Original article

Measurement and modelling

of the photosynthetically active radiation
transmitted in a canopy of maritime pine

P Hassika P Berbigier, JM Bonnefond

Laboratoire de bioclimatologie Inra, domaine de la Grande-Ferrade, BP 81,
33883 Villenave-d’Ornon cedex, France

(Received 20 May 1996; accepted 20 May 1997)

Summary - Modelling the photosynthesis of a forest requires the evaluation of the quantity of pho-
tosynthetically active radiation (PAR) absorbed by the crowns and the understorey. In this article a
semi-empirical model, based on Beer’s law is used to study PAR absorption and its seasonal varia-
tion. Our purpose was to confirm that the PAR and the solar radiation follow the same interception
laws for both the direct and diffuse part, using correct values of needle transmission and reflection coef-
ficients. The model developed took into account the direct and the diffuse radiation. The radiation
rescattered by the crowns was neglected following an estimation using the Kubelka-Munk equa-
tions, which indicated that the term was small. The model was calibrated and tested from the mea-
surements taken in a maritime pine forest during the summer and autumn of 1995. The comparison
between the results of the model and the measurements was satisfactory for the direct radiation as well
as for the diffuse radiation. In conclusion, although the measurement wavebands are different, the pen-
etration of the PAR can be estimated using the same simple semi-empirical model already estab-
lished for solar radiation.

model / solar radiation / photosynthetically active radiation / penetration / maritime pine

Résumé — Mesure et modélisation du rayonnement utile à la photosynthèse transmis dans un

couvert de pin maritime. Pour la modélisation de la photosynthèse d’un couvert végétal, il est
important de connaître la quantité de rayonnement utile à la photosynthèse (PAR) absorbé par les cou-
ronnes et le sous-bois. Dans cet article, un modèle semi-empirique, exploitant la loi de Beer, ainsi que
les variations saisonnières du PAR sont présentés. L’objectif de l’étude est de confirmer que le
rayonnement utile à la photosynthèse et le rayonnement solaire suivent les mêmes lois d’interception
pour le direct et pour le diffus en intégrant les valeurs mesurées de reflectance et de transmitance. Le
modèle établi prend en compte le rayonnement direct et le rayonnement diffus. Le rayonnement

*
Correspondence and reprints
Tel: (33) 05 56 84 31 87; fax: (33) 05 56 84 31 35; e-mail: hassika@bordeaux.inra.fr
rediffusé par le houppier est estimé à partir des équations de Kubelka-Munk. Lorsque ce terme est
négligé, on montre que l’erreur induite sur le bilan radiatif est faible. Les entrées du modèle sont
déduites des mesures effectuées sur une forêt de pin maritime durant l’été et l’automne 1995. La
comparaison entre les résultats du modèle et les mesures est satisfaisante aussi bien pour le rayonnement
direct que pour le rayonnement diffus. En conclusion, bien que les ordres de grandeurs et les domaines
spectraux des mesures soient différents, la pénétration du rayonnement utile à la photosynthèse peut
être estimé par un simple modèle semi-empirique déjà établi pour le rayonnement solaire.

modèle / rayonnement solaire / rayonnement utile à la photosynthèse / pénétration /

