214 L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230
et al., 1982; Ritchie and NeSmith, 1991. The concept of thermal time assumes a strong correlation between
air temperature and that sensed by the plant Durand et al., 1982. But in maize, like in many monocot crop
plants, the specific locations where temperature influ- ences development — i.e. the zones where cell divi-
sion and expansion are occurring Kleinendorst and Brouwer, 1970; Watts, 1972b; Peacock, 1975 — are
close to the soil surface during early growth. In these conditions, the development rates leaf initiation, leaf
appearance or reproductive initiation rate are not ac- curately related to air temperature Beauchamp and
Lathwell, 1966; Brouwer et al., 1970; Aston, 1987. Duburcq et al. 1983 have shown that the develop-
ment rate of maize until male floral initiation was bet- ter related to soil temperature than to air temperature.
Swan et al. 1987 found that the development rate of maize was best described using soil temperature until
the sixth leaf was fully developed. More recently, Shar- ratt 1991 over barley and Bollero et al. 1996 over
maize observed different development rates under dif- ferent controlled soil temperatures. Moreover, looking
directly at plant temperature, either in growth-chamber or in field conditions, Ben Haj Salah and Tardieu
1996 observed that leaf elongation rate was corre- lated better with meristematic apex temperature than
with air temperature. Similarly, Jamieson et al. 1995 calculated thermal time based on plant temperature.
They concluded that ‘a model of leaf appearance based on near surface temperature and canopy temperature
gave superior prediction than others based on air tem- perature’.
Cellier et al. 1993 have shown that the tempera- ture of the meristem was significantly different from
both air and soil surface temperatures. The differences between air temperature at screen height and meris-
tem temperature reached almost 6 K for a daytime average, which means that hourly values were much
larger. Thus, accounting for the influence of tempera- ture on growth and development should be improved
by using the actual temperature of the extension zones. Beauchamp and Torrance 1969 proposed a model for
estimating the internal temperature of a young maize plant. The maize stem was represented as a vertical
cylindrical bar with one end in the soil considered as an infinite source of heat. This model overestimated
the temperature of the plant certainly because neither the circulation of water in the stem nor the transpi-
ration was considered. Cellier et al. 1993 proposed a model — based on a energy balance equation —
to predict the differences between air and meristem temperatures from standard meteorological data dur-
ing the early growth of a maize plant. However, this model presented some limits. The radiation balance
neglected the shade of leaves, and in the absence of any references, the stomatal conductance of the meris-
tematic zones was a fitting parameter. Furthermore, the output data are averages of day and night temperatures
with no way to estimate maximum or minimum which may be the most relevant temperatures for explaining
differences in development rate Weaich et al., 1996.
In this paper, we proposed a model based also on an energy balance approach, for estimating the temper-
ature of the extension zones of a young maize. This model works at hourly time steps, from standard me-
teorological data. The main improvements compared to the original model of Cellier et al. 1993 are related
to the radiation balance, the stomatal conductance pa- rameterization and the air temperature profile near the
soil surface.
2. Methods
2.1. Model The extension zones consisting of both leaves and
apical meristem which are often called ‘pseudo-stem’, will be referred to as ‘apex’ in the following text. The
apex temperature, denoted T
m
, is calculated from the energy balance of the apex, considered as a vertical
cylinder whose temperature is considered as uniform and homogeneous over the time steps of the model.
This model aims at estimating the apex temperature for such uses as integration in crop growth models
instead of the air temperature. To set up such an op- erational model, a compromise needs to be found be-
tween a realistic description of the energy exchanges based on mathematical expressions and the use of
readily available data and parameters. The amount of calculations is no longer a problem today, and a large
amount of work has been done in physical ecology to relate energy exchanges to plants and meteoro-
logical parameters and variables. Consequently, the main problem for such a model is to use only readily
available data.
L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230 215
During daylight, the main energy input to the apex is radiation, both solar and long-wave radiation. A part of
this energy is released by evaporation through stomata. If apex temperature is different from air temperature at
the same height, energy may be absorbed or released as sensible heat by convection. Moreover, energy may be
transferred through the apex in a vertical direction by convection andor conduction. During the night, most
of these fluxes change sign. The radiation balance is negative, and water vapor may condense on the apex.
