L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230 219
in the others, 4 air relative humidity at 2 m with a HMP35 capacitive hygrometer Vaisala, Helsinki,
Finland, 5 apex temperatures using thermocouples AWG30 inserted into the plant, with a variable num-
ber of replications according to the experiment six in Grignon90, nine in Grignon93, and four in Brosses
and Lacour. The thermocouples were inserted at heights between the soil surface and a height of 3 cm.
Additional measurements were made during the Grignon experiments. Soil surface temperature was
measured, using six copper–constantan thermocou- ples fixed on the soil surface with a thin plastic stem.
The sensors were previously coated with a thin layer of mud in order to have optical properties similar to
the soil. In Grignon93B, the photosynthetic active ra- diation received by the apex was measured using five
photovoltaic amorphous silicon cells Chartier et al., 1989 SOLEMS, Palaiseau, France put vertically
near the apex, two of them facing north, the three others facing, respectively, south, east and west. The
PAR reaching the apex was estimated as the aver- age of these five measurements, the two facing north
being averaged to give one single value.
All these data were collected every 10 s on a dat- alogger Campbell Scientific, Shepshed, UK and av-
eraged over 30 min.
2.2.3. Stomatal conductance Many studies have been published on the stomatal
conductance of maize leaves but, to our knowledge, no reference was available on the conductance of the
sheath of maize leaves, or of such a system as the apex, made of rolled leaves, whose external face is
composed of the sheaths of leaves. Therefore, obser- vations were made in order to i check if stomata
were present at the apex surface, ii estimate their density, and iii get some values of stomatal conduc-
tance of the apex, in order to integrate minimum g
sm
and maximum g
sM
values in Eq. 10. The stomatal density number of stomata per mm
2
was determined on the sheath or on the limb by press- ing small pieces of sheath or limb onto a rhodo¨ıd®
plate softened with acetone Schoch and Silvy, 1978. The prints of leaf epidermis, were observed under a
microscope amplification of 125. The stomatal den- sity of ten leaves was determined in ten different parts
of the same print. The stomatal conductance of the apex was measured
with a LI-700 porometer LI-COR, Lincoln, Nebraska, USA, by applying the measurement chamber on the
sheath of the first leaves, between 0 and 5 cm above the soil surface. Measurements were made on several
days, at different times of the day with various solar radiation densities. During two clear days, we related
g
s
to the PAR received by the apex. Each stomatal conductance measurement was coupled with a mea-
surement of the PAR, using a photovoltaic amorphous silicon cell Chartier et al., 1989 put vertically near
the apex.
3. Results
3.1. Experimental results 3.1.1. Observed apex temperatures
We compared the range of observed apex temper- atures with air and soil surface temperatures for two
days with different meteorological conditions during Grignon90 and Grignon93 experiments Fig. 2. Solar
radiation was high 28.2 MJ m
− 2
for the day on 26 May 1990 at Grignon Fig. 2a, and it was much less
on 14 July 1993 7.7 MJ m
− 2
, Fig. 2b. As solar radi- ation was high on Fig. 2a, the soil surface temperature
became much higher than air temperature, and conse- quently air temperature at apex height and apex tem-
perature increased, too. The temperature differences between air and soil surface and between air and apex
reached 21.3 and 7.3 K, respectively. These differences were not exceptional: over the five datasets mentioned
Fig. 2. Diurnal variation of air temperature, minimum and max- imum apex temperatures and soil surface temperature measured
at Grignon on 26 May 1990 a and 14 July 1993 b. UT is universal time.
220 L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230
above representing 48 days of measurements, the max- imum temperature difference between the apex and air
at 2 m was more than 10 K for 4 days, 7 K for 21 days and 5 K for 35 days. It was less than 4 K for only 5
days. Apex temperatures were also higher than air tem- perature during an overcast day Fig. 2b. Even with
low solar radiation, the apex temperature was clearly different from air temperature at screen height. The
difference was larger than 2 K near midday.
Compared to the difference between apex and air temperature, the variability of apex temperatures, es-
timated from the replicates, was low. The largest am- plitude was less than 2 K, which is much less than the
difference with air temperature. This will allow us to consider only the average apex temperature for testing
and validating the model.
