IllðÞdl:ð7Þ
After substituting the expression for m
from Eq. 6
into Eq. 7, it becomes clear that spectral errors
7909PPhotosynthetically Active Radiation: Measurement and Modeling
disappear if (1) the sensor has a response function
identical to that of the ideal sensor, e(l)e
(l), or
(2) the irradiance conditions match the calibration
lamp spectrum, I
(l) in the spectral inter-
val from l
to l
. The magnitude of the actual
spectral error varies with sensor type. While it is rea-
sonably small for the LI-190SA sensor, usually less than
1% for natural irradiance conditions, many other sen-
sor exhibit considerably larger errors, especially under
artiﬁcial illumination [11].
If the spectral composition of incident radiation or,
more speciﬁcally, the difference between the spectral
composition of radiation occurring during ﬁeld mea-
surements and during calibration, spectral error can be
eliminated by using a spectral correction. It is evident
that in the presence of the spectral error, multiplying
the measurement result by the inverse of b
(Eq. 7)
would compensate completely for the differences in
the spectra of incident radiation. Thus, if the actual
spectral irradiance I
(l) is known, a spectral correction
can be easily calculated. However, since I
(l) is usually
not available, a general value characterizing the illumi-
nation conditions (clear or cloudy sky, different artiﬁ-
cial light sources), I
(l), is used instead. Thus, the
spectral correction factor is calculated as the reciprocal
of b
after replacing I
(l)inEq. 7.
Therefore, when taking a measurement, the instru-
ment reading is ﬁrst multiplied by the calibration coef-
ﬁcient (m
or m
, calculated individually for each
sensor) and, optionally, by a spectral correction (calcu-
lated for a whole instrument class or model). As only
the average spectral irradiance distribution for typical
conditions is known, it is often preferable to ignore
spectral corrections.
Another possibility to calibrate the sensors is to
compare them with a reference sensor (or
a spectroradiometer) with a reliable calibration by the
manufacturer. When performing calibration under
irradiance conditions reasonably close to those occur-
ring under true measurement situations, spectral cor-
rections are not required. For example, ﬁeld
calibrations of radiation measuring instruments are
standard for the Baseline Surface Radiation Network
(BSRN, [42]), an international network for global mea-
surements of solar and atmospheric radiation at the
highest available accuracy. Additionally, all PAR sensors
continuously exposed to outdoor conditions should be
checked regularly against well-maintained reference
instruments. The sensitivity of sensors is apt to change
due the aging of the diffuser and ﬁlters. Such aging is
usually also documented in the instrument manual.
When a frequently and reliably calibrated instrument
is not available, it is strongly recommended to have
a reference instrument stored under controlled condi-
tions for periodical comparisons with the operating
Measurement Errors
As with all measurements, errors are inevitable and
arise from (1) the impossibility of controlling all the
physical processes that determine the measurement
result, (2) the non-perfect construction of the measur-
ing apparatus, and (3) the spectral composition of
incident radiation. Since the last error source (spectral
errors) was covered in section “Calibration and Spec-
tral Corrections, only the ﬁrst two categories are
brieﬂy discussed here.
Measurement errors can be reduced by carefully
following the instructions for performing the measure-
ments (usually provided by the manufacturer), using
proper installment and maintenance procedures (e.g.,
checking for the directionality and leveling of the
instrument), checking the performance of the instru-
ment regularly, and accounting for material degrada-
tion and changes in operating environment (ambient
temperature, irradiance conditions, humidity, etc.).
Flux measurements with a hemispherically integrating
sensor suffer from directionality effects: the sensor is
not equally sensitive to radiation arriving from differ-
ent directions. While manufacturing imperfections or
physical damage may cause an instrument to have
random sensitivity ﬂuctuations with the azimuth
angle of an incident beam, sensitivity to polar angle
(or zenith angle for a leveled sensor looking upward) of
the radiation source is usually more systematic. The
dependence of sensitivity with the polar angle is called
the cosine response of the sensor and the
corresponding correction a cosine correction. The
cosine response characteristics of several sensors
designed for irradiance measurements, including two
LI-COR 190 PAR sensors, are given in [43]. Cosine
effects, together with leveling inaccuracies, are espe-
cially inﬂuential when a strong directional radiation
7910 PPhotosynthetically Active Radiation: Measurement and Modeling
source is present, such as the direct solar radiation beam
on a clear day. All these errors, some systematic and
some random, can add to the spectral errors affecting
instruments designed for measuring radiation in
a spectral waveband as discussed in the previous section.
The ofﬁcial relative uncertainty of PAR instruments
claimed by manufacturers, about 5%, can only be
achieved under optimal conditions. During routine
measurements, even if performed by trained specialists,
the uncertainty can be considerably larger. For exam-
ple, [44] gives an estimate of 10% uncertainty for PAR
measurements in the FLUXNET network;
a comparison performed by BSRN found signiﬁcant
systematic differences between different PAR sensor
models and up to 20% spread within the group of
11 tested LI-190SA sensors [45].
PAR in Various Environments
PAR Below the Atmosphere
Without the inﬂuence of the atmosphere, the PAR
irradiance would be determined by the solar spectrum
and geometric conditions like the slightly varying dis-
tance from the earth to the sun, local solar elevation,
and topographic shadowing. The spectral composition
of radiation would be constant to the accuracy of the
multiple scattering contribution of non-ﬂat topogra-
phy (illuminated slopes of mountains and valleys).
Such direct topographic effects, although signiﬁcant
in shadow areas, are usually small when direct solar
radiation is present and will be ignored hereafter.
Under natural conditions, the amount and spectral
composition of radiation in the PAR spectral band, in
addition to the distance from the sun to the earth and
solar elevation angle, is mainly determined by the pres-
ence of clouds, the amount and optical properties of
aerosols, and, to a lesser extent, the chemical composi-
tion of the atmosphere.
Due to its universal nature, radiative transfer theory
(RTT, section Fundamentals of Radiation Transfer
Theory”) can be (and also has been) applied to predict
the irradiation conditions under all possible atmo-
spheric conditions. The actual precision of prediction
is limited by the availability of input data and computer
power. Models based on RTT can be used to calculate
accurately the spectral irradiance for the different
wavelengths comprising PAR, with subsequent
integration to obtain I
. For many practical pur-
poses, however, simpler models applicable to longer
timescales (hours, days, growing seasons) are sought
and thus different broad-band models or physically
based parametrizations are often used. For clear skies,
the accuracy of the best broadband models is compa-
rable to that of routine irradiance measurements in
existing networks [46].
Models developed for predicting the behavior of sun-
light in the atmosphere deal not only with PAR but with
the whole shortwave spectral region. The shortwave spec-
tral region is loosely deﬁned as the range of wavelengths
containing the bulk of the solar spectrum (magnitude
wise), usually between 300 and 4,000 nm. The simplest
case, global shortwave irradiance under a cloudless atmo-
sphere, can be very accurately predicted when the follow-
ing parameters are known (REST2 model, [46]): solar
zenith angle, A
¨m turbidity coefﬁcient (i.e., aero-
sol optical depth at 1,000 nm), A
¨m wavelength
exponents, aerosol single-scattering albedo, air pres-
sure, amounts of precipitable water and ozone, and
ground albedo. These parameters allow to calculate
the irradiance in two separate wavebands, PAR and
short-wave infrared. To predict only PAR irradiance,
a few parameters less are required, since ozone and
water vapor have little inﬂuence on PAR.
Because not all of the listed atmospheric parameters
are readily available, models based on easily measurable
radiation ﬁeld characteristics have also been developed
[24,47,48]. Usually, parametrizations are based on
approximately four parameters. While one parameter
is always solar elevation, others describe the state of the
atmosphere and can be either obtained from radiation
measurements (e.g., ratio of diffuse to direct shortwave
irradiance) [49] or routine meteorological data (e.g.,
dew point temperature). The variables explaining the
majority of variance in PAR availability and the spectral
quality of PAR (Q
ratio) include solar elevation
and a parameter to describe the turbidity of the atmo-
sphere (e.g., a sky clearness parameter or the A
turbidity coefﬁcient) [39,47,48,50,51].
