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
The experimental results showed that the apex tem- perature was very different from air temperature mea-
sured at screen height. This is mainly because, during the early growth stages, i.e. the first weeks after sow-
ing, the apex is near the soil surface, which is much warmer than the air at 2 m. During the Grignon90 ex-
periment, the temperature difference between the soil surface and air at screen height was more than 15–20 K
every day near midday. For a given air temperature, the apex temperature can be similar to air tempera-
ture at screen height in the case of a cloudy day, or
224 L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230
be 5–10 K warmer during day and 2–3 K lower during night in the case of a cloudless day. Therefore, the re-
lation between apex temperature and air temperature in a meteorological station is not straightforward. It
may be different both for average and extreme tem- peratures. This difference should be considered when
analyzing the response of a maize crop to either high temperatures — which may diminish photosynthesis
— or low temperatures frost. Due to the asymmetry of the temperature difference, the daily average over
24 h of apex temperature is larger than that of air temperature. The difference ranged from 0 to 2 K on
our experimental datasets. Such differences may have strong implications for accounting for the effects of
temperature on growth and development.
The model that is presented in this paper should al- low replacement of air temperature by an apex tem-
perature in crop models, or for estimating the risk of climatic stress frost, heat stress. It is particularly
adapted for operational application since 1 it uses only standard meteorological data and 2 some impre-
cision in the plant parameters is permitted, because the sensitivity study showed that the model was insensi-
tive to the plant parameters. The good agreement after fitting between calculated and measured apex temper-
ature at any time in the day on the Grignon90 dataset showed that the energy balance approach was well
adapted to this application. The model behaved fairly well under both daytime and night-time conditions,
which are very different from an energy balance point of view: stable atmospheric conditions, no evaporation
and a radiation deficit occur during the night, while daytime is characterized by a high radiation input,
evaporation regulated by stomata, larger wind speed, and very large soil surface temperatures. In particular,
the fair agreement between calculated and measured apex temperature near sunset and sunrise, when tem-
perature changes rapidly, shows that the hypothesis of stationarity of the energy balance over the considered
time step 30 min was reasonable. This allows one to estimate with a good accuracy the average, minimum,
and maximum temperatures.
Such a model also helps in interpreting apex tem- perature and factors that determine it. A surprising
result was the low sensitivity of the model to stomatal conductance. This is mainly because evaporation is a
minor term of the energy balance in the case of a maize apex. In fact, due to shading by leaves, and to the low
transmittance of the leaves for PAR, the stomatal con- ductance was low and the evaporation, too. The tem-
perature is then mainly determined by an equilibrium between net radiation, R
nm
, and sensible heat flux, H
m
, which is large for small temperature differences. Over the Grignon90 dataset, the calculated sensible
heat flux was approximately proportional to the calculated
temperature difference
between the
apex and the air at apex height, with a slope of 220 W m
− 2
K
− 1
. Net radiation was always less than 250 W m
− 2
. An uncertainty of ±50 on apex tran- spiration — which would result in a flux error of
approximately 50 W m
− 2
as calculated by the model on the Grignon90 data — would be compensated by
a variation in H
m
with a change of 0.2 K in apex temperature. Another result of the sensitivity study,
was the relatively low response of apex temperature to solar radiation 0.8 K for a change in solar ra-
diation of ±20. This may also be explained by the high aerodynamic conductance of the apex, but
also by the change in stomatal conductance. The PAR radiation reaching the apex was always low
500
m
mol m
− 2
s
− 1
, a level where stomatal conduc- tance is still increasing with increasing PAR see Fig.
3. Thus, any increase in solar radiation was partly compensated by an increase in evaporation, which
makes the apex temperature generally close to the air temperature at the same height. The calculated tem-
perature differences between the apex and air at the same height on the Grignon90 dataset were always
less than 0.8 K, whereas the temperature difference between the air at the apex height 2 cm above soil
surface and air at the reference height 2 m often reached 6 K near midday.
