Measurement and prediction of solar radiation distribution in full-scale greenhouse tunnels

Abstract

Radiative heterogeneity in greenhouses significantly influences crop activity, particularly transpiration and photosynthesis. This is especially true for plastic tunnels, which are the most commonly used greenhouse type in the Mediterranean basin. A computer model was generated for this study based on sun movement, greenhouse geometry, transmittance of the cover and weather conditions. Experiments to test model accuracy were performed in a standard 8 m wide east-west orientated lettuce tunnel located near Avignon (southern France). Solar radiation distribution was studied using 32 solar cells placed on the soil surface along 4 sections situated either in the tunnel centre or near the west gable end. Measured and simulated data of transmittance were close together for both cloudy and clear sky weather conditions. The tested model was then used to simulate solar radiation intensity distribution at the soil level in various tunnel types for different periods of the year. Simulated results revealed high radiative heterogeneity in tunnels, mainly due to effects of gable ends, vent openings and frames. Statistical analysis indicated that solar radiation inside the greenhouse at ground level was higher in the N-S orientated tunnel than in the E-W orientated tunnel in March and June, but radiative heterogeneity was higher in the N-S orientated tunnel, especially in June. Transversal heterogeneity in the E-W orientated tunnel was much higher than longitudinal heterogeneity. Global heterogeneity increased from March to June for both tunnel positions although its relative value remained approximately unchanged.

Full text

Agriculture and Environment
Original article
Measurement and prediction of solar radiation
distribution in full-scale greenhouse tunnels
Shaojin WANG, Thierry BOULARD
*
Unité de Bioclimatologie, INRA, Site Agroparc, Domaine Saint-Paul, 84914 Avignon Cedex 9, France
(Received 20 July 1999; accepted 18 November 1999)
Abstract. Radiative heterogeneity in greenhouses significantly influences crop activity, particularly transpiration and
photosynthesis. This is especially true for plastic tunnels, which are the most commonly used greenhouse type in the
Mediterranean basin. A computer model was generated for this study based on sun movement, greenhouse geometry,
transmittance of the cover and weather conditions. Experiments to test model accuracy were performed in a standard
8 m wide east-west orientated lettuce tunnel located near Avignon (southern France). Solar radiation distribution was
studied using 32 solar cells placed on the soil surface along 4 sections situated either in the tunnel centre or near the
west gable end. Measured and simulated data of transmittance were close together for both cloudy and clear sky weath-
er conditions. The tested model was then used to simulate solar radiation intensity distribution at the soil level in vari-
ous tunnel types for different periods of the year. Simulated results revealed high radiative heterogeneity in tunnels,
mainly due to effects of gable ends, vent openings and frames. Statistical analysis indicated that solar radiation inside
the greenhouse at ground level was higher in the N-S orientated tunnel than in the E-W orientated tunnel in March and
June, but radiative heterogeneity was higher in the N-S orientated tunnel, especially in June. Transversal heterogeneity
in the E-W orientated tunnel was much higher than longitudinal heterogeneity. Global heterogeneity increased from
March to June for both tunnel positions although its relative value remained approximately unchanged.
Greenhouse tunnel / radiative heterogeneity / computer model / simulation
Résumé – Mesure et simulation de la distribution du rayonnement solaire dans les serres tunnels. L'hétérogénéité
radiative sous serre influence fortement l'activité du couvert et plus particulièrement la photosynthèse et la transpiration.
En ce qui concerne le tunnel, le type de serre le plus répandu dans la région méditerranéenne, l'absence de données
expérimentales ainsi que la complexité des échanges radiatifs expliquent pourquoi la répartition fine du climat radiatif
demeure mal connue et pourquoi elle est rarement prise en compte dans les modèles de simulation numérique. Dans
cette étude, un modèle informatique de transfert radiatif sous tunnel a été développé. Il tient compte de la position du
soleil dans le ciel, de la géométrie du couvert et de la présence d'ouvertures, de la présence de structures et de petits bois
Agronomie 20 (2000) 41–50 41
© INRA, EDP Sciences
Communicated by Gérard Guyot (Avignon, France)
* Correspondence and reprints
boulard@avignon.inra.fr