Two downwelling PAR ﬁeld components can be
distinguished under a clear sky: the quasi-parallel
direct beam arriving from the direction of the sun
(with PAR irradiance on a horizontal surface I
and the diffuse sky radiation arriving from all upward
directions not blocked by topography (I
7911PPhotosynthetically Active Radiation: Measurement and Modeling
The sum of the two components is called global PAR,
. Depending on aerosol load and
solar elevation, the ratio of diffuse PAR to global PAR
irradiance on a horizontal surface ranges between 20%
and 40% [52]. The presence of clouds decreases the
global PAR irradiance usually by up to 80% [41] and
the contribution of diffuse PAR irradiance may take
any value between that corresponding to a clear sky and
100%. If the cloud cover is broken, the existence of the
direct beam depends on the locations of gaps between
clouds. Thus, two temporally and spatially variable
phenomena have great inﬂuence on the amount of
diffuse PAR: aerosol loading and clouds. Although the
effect of aerosols may be dominating in places with low
average cloud cover, it is expected that the contribution
of clouds as the source of variations in diffuse PAR is
larger for most locations.
The fraction of PAR in global shortwave irradiation
varies little and is usually between 40% and
50% [53,54]; values above 50% occur under very low
sun, thick cloud cover, or rain [14]. As an example,
measurements at To
˜ravere actinometric station
(Estonia) are presented in Fig. 3 for variable cloud
conditions during June 2009. The global PAR irradi-
ance can be relatively reliably predicted from global
shortwave irradiance, I
= 0.43 I
. The contribution
of diffuse PAR irradiance I
to global shortwave
irradiance, on the other hand, was more variable
(Fig. 3). Under completely overcast skies, the diffuse
PAR irradiance I
equals the global PAR irradi-
ance I
, which, as usual, contributed about 43% of
global shortwave irradiance. Under clear skies, I
is signiﬁcantly smaller than I
:inFig. 3 the data
points corresponding to clear sky form the lower clus-
ter. Broken cloud cover conditions are represented by
values between the two extremes when plotted
against I
Some variation in I
with elevation above sea
level is expected, but this variation is difﬁcult to detect
[52]. However, using measurement sites at 550, 900,
and 1,500 m above sea level, an increasing trend was
noted with altitude, of 3.6% per km for hourly values of
under clear skies [55]. An inverse trend was
found for hourly Q
under cloudy weather con-
ditions: Q
decreased at a rate of 1.8% per km.
The spectral composition of global PAR is relatively
stable [56]. It is reﬂected in the near-constant value of
the ratio of PPFD to PAR irradiance, Q
(Eq. 3).
The classical value of Q
= 4.57 mmol s
for global PAR proposed by McCree [2] has been ver-
iﬁed by several later studies. For example, [57] reported
that while 1-min average of Q
varied from 4.23
to 4.68 mmol s
, 1-h averages were relatively
insensitive to atmospheric composition with Q
= 4.56 mmol s
for global PAR.
For the diffuse radiation ﬁeld component, the ratio
depends on atmospheric conditions. Under a blue sky, an
average value of Q
= 4.28 mmol s
was reported [52] along with the observation that the
ratio increases with aerosol load. In the presence of
clouds, Q
increases with increasing
cloud cover from 4.24 mmol s
(a value charac-
teristic of blue sky) to the constant value for global
radiation, Q
= 4.57 mmol s
under an
overcast sky [57]. The value of Q
(or Q
) describes the color of light: the smaller the
ratio, the bluer the light looks to the human eye.
The angular distribution of PAR radiance can
be approximated using models applicable to visible
PAR Irradiance, IPAR (W m2)
0 1000
clear sky
overcast sky
Global shortwave irradiance, Isw (W m2)
Global PAR Diffuse PAR
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 3
Global and diffuse PAR irradiance as functions of global
shortwave irradiance in To
˜ravere, Estonia, in June 2009. Sky
condition varied from clear to completely overcast. The
labels “clear sky” and “overcast sky” indicate the
characteristic values of diffuse PAR irradiance for the two
atmospheric conditions
7912 PPhotosynthetically Active Radiation: Measurement and Modeling
light [16]. Additionally, several approximations exist
for predicting the angular distribution of shortwave
radiation. These models have been parametrized for
use in the PAR waveband [40,41] for different atmo-
spheric conditions ranging from completely clear to
overcast sky. The angular models describe sky radiance
relative to the nadir direction and cannot be generally
used to describe global PAR irradiance or PPFD.
A ﬁnal remark on the spectral quality of PAR at the
bottom of the atmosphere can be made based on the
spectral composition of extraterrestrial solar radiation.
The I
ratio outside the atmosphere based on the
solar constant of I
= 136 7 W m
equals 38.8% [51].
Using Q
= 2426 mmol s
for the extraterres-
trial irradiance on a surface perpendicular to sunrays
[48], we obtain that the Q
ratio outside the
atmosphere equals 4.57 mmol s
– exactly that
proposed by McCree [2]. While it may be concluded
that the atmosphere has little effect on the spectral
quality of PAR, the exact coincidence is most likely
due to chance: an accuracy of two decimals is clearly
beyond the uncertainties inherent in radiation
Description of PAR in Water
The waveband of radiation allowing phytoplankton
to carry out photosynthesis (i.e., PAR) corresponds
approximately to the same spectral band of electro-
magnetic radiation that penetrates into water. Pure
water absorbs strongly in the ultraviolet (l<400 nm)
and near-infrared (l>700 nm) spectral regions
[58]. Otherwise, the underwater light ﬁeld is deter-
mined by the incident irradiance (see section “PA R
Below the Atmosphere”), the state and composition
of the water body, and the optical properties of its
The spectrum of solar radiation penetrating a water
body changes drastically as its irradiance diminishes
with depth. While the scattering of radiation is com-
monly rather insensitive to wavelength in the PAR
waveband, absorption by different components has
a very strong spectral effect. The components having
an optical effect are dissolved organic substances (also
known as yellow substance), different species of phyto-
plankton, and inert particulate matter (Fig. 4). Since
the concentration of these is highly variable, the
spectral distribution of underwater irradiance in the
PAR waveband can change rapidly.
In a vertically homogeneous water body, the value
of the downwelling spectral irradiance I
approximately exponentially with depth z, that is,
Beer’s law holds (see also Eq. 8):
IlðzÞ¼Ilð0Þexp Zz
Kdiff l;z0
where K
(l,z) is the diffuse attenuation coefﬁcient,
a parameter often used to describe the optical proper-
ties of natural water bodies [6264].
In addition to the spectral PAR irradiance I
PPFD, a quantity called spectral ﬂuence rate, or spectral
spherical irradiance, is sometimes used to describe
the amount of radiation in water. It is deﬁned as the
total amount of photons incident in unit time interval
from all directions on a small sphere, divided by the
400 500 600
Wavelength (nm)
Absorption coefficient (m1)
Detritus Phytoplankton
Yellow substance Water TOTAL
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 4
Decomposing the absorption spectrum of a water sample.
Spectra of the absorption coefficients corresponding to
pure fresh water [59]; 1.0 10
mg m
substance (specific absorption coefficient at 380 nm
0.565 L mg
); 1.0 mg m
(phytoplankton, [60]); and detritus (from the measured
data of [61]). The total absorption of the water sample is
plotted with a bold line
7913PPhotosynthetically Active Radiation: Measurement and Modeling
cross-sectional area of the sphere. Analogously to the
PAR irradiance I
, the PAR ﬂuence rate may be
deﬁned by integrating over the PAR waveband. As
both ﬂuence rate and irradiance describe the amount
of PAR in water, Beer’s law can (with a different atten-
uation coefﬁcient) also be applied to describe the
change in spectral ﬂuence rate with depth.
Beer’s law is valid only for the spectral irradiance
I(l), that is, the irradiance in a narrow spectral interval
around wavelength l. Many authors have shown that
the exponential law fails when a single value of K
applied over the whole PAR waveband. The reason for
this failure lies in the change of spectral composition of
PAR with depth. This can be illustrated using the wave-
length corresponding to maximum penetration, l
and the Q
ratio. In clear oceanic waters, l
corresponds to the maximum in the extraterrestrial
solar spectrum (460 nm). When increasing the
amount of optically active substances in water, l
shifted toward larger values, as shown in Table 1, and
can be even larger than 700 nm in brownish boreal
lakes [65].
Photosynthesis in water takes place mainly in the
so-called euphotic layer near the surface. At the bottom
of the euphotic layer, the downward PAR irradiance has
decreased to 1% of its value just below the surface [66].
In clear oceanic waters, the thickness of the euphotic
layer can be of the order of a hundred meters. As
a contrast, in turbid lakes, the layer may be only half
a meter thick. Ice cover, and especially ice covered with
snow, may substantially decrease the amount of PAR in
water to a level not sufﬁcient for even the minimum
amount of photosynthetic activity, thus creating anoxic
conditions [67].