The energy balance of the apex can be written R
nm
+ G
m
+ H
m
+ λE
m
= 1
where R
nm
is the net radiation, H
m
and λE
m
are the sensible heat and the latent heat fluxes between the
apex and the surrounding air. G
m
is the transport of heat along the apex by conduction through the
plant tissues or convection by sap flow. The values of the parameters mentioned in the following equa-
tions are summarized in Table 1, and the notations are recapitulated in Appendix A. All the input data
of the model are 1 data measured by a standard meteorological station and 2 plant characteristics
with fixed values. The model calculates apex tem- perature over short time steps 1 h or less. It is the
only time step for which the hypothesis of stationarity of the energy balance and several parameterizations
such as that of stomatal conductance or temperature profiles see below are valid. This model runs in
the early growth stages, when leaf area index LAI is less than 0.5 m
2
m
− 2
. This limitation is imposed by the parameterization of both radiative and con-
vective schemes. With taller crops a more complex
Table 1 Values and origin of the constants used in the model
Symbol Significance
Value Unit
Source a
m
apex albedo 0.29
– Davies and Buttimor 1969
d
m
apex diameter 0.01
m Experiment
g
sm
minimum stomatal conductance 0.1
mm s
− 1
Bethenod and Tardieu 1990 g
sM
maximum stomatal conductance 5
mm s
− 1
Bethenod and Tardieu 1990 K
PAR
coefficient of Eq. 10 379
m
mol m
− 2
s
− 1
Olioso et al. 1995 K
D
coefficient of Eq. 10 61
hPa Olioso et al. 1995
z
o
roughness length 0.3
mm Fitted
z
m
apex height 20
mm Experiment
α coefficient of Eq. 4d
0.46 –
Weiss and Norman 1985 ε
m
apex emissivity 1.00
– τ
NIR
leaf near infrared transmissivity 0.20
– τ
PAR
leaf PAR transmissivity 0.03
– Fitted
radiative transfer model should be used, including some plant characteristics LAI, leaf angles, . . . .
For convective processes, wind and temperature pro- files in the canopy would be too strongly modified
compared to classical profiles observed over bare soil.
The energy balance is based on the description of the local energy exchanges depending on microclimatic
variables at apex height. More precisely, the model es- timates the temperature difference between the apex
and the air at apex height. This means that estimating air temperature at apex height is a determining step in
this apex temperature model. This is especially diffi- cult in early stages of development. Indeed, the soil
surface is only sparsely covered with vegetation, and when the weather is dry, the temperature gradient near
the soil surface can be very steep. Consequently, mod- eling apex temperature can be divided into two steps:
the first one consists in determining the air tempera- ture at apex height, i.e. the difference in air tempera-
ture between screen height and apex height, and the second one consists in estimating the temperature dif-
ference between the apex and the surrounding air. The first step requires knowledge of micrometeorological
conditions at field scale. The second needs to account for local characteristics of the microclimate or of sur-
face conditions near the apex. The importance of both steps might be very variable depending on the part of
the vegetation being considered. For a shaded evapo- rating organ, the temperature difference between the
organ and the air second step is expected to be small because the organ receives low energy, and a large
fraction of it can be dissipated into latent heat. For an organ directly exposed to solar radiation e.g. wheat
216 L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230
ear, pea flower, top leaves the temperature difference should be much larger, especially in the case of a
non-evaporating organ e.g. a bud before bud burst. On the other hand, the temperature difference between
the air at screen height and the air surrounding the apex first step can also be very variable according
to the field conditions: from several degrees or tens of degrees over a bare dry soil Garratt, 1988; Cellier et
al., 1996 to several tenths of degrees over an evap- orating vegetation or a wet soil. Consequently, both
temperature differences must be considered to build a model adapted to a wide range of vegetation and me-
teorological conditions and to be able to analyze what determines plant temperature.