S. Wang, T. Boulard
42
1. Introduction
Solar radiation distribution in greenhouses is an
important factor influencing crop transpiration and
photosynthesis. It is highly dependent on green-
house design, radiative capacity of the covering
material and weather conditions. Radiative hetero-
geneity is particularly important in tunnel green-
houses, the most commonly used greenhouse type
in the Mediterranean basin. This variability severe-
ly effects plant activity and often leads growers to
over fertilize, as has been observed for lettuce
crops [6].
A number of experimental and theoretical stud-
ies on solar transmittance in different greenhouse
types have already been performed. Spectral prop-
erties of several greenhouse cover materials have
been measured both in laboratory [12] and field
conditions [7]. Solar radiation transmittance of a
single span greenhouse has also been investigated
experimentally using a scale model [13].
Modelling solar radiation transmittance was car-
ried out in early 1970s. Smith and Kingham [14]
computed direct and hemispherical radiation trans-
mittance by evaluating the fraction of ground area
irradiated by a transmitted beam and Kozai and his
co-workers [8, 9] performed a study on radiation
transmittance in single and multi-span greenhous-
es. Their model ignores all reflected light and
effects of polarisation. But later Thomas [15] stud-
ied the effect of a speculatively reflecting material
on the north wall of an E-W single span green-
house. His model accounts a sophisticated method
of ray tracing. Amsen [1] established an interesting
technique of projecting light-obstructing areas on
to a hemisphere, to calculate the light loss to the
crop under diffuse light conditions. A series of pre-
dictions for solar transmittance in east-west (E-W)
and north-south (N-S) orientated greenhouses have
been generated using computer modelling at
United Kingdom latitudes [2–4]. Solar radiation
distributions in either single or multi-span plastic
tunnels are much less well understood although
Kurata et al. [10] and de Tourdonnet [6] have made
some headway. However, no results have been
reported on solar radiation distribution in full-scale
tunnels with vent openings, side walls and gable
end effects.
The objectives of this study were to generate a
computer model to simulate radiative heterogene-
ity at the greenhouse floor level as a function of
greenhouse geometry, covering material and
weather conditions. Solar radiation distribution at
the greenhouse floor level was defined using both
measurements and simulations to demonstrate the
theoretical model's accuracy and to compare results
with simulations performed for different tunnel ori-
entations and covering materials. Simulation
results were first experimentally tested based on
solar radiation measurements using 32 solar cells
at the soil surface along 4 vertical sections, either
in the tunnel centre or near the west gable end. The
validated model was then used to map radiative
heterogeneity in both E-W and N-S orientated tun-
nels under different typical radiative conditions
during various periods of the year near Avignon
(latitude: 44° N, southern France).
et enfin de la répartition du rayonnement incident en rayonnement direct et diffus. On a procédé à une validation de ce
modèle dans un tunnel de 8 m de laitues situé à Avignon dans le sud de la France. La distribution du rayonnement solai-
re à la surface du sol a été mesurée à l'aide de 32 cellules solaires disposées selon 4 sections situées soit au centre du
tunnel, soit à proximité du pignon ouest du tunnel. La comparaison entre les valeurs mesurées et calculées montre que le
modèle fonctionne convenablement, à la fois les jours couverts et ensoleillés. Le modèle ayant été validé de façon satis-
faisante, il a ensuite été utilisé pour simuler la répartition spatiale du rayonnement à la surface du sol, pour différentes
orientations et pendants différentes périodes de l'année. On a mis ainsi en évidence une forte hétérogénéité spatiale qui
était liée à la forme du tunnel et surtout à la présence d'ouvrants et d'ombres portées par les structures.
Serre tunnel / hétérogénéité radiative / modèles / simulation