Similarly to other environments, the PAR
irradiance in water can be given in energy units
) or quantum units (Q
,mmol s
). The quanta-to-energy ratio Q
) changes with the variation of the spectral
distribution of irradiance. Above water, Q
practically constant with an average value Q
4.57 mmol s
over a wide range of conditions (see
section “PAR Below the Atmosphere”). In clear oceanic
water, Q
decreases with depth. As a contrast, in
turbid coastal waters and lakes, it increases with depth
and approaches an asymptotic value. Thus, sufﬁciently
deep below the surface of turbid waters, the spectral
distribution of PAR, but not the value of PAR irradi-
ance, can be considered almost constant. The
average value of Q
there has been estimated at
4.15 0.40 mmol s
[68]; a value of Q
4.45 0.48 mmol s
has been suggested for
Norwegian coastal waters [69]. In lakes, Q
varies from 4.72 to 5.86 mmol s
[65]. Addition-
ally, there is a strong linear correlation between Q
and K
(r= 0.95) and, in deeper waters, Q
can be estimated using K
measurements in the
surface layer [65].
Measurement Stations and Networks
Unfortunately, no international network to measuring
PAR currently exists. As can be seen from their docu-
mentation, large international radiation measurement
networks like the Baseline Surface Radiation Network
(BSRN[70] have
discussed the subject of PAR measurements, but stan-
dardized measurements have not started. The PAR
irradiance (and also APAR) is recorded as a by-product
in some networks specialized in other measurements.
For example, the FLUXNET project (http://daac.ornl.
gov/FLUXNET/)[71,72], which is aimed at
Photosynthetically Active Radiation: Measurement and Modeling. Table 1 Wavelength of maximum penetration l
ratio Q
, and relative difference Dof Q
from its value above the surface for different water types as classiﬁed
by [62]
Water type I II III 13579
(nm) 465 480 505 530 540 547 565 582
(mmol s
) 3.9 4.0 4.2 4.4 4.5 4.5 4.7 4.9
D(%) 1614942226
7914 PPhotosynthetically Active Radiation: Measurement and Modeling
quantifying the exchanges of carbon dioxide, water
vapor, and energy between the biosphere and atmo-
sphere, has PAR data available for many sites. The solar
radiation budget network SURFRAD (http://www.srrb.[73] measures, among other vari-
ables, the incident PAR irradiance. A promising
start is SolRad-Net (,
a companion to the successful global AERONET aero-
sol network. However, the number of SolRad-Net sites
where PAR is measured today is still very small. Routine
monitoring of PAR and APAR as key factors in global
photosynthetic productivity [74] has been proposed
several times. Currently, the only global data sets
available are those based on remote sensing data
(see section “APAR and fAPAR from Satellite Observa-
tions”). Although remote sensing can provide excellent
spatial coverage unachievable in any ground-based
network, indirect remote retrievals should still be val-
idated against direct measurements of the variable
under investigation.
PAR in Vegetation Canopies
PAR Absorption by Leaves
PAR Absorption by Leaf Pigments Electromagnetic
radiation in the PAR spectral domain is mainly
absorbed by photosynthetic pigments in the leaf.
Among these, chlorophylls a and b are the most impor-
tant. They are found across a wide range of species,
from algae to higher plants, and they participate in
transforming radiation into energy, which is later
stored as chemical bonds of carbohydrates. Chloro-
phylls are characterized by two absorption peaks at
450 and 670 nm corresponding to the blue and red
color, respectively, explaining the green color of leaves
(Fig. 5). Besides chlorophylls, green leaves contain also
other pigments. Pigments such as carotenes and xan-
thophylls belonging to the carotenoid family associated
with chlorophylls are known to improve radiation
harvesting. They mainly absorb in the blue region
with absorption peaks at 450 and 470 nm making
them look orange or yellow. Additionally, carotenoids
prevent oxidation of the photosynthetic system in case
of excess incident radiation. Other pigments like
anthocyans absorb radiation in the PAR waveband
with maximum absorption between 450 and 600 nm
[77]. They protect the leaf against UV radiation by
preventing formation of free radicals and are responsi-
ble for the reddish colors of some leaves during the
autumn. The rest of the biochemical leaf constituents
responsible for the brown color (such as polyphenols,
which develop during leaf senescence), although
absorbing in the PAR waveband (Fig. 5), have no direct
role in photosynthetic processes.
The Role of Leaf Structure The efﬁciency with which
a leaf absorbs visible radiation depends not only on
chlorophyll content per unit leaf area, but also on the
speciﬁc mechanisms plants have developed to utilize
radiation. Chlorophylls are concentrated in chloro-
plasts, mainly located in the palisade mesophyll
consisting of tightly packed elongated cells just under
the upper epidermis (Fig. 6). The tubular shape of
palisade cells enhances the forward propagation of
PAR, thus directing photons to the chloroplasts located
at the bottom of the palisade. In a number of species,
the epidermis cells act as lens focusing radiation on the
chloroplasts thus increasing radiation absorption by
the photosynthetic pigments [78]. The spongy meso-
phyll of higher plants contains little PAR-absorbing
pigments. Instead, the numerous voids in this layer
act as a mirror to scatter back a large fraction of the
radiation transmitted through the palisade mesophyll,
further improving absorption of radiation by
th (nm)
Chlorophyll, Carotenoids (cm2/μg)
Brown pigments (relative units)
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 5
Specific absorption coefficients of chlorophyll (a + b),
carotenoids and brown pigments from the PROSPECT
model [75,76]
7915PPhotosynthetically Active Radiation: Measurement and Modeling
When the capacity of the leaf to use the available
PAR is exhausted by drought or nutrient stress, plants
may use different strategies to minimize absorbed radi-
ation. Besides changing the orientation of a leaf away
from direct sunlight, adaptations have been developed
at the upper epidermis level. The cuticle may turn to
crystalline and the amount of hair on the leaf surface
may increase, thus also increasing the leaf reﬂectivity
and directing radiation away from chloroplasts.
The Fate of Absorbed PAR in the Leaf The energy
carried by photons absorbed by the leaf is transformed
into several types of energy. The dominant type is heat,
accounting for more than 75% of the absorbed PAR
energy. Therefore, only a maximum of 25% of APAR is
left for photosynthesis. When photosynthesis is limited
by temperature, water, or nutrient availability, the radi-
ation use efﬁciency of a leaf decreases even further.
Additionally, a part of the excess PAR energy absorbed
by the pigments may be dissipated as ﬂuorescence, that
is, reradiated as photons with different, longer
Under optimal water, temperature, and nutrient
conditions, the efﬁciency of photosynthesis at the leaf
level is determined both by the absorbed PPFD and the
concentration in the leaf [79]. Figure 7 shows that
the photosynthetic rate increases almost linearly with
incident PPFD up to some threshold value. After the
threshold is reached, the rate of photosynthesis
becomes constant, limited by the CO
in the leaf. This concentration in the leaf, in turn, is
driven by the CO
concentration in the atmosphere
and the stomatal conductance of the leaf, itself deter-
mined by the hydraulic status of the leaf and the plant
as a whole [80]. The maximum photosynthetic rate,
achieved at large PPFD values, also strongly depends on
the fraction of the incident PAR absorbed by the leaf
[81], which is determined mostly by leaf chlorophyll
Upper epidermis
Lower epidermis
Palisade mesophyll
Spongy mesophyll
1 mm
Photosynthetically Active Radiation: Measurement and Modeling. Figure 6
Structure of a typical dicotyledon leaf (young maple)
Ci (mmol mol1)
100 500 1000
PAR (μmol m2 s1)
Photosynthetic rate (μmol m2 s1)
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 7
Relation between incident PAR photon flux density and
photosynthesis rate at different intercellular
concentration of CO
), simulated using model of C3
photosynthesis [79]
7916 PPhotosynthetically Active Radiation: Measurement and Modeling
Since chlorophyll absorbs the majority of incident
PAR and uses only a small fraction of it for photosyn-
thesis, the excess energy must be dissipated in a way
that keeps the photosynthetic apparatus functional. For
this purpose, plants have developed several
photoprotection mechanisms. One of such mecha-
nisms is based on xanthophyll pigments: the conver-
sion of violaxanthin into zeaxanthin can remove the
excess energy from chlorophyll and dissipate it as heat.
When conditions become more favorable, this conver-
sion is reversed, and zeaxanthin is changed back to
violaxanthin. The status of the xanthophyll cycle may
be used to evaluate the various stresses experienced by
plants, since it affects the leaf optical properties, or leaf
reﬂectance spectrum, in the 500–600 nm spectral
region [82].