pin maritime

INTRODUCTION parallelepipeds (Sinoquet, 1993). A Monte-

Carlo simulation can be used to calculate
the direct solar radiation at different points
Studying the evapotranspiration and the pho- in a canopy (Oker-Blom, 1984).
tosynthesis of plants is useful in many fields,
such as plant physiology, biomass produc- However, very few studies have focused
tion on a large scale and interaction with on the photosynthetically active radiation
the overall climate of the earth. When (PAR) of the solar spectrum (Sinclair and
extrapolating from a foliage element to the Lemon, 1974; Sinclair and Knoerr, 1982;
whole plant, the interception profile of radi- Pukkala et al, 1991). Other teams (Alados et
ation has the largest vertical gradient, and al, 1995 ; Papaioannou et al, 1996) have
is thus essential for scaling-up. In forest studied the relationship between the PAR
canopies, in contrast, vertical gradients of and the solar radiation. These studies tend to
temperature, concentration of water vapour show that the ratio between the PAR and
and CO
2 are very low. The photosynthetic the solar radiation depends on solar eleva-
activity depends first of all on the photo- tion, sky conditions and dewpoint tempera-
synthetically active radiation (PAR) inter- ture. Spitters et al (1986) also established
cepted and the combined effects of water an empirical relationship between global
vapour concentration and air temperature. and diffuse PAR.
Internal CO
2 concentrations in the intercel-
lular spaces of the leaves and the water stress In this paper we applied the model devel-
of the canopy also play a role (Jones, 1992). oped by Berbigier and Bonnefond (1995)
for solar radiation forest canopy (Les
on a
The numerous interception models of Landes, France) the PAR. The objective
to
radiation by plants vary from simple mod- of this model is to predict the proportion of
elling based on Beer’s law (Bonhomme and direct and diffuse PAR reaching the under-
Varlet-Grancher, 1977) to more complex storey using measurements of incident
models characterized by a discretization of global and diffuse PAR above the canopy.
the canopy into elementary volumes or cells. This very simple semi-empirical model rep-
These cells have a known geometrical shape resents the canopy as a horizontally homo-
and a known location in space. In general, geneous diffusing layer. The direct and dif-
these models do not take the multiple scat- fuse radiation penetrates according to Beer’s
tering between these different cells into law. The scattered radiation is estimated
account. These cells can be ellipsoids (Nor- from the Kubelka-Munk ( 1931 ) equations,
man and Welles, 1983), cones (Wang and which have also been used by Bonhomme
Jarvis, 1990), rows of cylinders and cones and Varlet-Grancher (1977). This model is
(Jackson and Palmer, 1972), ellipsoids semi-empirical since the extinction coeffi-
(Charles-Edwards and Thorpe, 1976), or cient is adjusted from measurements.
 The outputs of the model were validated voltage proportional to the incident radiation. To
measure this potential difference we used a resis-
using data collected during a series of mea- tance of 18 ohms. To reduce the specular reflec-
surements in summer and autumn 1995.
tion, a tarnished filter, which only allowed the
In this paper we divide the global PAR or spectrum between 400 and 700 nm to pass, was
incident PAR into a direct part (direct PAR) stuck above each cell.
and a diffuse part (diffuse PAR). The A number of sensors were mounted above
reflected to incident PAR ratio will be called the canopy on a 25-m-high scaffolding. At this
PAR reflectance. level at the end of a 2-m-long rod, two cells, one
facing upward and the other downward, mea-
sured the global PAR and the reflected PAR.

MATERIAL AND METHODS On the same site, at 2 m above the ground

and at the top of the scaffolding, two cells locally
measured the diffuse PAR below and above the
Experimental data were collected during sum-
mer 1995 in a maritime pine forest planted in canopy, respectively. The diffuse PAR was
obtained by using a shadow band, which stopped
1969. The plantation is located 20 km south-west
the direct PAR. The error induced on the mea-
of Bordeaux (latitude 44° 42’ N, longitude 0°
surement was small: to account for the effect of
46’ W).
the part of the sky vault hidden by the shadow
On a 1-ha stand, the trees were planted in par- band, a multiplier of 1.084 given by the manu-
allel rows. The mean height of the trees was facturer was applied.
approximately 16 m. The maximum height was At 1 m above the ground, a trolley rolling at
18 m and the mean height of the bases of the
crowns was 9 m. Tree density was 660 trees per
a speed of 2 m/min on a 22-m railway parallel to
the row carried five two-sided (one facing upward
hectare. The soil was completely covered with
and one facing downward) sensors located on a
clumps of grass approximately 0.7 m high, which transversal rod whose length was equal to the
were completely green at the time of measure-
width of the inter-row (4 m). Every 15 min this
ments. In a first approximation this forest can be
described by two distinct plant
-layers, ie, the experimental device calculated the mean of the
values measured every 10 s (Bonnefond, 1993).
crowns of the pines and the gramineae of the
This system allowed us to perform a space-time
understorey. The trees were planted along an average of the measurements and to smooth the
axis NE-SW. The leaf area index (LAI) varied
effect of the rows.
between 3.4 and 3 during the measurement sea-
son (July-October). This LAI was measured Cells were calibrated against a CM11, Kipp
using a Demon system (Lang, 1987), according and Zonen thermopile during very clear weather
to the method proposed by Lang et al (1991) and at maximum solar elevation. Under these
where the total surface area index was estimated conditions it is possible to calibrate quantum sen-
from gap frequencies. These frequencies were sors against solar energy sensors because the