Solar radiation distribution in greenhouse tunnels
43
2. Computer model
Modelling solar radiation transmittance in a
plastic tunnel is a very complicated task due to the
influence of covering material, greenhouse struc-
ture (frames, vent openings, side walls and gable
ends) and weather conditions. To simplify the
model, continuous curved surfaces of the arched
tunnel were approximated using a finite number of
small flat planes. Secondary reflections from inner
cover surfaces and soil surface were omitted.
Global solar radiation transmitted through a given
surface (A'B'C'D') with a slope angle β in rad [11]
was then calculated and projected as a “shadow
area” (ABCD) on the soil surface (Fig. 1):
(1)
with
S
D
= S
g
– S
d
(2)
where x', y' and z' are the Cartesian co-ordinates
for positions on the cover surface, S
d
and S
D
are
external diffuse and direct solar radiations (W·m
-2
),
S
g
and S
g
(x', y', z') are external and internal global
solar radiations (W·m
-2
), τ
d
and τ
D
are diffuse solar
and direct transmittances of the tunnel's elementary
surface (A'B'C'D').
To further simplify the model, it was assumed
that radiation transmittance was zero for tunnel
frames and 1 for vent openings. The experimental
value of the transmittance of the plastic cover used
in this study was a function of incidence angle α in
rad of radiation determined by Nijskens et al. [12].
Transmittance values of 0.69, 0.64, 0.62, 0.59, 0.29
and 0 for direct solar radiation at incidence angles
of 0°, 15°, 30°, 45°, 60° 75° and 90° with 0.69 for
diffuse solar radiation were used in this study. The
actual direct solar transmittance as a function of
the incidence angle was linearly interpolated. This
incidence angle for a surface is given by de
Halleux [5] and Kurata et al. [10] as follows:
α
= arccos[cos
γ
cos(
θ
–
ψ
) sin
γ
cos
β
] (3)
where γ (rad) is solar altitude angle, ψ (rad) is solar
azimuth and θ (rad) is orientation angle of each of
the cover's elementary planes relative to S-N axis.
If the co-ordinate system is assumed to originate
from the north-east corner of the tunnel, a solar
beam transmitted by the cover from position A'(x',
y', z') reaches position A(x, y) on the soil surface.
For each position on the level of the cover (x', y',
z') and for each solar position (γ and ψ), the x and
y co-ordinates can be determined as follows:
x = x' + z' cos
ψ
/ tg
γ
(4)
y = y' – z' sin
ψ
/ tg
γ
. (5)
It should be pointed out that the direct solar radia-
tion was not calculated if the tunnel cover's ele-
ments were projected outside the greenhouse but
the diffuse solar radiation was still taken into
account. A computer model in Quick Basic was
derived from relationships (1) to (5). The main
steps of the algorithm are as follows:
1) Initialization of the date, solar time, tunnel
location and orientation along together with the co-
ordinates of each of the cover's elementary planes
(A'B'C'D');
Agriculture and Environment
S
g
x
',
y
',
z
'
=
τ
D
⋅S
D
+
τ
d
⋅S
d
⋅
1 +cos
β
2
Figure 1. Definition of angles related to the sun's posi-
tion and schematic illustration of solar radiation trans-
mitted and reaching on the soil surface (α: incidence
angle of the area A'B'C'D'; β: slope angle of the surface;
γ: solar altitude angle; ψ: solar azimuth).

S. Wang, T. Boulard
44
2) Calculation of solar height γ and azimuth ψ;
3) Calculation of slope β and orientation θ,
angles for each of the tunnel cover's elementary
planes;
4) Determination of the incidence angle of direct
solar radiation α, using relationship (3) for each of
the cover's elementary planes;
5) Computation of internal global solar radiation
S
g
(x', y', z') for each of the cover's elementary
planes using relationship (1);
6) Determination of the “shadow area” projected
by each of the cover's elementary planes on the
tunnel's soil surface using relationships (4) and (5);
7) Calculation of averaged daily global solar
radiation by integrating and averaging daily solar
radiation received at a given position on the soil
surface. Finally, average daily transmittance of
global solar radiation was deduced for each posi-
tion using the ratio of daily integral global solar
radiation on the soil surface in the tunnel to outside
radiation.
3. Experimental design
3.1. Site and tunnel description
Measurements were conducted in a standard 8 m
wide E-W orientated lettuce tunnel situated near
Avignon in southern France (44° latitude). Tunnel
dimensions were 8 × 60 m with a top height of
3.1 m. Traditional discontinuous vent openings
were included. They were formed by separating
plastic sheets using 0.4 m long pieces of wood
placed every two meters along both sides of the
tunnel. A layout of the tunnel illustrating vent
openings is shown in Figure 2.
3.2. Measurement instruments
Solar radiation distributions were measured
using 32 silicon solar cells set up along four sec-
tions in the middle of the tunnel or near the west
gable end (Fig. 2). Extensive tests were performed
prior to using these solar cells to check that output
signals were in line with solar radiation.
Figure 2. Layout of 32 experimental solar cells (+) distributed in the tunnel centre or near the west wall (all dimensions
are in m).