The second pathway for dissipating excess energy
absorbed by photosynthetic pigments is ﬂuorescence.
When photosynthesis is limited by stress factors or
when a leaf is exposed to too high irradiance, a small
but measurable fraction of the excess energy is
reemitted at a longer wavelength than that of absorp-
tion. The peak of chlorophyll ﬂuorescence emission is
in the blue-green (455 nm), red (685 nm), and far-red
(735 nm) spectral regions [83]. The energy lost in this
process amounts to a few percent of the total PAR
energy absorbed by the leaf [84].
Quantitative Description of PAR in Vegetation
Radiative Transfer in Plant Canopies When dealing
with PAR in vegetation canopies [85,86], it is assumed
that the only scatterers are plant leaves (or needles,
shoots, etc.), that radiation originates from the sun
only, and that thermal emission can be ignored. Ther-
mal emission in the PAR waveband is indeed negligible
(nonexistent for all practical purposes) at temperatures
suitable for photosynthesis. The existence of ﬂuores-
cence by green leaves, an emission source concurrent
with photosynthesis, assumes the presence of incident
PAR. The energy contribution of ﬂuorescence is small
compared to that of scattered PAR, and is generally
masked by scattered radiation [87].
When using RTT, the optical thickness of a canopy
is often described by its leaf area index (LAI): one-sided
leaf area (or half of the total leaf area for plants with
non-ﬂat leaves) per unit ground area. Quite commonly,
the downward cumulative LAI, L(z), calculated as LAI
above height z, is used instead of the geometric vertical
coordinate z. At the top of the canopy, L(z
) equals 0,
then increases with depth inside the canopy. Finally,
below the plant layer, L(0) = LAI.
Radiation Interception When RTT is applied to
describe the attenuation of radiation in vegetation,
a well-known result is obtained. In an environment
where the scattering elements ﬁll a volume uniformly
and randomly, and are inﬁnitesimally small, the radi-
ance decreases exponentially:
ekx ;ð8Þ
where R
) is the radiance before entering the
scattering medium, kis the attenuation coefﬁcient,
and xis the distance from the point where radiation
enters the medium (depth inside the canopy). The
exponential decay described by Eq. 8 is commonly
known as Beer’s law, sometimes called Beer–Lambert’s
or Beer–Lambert–Bouguer’s law. The terms attenua-
tion and interception are used interchangeably: inter-
ception of radiation attenuates the unscattered
radiation ﬁeld.
The tradition of using Beer law for radiation trans-
mission in vegetation canopies consisting of ﬂat leaves
started with the classic work by Monsi and Saeki
[88,89]. They plotted the logarithms of light transmit-
tance of vegetation canopies during overcast days
against the LAI of the canopy, and obtained straight
lines (Fig. 8). They explained the variations in the
slopes of the lines (i.e., attenuation coefﬁcients) theo-
retically, using leaf inclination angles. Since then, Beer’s
law has been routinely applied to approximate PAR
availability in plant canopies [90,91].
Generally, Beer’s law is exactly valid for monochro-
matic radiation only and is not directly applicable
to radiation arriving from the whole hemisphere
(i.e., irradiance I
). To obtain non-intercepted PAR
irradiance on a horizontal surface below a plant can-
opy, Beer’s law (Eq. 8) has to be integrated over the
upper hemisphere:
IPAR ¼Zp=2
RPARðztop ;#;fÞekð#;fÞx#;fðÞ
cos #sin #dydf;
7917PPhotosynthetically Active Radiation: Measurement and Modeling
where #and fare the zenith and azimuth coordinates
describing a direction in the upper hemisphere, respec-
tively. The distance from the bottom to the top of the
canopy in the direction (#,f) depends mostly on the
zenith angle #. For a canopy layer of uniform thickness,
x(#,f) = 1/cos #.Equation 9 is identical to the equa-
tion relating irradiance and radiance, Eq. 4. The former
can be obtained from the latter by expressing radiance
as a function of canopy transmittance (which is Beer’s
law for vegetation canopies, Eq. 8) and considering that
the differential of a solid angle can be expressed in polar
coordinates as dO= sin #dydf. Computations involv-
ing numerical integrations of canopy interceptance
over the upper hemisphere similar to Eq. 9 are com-
mon in optical estimations of LAI [92,93].
In most applications of RTT, the probability of
a scattering event, and thus the extinction coefﬁcient
k, does not depend on the direction (#,f) of photon
travel. However, this does not generally hold in
a vegetation canopy of ﬂat leaves. For example, in
a canopy consisting of mainly horizontal leaves, the
probability of hitting a leaf is much larger for
a photon traveling in the vertical direction than for
one traveling in the horizontal direction. Thus, the
Ross–Nilson G-function (a function returning a value
between zero and one for every direction) is used to
describe the effect of foliage orientation: it equals the
ratio of leaf area projected in a given direction (#,f)to
the total leaf area [85].
The distribution of foliage inside a natural canopy
is not uniform and the assumptions of Beer’s law are
not fulﬁlled. To accurately describe the attenuation of
radiation (including PAR) inside vegetation, more
complex methods have to be used, and one must take
into account the structure of the vegetation layer. In
addition to the above-mentioned angular distribution
of foliage, additional variables describing the geometric
properties of plants at various levels (shoot, branch,
crown, etc.) have to be used. Introduction of larger-
scale structures decreases interception at the top of
the canopy and increases it in middle canopy layers
Leaf area index
K = 1
Light intensity (%)
K = 1
Leaf area index
Light intensity (%)
Photosynthetically Active Radiation: Measurement and Modeling. Figure 8
Light intensity–leaf area index curves of some plant communities measured under mostly overcast conditions on different
days (Reprinted from [89]). (a) The communities of the Kirigamine montane meadow; (b) the communities of the
Tazima meadow and in the vicinity of Tokyo. Light intensity, a good proxy for PAR irradiance, decreases near-exponentially
(See the original article for more details. Published with permission from Oxford University Press)
7918 PPhotosynthetically Active Radiation: Measurement and Modeling
Scattering Inside the Canopy The small fraction of
photons in the PAR waveband not absorbed when
hitting a leaf give rise to a phenomenon commonly
known as beam enrichment. After one or two scatter-
ings in the canopy (very few photons in the PAR
waveband survive more), photons may be inserted
back into the beam traveling in the direction of the
receiver. In other words, as plant leaves are not black
(completely absorbing), the downward ﬂux of radia-
tion is “enriched” by scattered photons. Naturally, the
amplitude of this effect depends on the scattering prop-
erties of the scattering elements, leaves, and needles.
To describe the reﬂectance and transmittance prop-
erties of plant leaves, they are usually assumed to be
Lambertian surfaces – the angular distribution of
reﬂected (or transmitted) radiance does not depend on
the direction of scattering. Actual leaves deviate from
Lambertian surfaces, mainly due to the specular (mir-
ror-like) reﬂectance from the wax coating. However, for
practical purposes, there is no information that the
assumption of Lambertian scattering would lead to
considerable errors [96]. Therefore, the scattering prop-
erties of ﬂat leaves are generally described by up to three
numbers: the two leaf reﬂectance values for the abaxial
and adaxial leaf sides, and one leaf transmittance (the
general reciprocity relations require for the two sides of
a Lambertian surface to have identical transmittance
[95]). However, quite often reﬂectances are not avail-
able separately for the two leaf sides and the reﬂec-
tances of the adaxial and abaxial sides are taken equal.
The reﬂectance properties of leaves depend some-
what on species, growing conditions, and leaf status.
Some approximate values are given in the literature. In
his seminal book, Ross used the values 0.06 and 0.09 for
leaf reﬂectance and transmittance in the PAR region,
respectively [85]. Relatively little between-species vari-
ability in leaf optical properties, compared to within-
species variability, was found during an extensive study
in Texas, USA [97], indicating that the leaf optical
properties in this spectral region are dynamically stable
along a pronounced climate gradient. For trees and
shrubs, a leaf reﬂectance of 0.09 (standard deviation
0.01) and a leaf transmittance of 0.06 (0.03) was
proposed; for grasses the resulting numbers were 0.12
(0.01) for reﬂectance and 0.06 (0.02) for transmit-
tance [97]. Although the measurements were
performed in the spectral interval of channel 1 of the
AVHRR satellite sensor (550–700 nm) which corre-
sponds to the green–red part of PAR, they can also be
used to approximate the leaf optical properties in the
whole PAR waveband with reasonably small errors.
