Plant Distribution
Resume:
Int J Biometeorol (****) **: *** ***
ORIGINA L ARTI CLE
Xiping Wang . Yan Guo . Baoguo Li .
Xiyong Wang . Yuntao Ma
Evaluating a three dimensional model of diffuse
photosynthetically active radiation in maize canopies
Received: 18 July 2005 / Revised: 25 February 2006 / Accepted: 8 March 2006 / Published online: 9 May 2006
# ISB 2006
Abstract Diffuse photosynthetically active radiation against DPAR measurements made in an actual maize (Zea
(DPAR) is important during overcast days and for plant mays L.) canopy over selected days during the early filling
parts shaded from the direct beam radiation. Simulation of stage. The simulated and measured DPAR at different
canopy depths showed a good agreement with a R2
DPAR interception by individual plant parts of a canopy,
separately from direct beam photosynthetically active equaling 0.78 (n=120).
radiation (PAR), may give important insights into plant
Keywords Canopy . Diffuse photosynthetically active
ecology. This paper presents a model to simulate the
radiation . Maize . Model . Plant architecture
interception of DPAR in plant canopies. A sub-model of a
virtual maize canopy was reconstructed. Plant surfaces
were represented as small triangular facets positioned
Introduction
according to three-dimensionally (3D) digitized data
collected in the field. Then a second sub-model to simulate
the 3D DPAR distribution in the canopy was developed by Incoming solar radiation is a very important aspect of crop
dividing the sky hemisphere into a grid of fine cells that eco-physiology because it is a major element in the energy
allowed for the anisotropic distribution of DPAR over balance and the only source of energy for photosynthesis.
the sky hemisphere. This model, DSHP (Dividing Sky There are two components of this radiation into canopies,
Hemisphere with Projecting), simulates which DSH i.e. direct and diffuse solar radiation. The diffuse radiation
(Divided Sky Hemisphere) cells are directly visible from into plant canopies comes from both the sky diffuse
a facet in the virtual canopy, i.e. not obscured by other radiation penetrating directly through canopy gaps and
facets. The DPAR reaching the center of a facet was from complementary radiation scattered by phytoelements.
calculated by summing the amounts of DPAR present in For photosynthetically active radiation (PAR), the incident
every DSH cell. The distribution of DPAR in a canopy was sky diffuse radiation penetrating through canopy gaps may
obtained from the calculated DPARs intercepted by all be considered as the predominant component of diffuse
facets in the canopy. This DSHP model was validated PAR (DPAR) into crop canopies and the scattered compo-
nent may be omitted in the estimation of the total PAR into
plant canopies (Brunner 1998; Sinoquet et al. 1998; Grant
X. Wang . Y. Guo . B. Li . Y. Ma 1999; Alados et al. 2002).
It is difficult to make an accurate representation of the
Key Laboratory of Plant-Soil Interaction,
Ministry of Education, College of Resources and Environment, diffuse radiation distribution into canopies because of the
China Agricultural University, complexity of the distribution of diffuse radiation over the sky
Beijing, 100094, People s Republic of China
and the complexity of crop architecture (Ross 1981; Grant
e-mail: ****@***.***.**
1997, 1999; Brunner 1998; Alados et al. 2002; Jonckheere et
Tel.: +86-10-062******
Fax: +86-10-627***** al. 2004). Furthermore, the intensity of sky DPAR is usually
much less than that of direct beam PAR under clear sky
X. Wang
conditions (Grant and Heisler 1996; Grant 1999; Wang et
College of Resources and Environmental Sciences,
al. 2004). Thus, research into the distribution of diffuse
Hebei Normal University,
Shijiazhuang, 050016, People s Republic of China radiation is limited and the penetration of diffuse radiation
into canopies has been arbitrarily simplified to an
X. Wang
exponential or other statistical extinction functions in
Department of Computer and Information Science
the canopy (Ross 1981; Ross and M ttus 2001; Zhao et al.
and Engineering, University of Florida,
2003; Annandale et al. 2004).