Solar radiation distribution in greenhouse tunnels
45
Calibration was performed by comparing a quan-
tum sensor LI-200SB and a pyranometer under dif-
ferent weather conditions. Linear relationships
between each solar cell and the quantum sensor
were derived which were later used to correct solar
radiation distribution measurements. During mea-
suring, external global and diffuse solar radiations
were also recorded near the tunnel using pyra-
nometers attached to a 3 m high mast. All measure-
ments were taken every 10 s and averaged on-line
over 10 minutes then stored in a portable data log-
ger (DELTA-T, Cambridge, UK).
4. Results and analysis
4.1. Model accuracy
Measurements and simulations were first com-
pared based on measurements taken from the tun-
nel's center. Validation was performed over four
days under both cloudy (February 24 and March 4,
1999) and sunny (February 25 and March 7, 1999)
conditions (Fig. 3). Outside global and diffuse
solar radiations were used as input parameters for
the computer model. An example of average daily
transmittances of global solar radiation obtained
through experiments and simulations along four
sections situated in the tunnel center under a
cloudy condition is shown in Figure 4. Measured
transmittance in the section situated below the vent
opening (Sect. 1) was higher due to vent opening
(Fig. 4a) and much lower near the south and north
borders due to larger incidence angles. On average,
transmittance variation data as a function of tunnel
width was similar whether obtained through exper-
iments or simulations. However, an underestima-
tion of simulated transmittance in the north part of
the tunnel was observed. Similar results were
obtained for Sections 2, 3 and 4. However, no dif-
ferences in transmittance were detected for loca-
tions on the south side just below the openings
(Sect. 1) or at similar positions situated between
two successive openings below the cover (Sect. 3).
Larger discrepancies were found on the north side
(Figs. 4 and 5), probably because secondary
reflectance on the north inner cover surfaces was
omitted in simulations. This secondary reflectance
yielded an important effect as the inner surface of
the north side, which was shaped like a parabolic
mirror, focused reflected solar radiation on the tun-
nel soil surface near the north wall.
Agriculture and Environment
Figure 3. Outside global () and diffuse (—) solar
radiation under cloudy and clear skies during measure-
ments.
Figure 4. Measured (+) and calculated (  ) daily aver-
aged transmittances of global solar radiation in the tun-
nel centre along Sections 1 (a), 2 (b), 3 (c) and 4 (d)
under cloudy weather conditions (Feb. 24).