Radiation Field Inside a Vegetation Canopy Canopy
photosynthesis depends not only on the amount of
available PAR, but also on how the irradiance is dis-
tributed: high and low PAR irradiance levels have dif-
ferent photosynthetic potentials. Without going into
further details, it is possible to divide the locations
inside a plant canopy into three groups.
1. Full sunlight. In areas inside the canopy where the
sun is completely visible, or “sunﬂecks,” the radia-
tion ﬁeld is strongly dominated by the direct solar
radiation beam. Under natural conditions, one can
safely ignore the contribution of scattered PAR and
assume that the spectral distribution of radiation is
identical to that above the canopy.
2. Penumbra. Due to the nonzero diameter of the
solar disc, shadows cast by sunrays do not have
sharp edges. Full sunlight and complete shadow
are always separated by a narrow strip with
smoothly varying irradiance. If the angular dimen-
sions of the shadowing object are smaller than the
apparent diameter of the solar disc, for example, the
object is far from the receiver, no complete
shadowing can occur. Depending on the fraction
of the solar disc visible, the PAR ﬂux and spectrum
in penumbra may be close to what they would be
under either direct sunlight or complete shadow.
3. Shadow (umbra). Behind large objects or sufﬁ-
ciently deep down into the canopy, the direct solar
irradiance can be considered zero. Thus, the radia-
tion conditions in umbra are determined by the
possible presence of diffuse sky radiation, radiation
scattered by plant elements, and radiation reﬂected
by the underlying soil. The spectral composition of
radiation depends on skylight conditions, the
amount of visible sky, and the spectral properties
of canopy elements. On an overcast day, the whole
canopy is effectively in a shadow cast by clouds.
The division as given above is just one of the pos-
sible approaches to categorizing the radiation ﬁeld. No
standard practice has emerged yet in the scientiﬁc lit-
erature: the word “sunﬂeck” is the general term used to
7919PPhotosynthetically Active Radiation: Measurement and Modeling
describe areas with increased irradiance, whereas the
penumbra is often ignored. Depending on application,
the penumbra may be treated as either an area where
the sun is obstructed (i.e., shadow) or, in contrast, an
area where the irradiance is above the threshold deter-
mined by the reading below a dense canopy (i.e.,
Due to the dynamic nature of sunﬂecks, the radia-
tion ﬁeld inside a canopy can be highly variable, both
spatially and temporally [98]. Variations in the diffuse
ﬁeld are generally much smaller, and thus global irra-
diance in umbra is much easier to measure. For this
reason, canopy transmittance measurements made on
a cloudy day are much more representative. For exam-
ple, 412 radiometers would be required to estimate the
instantaneous downward radiation ﬂux in a pine stand
with a maximum error of 10% in the midday ﬂux above
the canopy, whereas just one instrument is needed for
a full-day average in a hardwood canopy [99]. When
averaged over the path, the sun follows on a day or
a growing season, the mean transmittance of direct
radiation can be approximated by a single measure-
ment of transmittance of diffuse sky radiation. How-
ever, due to natural limitations in the solar elevation
and azimuth angles which are speciﬁc to each geo-
graphic location, systematic errors may occur [90].
Even if one has sufﬁcient data to quantify the aver-
age PAR irradiance inside and below a vegetation can-
opy, this will not sufﬁce for photosynthesis modeling
purposes. It has been known for a long time that the
photosynthetic response of a leaf is not linear with PAR
irradiance (see section “PAR in Vegetation Canopies”).
Thus, the radiation ﬁeld is commonly described as
composed of two ﬂuxes, direct and diffuse PAR, and
PPFD values at leaf surfaces are calculated separately
for the two ﬂuxes [100]. Beside atmospheric condi-
tions, the availability of direct solar radiation depends
only on canopy structure. In contrast, diffuse radiation
is generated via more numerous mechanisms.
The ﬁrst source of what can be called diffuse radi-
ation, or radiation of diminished radiance compared
with direct solar radiance above the vegetation canopy,
is penumbra. Penumbral effects are purely geometric
and are most evident in a tall canopy of small scatterers,
for example, in a needle-leaf boreal forest. At high
latitudes, low sun angles further increase the
pathlength of direct solar beam in the canopy, thus
making the penumbra dominate the radiation ﬁeld
on a clear day. In a canopy consisting of shoots, the
penumbral effect alters the irradiance distribution, but
also vertically redistributes the photosynthetic poten-
tial inside the canopy [101]. Coupling the nonzero
angular diameter of the sun and the three-dimensional
structure of the vegetation canopy can lead (at least in
model calculations) to an increase in canopy photo-
synthetic capacity by tens of percent [102,103]. Such
computations are rare in the scientiﬁc literature since
the correct prediction of penumbral irradiation
assumes nonzero scatterer sizes, which is beyond the
scope of traditional RTT.
The second source of diffuse radiation, multiple scat-
tering inside vegetation, depends on the canopy structure
and cannot be easily predicted without a radiative trans-
fer model. However, whereas modeling penumbra
requires special consideration for both the spatial distri-
bution and the dimensions of canopy elements, the
dimensions of leaves are usually ignored when calculating
multiple scattered radiation ﬂuxes. Assuming inﬁnitesi-
mally small leaves makes it possible to apply the tradi-
tional methods for solving RTT [85,86].
The third component of the diffuse PAR ﬁeld inside
a vegetation canopy is contributed by diffuse sky radi-
ation: some of the photons scattered by the atmosphere
can penetrate the vegetation layer without being
intercepted by canopy elements. Depending on cloud-
iness and other atmospheric conditions, the diffuse sky
irradiance can vary within large limits. The complica-
tions related to calculating this PAR component origi-
nate in the difﬁculties of correctly estimating the
variability of above-canopy diffuse radiance. In con-
trast, the canopy transmittance can be modeled from
simple structural assumptions or measured from hemi-
spheric photography.
The diffuse sky PAR irradiance is usually less than
one-third of the global PAR irradiance (section “PAR
Below the Atmosphere”). Considering that not all of
the sky is visible inside the canopy, the diffuse PAR
irradiance (on a horizontal surface) is at least one
order of magnitude smaller than the direct PAR irradi-
ance in a sunﬂeck. The adaptation of leaves in deeper
canopy layers (where sunﬂecks are rare) to low irradi-
ances makes diffuse sky radiation more effective in
inducing photosynthesis than direct PAR [104]. In
other words, the light use efﬁciency is generally larger
7920 PPhotosynthetically Active Radiation: Measurement and Modeling
for diffuse radiation than for direct irradiance: this
effect is sometimes termed diffuse-radiation fertiliza-
tion. Thus, an increase in diffuse PAR can lead to
increased carbon assimilation. This mechanism has
been proposed as the explanation of the decrease in
global CO
concentration after Mt. Pinatubo’s eruption
in 1991. Volcanic eruptions are known to increase the
amount of atmospheric aerosol for several years thus
enhancing diffuse sky radiation [105,106] and global
carbon assimilation. The adverse effect of decreasing
the amount of anthropogenic sulfate aerosol could
similarly lead to a decrease or fall in global photosyn-
thesis [107].
The spectral distribution of PAR above and below
a vegetation canopy is shown in Fig. 9. Four spectral
distributions are shown, corresponding to global and
diffuse radiation above and below a closed alder canopy
(LAI = 2). The distributions are normalized so that
their maximum value in the PAR waveband equals
unity. Whereas changes in the spectral distribution of
global PAR are relatively small, alteration of the spectral
distribution for the diffuse ﬁeld is quite signiﬁcant.
Above the canopy, the diffuse radiation spectrum
peaks at blue wavelengths. The diffuse PAR ﬁeld
below a canopy reaches its maximum at about
550 nm, which corresponds to green light. Further, in
the near-infrared (NIR) region, at wavelengths imme-
diately above 700 nm, the diffuse spectral irradiance
below the canopy increases to levels much higher than
those in the PAR waveband. Such an increase empha-
sizes the requirement to consider spectral errors with
care: if the sensor sensitivity cutoff at 700 nm is not
sharp enough, measurements of diffuse PAR inside
a vegetation canopy are contaminated by the high
NIR irradiance. Also, the differing spectral composi-
tion of diffuse radiation between the higher and lower
canopy layers must be taken into account when calcu-
lating the contribution of diffuse radiation to canopy
Explicit treatment of the total PAR available for
photosynthesis is thus a complex task [98]. Exact com-
putations require that many factors are taken into
account: dimensions of the solar disc and the scattering
elements, detailed structure of the vegetation canopy,
spectral properties of leaves, nongreen canopy elements
and soil, spectral and angular distributions of incident
radiation, etc. Due to the large spatial and temporal
variability of PAR inside a plant canopy, its measure-
ment and empirical analysis are also extremely compli-
cated and only a few examples are presented in the
literature [20,108].
