Measurement and prediction of solar radiation

distribution in full-scale greenhouse tunnels

Shaojin Wang, Thierry Boulard

To cite this version:

Shaojin Wang, Thierry Boulard. Measurement and prediction of solar radiation distribution in full-
scale greenhouse tunnels. Agronomie, EDP Sciences, 2000, 20 (1), pp.41-50. �10.1051/agro:2000107�.
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Agronomie 20 (2000) 41–50 41
© INRA, EDP Sciences

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

Communicated by Gérard Guyot (Avignon, France)

* Correspondence and reprints

boulard@avignon.inra.fr
42 S. Wang, T. Boulard

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

1. Introduction 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-
Solar radiation distribution in greenhouses is an dictions for solar transmittance in east-west (E-W)
important factor influencing crop transpiration and and north-south (N-S) orientated greenhouses have
photosynthesis. It is highly dependent on green- been generated using computer modelling at
house design, radiative capacity of the covering United Kingdom latitudes [2–4]. Solar radiation
material and weather conditions. Radiative hetero- distributions in either single or multi-span plastic
geneity is particularly important in tunnel green- tunnels are much less well understood although
houses, the most commonly used greenhouse type Kurata et al. [10] and de Tourdonnet [6] have made
in the Mediterranean basin. This variability severe- some headway. However, no results have been
ly effects plant activity and often leads growers to reported on solar radiation distribution in full-scale
over fertilize, as has been observed for lettuce tunnels with vent openings, side walls and gable
crops [6]. end effects.
A number of experimental and theoretical stud-
ies on solar transmittance in different greenhouse The objectives of this study were to generate a
types have already been performed. Spectral prop- computer model to simulate radiative heterogene-
erties of several greenhouse cover materials have
ity at the greenhouse floor level as a function of
been measured both in laboratory [12] and field
greenhouse geometry, covering material and
conditions [7]. Solar radiation transmittance of a
weather conditions. Solar radiation distribution at
single span greenhouse has also been investigated
the greenhouse floor level was defined using both
experimentally using a scale model [13].
Modelling solar radiation transmittance was car- measurements and simulations to demonstrate the
ried out in early 1970s. Smith and Kingham [14] theoretical model's accuracy and to compare results
computed direct and hemispherical radiation trans- with simulations performed for different tunnel ori-
mittance by evaluating the fraction of ground area entations and covering materials. Simulation
irradiated by a transmitted beam and Kozai and his results were first experimentally tested based on
co-workers [8, 9] performed a study on radiation solar radiation measurements using 32 solar cells
transmittance in single and multi-span greenhous- at the soil surface along 4 vertical sections, either
es. Their model ignores all reflected light and in the tunnel centre or near the west gable end. The
effects of polarisation. But later Thomas [15] stud- validated model was then used to map radiative
ied the effect of a speculatively reflecting material heterogeneity in both E-W and N-S orientated tun-
on the north wall of an E-W single span green- nels under different typical radiative conditions
house. His model accounts a sophisticated method during various periods of the year near Avignon
of ray tracing. Amsen [1] established an interesting (latitude: 44° N, southern France).
 Solar radiation distribution in greenhouse tunnels 43

Agriculture and Environment

2. Computer model where x', y' and z' are the Cartesian co-ordinates
for positions on the cover surface, Sd and SD are
external diffuse and direct solar radiations (W·m-2),
Modelling solar radiation transmittance in a Sg and Sg(x', y', z') are external and internal global
plastic tunnel is a very complicated task due to the solar radiations (W·m-2), τd and τD are diffuse solar
influence of covering material, greenhouse struc- and direct transmittances of the tunnel's elementary
ture (frames, vent openings, side walls and gable surface (A'B'C'D').
ends) and weather conditions. To simplify the To further simplify the model, it was assumed
model, continuous curved surfaces of the arched that radiation transmittance was zero for tunnel
tunnel were approximated using a finite number of frames and 1 for vent openings. The experimental
small flat planes. Secondary reflections from inner value of the transmittance of the plastic cover used
cover surfaces and soil surface were omitted. in this study was a function of incidence angle α in
Global solar radiation transmitted through a given rad of radiation determined by Nijskens et al. [12].
surface (A'B'C'D') with a slope angle β in rad [11] Transmittance values of 0.69, 0.64, 0.62, 0.59, 0.29
was then calculated and projected as a “shadow and 0 for direct solar radiation at incidence angles
area” (ABCD) on the soil surface (Fig. 1): of 0°, 15°, 30°, 45°, 60° 75° and 90° with 0.69 for
diffuse solar radiation were used in this study. The
1 + cosβ actual direct solar transmittance as a function of
S g x', y', z' = τ D⋅S D + τ d⋅S d⋅ (1) the incidence angle was linearly interpolated. This
2
incidence angle for a surface is given by de
Halleux [5] and Kurata et al. [10] as follows:
with
α = arccos[cosγ cos(θ – ψ) sinγ cosβ] (3)
SD = Sg – Sd (2)
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' cosψ / tgγ (4)
y = y' – z' sinψ / tgγ . (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:
Figure 1. Definition of angles related to the sun's posi-
tion and schematic illustration of solar radiation trans- 1) Initialization of the date, solar time, tunnel
mitted and reaching on the soil surface (α: incidence location and orientation along together with the co-
angle of the area A'B'C'D'; β: slope angle of the surface; ordinates of each of the cover's elementary planes
γ: solar altitude angle; ψ: solar azimuth). (A'B'C'D');
44 S. Wang, T. Boulard