S. Wang, T. Boulard
46
Average daily transmittances in the tunnel center
under a clear sky are shown in Figure 5.
Transmittance patterns obtained both through
experiments and simulations were generally simi-
lar to results for cloudy skies. Nevertheless, statis-
tical analysis revealed (Tab. 1) a substantial
increase in average solar transmittance under clear
skies compared to cloudy conditions in all sections.
This increase represented about 3.5% for the mea-
sured values and 4.7% for the simulations.
Figures 6 and 7 show average daily transmit-
tances near the west gable end of the tunnel under
cloudy and clear skies respectively. In both cases,
transmittance was much lower than in the tunnel
center, mainly due to the effects of the side wall
and gable ends, particularly in the afternoon.
Transmittance in the middle of Section 1 was high-
er than in all the other sections due to door opening
(2 m wide and 1.8 m high) during the diurnal peri-
od. Generally, agreement between the computed
and measured transmittances near the gable end
was good in all sections under both cloudy and
clear weather conditions (Figs. 6 and 7). Table II
shows average measured and simulated transmit-
tances during cloudy (0.40 compared to 0.42) and
sunny days (0.46 compared to 0.49).
Table II shows that transmittance loss near the
gable end was very high: 13% during cloudy days,
Figure 5. Measured (+) and calculated (  ) daily aver-
aged transmittances of global solar radiation in the tun-
nel centre along Sections 1 (a), 2 (b), 3 (c) and 4 (d)
under clear weather conditions (Feb. 25).
Figure 6. Measured (+) and calculated (  ) daily aver-
aged transmittances of global solar radiation near the
tunnel west wall along Sections 1 (a), 2 (b), 3 (c) and 4
(d) under cloudy weather conditions (March 4).
Table 1. Averaged transmittances in tunnel centre.
Cloudy conditions Sunny conditions
Sections (Feb. 24) (Feb. 25)
Measurement Simulation Measurement Simulation
1 0.53 0.54 0.57 0.59
2 0.53 0.54 0.56 0.58
3 0.54 0.53 0.56 0.58
4 0.52 0.53 0.57 0.58
Mean 0.53 0.54 0.56 0.58

Solar radiation distribution in greenhouse tunnels
47
10% during sunny days. However, this value was
slightly smaller than transmittance loss (16%)
observed between the middle of the tunnel and the
sides when transversal heterogeneity was consid-
ered.
4.2. Model application
Once the computer model was validated in the
tunnel centre and near the gable end under both
cloudy and clear conditions, it could reasonably
and reliably be used to predict solar radiation dis-
tribution in similar tunnel types with different ori-
entations at different seasons in Avignon latitude.
This simulated tunnel (22 × 8 m
2
) was assumed to
be equipped with discontinuous vent openings
made by separating plastic sheets every four
meters using 0.6 m long pieces of wood. As in
experiments, total daily radiation received at each
point on the soil surface was added together then
averaged out over the length of the diurnal period.
Figure 8 illustrates global solar radiation distri-
bution over the ground surface of full-scale E-W
and N-S orientated tunnels on March 21.
Considerable variations in global solar radiation
between both tunnels were observed. For both ori-
entations, higher solar radiation values at the soil
surface were due to higher radiative transmittance
through the vent openings while lower values were
caused by lower transmittance due to larger solar
radiation incidence angles. Due to the sun's lower
position, the largest heterogeneity was observed
along the transversal section of the E-W orientated
tunnel. Solar radiation distribution in the N-S ori-
entated tunnel was nearly symmetrical along the
tunnel axis and average transmittance was slightly
higher than in the E-W orientated tunnel. However,
higher contrasts were found between areas situated
below vent openings and in the center, character-
ized by high transmittance, and zones situated
along the sides and gable ends associated with
lower transmittance.
Solar radiation distributions over the ground sur-
face in both E-W and N-S orientated tunnels on
June 21 are shown in Figure 9. A side wall effect
can be observed in the E-W orientated tunnel on
both the south side and the two gable ends.
Average distribution of solar radiation was more
homogeneous than in N-S orientated tunnels.
Higher solar radiation values were observed in the
center of the N-S orientated tunnel during summer
due to a relatively smaller solar radiation angle of
incidence in the top part of the cover. Higher
Agriculture and Environment
Table 2. Averaged transmittances near tunnel side wall.
Cloudy conditions Sunny conditions
Sections (March 4) (March 7)
Measurement Simulation Measurement Simulation
1 0.37 0.41 0.43 0.47
2 0.41 0.41 0.46 0.50
3 0.41 0.43 0.46 0.49
4 0.42 0.43 0.48 0.50
Mean 0.40 0.42 0.46 0.49
Figure 7. Measured (+) and calculated (  ) daily aver-
aged transmittances of global solar radiation near the
tunnel west wall along Sections 1 (a), 2 (b), 3 (c) and 4
(d) under clear weather conditions (March 7).