Finally, it can be concluded that the lack of knowl- edge about the energy exchange parameters of a maize
apex is not a great problem for estimating apex temper- ature because it is not very sensitive to most plant pa-
rameters. This is mainly because i the apex receives a low amount of radiation due to the overlying leaves
protecting it from direct solar radiation, ii a sig- nificant fraction of this radiative energy is consumed
by evaporation, which transforms energy at constant temperature and iii the small aerodynamic resistance
makes the sensible heat flux increase rapidly when the apex temperature goes above air temperature.
Due to this small temperature difference between the air and the apex, it could be argued that the apex
L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230 225
energy balance module is not strictly necessary to esti- mate apex temperature under such conditions. In order
to check this, the model was run in a simplified ver- sion by considering that apex temperature was equal
to air temperature at the same height. The model then only consisted in the soil surface energy balance pre-
sented in Appendix A. As previously done for the complete model the surface roughness length was fit-
ted on the Grignon90 dataset. The best value is close to the previous one: 0.35 mm instead of 0.30 mm. How-
ever, both the absolute error and the residual stan- dard deviation are larger by approximately 0.1 K, i.e.
10–15 and 15–20, respectively, with this simpler model compared with the initial model. Using a rough-
ness length based on the canopy physical description, i.e. values comprised between 10 and 40 mm leads
to much worse results. Both the absolute error and the residual standard deviation are multiplied by more
than 2. Moreover, it must be emphasized that using only the soil surface energy balance model produces
a simplification only by reducing the number of equa- tions. The input meteorological variables, which are
the key-point for deciding whether a model is opera- tional or not, are the same for both models. The com-
plete model has the advantage of being more general and easily adaptable for calculating the range of apex
temperature i.e. shaded and sunlit apex or the tem- perature of any plant organ. For example, for an or-
gan placed near the top of the crop leaf, flower, ear, the solar radiation absorption and the stomatal con-
ductance would be much more relevant to estimate the organ temperature because the organ is directly ex-
posed to the solar radiation. Moreover, the difference between the temperature of the air at screen height
and the temperature of the air surrounding the organ should be less, because the organ is higher above the
soil surface.
Thus, modeling the temperature of a vegetation or- gan needs accurate modeling of the microclimate near
the considered organ. In this case, one must determine precisely the wind speed and air temperature at apex
height from the standard values taken at a reference height. The soil surface temperature must be deter-
mined accurately under all conditions: during night and day, with low or large solar radiation or wind
speed, with a wet or dry soil. It requires an account to be taken of the soil properties, because they influ-
ence greatly the soil surface energy balance. This is what makes the model difficult to apply under differ-
ent conditions. This is certainly the main reason why the model results were not so good in 1993 in Grignon,
or for the Lacour or Brosses experiments. The soils conditions were very different, with a chalky Brosses
and a sandy soil Lacour compared with a clay loam soil Grignon. The meteorological conditions were
also very different, with frequent rain. In such condi- tions, soil evaporation must be simulated well in or-
der to estimate soil surface temperature. Despite these constraints, the results remained satisfactory when the
model was applied under very different conditions, with no systematic deviation and a standard deviation
which is less than twice that of the calibration experi- ment Grignon90. This means that the calibrating fac-
tor, the roughness length, can be considered as robust enough to make the model applicable to different sites.
We obtained the least satisfactory results in the La- cour experiment. This might be because the soil was
much more sandy, but more likely because this field was irrigated. Irrigation caused very rapid changes in
temperatures, and wetted the apex, which created in- consistent datasets, with a wet apex at the same time
as the solar radiation was large. This case is critical because the model does not account for water inter-
ception by the apex. Under a natural climate, the apex is only wet when it rains, and, in this case, its tem-
perature cannot be much higher than air temperature due to low solar radiation in addition to wetness and
large soil evaporation. When solar radiation is large and the apex is wet, its temperature cannot be much
larger than air temperature as expected, because of a large energy consumption by evaporation. Thus, ne-
glecting water interception is not critical in the model under most conditions, unless the crop is irrigated.
5. Concluding remarks