deduced from the penetration of direct sunbeams. spectrum distribution of the solar energy remains
This method is based on Cauchy’s theorems constant (Varlet-Grancher et al, 1981). In inter-
(Lang, 1991). national units (SI) the density of the solar energy
flow is measured in watts per square meter
). The flux density of the PAR (photo-
-2
(W.m
Measurements of the synthetic photon flux density (PPFD): 400-700
photosynthetically nm) is usually defined in moles of photons per
active radiation surface unit and per unit of time (photon.m
).
-1
.s
-2
We found that, in the case of clear days, 2.02
The tools generally used for measuring PAR are μmol m
-2 s
-1 of PAR were equal to 1 W.m -2of
cells containing crystalline silicon, such as those global radiation.
manufactured by Licor (LI 190S), which respond All sensors had similar calibration coeffi-
almost instantaneously to small or sudden vari- cients. In order to avoid any measurement error
ations in light intensity. due to sensor failure (ageing, loss of sensitivity,
For this experiment, 25 cells were prepared in contact defect) a new calibration was made under
the laboratory using the method developed by similar conditions at the end of the season.
Chartier et al (1993). These sensors delivered a Results appeared to be identical.
 In parallel with PAR measurements, the net This theory has already been developed
and global radiation above the forest as well as its for solar radiation, by Berbigier and Bon-
PAR reflectance were measured for the whole nefond (1995). The aim of the model is to
solar spectrum (table I).
calculate the PAR transmitted and absorbed
Data recorded on a data acquisition sys-
were
from measurements of the incident direct
tem of the Campbell 21X type (Campbell Sci- and diffuse PAR.
entific, Logan, UT). As for the mobile measure-
ments, the recorded values were the 15-min
average of measurements taken every 10 s.
For this study we had a complete set of mea- Non-intercepted direct PAR
surements (direct and diffuse PAR at the lower
and higher levels) for clear days 189 and 193. The non-intercepted direct PAR is simply
For days 275, 279, 280 and 281 (clear sky) the modelled by Beer-Bouguer’s law, which
measurement of the lower diffuse radiation was
can be written as:
missing.
We also had a complete set of measurements
for two days with a partially or totally overcast
sky (190 and 192). where R (λ) (μmol m
b -2 ) -1 is the direct
s
Lastly, for days 247, 249, 250, 265-273, PAR at a given level within the crown, R (0)
b
276-278 and 282 (totally or partially overcast is the direct PAR above the canopy, λ is the
days) the measurement of the lower diffuse PAR LAI integrated from the top of the canopy to
was missing, whereas for days 187, 188, 191 and
194-198 the measurement of the lower global
the point where R (λ) is defined,β is the
b
PAR solar elevation angle and K a non-dimen-
was missing.
sional extinction coefficient. When the
The direct PAR above the canopy R (0) was
b
obtained by the difference between the mea- whole crown is considered, λ L is the LAI
=

surements of the diffuse and global PAR above of the canopy. Thus, when using Beer’s law,
the canopy: R
(0) R
b (0) - R
s =
(0).
d the only parameter required is the extinc-
tion coefficient (K) of the canopy.

THEORY
Non-intercepted diffuse PAR
The forest of Les Landes is modelled as two
well-separated plant layers, ie, the under- Distribution laws of luminance corre-
storey and the crowns. We focused on the sponding to clear or overcast lighting con-
amount of PAR transmitted through the ditions are very different. For the sake of
crown layer. simplicity we used the standard overcast
sky (SOC) law proposed by Steven and maritime pines have already been measured
Unsworth (1980). For clear weather, strictly by Berbigier and Bonnefond (1995)
speaking this law is not correct because there
is a strong circumsolar diffuse PAR. How-
ever, since the diffuse PAR represents only
approximately 15% of the global PAR, this The scattered radiation was deduced for each
error is acceptable as a first approximation.
elementary layer, when the radiation bal-
The expression of this law proposed ance is integrated from λ
= 0 to λ L. These
=
by
Steven and Unsworth (1980) is: values made it possible to obtain the total
diffuse PAR of the crown (Bonhomme and
Varlet-Grancher, 1977; Sinoquet et al,
1993).
where N(β,&phis;) is the luminance value,
The analytical solution of these equations
N(π/2,0) the luminance value at zenith and
the angular source azimuth. R
was given by Bonhomme and Varlet-
(0) is the mea-
d Grancher (1977) for a canopy of maize when
sured value of the incident diffuse PAR. As
a consequence of equation [2], the density of p = τ and by Berbigier and Bonnefond
the diffuse PAR above the canopy is written: (1995) for a canopy of maritime pines when
ρ ≠ τ. We used the solution established by
the last authors.