2.1.1. Temperature and wind speed profiles above the soil surface
Due to interactions between free and forced convec- tion air temperature and wind speed profiles cannot be
determined independently from each other. Moreover, both air temperature T
am
, and wind speed, U
m
, at apex height are required in some fluxes of the energy bal-
ance equation. Wind speed and air temperature varia- tion with height are generally described by using the
flux-gradient relationships given by Dyer and Hicks 1970
uz = u
∗
k ln
z z
o
− 9
M
z − z
o
L 2
T z − T
o
= T
∗
k ln
z z
oh
− 9
H
z − z
oh
L 3
where uz and Tz are the wind speed and air temper- ature at height z; u
∗
is friction velocity, T
∗
a scale tem- perature, and z
o
and z
oh
are the roughness lengths for momentum and heat transfer. As generally assumed,
z
oh
was taken equal to 0.1z
o
Brutsaert, 1982. The Monin–Obukhov length, L, is related to u
∗
and T
∗
by L = Tkg u
2 ∗
T
∗
. The stability functions 9
M
and 9
H
account for the effects of vertical temperature gradient on convective transfer Dyer and Hicks, 1970. Their
expressions were derived by Paulson 1970. Determining the wind and temperature profiles re-
quires calculation of u
∗
, T
∗
and L using Eq. 3 and analogous equations. For this, the air temperature at
z
oh
, T
o
, must be determined. This was done using an energy balance of the soil surface, including a soil sur-
face water balance as described in Appendix B. This method makes it possible to account for the variations
of soil surface temperature due to meteorological con- ditions and soil wettingdrying according to the cli-
matic factors and capillary water transfer in the top soil. The height where T
am
and U
m
are calculated as that of the apex, z
m
was taken as 0.02 m. 2.1.2. Radiation balance
The radiation balance is divided into short-wave and long-wave radiation balances. Visual observation
showed that for most of the day, the apex was shad- owed by its own leaves or those of the neighbouring
plants in the same row. This is especially true when the solar elevation is high, i.e. when solar radiation is at
this peak. We could then consider that short-wave radi- ation reaching the apex was either transmitted through
the leaves or reflected from the soil Fig. 1. In both cases, it is diffuse radiation. As leaf transmittance is
different for photosynthetically active PAR and near infrared radiation NIR, these spectral intervals have
to be considered separately. Moreover, PAR radiation is required for calculating stomatal conductance see
below. Due to shadowing by leaves, no directional ef- fect of radiation was considered. Short-wave radiation
balance, R
SWm
, may then be expressed as R
SWm
= 1 − a
m
R
PARm
+ R
NIRm
4a with
R
PARm
= τ
PAR
+ a
s
R
PAR
4b and
R
NIRm
= τ
NIR
+ a
s
R
NIR
4c where a
m
and a
s
are the plant and soil albedos. Also τ
PAR
and τ
NIR
are the transmittances of leaves in the PAR and near infrared wavelength ranges. R
PAR
and R
NIR
are the PAR and NIR inputs over the canopy obtained from the solar radiation R
s
by R
PAR
= αR
s
4d R
NIR
= 1 − αR
s
4e Following Weiss and Norman 1985, α was taken
equal to 0.46. All radiation components are expressed in units of W m
− 2
. In R
PARm
and R
NIRm
the index ‘m’ refers to the incident radiation on the apex.
L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230 217
Fig. 1. Schematic representation of the short-wave radiation balance of the apex R
s
, solar radiation; R
PAR
, R
NIR
incident PAR and incident NIR above the crop; R
PARm
, R
NIRm
, PAR and NIR at the apex surface; a
m
apex albedo; a
s
soil albedo; τ
PAR
, τ
NIR
, leaf transmissivity for PAR and NIR.
The long-wave radiation balance is written R
LWm
= ε
m
R
am
− σ T
4 m
5 The first term on the right-hand-side of Eq. 5, R
am
, is the long-wave radiation input from the surround-
ing environment sky, leaves, soil. This flux was ex- pressed as
R
am
= σ T
4 a
+ σ T
4 s
2 6
where T
a
is air temperature K measured at screen height and T
s
is the soil surface temperature. The first term on the right-hand side of Eq. 6 is σ T
4 a
instead of atmospheric radiation because it can be considered
that the apex mainly ‘looks at’ the lower atmosphere at large angles from the zenith and maize leaves whose
temperature is close to air at screen height at low angles Fig. 1. The second term in the right-hand-side
of Eq. 5 represents the long-wave radiation losses linked to the apex temperature. The apex emissivity,
ε
m
, is taken equal to 1.00, as usually done for most vegetation, and the soil emissivity too.
2.1.3. Sensible heat exchanges The transfer of sensible heat from the apex to the
surrounding air is considered as proportional to the temperature difference between the apex and the air
at apex height H
m
= ρc
p
g
m
T
m
− T
am
7 where T
am
is air temperature at apex height, and g
m
is a thermal diffusion conductance. Its value depends on
the wind speed at apex height, U
m
, and on the apex diameter, d
m
. It can be expressed according to the expression given by Finnigan and Raupach 1987.
g
m
= 0.54
U
m
d
m 12
8 T
am
and U
m
were calculated from air temperature and wind speed profiles as previously described.