Measurement of PAR Absorbed by Canopies
Direct Measurement of APAR The PAR ﬂux
absorbed by plant canopies (APAR) may be either
measured directly using PAR sensors or estimated indi-
rectly, based on canopy gap fraction measurements.
Leaf area index (LAI) measurements may also be used
to estimate the PAR absorbed by the canopy. First,
a description of direct PAR measurements is given.
The PAR absorbed by vegetation equals the total
amount of radiative energy absorbed by all plant sur-
faces and can thus be measured in either quantum or
energy units. The formulation of the problem is iden-
tical for the two representations. Here, the quantum
PARÞis used as an example. Due to the differ-
ent spectral compositions of PAR that is incident or
reﬂected and transmitted by a vegetation canopy,
Relative irradiance
400 500
Wavelength (nm)
600 700 800
Global, sky Diffuse, sky
Global, vegetation Diffuse, vegetation
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 9
Spectral distribution of radiation on a clear day above and
below a vegetation canopy. Measurements were made
inside and next to a gray alder (Alnus incana) plantation
(leaf area index L= 2.1) in To
˜ravere, Estonia
7921PPhotosynthetically Active Radiation: Measurement and Modeling
converting between QA
PAR and its companion quantity
in energy units, IA
PAR, is not a straightforward task.
Thus, estimates of fAPAR from quantum measure-
ments are not directly comparable with fAPAR values
calculated in energy units. However, considering the
measurement uncertainties and the errors related to
retrieval of fAPAR from remote sensing measurements,
the differences are ignored here.
PAR is computed from the energy conservation law
in the canopy using hemispherical ﬂuxes:
PAR ztop
PAR ztop
where Q
PARðzÞrepresents downward Q#
upward Q"
PARðzÞhemispherical PAR ﬂuxes at the bot-
tom (z= 0) or top (z=z
) of the canopy. Therefore,
the hemispherical PAR sensors should be precisely
located to obtain representative measurements of the
several terms in the PAR balance:
PAR ztop
, the incident PAR at the top of the
canopy is measured using upward-looking sensors
at the top of the canopy
PAR ztop
, the reﬂected PAR is measured using
downward-looking sensors at the top of the canopy
PARð0Þ, the transmitted PAR is measured by
upward-looking sensors placed at the bottom of
the canopy
PARð0Þ, the PAR reﬂected by the soil is measured
using downward-looking sensors at the bottom of
the canopy
The number of sensors used to measure the several
terms in a representative way depends mainly on the
heterogeneity of the canopy and on the typical foot-
print of the sensor. About half of the ﬂux collected
by a hemispherical sensor comes from inside a circle
whose radius equals the distance of the sensor from
the object it is looking at [109]; about 96% of the signal
originates from inside a circle with a radius of ﬁve times
the distance. Therefore, many sensors (between 5
and 50) are required to properly measure all the terms
in Eq. 10 at the bottom of the canopy: the distance from
the sensor to the bottom of the canopy (when measur-
ing Q#
PARð0Þ) or the soil (when measuring Q"
is generally limited. Conversely, just one sensor is
required for the incoming PAR, Q#
PAR ztop
, and only
a few for the reﬂected PAR, Q"
PAR ztop
, depending on
the distance between the sensor and the top of the
canopy (Fig. 10).
The fraction of absorbed PAR fAPAR;FA
, may
be derived from Eq. 10 by dividing all the terms by the
incident PAR:
where r
is the reﬂectance of the canopy, t
is the
transmittance of the canopy, and r
is the soil reﬂec-
tance. As mentioned above, FA
PAR is used here to denote
the quantum fAPAR, or the absorbed fraction of inci-
dent photons in the PAR waveband. Note that all these
variables are bihemispherical quantities [110,111],
although the directional integration of incident radia-
tion requires, as a minimum, weighing the direct and
diffuse components of canopy transmittance.
According to Eq. 11, fAPAR is a very convenient quan-
tity: it is independent on the magnitude of the incident
irradiance. However, fAPAR is somewhat sensitive to
the irradiance geometry: the attenuation of the direct
component of the incident radiation ﬁeld varies
strongly with the direction of the sun as well as canopy
QPAR (ztop)QPA R (ztop)
QPAR (0) QPAR (0)
z = ztop
z = 0
Photosynthetically Active Radiation: Measurement and
Modeling. Figure 10
Configuration of PAR sensors to measure APAR and fAPAR.
Sensor A measures the incident PAR Q#
PAR ztop
, sensor B
measures the reflected PAR Q"
PAR ztop
, sensor C
measures the transmitted PAR Q#
, and sensor D
(usually omitted) measures the soil reflectance Q"
7922 PPhotosynthetically Active Radiation: Measurement and Modeling
If the soil reﬂectance r
is assumed to be known,
the PAR balance may be approximated by using
measurement data for the three ﬁrst terms only, that
is, the incident Q#
PAR ztop
, reﬂected Q"
PAR ztop
and transmitted Q#
radiation. Equation 11
may further be simpliﬁed as in the PAR domain,
where very little multiple scattering is expected,
where r
is the asymptotic value of canopy reﬂectance
when the leaf area index, L, tends toward inﬁnity.
Values of r
are generally small in the PAR domain
(around 0.06 [112]) since most photons are absorbed
by the green leaves. In these conditions, the PAR bal-
ance, Eq. 10, may be approximated by measuring
only the incident Q#
PAR ztop
and the transmitted
terms. It is thus possible to avoid problems
in measuring the soil reﬂectance r
: as highlighted
earlier, many sensors are required due to the small
distance between soil and sensor and the possible effect
of the sensor shadow in its footprint. It also avoids
problems related to the dependence of r
on the
directionality of incident radiation.
Because the PAR balance and thus fAPAR both
depend on the varying illumination geometry, contin-
uous measurements are required. Furthermore, fAPAR
measurements are generally used in light-use efﬁciency
models [3,113] which require daily and even seasonally
integrated fAPAR values. The PAR radiance measure-
ment system thus needs to be set in place from several
days up to several months. In practice, this calls for
weatherproof systems with sufﬁcient autonomy both in
terms of energy and memory. Affordable systems meet-
ing these requirements and able to replicate individual
observations for improved spatial sampling have been
developed only recently. However, instantaneous mea-
surements using several view directions may be
achieved by different existing systems, allowing the
reconstruction of fAPAR values for any (possibly
modeled) illumination geometry.
In all situations, the approach based on radiation
balance assesses the value of PAR absorbed by the can-
opy, independently of the nature of the radiation
intercepting elements. As a consequence, when
non-photosynthetic material (such as trunks, branches,
or senescent leaves) constitutes a signiﬁcant fraction of
canopy, the true fAPAR, or PAR absorbed by the green
photosynthetically active elements, is overestimated.
Estimation of fAPAR from fIPAR Green leaves gen-
erally absorb a very large fraction of light in the PAR
domain, that is, they appear almost black from a pure
radiative standpoint. Considering this, the fraction of
absorbed PAR may be approximated by the fraction
of intercepted PAR fIPAR;FI
PAR ¼1tCAN :ð13Þ
Combining Eqs. 12 and 13 provides a relation
between the fraction of absorbed PAR and the
intercepted fraction:
PAR 1r1
The validity of this approximation has been exten-
sively investigated and found to hold with reasonable
accuracy [114117].
Instruments for Measuring fAPAR
Directional and Flux Measurements Based on the
directionality of measurements, fAPAR sensors can be
divided into two subgroups. The ﬁrst group contains
instruments that disregard the directional distribution of
incident PAR (either by integrating over the upper hemi-
sphere or looking into only one particular direction); the
second group consists of instruments measuring with
a ﬁeld of view divided between different directions
(multidirectional devices). Generally, the lack of direc-
tional sampling by instruments in the ﬁrst group must
be compensated by increased spatial sampling.
Ceptometers are devices consisting of an array of
hemispherical sensors aligned on a single support,
allowing for spatial representativeness. They are partic-
ularly well suited for crops: a ceptometer covering
a transect representative of a forest canopy would be
too long to be moved easily between the measurement
locations. While a ceptometer is used to measure radi-
ation below the canopy, the incident PAR can be simul-
taneously recorded with an additional PAR sensor.