RESULTS AND DISCUSSION

where u = sinβ.
This integral has no analytical solution.
Experimental measurements
However, its numerical value can be closely
adjusted to a function Y = exp(-K’λ) using
the least-squares method (Berbigier and Figure I shows the different terms of the
radiation balance in the PAR above and
Bonnefond, 1995). We obtained K’ = 0.467.
below the canopy for clear weather (day
193) as a function of the hour of the day.
The transmission of the incident PAR varies
Scattered PAR
with the solar elevation and is much lower
for low incident angle incidences. Apart
Measurements showed that the diffuse PAR
from a cloudy period at approximately1400
reaching the understorey is spatially homo- hours UT, which explains the fall in the
geneous even in a discontinuous canopy.
As with the non-intercepted PAR, the rescat-
global PAR and the increase in the incident
diffuse PAR, the curves show the expected
tered radiation can be treated a fortiori with
the hypothesis that the canopy is continu- shape. The incident global PAR reached
a maximum of approximately 1900
ous.
-1 in the middle of the day. The
.s
-2
μmol.m
The method consists in writing the radi- global PAR below the crowns reached a
ation balance of an elementary horizontal peak at approximately 700 μmol.m
-1
.s
-2
layer with a thickness dλ. The rescattered around 1300 hours (denoted ’1’ in fig 1),
radiation depends on the reflectance and the which corresponds to the presence of the
transmittance of the foliage elements (ρ and sun between the rows. The effects of the
as well as on the PAR reflectance of the
τ) two adjacent rows of crowns can also be
understorey. Reflectance (p) and transmit- seen on the measurements (denoted ’2’ in
tance (τ) in the PAR waveband on needles of fig 1).
 To estimate the scattered PAR it is nec- of the reflected PAR are extremely low (less
essary to know the PAR reflectance of the than 3 μmol m
-2 ).-1 When the understorey
s
understorey. This PAR reflectance is defined average PAR reflectance could be measured,
as the ratio between incident PAR and it reached approximately 0.05.
reflected PAR. An example of variations
with time for a day of measurements of the The daily value of the canopy PAR
PAR reflectance of the canopy and the reflectance is defined as the ratio between
understorey is presented in figure 2. the sum of daily incident PAR and the sum
of daily reflected PAR above the canopy.
The increase in the canopy PAR
We deduce PAR reflectance and the ratio
reflectance at the beginning and at the end of
of incident diffuse PAR on incident global
the day is due to the interception of the top
PAR by using the daily sums, since the
of the plant canopy. For this day the average
direct PAR depends more closely on the
PAR reflectance above this forest reached
solar elevation angle.
approximately 0.06. This value represents
less than half of the PAR reflectance of the In figure 3a a regular increase in the
solar radiation when the whole spectrum is
canopy PAR reflectance was observed on
taken into account (fig 2). Although this the forest, during the seasonal measurement.
value seems low, this result is coherent with The forest PAR reflectance reached approx-
another study (Gash et al, 1989).
imately 0.05 at the beginning of July and
For the understorey PAR reflectance the 0.07 at the beginning of October. This
values at the beginning and the end of the increase could be due to the increased stand
day are not representative because the values reflectivity at low incidences, which has
already been mentioned, and perhaps to the Variations in diffuse PAR and global
death of 3-year old needles. PAR daily means are presented in figure 4
for the period from 5 July to 9 October 1995
Figure 3b shows the variation curve of
the understorey PAR reflectance. A maxi- (days 186-282). It shows a divergence
be observed in the mean value between the trends of the global and the dif-
mum can
fuse PAR, probably due to the mean
between days 235 and 255. This increase
decrease in solar elevation. Since the ratio
was possibly due to a short period of water
between the diffuse and global PAR pre-
deficiency in the summer of 1995: the sents more intra-day variations, we do not
graminea were dry and had lost their green show a curve of the 15-min ratios, which
colour unlike the needles which remained
were much more variable.
green. After rainfall, a decrease was
observed. The mean forest and understorey Table II shows the values of the propor-
PAR reflectance was 0.06 and 0.05, respec- tions between the diffuse PAR and the
tively, over this period. These two values global PAR, which were measured for clear
of the PAR reflectance are not additive and variable weather throughout the season.
because the reflected PAR above the canopy For clear days the density of the diffuse PAR
is not the sum of the PAR reflected by the represented approximately 15% of the global
understorey and crowns. PAR. This ratio was 40% for the variable
days and 30% for all the days. These val- the PAR can be estimated from measure-
ues imply that the proportion of diffuse PAR ments of radiation with short wavelengths
in the global PAR was almost equivalent to
using the following relation:
the proportion of diffuse radiation in the
global solar radiation.
This result has to be compared to other
studies (Efimova, 1967) which suggest that
The difference observed in our study (30% for which all the data were available. These
versus 57% in the former) can be explained days were chosen close to the summer sol-
by the fact that our study was performed stice in order to have a maximum variation
during a rather sunny part of the year. A in the solar height. The different parts of the
more precise estimation of these values is model were then validated with the corre-
currently being studied. sponding measurements of the other days
between days 188 and 282.
However, since measuring the diffuse
PAR routinely is relatively complicated, it is
also of interest to search for a semi-empiri-
cal relation between the diffuse PAR and Direct radiation
the global PAR, which could avoid mea-
suring the diffuse PAR. Spitters et al ( 1986) The extinction coefficient K of the foliage
also established an empirical relationship elements can be deduced from Beer’s law
between global and diffuse PAR, taking into and written as:
account sunshine duration. Unlike the solar
radiation this type of relation has never been
established for PAR in our region. This rela-
tionship is currently being studied in our
laboratory. where R (0) and R
b (λ) represent the direct
b
PAR below and above the crowns, respec-
tively. In figure 5 a relationship between K
Modelling and the angles of solar elevation is observed.
Strictly speaking, K cannot be assumed con-
The model was adjusted on three days with stant since it varies with sun angular eleva-
clear and overcast sky (days 189, 190, 192) tion (de Wit, 1965).
 On days 189, 190 and 192 K was calcu- surements and the outputs of the model for
lated for solar elevation angles greater than one of the days used to adjust equation [1].
30°. The mean values are given in table III. The deviations to the model are represented
The overall average is: with a linear regression forced to the ori-
gin. The slope of this line is 0.95 for R
2 =

