260 H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263
are not shown since both measured and simulated val- ues ranged between 0 and 0.02.
5. Discussion
5.1. Methodology for model testing This study was aimed at addressing the question of
light partitioning between several species in a mixed canopy, especially grass–legume mixtures. The ques-
tion of light partitioning in well-mixed canopies i.e. where foliages of the species are intermingled in the
same canopy volume cannot be addressed from light measurements, because there is no experimental de-
sign to estimate the radiation balance of a given com- ponent in these conditions. The only way should be
to use sensors attached to leaves. This was attempted to estimate light partitioning between shoots in a tree
canopy Sinoquet et al., 1997. Despite the number of sensors 60, the confidence in measurements was
very low due to the large variability in leaf irradiance measurements. Moreover in case of small canopies
like grass–legume mixtures, sensor settlement would be extremely difficult without disrupting canopy struc-
ture. That is the reason why we chose to test the sim- ple models against simulations of the more complex
SIRASCA model. Notice that Wallace 1997 did the same to test his ERIN model but he used a smaller
range of conditions. As SIRASCA is a 1D version of a radiation transfer model that has been used and
tested in a number of contrasting situations as men- tioned earlier, it was assumed to be able to serve as
a reference model.
Model comparison was made from canopy structure data taken from the literature. In the reported experi-
ments, LAI ranged from 1 to 12. Although this range might be regarded as a wide range, it corresponds to
values that are found in natural conditions. The test was thought to be more powerful if it applies to a range
of realistic values. The same applies to leaf scatter- ing coefficients, the range of which 0.2–0.8 approxi-
mately corresponds to values found for leaves: 0.2 and 0.8 are typical values for the PAR and NIR wavebands,
respectively. Testing the models in the PAR waveband is useful for primary production analysis e.g. Mon-
teith, 1972 while NIR domain should be included to compute the energy balance.
5.2. Use of simple models for estimating light partitioning between species
5.2.1. KMS model The KMS model accurately summarised the de-
tailed model SIRASCA under low scattering condi- tions in the case of various multispecies canopies:
two-species monolayer Fig. 1, two-species mul- tilayer Figs. 3 and 4 and multispecies multilayer
canopies Fig. 5. This model could therefore be used in growth analysis methods and simulation models
dealing with horizontally homogeneous multispecies canopies, especially those requiring partitioning in
the PAR domain. In comparison with other simple light models devoted to partitioning see Section 1,
KMS is able to adapt to a wide range of canopies and to explicitly take into account the main deter-
minants of light microclimate: canopy structure i.e. LAI and mean leaf inclination of each species in
each canopy layer and optical properties of leaves of each species and the soil surface. In the version
proposed in this paper, the model assumes overcast sky conditions. This is because the model is aimed
at simulating light partitioning between species at a daily scale. Several studies showed that light absorp-
tion at a daily scale is correctly approximated by a single run in overcast conditions in both monospecies
and multispecies canopies Varlet-Grancher and Bon- homme, 1979; Sinoquet et al., 1990. In order to use
the model at smaller time steps, direct beam flux should be included in the model, in a way similar to
Bonhomme and Varlet-Grancher 1977 in the case of monocrops. Last but not least, the model is easily
implemented since it only includes Eqs. 6 and 8 for the extinction coefficient as a function of leaf
inclination and leaf optical properties, Eq. 9 for coefficients α and β, and the recursive use of Eqs.
22, 24, 18 and 19 to compute light balance and partitioning in each canopy layer.
The derivation of the KMS model made it possi- ble to bridge the Kubelka–Munk theory and the model
by Goudriaan 1977, where scattering is taken into account by correcting the extinction coefficient by a
factor √
1−σ
i
. Goudriaan’s proposal avoids compli- cated computations of light scattering and has proved
to be efficient Cohen and Fuchs, 1987; Campbell and Van Evert, 1994; Tournebize and Sinoquet, 1995.
From Eq. 21a applied to monocrops, it appears that
H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263 261
Goudriaan’s model can be interpreted as a two-flux KM model upwarddownward where exp−K
′
z is neglected with regard to expK
′
z. Reciprocally the KMS model proposed in this paper can be regarded as
an extension of Goudriaan’s to the case of multilayer multispecies canopies.