3.1.2. Stomatal conductance Visual observations showed the presence of stomata
on the leaf limb, but also on the external face of the sheath. However, the stomatal density was lower on
the sheath 28 ± 12 stomata mm
− 2
than on the leaf limb 98 ± 20 on the lower face and 51 ± 18 on the up-
per face. Stomatal conductance measurements were made over a wide range of radiation, from 0 to more
than 1400
m
mol m
− 2
s
− 1
. At any radiation, low stom- atal conductances were observed less than 5 mm s
− 1
. The maximum values were observed for radiations
above 800
m
mol m
− 2
s
− 1
. The large variability in Fig. 3 has been classically observed in many previous stud-
ies see, e.g., Jones 1992 and Bethenod and Tardieu 1990. It may be due to either other limiting factors
soil water potential, vapor pressure deficit or due to a technical problem such as leaks when using the dif-
fusion porometer, which is not adapted to the shape of the apex Turner, 1991. However, despite the lower
stomatal density, the change in stomatal conductance with radiation and the maximum values were similar
to previously published values. Thus, we considered that the apex behaved like a leaf, and we chose for the
maximum stomatal conductance in Eq. 10 the values given by Bethenod and Tardieu 1990 see Table 1.
3.1.3. PAR reaching the apex In Fig. 4 are compared the PAR balance of the apex
measured using the five silicium cells and that esti- mated using Eqs. 4b and 4d, for 11 days during
Fig. 3. Stomatal conductance estimated with a diffusion porometer as a function of PAR near the apex. The curve is the relation
between PAR and stomatal conductance as expressed by Eq. 10, excluding the vapor pressure deficit effect D = 0.
Grignon93B. The best fit between measured and cal- culated values was obtained with a PAR transmissivity
of 0.03. This value for τ
PAR
is consistent with most published values, which range from 0.01 to 0.05. The
global trend is around the 1 : 1 line, but with large dispersion at high values. Most values underestimated
by Eq. 4b came from data collected early in the morning, when direct solar radiation reaches the apex,
which is not accounted for in the model. These data,
Fig. 4. Comparison between half hourly values of measured and calculated PAR at apex height.
L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230 221
Fig. 5. Sensitivity of the model to the plant parameters: a apex albedo, b apex diameter and maximum stomatal conductance, c apex height above the soil surface and to the forcing variables, d solar radiation and wind speed and e air and dew point temperature.
corresponding to hours before 9 a.m., are plotted with crosses. On the contrary, PAR calculated near mid-
day overestimated the measurements because a larger fraction of the soil is shadowed by the leaves of the
maize canopy, and consequently the reflected PAR is certainly less than assumed in Eq. 4b. These data
are represented as open circles in Fig. 4. Despite these limitations, the comparison was considered as satisfac-
tory for our application, with such simple input data.
3.2. Sensitivity study The sensitivity of the model to either the forcing
variables, i.e. the input meteorological data, or to the plant parameters albedo, diameter, maximum stom-
atal conductance and apex height was analyzed. The model was run using the parameters given in Table 1,
by changing only one variable or parameter by more than twice the uncertainty on it. The chosen ranges
of variation were ±20 for solar radiation and wind speed, ±2 K for air and dew point temperature, ±50
for maximum stomatal conductance and apex diame- ter, ±10 mm for apex height and ±0.05 for albedo. The
average values given in Table 1 are either taken from the scientific literature or fitted to our experimental
data see next section. The input meteorological data are those from the Grignon90 experiment which, were
also used for calibrating the model see next Section. They come from fine weather days with high solar ra-
diation and large temperature differences between the apex and air. Under such conditions, the effect of any
parameter or variable should be most evident. The re- sults are plotted in Fig. 5a–e.
Concerning the parameters Fig. 5a–c, the apex albedo and diameter have a negligible effect on apex
temperature. Stomatal conductance has a larger effect, but it remains surprisingly low, when one considers
its importance in most crop microclimate models.
222 L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230
Finally, the only plant parameter to which the model is sensitive, is the apex height. This is the conse-
quence of the steep air temperature variation with height near the soil surface.
For the meteorological variables Fig. 5d–e, the sensitivity is larger. It remains low for the dew point
temperature. It is slightly larger for wind speed. The sensitivity to solar radiation is large ±0.8 K for a
change in solar radiation of 20, but the calculated apex temperature is most sensitive to the air tempera-
ture ±1.8 K for a change in air temperature of ±2 K.