0.9. An increasing dispersion is observed

for the high values, which is due to rows.
On the same experimental site Berbigier and
Bonnefond (1995) have found the same However, figure 7 shows that the com-

value in a study of solar radiation. Conse- parison between all the measurements of all
the days not used to adjust the model and
quently, with the same hypotheses, Beer’s the outputs of the model may be represented
law in this forest has a unique extinction
with a linear regression forced to the ori-
coefficient for the PAR as well as the solar
radiation. gin. It can be noted that the model slightly
overestimates the measurements since the
However, without assuming that the slope of this line is 0.96 for R
2 0.91. This
=

foliage index is horizontally homogeneous, bias may result from the hypothesis of a
the effect of the angular distribution of the constant K, which does not exactly repre-
needle must be included. Nevertheless we sent the reality.
checked this using the ellipsoidal distribution
of the needle orientations suggested by Diffuse PAR
Campbell (1986). This did not give better
results, which justifies the use of a constant The diffuse PAR measured below the
K.
canopy is the sum of the sky diffuse PAR
Figure 6a shows a comparison between having crossed the canopy without being
the measurements of the direct PAR and the intercepted and the PAR scattered by the
modelled direct PAR using equation [6] on elements of the crown. We first studied the
day 193. Variations in the direct PAR in the scattered part of the PAR.
understorey resulting from the presence of The model is applied for evaluating the
rows cannot be seen from the results of the scattered PAR to all the days. The values
model, which is based on the assumption obtained are lower than 5 ± 0.025
of a continuous horizontal canopy. -1 on average, ie, less than 4%
.s
-2
μmol.m
6b of the lower diffuse radiation.
Figure gives example of the out-
an