When applied to high scattering conditions, KMS correctly simulated light absorption of planophile
Species 1 but significantly underestimated light in- terception by the erectophile Species 2. When using
the complete KM equations, the same behaviour was observed data not shown. As previously pointed out
by Myneni et al. 1989, the KM approach does not take into account differences in directional light in-
terception. By dealing with hemispherical fluxes, the KM approach implicitly assumes that the directional
distribution of radiation fluxes does not change within the canopy, while it does in real canopies. Varia-
tions in extinction coefficients with beam direction depend on foliage inclination see e.g. Ross, 1981.
Planophile foliage shows less change in extinction coefficients with beam direction than erectophile fo-
liage in particular, the projection coefficient of hor- izontal leaves is unity whatever the beam direction,
Ross, 1981. The large directional variations of light extinction in erectophile canopies result in modifica-
tion of the directional distribution of radiation fluxes within the canopy while the extinction coefficient of
the canopy see Eq. 6 is calculated according to the radiance distribution above the canopy. In agreement
with Myneni et al. 1989 this suggests that models based on the KM equations would poorly estimate the
radiation balance of erectophile canopies, especially under high scattering conditions.
5.2.2. ERIN model When applied to monolayer mixed canopies, the
ERIN model correctly simulated light partitioning be- tween species in some, but not in all, conditions Figs.
1 and 2. This is because ERIN shares light between canopy components according to their height rather
than their LAI Wallace, 1997. In case of a monolayer canopy, the two components have the same height, so
that the fraction of light absorbed by component i is simply the mean value between maximal and mini-
mal values i.e. ε
i max
and ε
i min
computed in case of dominance of either one or the other species, see Eq.
3. This estimation is correct when the difference be- tween ε
i min
and ε
i max
is low, i.e. when the companion species have a reduced competitive ability namely a
small LAI. The ERIN model can also give correct es- timations if the species ability to capture radiation i.e.
the term K
i
L
i
1−σ
i
is the same for the two species. Wallace 1997 compared ERIN with SIRASCA in
conditions of equal LAI and leaf inclination, and he found a good agreement between the two models. This
behaviour of ERIN can also be seen in Fig. 2a: ERIN lines cross SIRASCA lines when the LAI of the two
species are similar. In contrast, ERIN fails in simulat- ing light partitioning between species when the two
species have high but different LAI Fig. 2. Due to the equal height of the two species in the monolayer
canopy, light competition as simulated by ERIN is less intense than that computed from SIRASCA Fig. 2.
In case of high scattering conditions, ERIN greatly overestimated light absorption by the two canopy com-
ponents, mostly because upward radiation fluxes are not taken into account while they largely contribute
to radiation lost by the canopy i.e. reflected to the sky.
5.3. Requirements in canopy structure parameters Reducing the requirements for canopy structure
parameters in a light model considerably simplifies the inclusion of light partitioning in crop simulation
models. Due to low requirements for canopy struc- ture parameters, ERIN would be the best model for
inclusion in crop simulation models. However parti- tioning light according only to height difference Eq.
4 leads to large underestimation of light compe- tition, i.e. between-component differences in light
absorption are underestimated.
Several authors have described the structure of multispecies canopies as a multilayer canopy where
the layer boundaries were defined by the height of the vegetation components Rimmington, 1985; Graf
et al., 1990. This means that a mixture where com- ponents have the same height could be described
as a monolayer. Fig. 3 shows the significant effect of the vertical distribution of leaf area in the case
of similar heights for the components. Indeed disre- garding the vertical distribution of leaf area leads to
underestimate competition between the two species.
262 H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263
This effect also exists, but to a lesser extent, when the components have different heights. These results
are not fully consistent with previous simulation re- sults, where Sinoquet and Caldwell 1995 showed
that the main determinants of light partitioning in two-species mixtures were: i the relative height of
the two components and ii differences in leaf incli- nation. The vertical profile of leaf area density was
claimed to be of least importance. These conclusions were drawn from computations with the SIRASCA
model involving theoretical vertical profiles of leaf area density. Such results would have suggested that
describing the canopy as a monolayer or a two-layer canopy would be enough. In another approach, Faurie
et al. 1996 proposed that light partitioning between species be related to their relative contribution to the
upper canopy layer of total LAI equal to 3, because light transmission below a LAI of 3 is negligible. Al-
though useful, such an approach requires knowledge of the vertical profile of leaf area in order to define the
upper layer of LAI equal to 3, and the contribution of the vegetation components to this layer.
Finally, it appears that a simplified description of canopy structure leads to biased estimation of light
partitioning between species. This means that a de- scription of canopy structure in terms of LAI of each
component in each layer would be necessary. How- ever, current crop simulation models for multispecies
canopies are unable to simulate canopy structure to the required degree.
6. Conclusion