Gainesville, FL 32611, USA
350
environment. This approach was a great step forward in
Nonetheless, diffuse radiation is able to penetrate into
the precise modelling of radiation into canopies and would
parts of canopies shaded from direct beam radiation and it
be a significant aid to physiological crop modelling.
is the dominant form of solar radiation on cloudy days. It is
However, with direct and diffuse radiation combined
especially important for solar radiation in canopies of high
together as the radiosity environment, the calculation of
planting density into which direct beam radiation pene-
sky diffuse radiation into canopies was very complex and
trates relatively little (Grant 1997; M ttus 2004; Wang et
computationally demanding. In addition, it was difficult for
al. 2004, 2005). Therefore, it is essential to understand how
it to be parameterized for real crops (Chelle and Andrieu
the diffuse radiation component varies in estimating the
1998, 1999).
radiation distribution in plant canopies.
Diffuse radiation is usually assumed unrealistically to be
Modelling is widely used as an efficient way to obtain
isotropically distributed across the sky (Hanan and Begue
the necessary information on the distribution of solar
1995; Chelle and Andrieu 1998; Sinoquet et al. 1998; Zhao
radiation in canopies (Chen et al. 2000; Zhao et al. 2003;
et al. 2003), or the anisotropic distribution of diffuse
Annandale et al. 2004; Choudhury 2001; M ttus 2004).
radiation is dealt with in a simple manner in order to model
Statistical models are efficient ways to obtain information
the distribution of diffuse radiation in canopies (Dauzat and
on the vertical distribution of diffuse radiation in canopies.
Eroy 1997; Dauzat et al. 2001). However, the anisotropy of
However, these models do not contain detailed representa-
tions of how diffuse radiation varies between different diffuse radiation under overcast conditions tends to vary
plant parts (Ross 1981; Grant and Heisler 1996; Thornley with air quality, types and distribution patterns of clouds in
1998, 2004; Grant 1999; Ross and M ttus 2001; Zhao et al. the sky. In clear skies, diffuse radiation is much more
2003; Annandale et al. 2004). anisotropic and its maximum intensity is found close to the
It is possible to simulate the DPAR regime in canopies position of the sun (Temps and Coulson 1977, Grant 1999).
based on a three-dimensional (3D) canopy structure and the Consequently, to simulate diffuse radiation in plant
directional distribution of DPAR over the sky. A more canopies sufficiently precise for crop eco-physiology
detailed kind of diffuse radiation modelling in plant studies, it is essential to combine the anisotropical distri-
canopies is the hemisphere photograph model (Fournier bution of sky diffuse radiation with its precise interactions
et al. 1996; Sinoquet et al. 1998; Brunner 1998; Dauzat et with phytoelements.
al. 2001; Frazer et al. 2001; Jonckheere et al. 2004). Our study reports on the development and validation of a
Generally, these models estimate the penetrated diffuse model, the Dividing Sky Hemisphere with Projection
radiation through the calculation of the gap fraction over (DSHP) model, used to simulate the 3D distribution of
the sky hemisphere based on plant geometry models. They incident DPAR into plant canopies. That model calculated
can give more detailed representations of crop geometry the fraction of viewable sky by using a particular divided
and diffuse radiation distribution in canopies than statistical grid sky hemisphere with the centre projection of
models. For example, the TURTLE model originated by phytoelement. The DSHP model divided the sky hemi-
Den Dulk (Sinoquet et al. 1998, Dauzat et al. 2001), in sphere into fine grid cells and was able to handle both the
which the sky hemisphere was divided into 46 hexagonal anisotropic distribution of sky diffuse radiation and the
sections like a turtle shell, has been widely used in diffuse heterogeneous distributions of canopy elements. The 3D
radiation modelling. Plant images were projected onto crop structure in this model was reconstructed from 3D
every section of the turtle hemisphere based on various digitizer measurements of plant architecture in the field.