3.3. Model calibration The sources of uncertainty in this model can be
classified as relative to either the local energy balance of the apex, or to the way of estimating the micro-
climatic variables at apex height. Most parameters in the local energy balance could be directly determined
size, soil albedo, or chosen from the literature apex albedo, emissivity, maximum stomatal conductance
Table 1. Moreover, the sensitivity study showed that the calculated apex temperature was not very sensi-
tive to these parameters, but was very sensitive to air temperature.
Consequently, the air temperature at apex height must be determined as precisely as possible. For this,
the main parameter to know is the roughness length Eq. 2. However, it is not possible to use an aero-
dynamic roughness length directly estimated from the physical characteristics of the soil surface and the
maize crop, using simple relations with the physi- cal surface roughness height of obstacles; . . . for
two reasons. First, the logarithmic wind and temper- ature profiles cannot be extended down to the apex
height, because the flux-gradient relationships are not strictly valid at low zz
o
ratios Tennekes, 1973; Cel- lier and Brunet, 1992. Secondly, it is not straight-
forward to derive one roughness height for the whole wind and temperature profile from the reference height
to the soil surface, when two flows should be con- sidered: one above the canopy and another near the
soil surface the maize crop was generally taller than 0.3–0.4 m when the LAI reached 0.5. Thus, as it could
not be determined a priori, the roughness length was used as a fitting parameter for the model. For the rea-
sons expressed above, it could not be considered as
Fig. 6. Roughness length dependence of the average and of the standard deviation of the absolute value of the difference between
calculated and measured apex temperatures. The input data are those from the Grignon90 experiment.
a realistic roughness length but only as a way to re- late air temperature at apex height to air temperature
at screen height. Classical flux-gradient relationships Eqs. 2–3 were used in order to account for the in-
fluence of the surface energy balance and the turbulent flow characteristics on the temperature profile. Using
the Grignon90 experiment, the roughness length giv- ing the best fit between calculated and observed apex
temperatures was determined. The observed temper- ature was taken as the average of the six apex tem-
peratures measured in this experiment. In Fig. 6 are plotted the average and the standard deviation of the
absolute value of the difference between calculated and measured apex temperatures. Both curves show
an optimum for roughness lengths between 0.2 and 0.6 mm, with a minimum value at 0.3 mm. Thus, a
roughness length of 0.3 mm was chosen. It is much less than the roughness length that could have been
determined from the crop height and leaf area den- sity, i.e. 10–40 mm. This confirms that this roughness
length is nothing more than a fitting parameter.
On Fig. 7 are presented the observed and calculated apex temperatures during the Grignon90 experiment
with z
o
= 0.3 mm. It can be seen that the model gives
a fair estimate of the actual apex temperature at any time in the day, with no drift during the experimental
period. The maximum during the day and the response to changes in solar radiation are well simulated. This
L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230 223
Fig. 7. Air temperature, measured and calculated apex temperature during the Grignon90 experiment.
is important because it is during fine weather days that the temperature difference between apex and air is at
its largest. The gradual temperature decrease in the night and the minimum are also well simulated, even
though the energy transfer processes are very different during day and night.
3.4. Model validation with other datasets The model with the roughness length determined
over the Grignon90 experiment has been applied to the other independent datasets presented previously. This
comparison was made only on the daytime period, between sunrise and sunset, because this is the pe-
riod when the temperature differences are the largest. Moreover, it is often biased to compare averages cal-
culated over a 24 h period, because the energy transfer processes are opposite between day and night. Thus,
a bad account of energy transfers could give the same average, while the temperature may be underestimated
during day and overestimated during night, or the re- verse. The results are given in Fig. 8 and Table 2. The
averages and dispersion are larger on these experi-
Table 2 Average and standard deviation K of the difference between observed and calculated apex temperature during the day R
s
≥ 50 W m
− 2
Experiment Grignon90
Grignon93A Grignon93B
Brosses Lacour
Number of values 168
389 299
161 161
Average 0.20
0.06 −
0.50 −
0.30 0.64
Standard deviation 0.69
1.27 1.17
1.36 1.93
Fig. 8. Comparison of half hourly values of calculated and measured temperature difference between the apex and air at
screen level, for a Lacour, b Brosses, c Grignon93A and d Grignon93B experiments.
ments than on Grignon90. This is, of course, partly be- cause the model was calibrated with Grignon90 data,
but also because the weather was much more chang- ing over these experiments, with frequent rainfall and
changes in solar radiation, which induced a great vari- ability in air and soil surface temperatures.
4. Discussion
