138 S. Khabba et al. Agricultural and Forest Meteorology 106 2001 131–146
Fig. 3. Vertical and a cross-row distributions of leaf area density. The number N
z
of layers was 6 in Morocco and 10 in Belgium, the number N
x
of slices was 5. The geometrical structure of the canopy is assumed symmetrical on both sides of inter-rows line.
The layer numbers refer to heights from the bottom to the top. The slice numbers refer to a cross-row, from the row to the inter-row
Fig. 2.
slices were taken between two rows for the two ex- periments. The geometrical structure of the canopy
was assumed symmetric on both sides of the row.
4. Results and discussion
4.1. Comparisons between radiation measured and simulated on horizontal plane at ear position
Before using the proposed model to estimate the ear stomatal resistance, the method used to calculate ear
radiation balance was tested. Measured and simulated downward and upward radiation, at ear position, are
presented in Fig. 5. The agreement between calculated and observed values was tested with linear regression.
For daytime measurements, slope of the regression lines was 1.06, the intercept 36.7 and r
2
= 0.87, and
Fig. 4. Vertical and cross-row distributions of mean leaf angle. The number N
z
of layers was 6 in Morocco and 10 in Belgium, the number N
x
of slices was 5. The geometrical structure of the canopy is assumed symmetrical on both sides of inter-rows line.
The layer numbers refer to heights from the bottom to the top. The slice numbers refer to a cross-row, from the row to the inter-row
Fig. 2.
Fig. 5. Comparison between measured and calculated sum of downward and upward radiation on a horizontal plane situated at
the same level as the ear. Calculations were made with Eq. 24
j
and + are hourly averages of 1 min readings, respectively, for daytime and night-time. Measurements were made in Belgium
from 14 to 23 September 1998. Line is X = Y . The equation of the regression line is presented.
S. Khabba et al. Agricultural and Forest Meteorology 106 2001 131–146 139
for night-time R
s
= 0, the values were 1.03, 18.2
and 0.90, respectively. 4.2. Stomatal resistance
In the absence of reference values for the stomatal resistance, our estimation was made by inverting the
model using measurements of ear temperatures in day- time conditions. We used ear temperatures data from
alternate days, i.e. 13, 15, 17, 19, 21 and 23 Septem- ber 1998 to determine mean hourly values of stom-
atal resistance of the husk leaves method described above. The data on ear temperatures from the other
days were used to test the model.
Stomatal resistance is affected by environmental factors among which solar radiation, R
s
, and water vapour deficit are the most important. Water vapour
deficit was represented by the difference between dew point and air temperatures. The difference T
a
− T
d
is partly related to R
s
. Since, stomatal resistance is inversely proportional to the solar radiation Norman,
1979, r
i
was plotted against T
a
− T
d
R
− 1
s
Fig. 6. The values less than 30 s m
− 1
correspond to rainy days 13 and 15 September 1998. These low values
of r
i
are linked to the presence of liquid water on the ear surface. Such increasing trends have often been
observed Carlson, 1991; Turner, 1991; Collatz et al., 1991; Cellier et al., 1993 but the most surprising
features of this figure are the low values taken by r
i
Fig. 6. Relation between ear stomatal resistance r
i
and the rela- tionship T
a
− T
d
R
− 1
s
. Each point is an hourly average. The equa- tion of the line is used to estimate r
i
in the model. T
a
, T
d
and R
s
are air temperature, dew point temperature and solar irradiance, respectively.
and the presence of an upper threshold. Some expla- nations can be put forward. 1 First, water vapour
could come from the inner of the ear and even from the gaps between the husk leaves; as a consequence,
the source surface for water vapour would be much larger than the simple external surface of the ear. 2
Second, the presence of dew accumulated inside the ear whose evaporation consumes a noticeable part of
incident radiation. 3 Third, particular physiological characteristics of the husk leaves may interfere; unfor-
tunately, we have no precise information on this point; 4 Fourth, neglecting the energy fluxes by stem flow
in and from the ear overestimates the available energy.
Stomatal resistance was assumed to follow a linear trend up to T
a
− T
d
R
− 1
s
= 2.4 and having a con-
stant value above that limit. The regression line drawn through the experimental points of Fig. 6 was
r
i
= 49.2±1.1T
a
− T
d
R
− 1
s
− 22.4±2.7
r
2
= 0.96, d.d.l. = 57
23 This relation was used in the model to calculate the
diurnal ear temperatures. During the night, a value of r
i
= 3000 s m
− 1
was chosen in order to account for the stomatal closure Norman, 1979.