Examples of such sensor arrays are AccuPAR (Decagon,
USA), SunScan (Delta-T, UK), and PAR/LE (Solems,
7923PPhotosynthetically Active Radiation: Measurement and Modeling
Other specialized multipoint radiation measure-
ment systems have been developed (for mainly in-
house use) on various scales. For example, spatial
distributions of the radiation ﬁeld (with focus on
PAR) affecting a conifer shoot have been measured
using optical ﬁbers and a CCD matrix [118]. At the
other end of the scale are systems capable of character-
izing tree-level heterogeneity using hundreds of sensors
attached to 5-m-long booms [119]. PAR @METER
[120] is a recently developed device capable of contin-
uously monitoring the transmitted PAR at different
points inside and above a vegetation canopy. Incident
and transmitted PAR are simultaneously recorded and
stored in a network of sensors placed according to
a predeﬁned spatial sampling scheme using wireless
computer connections.
Directional devices are generally less common than
the hemispherical instruments listed above. Examples
of directional, below-canopy radiation measuring
devices are TRAC (Natural Resources, Canada) and
DEMON (CSIRO, Australia). They measure direct sun-
light and use different approximations to characterize
the plant architecture. TRAC inverts the light transmit-
tance proﬁles obtained on a transect based on a model
of canopy gap size distribution [121]. It accounts for
the nonhomogeneous distribution of foliage in certain
canopies (also called clumping effect [122]) by
inverting the measured sunﬂeck length distribution.
DEMON makes use of Beer’s law and a special zenith
angle at which canopy transmittance does not depend
on leaf orientation [123] to retrieve LAI from incident
and transmitted PAR measurements.
The instruments mentioned above are designed for
measurements of transmitted PAR. However, by adding
canopy reﬂectance measurements, the complete PAR
balance can be obtained (Fig. 10). From such balance
measurements, it is also possible to calculate the frac-
tion of absorbed PAR, fAPAR.
Multidirectional Transmission Instruments The
incoming PAR may be decomposed into the direct
component coming from the sun and the diffuse com-
ponent due to light scattering in the atmosphere. For
each of those components, a fAPAR value can be asso-
ciated. The total fAPAR can then be written as:
PAR ¼1fdiff
ðÞþfdiff FA
PAR 2pþ
where f
is the diffuse fraction of radiation in global
irradiance, O
is the direction of the sun, and 2p
used to denote the upper hemisphere; FA
PAR 2pþ
ðÞare thus the fAPAR values for direct-only or
diffuse-only incidence, respectively. Sometimes,
ðÞis called the black-sky fAPAR and corre-
spondingly, FA
PAR 2pþ
ðÞthe white-sky fAPAR. To apply
Eq. 14 to the calculation of FA
PAR for all sky conditions,
the directional characteristics of t
(O) have to be
Directional devices provide measurements of can-
opy transmittance, t
(O), in a number of directions
O=(#,f). Two types of devices are mainly used: the
LAI-2000 instrument [124] and digital hemispherical
cameras (DHC) [125,126]. Lidar systems may also
access the directional variation of light transmittance,
although the technique might be better suited for other
applications related to detailed characterization of can-
opy architecture. The LAI-2000 instrument measures
light transmitted in the blue wavelengths to the bottom
of the canopy in ﬁve concentric rings of 15in the range
0<#<70. For each ring, all azimuths directions are
accounted for. Measurements are generally taken under
diffuse conditions to prevent an unwanted sensitivity to
the speciﬁc sun direction, while minimizing any possi-
ble sun glint on the leaves. The blue spectral region is
used since, at these wavelengths, leaves appear almost
black and diffuse sky scattering is at its peak. The view
azimuth angle can be modiﬁed using a series of view-
limiting caps to block out a part of the sky or focus the
measurements toward speciﬁc directions of interest.
Hemispherical cameras provide estimates of the
gap fraction over the whole hemisphere. If the angular
distribution of incident radiation is known, the gap
fraction may be converted into canopy non-
interceptance. Again, assuming that leaves are black at
the visible wavelengths used by cameras, the canopy
interceptance is converted into canopy absorptance.
DHC usually involves a high-resolution digital camera
and an attached ﬁsheye lens. This ﬁsheye lens projects
the whole upper hemisphere onto the digital array of
the camera, producing circular images. However, his-
torical data recorded on black-and-white ﬁlm may still
be encountered and, in some cases, photographs made
using ordinary lens are used (i.e., any lens not covering
the whole hemisphere). The a posteriori processing of
digital images provides the fraction of the upper
7924 PPhotosynthetically Active Radiation: Measurement and Modeling
hemisphere covered by vegetation. This is done by
classifying each pixel as sky or non-sky, that is, applying
a threshold to divide the pixels constituting the image
into two classes [126].
Furthermore, the variations in vegetation canopy
transmittance with zenith (and sometimes also azi-
muth) angle may be used to reconstruct the diurnal
variation of fAPAR. Note that, similarly to sensors mea-
suring the transmitted PAR, no distinction is made
between green photosynthetically active elements and
the non-photosynthetic material. This may lead to an
overestimation of the actual value of the true fAPAR.
However, when using hemispherical photographs taken
from above canopies, it may be possible to distinguish
between green and nongreen elements. Unfortunately,
downward looking photography is limited to relatively
short canopies for obvious practicalreasons. DHC tech-
niques are very efﬁcient by allowing instantaneous mea-
surements that can be replicated multiple times to
improve the spatial sampling while accessing the diurnal
variation of fAPAR. However, such measurements are
only representative of the current canopy architecture,
and measurements should be repeated along the grow-
ing season to match the canopy architecture dynamics.
A novel approach consists in using digital cameras
as hemispherical radiation receivers [127,128]. Simi-
larly to the traditional DHC approach, a ﬁsh-eye lens
projects the whole hemisphere onto the sensor array.
However, instead of just applying a threshold to iden-
tify the gaps in the canopy, the new “calibrated camera
method treats the receiving surface of the camera as
a two-dimensional array of miniature quantum
receivers. Each array element receives radiation from
a single direction in the upper hemisphere. The spectral
sensitivity functions of the array elements have maxima
in the optical region of electromagnetic radiation, that
is, in the PAR waveband. Therefore, after proper labo-
ratory calibration, a raw digital image stored in the
camera can be treated as a (PAR) radiance measure-
ment result. However, these measurements must be
treated with care because modern consumer cameras
are complex optical systems designed for producing
visually good-looking images, not recording spectral
radiance values.
Relationships Between fAPAR and LAI The devices
described above are often used (or even designed) for
measuring canopy leaf area index (LAI) [92,93]. Gen-
erally, all techniques to estimate LAI from PAR trans-
mittance measurements rely on Beer’s law (Eq. 8). The
directional instruments allow for a more accurate inte-
gration over the hemisphere required for the accurate
application of Beer’s law. However, a direct use of it,
without spectral integration, is still quite common
when relating PAR irradiance and LAI [129]. The
opposite link is also often made: if the canopy LAI is
known, fAPAR can be modeled using the known opti-
cal properties of the elements constituting the vegeta-
tion canopy and some basic knowledge of canopy
structure. All these calculations are based on the
Beer’s law specially formulated for vegetation canopies,
as described in section “Quantitative Description of
PAR in Vegetation Canopies”.
APAR and fAPAR from Satellite Observations
The fraction of absorbed photosynthetically active
radiation, fAPAR was probably the ﬁrst biophysical
variable to be estimated from remote sensing observa-
tions from NDVI, the normalized difference vegetation
index computed as NDVI ¼rNIR rRED
, where r
and r
are the top-of-canopy reﬂectance in the
near-infrared (NIR) and red (RED) bands, respectively
[130]. The early empirical relationships were later
explained by investigating the radiative transfer in can-
opies [112,131]. Compared to other biophysical vari-
ables (such as LAI), fAPAR appears to be retrievable
much more accurately and robustly [132,133]. The
optimal conﬁguration for retrieving fAPAR includes
four spectral bands: red, near-infrared, green, and red
edge. Simple observations in the red and near-infrared
in view directions close to nadir were found to lead to
slightly degraded performance.
The optimal view angle for a satellite instrument is
not directly down (nadir), but in the principal solar
plane close to the hot spot (the direction of the sun,
corresponding to backward scattering), and in the per-
pendicular solar plane at zenith angles close that of the
sun [132,133]. Alternatively, directions around 60
from nadir in the backscattering direction or in the
perpendicular plane were also shown to be close to
optimal [134]. However, as these optimal conﬁgura-
tions are not generally available, most algorithms for
fAPAR retrieval focus on the minimization of
7925PPhotosynthetically Active Radiation: Measurement and Modeling
directional effects by simply making use of whatever
remote sensing data can be obtained.