plant geometry models, and the diffuse radiation penetra- In China, higher density planting of more compact plants
tion into canopies was calculated using gap proportion has increased maize yield significantly, and continued
statistics. In most cases, these models were used for large research into crop eco-physiology is still essential to
canopies, mainly of trees (Dauzat and Eroy 1997; Sinoquet maintain and improve maize production efficiency (Xue et
et al. 1998; Dauzat et al. 2001; Jonckheere et al. 2004). The al. 2002, Maddonni et al. 2002). During the later part of the
TURTLE model may lead to obvious bias in the statistics of growing season, the PAR distribution in a maize canopy is
the gap fraction when used for plants of small scale (like important for the yield, so the DSHP model was first built
most field crops) by using parallel projection to calculate and validated over selected days in the early grain filling
the gap fractions for the 46 turtle sections along with the stage of maize.
statistical assumptions for geometry models. This concern
is especially so for crop eco-physiological studies in which
Materials and methods
radiation inputs for individual organs are needed, like
maize (Zea mays) that has higher foliage densities and
relatively large and long leaves, for which radiation Field experiment
conditions at specific leaves or cobs are likely to have
greater impacts (Rosati and Dejong 2003). Modelling of The field experiment was carried out at the farming station
of China Agricultural University in Beijing (39 59 N, 116
diffuse radiation for such crops requires a much finer scale.
17 E), China. Maize (Zea mays L. variety ND108 ) was
Chelle and Andrieu (1998) made a nested radiosity
planted on 8 May 2002 in north south rows. There were
model with more detailed information of radiation prop-
agation into a crop canopy in which incident direct and two plant density treatments, both using 0.6-m row
diffuse solar radiation was computed as a radiosity spacing. Plant spacing was 0.3 m in the high-density (H)
351
treatment (standard farming density) and 0.6 m in the low- A mast (Fig. 1) for the AccuPAR ceptometer was built,
density (L) treatment (one-half standard density). There comprising a horizontal base plate, a vertical post 2.2 m in
were four plots, two low-density and two high-density, height, a horizontal arm 1.2 m in length that could move up
each 11 m (N S) 17 m (W E), lined up from south to and down the vertical post, a box to hold the AccuPAR
north (H-H-L-L). Maize, bean, cotton and grass were controller that could slide along the arm to make the PAR
growing in the area around the plots. The closest building measurement at different positions, and a base for the LI-
was 300 m to the west and was 3 m in height. 190SA at the top of the vertical post. There were rulers on
Plant architecture and intensity of PAR (PPFD, photo- both the vertical post and the horizontal arm for AccuPAR
synthetic photon flux density) were measured in sub-plots positioning. The support was painted black to minimize
(MSP) located in the middle of the most northerly of the light reflection.
high- and low-density plots. Each MSP contained 3 Measurements were made for a combination of heights
plants 4 rows in the low-density treatment, and 5 plants 4 and horizontal positions between the middle two rows of
rows in the high-density treatment. The areas of the MSPs the low-density and high-density MSPs. The heights were
were (3 plants 0.6 m) (4 rows 0.6 m)=4.32 m2 and (5 0.11 and 0.26 m, and at increments of 0.20 m to a
plants 0.3 m) (4 rows 0.6 m)=3.6 m2 for low and high maximum of 2.16 m in the low-density treatment, and
2.26 m in the high-density treatment for a total of 12
density treatment, respectively.
measurement heights in each canopy. Both have 12 height
The field measurements for model validation were made
levels. The horizontal positions were 0, 0.15, 0.3, 0.45,
between 7 and 16 August 2002. In and above canopy PAR
0.6 m from the eastern row for all the heights. It took about
was measured between 7 and 11 August and 3D canopy
30 min to complete a measurement for all levels. The
digitizing was taken between 12 and 16 August 2002. The
measurement for all the 12 levels was made every 2 h from
maize during this time was in the early grain filling stage
about 0800 to 1900 hours. It was bright sunshine with clean
and the canopy heights for the low-density and high-
air between 7 and 9 August and overcast with clean air on
density treatments were 2.4 and 2.6 m, respectively. There
were 13 15 green leaves on every stem in both densities. It 11 August 2002. There was little wind on those days.