2) Calculation of solar height γ and azimuth ψ; 3. Experimental design

3) Calculation of slope β and orientation θ,
angles for each of the tunnel cover's elementary 3.1. Site and tunnel description
planes;
Measurements were conducted in a standard 8 m
4) Determination of the incidence angle of direct wide E-W orientated lettuce tunnel situated near
solar radiation α, using relationship (3) for each of Avignon in southern France (44° latitude). Tunnel
the cover's elementary planes; dimensions were 8 × 60 m with a top height of
5) Computation of internal global solar radiation 3.1 m. Traditional discontinuous vent openings
Sg (x', y', z') for each of the cover's elementary were included. They were formed by separating
planes using relationship (1); plastic sheets using 0.4 m long pieces of wood
placed every two meters along both sides of the
6) Determination of the “shadow area” projected tunnel. A layout of the tunnel illustrating vent
by each of the cover's elementary planes on the openings is shown in Figure 2.
tunnel's soil surface using relationships (4) and (5);

7) Calculation of averaged daily global solar 3.2. Measurement instruments

radiation by integrating and averaging daily solar
radiation received at a given position on the soil Solar radiation distributions were measured
surface. Finally, average daily transmittance of using 32 silicon solar cells set up along four sec-
global solar radiation was deduced for each posi- tions in the middle of the tunnel or near the west
tion using the ratio of daily integral global solar gable end (Fig. 2). Extensive tests were performed
radiation on the soil surface in the tunnel to outside prior to using these solar cells to check that output
radiation. 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

Agriculture and Environment

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).
Figure 3. Outside global () and diffuse (—) solar
radiation under cloudy and clear skies during measure-
ments.
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- Figure 4. Measured (+) and calculated (  ) daily aver-
iments or simulations. However, an underestima- aged transmittances of global solar radiation in the tun-
tion of simulated transmittance in the north part of nel centre along Sections 1 (a), 2 (b), 3 (c) and 4 (d)
the tunnel was observed. Similar results were under cloudy weather conditions (Feb. 24).
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 omitted in simulations. This secondary reflectance
two successive openings below the cover (Sect. 3). yielded an important effect as the inner surface of
Larger discrepancies were found on the north side the north side, which was shaped like a parabolic
(Figs. 4 and 5), probably because secondary mirror, focused reflected solar radiation on the tun-
reflectance on the north inner cover surfaces was nel soil surface near the north wall.
46 S. Wang, T. Boulard

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

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).

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 Figure 6. Measured (+) and calculated (  ) daily aver-
cloudy and clear skies respectively. In both cases, aged transmittances of global solar radiation near the
transmittance was much lower than in the tunnel tunnel west wall along Sections 1 (a), 2 (b), 3 (c) and 4
(d) under cloudy weather conditions (March 4).
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- shows average measured and simulated transmit-
od. Generally, agreement between the computed tances during cloudy (0.40 compared to 0.42) and
and measured transmittances near the gable end sunny days (0.46 compared to 0.49).
was good in all sections under both cloudy and Table II shows that transmittance loss near the
clear weather conditions (Figs. 6 and 7). Table II gable end was very high: 13% during cloudy days,
 Solar radiation distribution in greenhouse tunnels 47

Agriculture and Environment

Table 2. Averaged transmittances near tunnel side wall. 4.2. Model application

Cloudy conditions Sunny conditions Once the computer model was validated in the
Sections (March 4) (March 7) tunnel centre and near the gable end under both
cloudy and clear conditions, it could reasonably
Measurement Simulation Measurement Simulation
and reliably be used to predict solar radiation dis-
tribution in similar tunnel types with different ori-
1 0.37 0.41 0.43 0.47 entations at different seasons in Avignon latitude.
2 0.41 0.41 0.46 0.50 This simulated tunnel (22 × 8 m2) was assumed to
3 0.41 0.43 0.46 0.49 be equipped with discontinuous vent openings
4 0.42 0.43 0.48 0.50 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
Mean 0.40 0.42 0.46 0.49 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.
Figure 7. Measured (+) and calculated (  ) daily aver-
aged transmittances of global solar radiation near the Solar radiation distributions over the ground sur-
tunnel west wall along Sections 1 (a), 2 (b), 3 (c) and 4 face in both E-W and N-S orientated tunnels on
(d) under clear weather conditions (March 7). 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
10% during sunny days. However, this value was homogeneous than in N-S orientated tunnels.
slightly smaller than transmittance loss (16%) Higher solar radiation values were observed in the
observed between the middle of the tunnel and the center of the N-S orientated tunnel during summer
sides when transversal heterogeneity was consid- due to a relatively smaller solar radiation angle of
ered. incidence in the top part of the cover. Higher
48 S. Wang, T. Boulard

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

values were also found for the same orientation comparing average values and standard deviations
below the vent openings where radiation penetra- (for the E-W and N-S orientated tunnels: Tab. III).
tion was heightened by the absence of a plastic If x and y represent respectively transversal and
cover. longitudinal directions at the soil surface, three dif-
Statistical analysis of radiative heterogeneity ferent standard deviations can be calculated:
was performed both on March 21 and June 21 by global, σx,y; transversal, σx,-y and longitudinal, σ-x,y.
 Solar radiation distribution in greenhouse tunnels 49

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).

Solar radiation in the N-S orientated tunnel was 5. Conclusions

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

reflectance on the inner surface of the north side [5] De Halleux D., Modèle dynamique des échanges
cover was omitted. énergétiques des serres : étude théorique et expérimen-
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