puts of the model direct PAR measure-

to These values are within the range of
ments on day 189. It compares the mea- absolute error of our sensors. Consequently,
this part can be neglected when modelling underestimation (slope 0.9), which may be
the radiation transmitted because the error due to geometrical effects of the crowns
induced is lower than 1 % on the estimation (rows, holes, preferential orientations of the
of the global radiation in the understorey. foliage elements).
The rescattered radiation is not accounted
for in the model.
It was shown above (equation [3]) that CONCLUSION
the non-intercepted diffuse PAR R d (λ) at Since the penetration of the PAR into plant
depth λ can be written as:
canopies is poorly documented, we tried, in
this paper, to apply a semi-empirical model
to the PAR. This model was previously

Regarding measurements and the simula- established for the solar radiation in a forest
tion of day 193 (fig 8a), the orientation of the of maritime pines. The daily variations of
rows does not seem to affect the proportion the incident and transmitted PAR were pre-
of diffuse PAR transmitted to the under- sented.
storey. The simulation example shown in A regular increase in the canopy PAR
fig 8a was made on a clear day (except from reflectance was observed, during the mea-
1400 to 1500 IST) in order to suppress the surement season. This value, approximately
disruptive effects of the clouds. 0.05 at the beginning of July, reached 0.065
in October. During the same time, for under-
Figure 8b shows that the diffuse PAR is
homogeneous. Thus, the diffuse radiation storey PAR reflectance an increase in the
smooths the effect of the rows. A linearity mean value between days 235 and 255 could

defect between the measurements and the be observed. This increase was due to a short
model can be seen. This bias may result period of water deficiency. Later we showed
from the hypothesis of a constant K, which that the reflectivity of the canopy was much
would affect K’. However, this angle was lower in the PAR than for the whole solar
observed on clear days, where the diffuse waveband.
PAR was very small (150
-1 at
.s
-2
μmol.m The proportions between the diffuse PAR
maximum). and the global PAR, which were measured
The model was validated on all the days by clear and variable weather throughout
not used to the season, were compared. The diffuse
adjust theK coefficient and for
PAR represented approximately 30% of the
which the lower diffuse PAR was measured.
Predictions were in agreement with the mea- global PAR.
surements and the maximum difference with The outputs of the model of the direct
the line 1:1 was approximately 26 PAR and the diffuse PAR transmitted to the
-1 (fig 9).
.s
-2
μmol.m soil showed a good correlation with the sea-
sonal measurements. This result enables us
to state that this model is a good tool for
Global PAR predicting the interception of the PAR in
the forest, ie, the partition of PAR between
crowns and understorey.
The outputs of the complete model can now
be compared to the measurements of the In a first approximation, the extinction
global PAR (fig 10) for all the experimental coefficient K is constant. The daily outputs
days where this measurement is available of the model of the direct PAR and the dif-
(1 350 points). A good agreement is fuse PAR transmitted to the soil were not
observed (R
2 0.94) in spite of a slight
= in agreement with measurements, but more
realistic models of K will be tested after- to Environmental Plant Physiology, 2 ed. Cam-
wards. bridge Univ Press, Cambridge
Kubelka P, Munk F (1931) Ein Beitrag zur Optik der
Nevertheless, this model may be useful Farbanstriche. Zeits Furtechn Physick 12, 593
forecophysiological studies. Lang ARG (1987) Simplified estimate of leaf area
index from transmittance of the sun’s beam. Agric
Acknowledgements: The authors thank Y
For Meteorol 41, 179-186
Brunet, I Champion and M Irvine for proof-read-
ing this article as well as A Kruszewski for con- Lang ARG, McMurtie RE, Benson ML (1991) Valid-
structing and installing sensors on the experi- ity of surface area indices of Pinus radiata esti-
mated from transmittance of the sun’s beam. Agric
mental site. This work was partially supported For Meteorol 55
by the Conseil regional of Aquitaine. Lang ARG (1991) Application of some of Cauchy’s
theorems to estimation of surface areas of leaves,
needles and branches of plants, and light transmit-
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