In another maize plot 15 m to the north of the
was assumed that the plants did not change during these
experimental site, where plants were at the 7 leaf stage
measurements.
with canopy height about 0.3 m, global PAR above the
canopy was measured between 7 and 11 August 2002 at
different solar times, from 0800 to 1900 hours, by fixing
Measurement of plant architecture
the AccuPAR probe 1.5 m above the ground with the
sensors upright. The sky DPAR was measured about every
For the measurement of above-ground architecture of all
2 h while holding a black disk of 0.1 m diameter at 0.6 m
the plants in the MSPs, the 3D spatial coordinates of points
above and shading some of the AccuPAR sensors. The
on leaves and cobs were recorded using a Fastrack 3D
digitizer (Polhemus, USA) connected to a laptop computer.
The average distance between measured points was
approximately 25 mm. On the leaves, points were selected
on both margins and on the median veins. The points were
closest together where the margins were most irregular. On
cobs, points were digitized along two lines from the base to
the tip on opposite sides of the cob, one line being along the
uppermost surface and the other along the lowermost
surface. All digitized points were referenced to the 3D
coordinates of the base of each plant that was in turn
referenced to its position in the MSP.
Measurement of PAR in and above maize canopy
PAR at numerous points at different levels in the canopy
between the middle two rows of MSPs was measured using
an AccuPAR Linear PAR/LAI ceptometer (Decagon
Devices, USA) on which there were 80 sensors (Photo-
diode type GaAsP) at 10-mm intervals along an 800-mm
probe. An above canopy PAR sensor (LI-190SA, Silicon
Photovoltaic Detector, LI-COR, USA) was also connected
to the AccuPAR. The AccuPAR was set to collect all the 81
PPFD (400 700 nm) values simultaneously by the 81 Fig. 1 The equipment used for measuring the 3D distribution of
sensors at every reading, from which the 81 values together PAR in maize (Zea mays) canopies. a Base plate, b vertical post,
were called one record. c horizontal arm, d AccuPAR and e LI-190SA sensor
352
shaded sensors measured sky diffuse PPFD (DPPFD) from
the whole sky dome except for the area covered by the disk.
The total sky DPPFD was obtained by a correction
depending on the solid angle covered by the disk. Sensors
not shaded by the disk gave the total PPFD.
Three-dimensional canopy reconstruction
A static virtual canopy was reconstructed by representing
all surfaces (leaves, stems, cobs, and the ground) as
triangular facets positioned according to the 3D coordinate
data collected in the field using the Fastrack digitiser
(Fig. 2; Wang et al. 2005). For all facets, the maximum
length of a side was 0.02 m. Leaf blades were divided into
facets fitted between the leaf edges and midribs positioned
Fig. 3 Projection method applied in calculation of the portions of
by linear interpolation and by fitting a B-spline to digitized the sky directly visible from the center (point O) of a facet in the
points (Fig. 2a). Cob and stem facets were positioned by canopy model. A hemisphere was considered centred on O and
assuming the geometrical shapes shown in Fig. 2b and c. triangles ABC and DEF are examples of two facets in the model.
Triangles A B C and D E F are projections of these facets onto the
The ground and horizontal planes at other heights were
hemisphere and represent areas of the sky from which radiation
represented as facets by subdivision into rectangles, which could not be received. This hemisphere projection method was
were then divided into triangles (Fig. 2d). based on Renaud et al. (1995)
DSHP modelling of distribution of DPAR in maize The intensity of DPAR in each portion of the sky was
canopies estimated by dividing the hemisphere representing the sky
dome into a grid of cells and then calculating the mean
The basic idea of the DSHP model was that the DPAR intensity of DPAR in each cell (Fig. 4). This method was
derived from the turtle sky concept of Den Dulk
reaching each facet in the model canopy was calculated
from the portions of sky directly viewable through gaps in (Sinoquet et al. 1998, Dauzat et al. 2001) who divided
the canopy combined with the intensity distribution of the sky hemisphere into 46 sectors. The model described in
DPAR on the sky hemisphere. Portions of the sky visible our study is more precise because it divides the sky
from the center point of every facet were the portions not hemisphere into much finer cells. The hemisphere was
obscured by any other facets over the sky dome. The divided into 5,000 quadrilateral cells by assuming the
obscured portions were calculated using method shown in presence of one set of 100 lines intersected by a second set
Fig. 3 (hemisphere projection algorithms referenced from of 100 lines [N=100 in Eq. (2)] in the model execution in
Renaud et al.1995). The diameter of the hemisphere was our model. There was an intersection located at the zenith.