2.1.4. Evaporation The transpiration from the apex is mainly regulated
by stomata. It may be expressed in a form similar to that of the sensible heat flux,
λE
m
= ρc
p
γ e
m
− e
am
1g
v
+ 1g
s
9 where e
am
is the vapor pressure at apex height and e
m
is the vapor pressure inside substomatal chambers of the leaves which constitute the external face of the
apex. It is taken equal to the saturation vapor pres- sure at apex temperature; e
am
can be calculated from a relationship similar to Eq. 3 where the tempera-
ture scale is replaced by a humidity scale determined from the soil evaporation calculated according to the
218 L. Guilioni et al. Agricultural and Forest Meteorology 100 2000 213–230
procedure described in Appendix B; g
v
is a thermal diffusion conductance, equal to 0.89g
m
Eq. 8. The stomatal conductance, g
s
, is controlled by dif- ferent environmental factors, among which radiation,
water vapor pressure deficit, soil water content and at- mospheric carbon dioxide concentration are the most
important Jarvis, 1976. Considering that, just after sowing, soil water content was rarely a limiting factor,
g
s
was modeled using only a regulation by solar ra- diation and water vapor deficit. The relation proposed
by Olioso et al. 1995 was used,
g
s
= g
sm
+ g
sM
− g
sm
1 − exp −Q
PAR
K
PAR
× 1 −
D K
D
10 where g
sm
and g
sM
are the minimum and maximum conductances m s
− 1
, D is the water vapor pressure air deficit at apex level; Q
PAR
is R
PARm
Eq. 4, but expressed in
m
mol m
− 2
s
− 1
; K
PAR
and K
D
are constant coefficients given by Olioso et al. 1995 see Table 1.
2.1.5. Heat flux through the stem Under daytime conditions, heat is transported from
the underlying warmer ground to the leaves by sap flow through the apex. Temperature measurements be-
low and above the apex showed that the amount of heat transported by this way was less than 10 of the
net radiation in all cases, and their difference, which represents the energy storage by the apex was much
less. Therefore, this flux was neglected.
2.1.6. Calculation of the apex temperature Using Eqs. 1 and 4–10, the energy balance
equation was solved at each time step using an itera- tive procedure. The iteration of apex temperature was
terminated when the energy balance closed to within 1 W m
− 2
. The same approach was used at the same time to calculate soil surface temperature and water
content, using Eqs. B.1–B.10. If not available, the soil water content was initialized to 75 of the field
capacity for the surface layer, and to the field capacity for the deep soil layer. The apex temperatures calcu-
lated during the first day were excluded from the anal- ysis so that the results might not be affected by badly
estimated initial soil water contents. 2.2. Field experiments
2.2.1. Field conditions This model was calibrated and tested with five
datasets, collected at three sites. Three experiments were conducted in Grignon, France 48
◦
51
′
N, 1
◦
58
′
E, altitude 125 m, one in 1990 and two in 1993, over
a 1.4 ha maize field Zea mays L. of the INRA ex- perimental station, with a clay-loam soil. The albedo
was 0.20 under dry conditions, and decreased to 0.15 after rainfall. In 1990, the maize was sown on 4 May
day of year DOY 124 and the measurements of apex temperatures were made from 23 May DOY
143 to 30 May DOY 150. In 1993, two sub-plots of 40 m × 40 m called A and B were sown in the same
field at two different dates in order to get different cli- matic conditions, especially temperature. The maize
was sown on 7 May 1993 on plot A and on 9 June on plot B. Apex temperatures were measured from 15 to
29 June for A and from 4 to 15 July for B. The three experiments performed in Grignon will be referred to
as Grignon90, Grignon93A, and Grignon93B.
Two other experiments were conducted in 1992 in two farmers’ fields near Pithiviers, France 48
◦
08
′
N, 2
◦
13
′
E, altitude 120 m. The first called ‘Brosses’ was on a calcareous loamy soil with small stones and
the second called ‘Lacour’ was on a loamy sand soil. The apex temperatures were measured from 22 to 29
May. Over both fields, the albedo was 0.30 when the soil surface was dry. After raining, it decreased to 0.20
at Lacour and 0.15 at Brosses.
In all experiments the maize variety was DEA, and the plant density was about 90,000 plants ha
− 1
. During all experimental periods, the maximum crop height
was between 0.1 and 0.4 m.
2.2.2. Micrometeorological measurements In all experiments, the following measurements
were made: 1 total downward solar radiation flux density on a horizontal surface R
s
, with a CM6 pyranometer Kipp and Zonen, Delft, Netherlands,
2 wind speed at 2 m above the soil surface, with a cup anemometer CE-155 CIMEL électronique, Paris,
France, 3 air temperature at 2 m above the soil sur- face, using a copper–constantan thermocouple AWG
24 placed in a radiation screen artificial ventilation in the Grignon experiments and natural ventilation
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