In addition to NDVI, indices have been developed
to correct for the contribution of soil to the measured
reﬂectance, or to use the more readily available top-of-
atmosphere reﬂectance instead of the top-of-canopy
value [116,134]. Further, look-up tables have been
used to derive fAPAR from MODIS top-of-canopy
reﬂectance observations after calibration with radiative
transfer model simulations [135]. However, when the
physically based algorithm (known as the main
algorithm) fails, a backup algorithm is triggered using
relationships between fAPAR and MODIS NDVI. Neu-
ral networks have also been used [120,136] to opera-
tionally retrieve fAPAR from satellite-measured
The main fAPAR products derived from satellite
observations (Table 2) thus demonstrate a wide range
of either empirical or physically based approaches. To
obtain these fAPAR products, the needed inputs are
either top-of-canopy or top-of-atmosphere reﬂectance
values observed in 2–13 reﬂectance bands. Some
Photosynthetically Active Radiation: Measurement and Modeling. Table 2 Examples of fAPAR values derived from
satellite-based reflectance measurements
Product name Approach Sensor Reference
NDVI Empirical linear regression AVHRR [130,137,140]
NDVI Linear regression of RT simulations AVHRR [112,141]
RDVI Linear regression of RT simulations POLDER [134]
JRC-FAPAR VI calibrated using RT simulations PARASOL, SEVIRI [116]
TOC-VEG NN calibrated using RT simulations MERIS [136]
TOA-VEG NN calibrated using RT simulations MERIS [142]
MODIS LUT from RT simulations MODIS [135]
CYCLOPES NN calibrated using RT simulations Vegetation [120]
GLOBCARBON Derived from LAI product Vegetation, MERIS, AATSR [143]
GEOLAND2 NN calibrated using other products Vegetation [144]
VI vegetation index, RT radiative transfer, NN neural network, LUT look-up table
00 0.2 0.4 0.6
RMSE = 0.12
0.8 1
00 0.2 0.4 0.6
RMSE = 0.10
0.8 1
Photosynthetically Active Radiation: Measurement and Modeling. Figure 11
Comparison of ground-measured (horizontal axis) and satellite (vertical axis) estimates (MODIS: left, CYCLOPES: right) of
7926 PPhotosynthetically Active Radiation: Measurement and Modeling
algorithms use a priori information on vegetation
type or rely on a land cover map. Most of the
algorithms provide an instantaneous black-sky
fAPAR value at the time of satellite overpass, while
a few others use multidirectional observations, to pro-
vide a daily integrated black-sky value. Note that most
of the polar orbiting sensors considered here are on
satellites in sun-synchronous orbits with equatorial
crossing time close to 10:00 local time. Under these
conditions, the instantaneous black-sky fAPAR value
is a good approximation of the daily integrated
fAPAR value.
Individual validation exercises have been reported
by several authors [116,137139]. They generally show
a reasonable agreement between ground-measured
fAPAR and satellite estimates, with RMSE values
around 0.10–0.15 (in fAPAR units) (Fig. 11). Consid-
ering the complex interactions between radiation and
vegetation canopies described above, fAPAR also has
a most desirable feature: it is almost independent of
scale. Values of fAPAR derived from algorithms applied
at higher spatial resolution and integrated over
a coarser spatial domain provide similar values to
those derived using the same algorithm applied directly
to the coarser spatial resolution [133]. Unfortunately,
the same cannot be said of any other vegetation param-
eter derived from remote sensing data.
Future Directions
The current research related to PAR measurement
(and, inevitably, modeling) is aimed at utilizing the
technological advances in (remote) sensing technology
to better characterize the environment we live in. Pho-
tosynthesis is the energy source for all life on earth. The
raw energy for life is originally dispersed in the form of
electromagnetic radiation arriving from our closest
star. Although the importance of photosynthesis, and
the role of shortwave radiation in it, has always been
acknowledged, there are still large gaps in our
From a more technical point of view, the most
evident and surprising gap is a lack of comprehensive
ground-based measurement network. Fortunately, this
lack of basic monitoring does not result in severe
ignorance of global PAR availability. This is evidenced
by the ongoing satellite measurements and the
simultaneous model developments – to convert satel-
lite sensor readings into radiation ﬂuxes absorbed by
vegetation hundreds of kilometers below. The progress
is also witnessed by the large number of scientiﬁc
articles with keywords such as fAPAR, satellite remote
sensing, and global productivity. The ultimate goal of
this research, however, is not only to give a detailed
quantitative measure of the health of our planet, but
also to provide the physical basis for describing and
understanding the very fundamental links between the
physical and biological environments.
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Photovoltaic Energy, Introduction
Institute of Research and Development of Photovoltaic
Energy, Chatou, Cedex, France
Article Outline
III-V Solar cells Solar cells based on compound com-
bining elements from the Ga and As columns
(III and V).
Cadmium telluride (CdTe) solar cells Solar cells
based on this compound, used in the form of thin
Chalcopyrite solar cells Solar cells based on the com-
pound Cu(In,Ga)Se
, also noted CIGS, in the form
of thin ﬁlms.
Dye sensitized solar cells (DSSC) Solar cells based on
mesoscopic tintanium oxide thin ﬁlm sensitized
with dye photoactive molecules and impregnated
by an electrolyte.
Hot carrier solar cell New high efﬁciency concept
allowing to convert high energy photons in electrical
charges in the external circuit without thermal losses.
Life cycle analysis (LCA) To quantify all the steps
from mining, utilization to recycling in terms of
energy consumption, material utilization, environ-
mental and health impacts.
Multijunction solar cell High efﬁciency solar cell
based on the association of several elementary
solar cells made of sing junctions.
Organic solar cells Solar cells based on organic com-
ponents like carbon fullerenes and polymers,
blended in the form of thin ﬁlms.
Pay back time Time needed by a solar cell under
operation to reimburse the total energy used for
its fabrication.
Photovoltaics Conversion of photon energy to
Siicon solar cells Solar cells based on silicon element,
either in crystalline or amorphous forms.
Solar cells Device allowing to absorb photon energy
and convert it to electricity in an external circuit.
Up, down conversion New high efﬁciency concept
using optical processes allowing to convert low
(resp. high) energy photons to medium visible
energy photons for maxium conversion efﬁciency.
Photovoltaics is the direct conversion of solar energy
into electricity. It results from the fundamental mech-
anism of absorption of photons in matter, with the
excitation of electrons from their equilibrium lower
energy state to a nonequilibrium excited state of
higher energy. That means that electrons are being
transferred to more negative electrical potential.
Then, they usually return to equilibrium by giving
back the initial photon energy in form of thermal
energy (with the interactions with phonons), light
with the emission of new photons via luminescence
processes or chemical species via electrochemical
oxydo reduction processes in the case of photosynthe-
sis. The uniqueness and beauty of photovoltaics is to
“plug” on the initial step when electrons are just excited
to a lower potential, and to have them directly trans-
ferred in an external circuit where the energy can be
used directly in the electrical form. The device to do it is
just a solar cell. However, to have it efﬁcient imposes to
be able to compete with the naturally occurring spon-
taneous processes! This was not easy and from the
discovery of the photovoltaic effect in 1839 by Edmond
Becquerel to the ﬁrst efﬁcient silicon solar cell in 1954 it
took more than one century and then 50 years more to
reach the years 2000s to assist to the large scale indus-
trial endeavor of photovoltaic conversion of solar
energy, bringing for the ﬁrst time in the human history
this new renewable energy technology as an alternative
to fossil fuels and nuclear utilizations. While laboratory
record efﬁciency for any photovoltaic cells is reaching
the incredible value of 43%, approaching the 50% level,
more than 20 GW of photovoltaic peak power sources
have been produced by the industry in 2010. This is the
7932 PPhotovoltaic Energy, Introduction
... Over the IMAGINES sites, only part of the sites' FAPAR corresponded to the instantaneous black-sky values at 10:00 AM, whereas the FAPAR values over other sites corresponded to the daily integrated black-sky FAPAR. Considering that instantaneous FAPAR at the time of the satellite overpass (around 10:00 AM) is a good approximation of daily integrated black-sky FAPAR [21,36], the instantaneous and daily integrated black-sky FAPAR values of high-resolution reference maps at the VALERI and IMAGINES sites were chosen to evaluate the MODIS, MUSES and EBR black-sky FAPAR products. Consequently, 58 high-resolution FAPAR reference maps over 36 VALERI and IMAGINES sites were used in this study. ...