Consider a point A (x, y, z) on the surface of the
4.0 m, chosen so as to fit the canopy calculation in the
model. hemisphere that represents one vertex of a projected facet
Fig. 2 The triangular facet
method in canopy reconstruc-
tion model applied to a leaves,
b cobs, c stems and d the plane
surface of maize
353
each cell along the i th contour line, Si, was obtained by
Eq. (5) in which S0 was the area of each cell on the top.
Si S0 sin (5)
Consider the facet ABC in Fig. 3 and its projection A B C
on to the surface of the hemisphere. All the cells within
triangle A B C on the surface of the hemisphere were
labeled as covered, indicating that no light could pass
through them. After all facets in the canopy models were
projected onto the hemisphere and the covered cells were
labeled, the remaining uncovered cells were identified.
The quantum of DPAR penetrating through every un-
covered cell could be determined according to the cell
direction originating from the center point O in Fig. 4, if the
distribution of sky DPAR was known. The amount of
DPAR reaching point O was then obtained by summing the
DPAR passing through all of the uncovered cells.
Edge effects would have led to major errors if the model
of an MSP alone had been used to represent the canopy of
the whole field. To overcome this, the DSHP model
Fig. 4 A simplified illustration of a quarter of the projection increased the virtual canopy size horizontally by copying
hemisphere divided into cells by crossed arcs of latitude (u) and
the model of each MSP (copied MSP, CMSP) so that the
longitude (v). O is the center of the projection hemisphere and P is
calculation MSP was surrounded by the copies of itself.
the zenith. The dashed lines (i) are contour lines for angles of
Increasing the number of CMSP is computationally
elevation of the centers of cells
expensive. For example, there were approximately
shown in Fig. 3. Its angle, representing the angle apart 114,000 facets in the model of the low-density MSP canopy.
For each of these, all the remaining facets in calculation
from the zenith P, can be found using Eq. (1).
MSP except the one under consideration, plus all the facets
in the surrounding CMSP model, need to be projected onto
y
arccos p (1) the hemisphere to calculate the incoming DPAR. Thus, there
x2 y2 z2 would be approximately 114,000 (25 114,000) calcula-
tions for the low-density treatment surrounded by 24
Contour lines for are shown in Fig. 4 in dotted lines. CMSPs. To find the minimum number of CMSPs
The serial number for these contour lines, i, can be surrounding the center MSP needed to give realistic results,
calculated using Eq. (2). the mean fraction of sky obscured was calculated for all
facets on virtual planes at heights of 0.2 and 1.4 m using 24,
N 80 and 288 CMSPs for the low-density treatment and 24 and
i (2)
=2 80 CMSPs for the high-density treatment.
Where N is the dividing line number and it equals to the Field validation of DSHP model
maximum of i in Eq. (2) and of u, v in Eq. (3, 4).