4.3. Comparison between predicted ear temperature and measured ear and air temperatures
Fig. 7 shows this comparison for the days 14, 16, 18, 20 and 22 September 1998. The calculated accu-
racy of the model estimations are practically identi- cal for different ear orientations east, south, west and
north. Agreement between computed and measured ear temperature is good: for daytime R
s
6= 0 and
night-time R
s
= 0, mean residuals difference, d,
between simulated and measured values were 0.5 and 0.3
◦
C, respectively, standard deviations of d were 0.7 and 0.5
◦
C, respectively, and r
2
values were 0.94 n = 13 020; 5 days × 4 polar positions ≈ 651 min per day
and 0.89 n = 15 780, respectively. For the rainy day 14 September 1998, the model overestimated the ob-
served values. This was probably due to the presence of water on the ear surface whose evaporation con-
sumes a noticeable part of incident radiation. For that day, r
2
= 0.85. These results are quite satisfactory for
such a model using simple meteorological data.
140 S. Khabba et al. Agricultural and Forest Meteorology 106 2001 131–146
Fig. 7. Comparison between air temperature measured at a weather station dashed line and ear temperature mid-length of ear and at centre of grain measured solid line, and calculated dotted line from our model of ear temperature for the data collected in Belgium
on 14, 16, 18, 20 and 22 September 1998.
Model predictions were also compared with values observed in Morocco. We used Eq. 23 to estimate
stomatal resistance. The results, plotted in Fig. 8, are similar to those obtained in Belgium: mean residual,
d, standard deviations and r
2
values were 0.6, 0.9 and 0.87
◦
C n = 405, respectively. This indicated that Eq. 23 was valid for this other data set. The data
were used to estimate the relationship between r
i
and T
a
− T
d
R
− 1
s
, and was found to be almost identical to Eq. 23:
S. Khabba et al. Agricultural and Forest Meteorology 106 2001 131–146 141
Fig. 8. Comparison between air temperature measured at a weather station dashed line and ear temperature mid-length of ear and at centre of grain measured solid line and calculated dotted line from our model of ear temperature for the data collected in Morocco
on 11, 12, 13, 14 and 15 June 1997.
r
i
= 48.3±2.1T
a
− T
d
R
− 1
s
− 21.0±1.8
r
2
= 0.94, d.d.l. = 61
24 Statistical analysis Coursol, 1983 showed that the
differences between the coefficients of the two corre- lations were not significant P ≤ 0.05.
In Belgium, the mean difference between ear and air temperatures, for daytime and night-time, were 1.1
and 0.6
◦
C, respectively. Standard deviations of the difference were 1.4 and 0.8
◦
C, and r
2
values were 0.85 and 0.86 for day and night, respectively. In Morocco
Fig. 8, these values were 1.8, 2.2 and 0.86
◦
C for
142 S. Khabba et al. Agricultural and Forest Meteorology 106 2001 131–146
Table 1 Values of the parameters used for the sensitivity test
a
Parameter Constant values
Variable values Leaf area density, a
k
β = 60
◦
, 1φ = 180
◦
a
kB
× 0.5, 0.75, 1, 1.25, 1.5
Sun elevation, β a
k B
, 1φ = 180
◦
40
◦
, 50
◦
, 60
◦
, 70
◦
, 80
◦
1φ = φ
s
− φ
e
a
k B
, β = 60
◦ ◦
, 45
◦
, 90
◦
, 135
◦
, 180
◦ a
a
k B
: distribution of the leaf area density shown in Fig. 3 in Belgium, β: sun elevation, and 1φ: difference between sun and ear azimuths.
difference, standard deviations and r
2
, respectively. Values of mean difference between measured ear and
air temperatures are generally higher between solar noon and sunset mean of d was 1.8
◦
C in Belgium and 2.4
◦
C in Morocco. After reaching a maximum, the temperature of the grains decreased at a slower
rate than air temperature. During the two periods of measurements, maximum difference between ear and
air temperatures were found between 13 and 16 h UT; the largest differences were 2.1 and 3.6
◦
C in Belgium and Morocco, respectively. This can be ex-
plained by the considerable thermal inertia of maize ear Ledent, 1988; Khabba et al., 1999a. These re-
sults show clearly that our three-dimensional model gives a better estimate of grain temperature.
The comparison of the measured grain temperatures against the temperature of the air surrounding the ear
shows that the model estimates of grain temperature are a greater improvement than using air temperature;
the average difference obtained were 1.3
◦
C in Bel- gium and 2.1
◦
C in Morocco. Standard deviations of the difference were 1.7 and 2.5
◦
C and r
2
values were 0.86 and 0.87, respectively.