S. Wang, T. Boulard
48
values were also found for the same orientation
below the vent openings where radiation penetra-
tion was heightened by the absence of a plastic
cover.
Statistical analysis of radiative heterogeneity
was performed both on March 21 and June 21 by
comparing average values and standard deviations
(for the E-W and N-S orientated tunnels: Tab. III).
If x and y represent respectively transversal and
longitudinal directions at the soil surface, three dif-
ferent standard deviations can be calculated:
global, σ
x,y
; transversal, σ
x,
-
y
and longitudinal, σ-
x,y
.
Figure 8. Simulated average
solar radiation distributions in
E-W (a) and N-S (b) orientated
tunnels on March 21 (Outside
average solar radiation was
196 W·m
-2
).
Table 3. Statistical results of global solar radiation (W·m
-2
) distributions in E-W and N-S orientated tunnels on March
21 and June 21.
Tunnels Date Mean Min. Max. Standard deviation
Outside Inside Global Longitudinal Transversal
E-W March 21 196 115.9 101.9 134.3 7.7 1.5 7.2
June 21 465 282.8 238.0 31.7 13.4 6.4 10.9
N-S March 21 196 121.9 94.7 146.4 9.8 6.4 6.7
June 21 465 289.6 246.8 331.6 18.2 12.8 11.5

Solar radiation distribution in greenhouse tunnels
49
Solar radiation in the N-S orientated tunnel was
higher than in the E-W orientated tunnel in March
and June. This difference was low in March (5%)
and June (2%). Conversely, radiative heterogeneity
was higher in the N-S orientated tunnel than in the
E-W orientated tunnel, especially in June.
Generally, global heterogeneity (σ
x,y
) increased
from March to June for both orientations, although
its relative value (σ
x,y
/ S
g
(x,y)) remained approxi-
mately unchanged. Transversal heterogeneity in
March (σ
x,
-
y
= 7.2 W·m
-2
) in the E-W orientated
tunnel was much higher than longitudinal hetero-
geneity (σ-
x,y
= 1.5 W·m
-2
). However, transversal
and longitudinal heterogeneities were nearly the
same for both March (6.4 and 6.7) and June (12.8
and 11.5) in simulations for the N-S orientated tun-
nel.
5. Conclusions
As radiative heterogeneity in greenhouses is cru-
cial for both crop transpiration and photosynthesis,
a computer model to calculate solar radiation dis-
tribution based on greenhouse structure, surface
transmittances and solar positions was generated.
Predicted results of solar transmittances were vali-
dated through comparison with experimental val-
ues obtained using 32 solar cells in a full-scale
E-W orientated tunnel in February and March.
Simulated transmittance variations over tunnel
width concurred with experimental results both
under cloudy and clear weather conditions.
However a slight underestimation was observed for
the north side of the tunnel as secondary
Agriculture and Environment
Figure 9. Simulated average
solar radiation distributions in
E-W (a) and N-S (b) orientated
tunnels on June 21 (outside
average solar radiation was
465 W·m
-2
).

S. Wang, T. Boulard
50
reflectance on the inner surface of the north side
cover was omitted.
The validated computer model was applied to
map solar radiation heterogeneity in E-W and N-S
orientated tunnels in Avignon on March 21 and
June 21. The results revealed considerable varia-
tions in global solar radiation over the tunnel
ground surface. These variations were mainly
caused by vent openings, gable ends and different
incidence angles for various cover surfaces.
Transmittance for the N-S orientated tunnel was
slightly higher than for the E-W tunnel. The E-W
orientated tunnel was primarily marked by a N-S
gradient, resulting in moderate global radiative het-
erogeneity. Heterogeneity in the N-S orientated
tunnel was higher, but more evenly distributed in
all directions.
Acknowledgements: The authors wish to express their
deepest thanks to J.C. L'Hotel for his technical support
with the measurement system and M. Keller for provid-
ing us with the measurement site in a greenhouse at the
“Lycée Agricole de Cantarel” in Avignon.
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