The grid coordinates (u, v) of point A with respect to the Assuming that intensities of reflected and transmitted PAR
origin at P are determined using Eq. (3) to (4) where i, u, v in green plant canopies were very low, the incident sky
are integers: DPAR was usually the major component of DPAR in
canopy (Grant 1999). Consequently, model calculations of
i x incident DPAR could be evaluated by comparison with
arcsin p
u (3)
=2 PAR measured in the field by AccuPAR sensors. When
x2 z2
there were no clouds in the sky, the flux intensity of DPAR
was less than the direct beam PAR. Consequently, when an
AccuPAR sensor registered radiation intensity was less
i z
arcsin p
v (4) than the direct solar PAR calculated from the reading of the
= 2 x2 z 2 LI-190SA sensor above the canopy, the AccuPAR sensor
was assumed to be shaded by plant elements and exposed
Finally, the sky hemisphere was divided into cells that to the DPPFD. For every measurement height in the
were the largest at the top of the hemisphere, being 1.57 canopy, the average of PPFD readings that were less than
times as large as cells around the base. Then the area of direct solar PAR were considered to be DPAR, and these
354
Table 2 Influence of the number of copied Measured Sub-Plot
values were compared with the simulated average DPPFD
(MSP) on the calculated gap fractions at different heights in the low-
to evaluate the model behavior. density virtual canopy
It took about 5 days to complete the calculation of DPAR
Height Number of copied Gap fraction of the MSP canopy
for the 12 planes at heights from 0.11 to 2.26 m using
DSHP model with 24 copied MSPs. To reduce the (m) MSPs computing time for model validation, as well as the
0.2 24 6.63
difficulty to treat the uncertainty of the regularity of DPAR
80 2.38
distribution over the sky in the days of measurement, it was
288 1.94
assumed that sky PAR was distributed uniformly over the
1.4 24 9.54
sky and was not affected by solar position in model
80 9.50
execution for validation. This reduced computation by
2.0 24 41.02
simplifying the calculation of DPAR to the fraction of the
80 40.78
viewable sky that was simply equal to the area percentage
of cells that was uncovered on the sky hemisphere.
To evaluate the influence of the anistropic distribution of
DPAR over the sky, the simulated canopy DPAR from an 0.44% when viewed from 0.2 m height. These results
assumed anistropic distribution pattern of DAPR over the suggested little increase in accuracy was obtained by
sky was compared to the isotropic simulated and measured increasing the number of copied plots beyond 24, so in all
DPAR in canopy. According to the general idea about the subsequent calculations 24 CMSPs were used.
distribution pattern of the sky diffuse radiation in sunshine
condition (Temps and Coulson 1977, McArthur and Hay
1981), the anistropic DPAR distribution was assumed to be Calculations of DPAR and validation of DSHP model
maximum around the direction of the sun, being 1.5 times
the mean DPAR flux intensity. The minimum was opposite Regression analysis from the measured PAR data in field
to the sun, being 0.5 times the mean DPAR flux intensity showed that the ratio of sky DPAR to global PAR were
(see details in Table 1). linearly related to global PAR above canopy. DPPFD above
A copy of the DSHP software may be obtained by the canopy could be calculated by Eq. (6).
emailing the author at "******@****.*****.***.**."
Qd0 Qt0 0:0336 Qt0 26:69 Qt0 100 (6)
2
R 0:68; n 71
Results
where Qt0 is the global PPFD ( mol m 2 s 1) above the
Determination of the number of CMSP to reduce the
edge effects canopy and Qd0 is sky DPPFD above the canopy. The
DPPFD intercepted by a facet, Qd, was calculated by
Increasing the number of CMSPs for the low-density multiplying the transmittance of sky DPAR, Rd that was
treatment from 24 to 80 resulted in 4.25% and 0.04% calculated from the DSHP model, by the sky DPAR above
changes in the fraction of sky obscured at 0.2 and 1.4 m, canopy (Qd0) (Eq. (7)).
respectively (Table 2). Increasing the number of CMSPs
Qd Qd0 Rd (7)
from 80 to 288 increased the fraction of sky obscured by
Table 1 Anisotropic distribution of diffuse photosynthetically
The DSHP model calculates the fraction of the viewable
active radiation (DPAR) over the sky as a function of varying
zenith and azimuth angles for around 1500 hours on 7 Aug 2002 sky, the transmittance of sky DPAR, the DPPFD for a
single point in the canopy, and their distributions in a MSP.
Direction Range of zenith Range of Ratio of DPAR
The simulation results could be visualized in various ways,
azimuth*a density relating to
e.g., Fig. 5 shows the distribution of intercepted DPAR in
different directions
the MSP canopy. The intensity of DPAR in the maize
40 55 240 canopies changed obviously with height from ground
Toward 1.5
(Fig. 6), but changed little horizontally as shown in Fig. 5,
sun 255
5 35 60 75 where the graded color changed very little at the same
Opposite 0.5
to sun*b height.