4.4. Sensitivity analysis of ear temperature The parameters included in the sensitivity were:
the values of the distribution of leaf area density a
k
, the sun elevation β and the difference between sun
and ear azimuths 1φ. The two first variables were chosen because they have a significant influence on
the probability of radiation interception Sinoquet and Bonhomme, 1992; De Castro and Fetcher, 1998.
The third parameter, 1φ, was chosen because it is an important factor in the absorption of solar radiation
Neveu, 1984. The values assigned to each parameter are given in Table 1. The values of each parameter
were varied, one at a time, while the others were maintained constant, and the model was run for each
combination of values. The model calculates the vari- ation in grain temperature for 4 h, at mid-length of
ear. The ear was assumed initially to be at a uniform temperature of 15
◦
C. The other parameter values were: u
e
= 0.5 m s
− 1
, R
s
= 600 W m
− 2
, R
d
R
s
= 0.3, T
a
= 18
◦
C,T
as
= 20
◦
C,T
d
= 12
◦
C,T
sol
= 10
◦
C,α = 30
◦
, φ
s
=
◦
. These values represent the optimum conditions, observed in Belgium, for ear
heating. The canopy characteristics considered were those for the experiment performed in Belgium.
4.4.1. Effect of the leaf area density Fig. 9 shows that ear temperature is highly influ-
enced by a
k
. The relationship is hyperbolic for all values used for the leaf area density. Using the val-
ues of a
k B
distribution measured in Belgium, Fig. 3,
Fig. 9. Relationship between simulated ear temperature, at mid-length of ear in the middle of grain, and the values of the dis-
tribution of the leaf area density a
k
indicated in the box. a
k B
is the distribution of leaf area density measured in Belgium Fig. 3.
Values of solar elevation, β, and difference between sun and ear azimuths, 1φ, were fixed at 60
◦
and 180
◦
, respectively. The ear was a uniform temperature 15
◦
C at time zero, and it was submit- ted to temperature and radiation conditions given in Section 4.4.
S. Khabba et al. Agricultural and Forest Meteorology 106 2001 131–146 143
Fig. 10. Relationship between simulated ear temperature, at mid-length of ear in the middle of grain, and sun elevation β.
Values of leaf area density, a
k
, are those shown in Fig. 3 and dif- ference between sun and ear azimuths, 1φ, is fixed at 180
◦
. The ear was a uniform temperature 15
◦
C at time zero, and it was submitted to temperature and radiation conditions given in Section
4.4.
ear temperature initially at 15
◦
C reached 21.5
◦
C after 4 h under the climatic conditions quoted below. When
a
k
was increased or decreased by half i.e. 1.5a
kB
or 0.5a
kB
the temperature estimated after 4 h was 19.2 and 22.7
◦
C, respectively. The effect of a
k
values on model results requires the use of accurate estimations
of the real values. However, measurements or estima- tions a
k
are time consuming Myneni, 1991. 4.4.2. Effect of the sun elevation
Calculated ear temperature increase with time was greater for higher sun elevations: β = 70 and 80
◦
Fig. 10. After 4 h, calculated ear temperature was 20.2, 21.5 and 22.2
◦
C for β = 40, 60 and 80
◦
, respec- tively. Higher sun elevation promotes good solar ra-
diation penetration within maize stands Sinoquet and Bonhomme, 1992.
4.4.3. Effect of the difference between sun and ear azimuths
Fig. 11 shows that this relationship was also hyper- bolic, but the effect of 1φ on ear temperature was less
important in comparison with a
k
and β. For 1φ = 90, 135 and 180
◦
, the difference between ear tempera- tures was not significant P ≤ 0.05. Values for these
angles were higher than those for 0 and 45
◦
. For 1φ between 90 and 180
◦
, direct radiation is almost per-
Fig. 11. Relationship between simulated ear temperature, at mid-length of ear in the middle of grain, and 1φ. Values of leaf
area density, a
k
, are those shown in Fig. 3 and sun elevation, β, is fixed at 60
◦
. The ear was a uniform temperature 15
◦
C at time zero, and it was submitted to temperature and radiation conditions
given in Section 4.4.
pendicular to the ear surface, giving higher radiation and a consequent increase in ear temperature. After
4 h, calculated ear temperatures were 20.6, 21.2 and 21.5
◦
C for 1φ = 0, 90 and 180
◦
, respectively.
5. Conclusion