There was a good agreement in trend between observed
Mean Whole sky dome except 1.0
and calculated DPPFD from both high- and low-density
over the the above zenith and
treatment (Fig. 6) and the correlation coefficient (R2) was
sky azimuth angles
0.76 (n=120; Fig. 7). The calculated values were
a
Azimuth is defined 0 at N and goes clockwise, 180 at S, 270
significantly less than observed values in the low-density
at W, etc.
canopy on clear days and close to solar noon. Generally,
b
The solar zenith and azimuth angles were around 45 and 250,
respectively
355
400
DPPFDsim = 0 .79DPPFDobs+ 0.29
R 2 = 0 .76 n =120 ME=20.78
1:1
300
DPPFD sim ( mol m -2 s-1)
200
100
0
DPPFDobs ( mol m -2 s-1 )
Fig. 7 Estimated vs. observed average diffuse PAR at different
Fig. 5 Calculated percentages of incident DPAR received by
heights in the low density (0.11 2.16 m) and high density (0.11
various parts of the virtual MSP model of the low-density canopy
2.26 m) maize canopies at different times of the day. DPPFDsim and
when it was surrounded by 24 copies of itself (CMSP). It looks
DPPFDobs are simulated and observed diffuse photosynthetic photon
horizontally homogeneous because the simulated DPPFD (Diffuse
flux density respectively
photosynthetic photon flux density) varied between 6 to more than
400 mol m 2 s 1 vertically from ground to the top of canopy, but
only varied with a range of less than 30 mol m 2 s 1horizontally
approximately under 1.6 m from ground, of the high-
density canopy.
simulated DPPFD was lower than measured with a mean As an example to illustrate the influence of the
error of ME=20.78 mol m 2 s 1 (Fig. 7). anisotropic distribution of sky DPAR on the DPAR
Figure 6 shows the same trend in measured and distribution in the canopy shown in Fig. 8, the trends of
simulated data for the plant density treatments. DPAR simulated DPPFD from both isotropic and anisotropic
penetrated more in the low-density canopy than in the high- distributions were generally similar in the lower density
density canopy, especially in the lower canopy layers. maize canopy for sunshine during the afternoon on 7
Also, the DPAR was very low in the lower canopy layers, August 2002. But the simulated DPPFD from anisotropic
450
Observed
400
Simulated
Low densit y t reatment High densit y t reatment
350
300
PPFD ( mol m -2 s-1 )
250
200
150
100
50
0
Aug 08 Aug 07 Aug 08 Aug 08 Aug 07 Aug 11 Aug 09 Aug 09 Aug 09 Aug 09 Date
18:00 08:00 16:00 10:00 14:00 16:00 18:00 16:00 09:00 12:00 T ime
Hours
6 4 4 2 2 4 6 4 3 0 departure
from noon
Fig. 6 Comparison of observed and simulated mean diffuse the sake of clarity. The heights were 0.11 and 0.26 m, and at
photosynthetic photon flux densities (DPPFD) at different heights increments of 0.20 m to a maximum of 2.16 m in the low-density
in low and high density maize canopies at different times of day. treatment, and 2.26 m in the high-density treatment for a total of 12
Results have been grouped according to different departures from measurement heights in each canopy. All observations were made
noon (approx. maximum solar elevation). Heights increased left to on cloudless days except for August 11, which was cloudy
right for every measurement and height scales have been omitted for
356
250
modelling. A strength of the DSHP model is that it
Ani-Sim provides the ability to take into account the anisotropic
Iso-Sim
200 DPAR distribution over the sky.
Obs.
DPPFD ( mol m -2 s-1)
A primary factor for the higher measured DPPFD over
the simulated DPPFD (with a ME equaling 20.78 mol
150
m 2 s 1) may be that the DSHP model did not take into
account multiple scattered radiation in the canopy. It was
100
reasonable to assume that this difference was more
apparent in the upper layers of the canopy, due to the
50 relative openness of this space compared to the lower,
denser canopy as shown in Figs. 6 and 7. From these
figures, one can see that the multiple scattering is a
0
significant component for DPAR estimation in the canopy.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
We are planning to incorporate the complementary DPAR
Height (m)
model in the next version of DSHP model.
Fig. 8 The comparison of observed (Obs) and simulated DPPFD Errors may have been introduced from the collection of
(diffuse photosynthetically photon flux density) at different heights field data. For example, a potential error may have come
in the lower density canopy by using isotropic (Iso-Sim) and
from the disturbance of the canopy during radiation
anisotropic (Ani-Sim) DPAR (diffuse photosynthetically active
measurement. The DSHP model requires detailed canopy
radiation) distributions over the sky dome around 1500 hours on 7
structure data. Future improvements in measuring the
August 2002. The anisotropic distribution was set according to
Table 1. It was assumed that the sky DPAR was the maximum canopy structure will open more opportunities for this
towards sun direction (1.5 times the mean DPAR intensity over the
model.
sky) and minimum opposite to sun direction (0.5 times of the mean
A modelling error may have also come from the
DPAR intensity over the sky)
statistical analysis of the field PAR data. Firstly, Eq. (6)
for the estimation of DPAR above the canopy was based on
distribution tended to be higher than that from isotropic. the data representative of the selected days in this study.
The results from the anisotropic distribution pattern were Another potential error may have come from the method-
better fitted the measured results. Both isotropic and ology to obtain DPAR from the sensors recording global
anisotropic simulation deviated from the measurements in PAR in the canopy. Particularly in the upper canopy, there
the higher canopy layers. were less shaded sensors from which the DPAR was
collected. So the sampled points at every height in the
upper canopy were fewer than in the lower canopy layers.
Discussion This sampling difference may have increased the random
error in the measured results.
The DSHP model used for calculating the intercepted Both the simulated and observed DPAR showed little
DPAR in canopies is based on the 3D measured canopy increase in the lowest canopy layers along with the height
structure, determinate 3D geometric calculations, and the above from ground (Figs. 7 and 8). The reason for this
physics of propagation of diffuse radiation into canopies. In result may be the increased gap fraction near horizontal due
theory, this model could calculate the penetrated DPAR to the sparse leaf distribution at the bottom of the canopy,
precisely at any position in a canopy. and it may be enhanced by the limited canopy size in this
There were several factors that could introduce errors in study. In general, the DPAR was very low (Fig. 6) in the
this model. The most important error source in the DSHP lower layers in high density treatment where the sunfleck
validation in this study was the assumption of a uniform distribution was also very low (Wang et al. 2004). This
distribution of DPAR across the sky hemisphere. The means that there would be little PAR distributed in the
anisotropy of the sky PAR distribution varies strongly with lower canopy layers when the plant density was high.
air conditions in a complicated way (Grant and Heisler In this study, we validated the DSHP model only with
1996; Grant 1999). In clean air, the maximum sky PAR is the data from the early filling stage of maize when the
distributed close to the direction of the sun and sky PAR plants had a stable structure. It allowed us to complete all
will always be at a minimum in a position in the sky dome the field measurement under almost the same crop canopy
opposite to the azimuth of the sun (Temps and Coulson structure.
1977; McArthur and Hay 1981). The field crop grows continuously. The topological plant
Comparing the simulated DPAR from the isotropic and architecture is different with different species. The leaf
anisotropic distribution patterns of DPAR in the sky reflectance and transmittance to PAR also varies with the
(Fig. 8), one can see that the simulated result was leaf age, plant development, species, etc, which influences
significantly improved by using an anisotropic distribution the amount of the complementary radiation in the canopy.
pattern. The anistropic distribution of DPAR over the sky Therefore, the DSHP model needs further evaluation under
was not measured in this study, thus the result in Fig. 8 was different development and environmental conditions.
only an example to show the influence of the DPAR The DSHP model presented here can be used to simulate
distribution pattern over the sky to the canopy DPAR global PAR in canopies by combining it with a model of
357
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