H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263 255
2.3. Simplified Kubelka–Munk equations KMS in a multispecies multilayer canopy
The multilayer canopy is described in terms of LAI L
ik
and mean leaf inclination θ
ik
of each vegeta- tion component i in each layer k k=1, . . . , M. Light
transmission is computed from the top to the bottom of the canopy by successive applications of Eq. 21a.
Light transmitted at the bottom of layer k is thus
T
k
=
k
Y
l=1
exp −K
′ l
22 Upward fluxes at the layer boundaries are then re-
cursively computed from the bottom to the top of the canopy by successive applications of Eq. 17. At
ground level i.e. the bottom of layer M,
A
M
= ρ
s
T
M
23 For other layers k,
A
k
= T
k
ρ
∞k
1 − ρ
∞k
A
k+1
T
k+1
+ A
k+1
T
k+1
− ρ
∞k
exp −2K
′ k
1 − ρ
∞k
A
k+1
T
k+1
+ ρ
∞k
A
k+1
T
k+1
− ρ
∞k
exp −2K
′ k
24 Eq. 24 is similar to Eq. 17 where incident radia-
tion is T
k
and soil reflectance ρ
s
is replaced by the ratio A
k +1
T
k +1
, i.e. equivalent to reflectance at the bottom of layer k+1. Notice that the reflectance of
the multilayer canopy can be computed from Eq. 24 with k=0.
Light absorption by vegetation layers and light partitioning between vegetation components are then
computed from fluxes T
k
and A
k
by using relation- ships similar to Eqs. 18 and 19.
3. Multispecies canopies for model application
3.1. Two-species monolayer canopies The light models were applied to theoretical mono-
layer canopies simulating well-mixed grass-legume mixtures. LAI of each species was varied between 0.25
and 5 in steps of 0.25, and all possible combinations of the two species were simulated. Leaf angle of Species
1 and 2 were assumed to be 25 and 65
◦
, i.e. those of a planophile and an erectophile species, such as
numerous legumes and grasses Ross, 1981, respec- tively. In a first series of simulation runs mimicking
low scattering, leaf scattering coefficient was set to 0.20 for both species and soil reflectance was 0.15. In
a second series of runs accounting for high scattering, leaf scattering coefficient and soil reflectance were set
to 0.80 and 0.40, respectively.
3.2. Multispecies multilayer canopies The light models were applied to multilayered mix-
tures from canopy structure data taken from the litera- ture. The first one was a grass-legume mixture made of
Lolium perenne and Trifolium repens, where the two components had similar heights Faurie et al., 1996.
Total LAI of the canopy ranged from 1.1 to 12.3. The plant canopy was divided into 2–6 horizontal layers
of variable thickness, depending of growth stage. Leaf area index of the two species and mean leaf inclina-
tion of L. perenne within each layer were computed from Faurie et al. 1996 see Figs. 1 and 2, p. 38.
Mean leaflet inclination of T. repens ranged from 25
◦
at the bottom of the canopy to 45
◦
in the upper layer Soussana et al., 1995.
The second canopy was a binary mixture of Vicia sativa and Avena sativa, Ouknider and Jacquard,
1989. Total LAI ranged from 5.6 to 12.3. One or the other component dominated, i.e. was taller, de-
pending on plant density, growth stage and nitrogen treatment. The canopy was divided into 3–6 layers of
20 cm where LAI of each component was measured Ouknider and Jacquard, 1989 see Figs. 4 and 5, p.
396. As leaf inclinations were not measured, they were assumed to range from the top to the bottom of
the canopy: from 40 to 25
◦
for V. sativa and from 40 to 65
◦
for A. sativa, according to the rather planophile and erectophile habit exhibited by the two species
in the deeper canopy, respectively Nichiporovitch, 1961.
The third canopy was a four-component mixture made of rice overgrown with three groups of weeds:
tall Cyperaceae, other Graminaceae and small di- cotyledons Graf et al., 1990. Total LAI ranged from
1.9 to 5.7. The multilayer canopy was built from height dynamics and vertical profiles of leaf density
256 H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263
Fig. 1. Comparison between SIRASCA and ERIN models in case of monolayer canopies: fraction of absorbed radiation by
planophile Species 1 a and erectophile Species 2 b under low scattering condition. See text for input parameters.
provided by Graf et al. 1990 see Fig. 2, p. 376 for each component. The canopy was divided into four
layers, the upper boundary of which corresponded to the height of the four components. The top layer only
included leaf area of the dominating rice, while the bottom one consisted of a mixture of the four compo-
nents. From the top to the bottom of the canopy, rice and grass weeds i.e. Cyperaceae and other Poaceae
were attributed leaf inclinations ranging from 40 to 70
◦
, according to Ito et al. 1973 and Sheehy and
Fig. 2. Simulated fraction of absorbed radiation by planophile Species 1 a and erectophile Species 2 b in a monolayer
canopy under low scattering conditions, as a function of species LAI, for three values of LAI of the other species: 1 open sym-
bols, 3 grey symbols, 5 black symbols. Comparison between SIRASCA
j
KMS
d
and ERIN
m
models. See text for input parameters.
Cooper 1973. Following Nichiporovitch 1961, leaf inclination of small dicots was assumed to be 25
◦
. For all three kinds of multilayer canopies, leaf scatt-
ering coefficient of every component and soil refle- ctance were assumed to be 0.20 and 0.15, respectively,
which are common values in the PAR waveband.
H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263 257
3.3. Model application to the multispecies canopies Light partitioning between species in all mixed
canopies described earlier was computed using SIR- ASCA Sinoquet et al., 1990, ERIN Wallace, 1997
and the KMS model proposed in this work. SIRASCA was assumed to provide the reference
computations, because it is a 1D version of a 3D model which has been tested against experimental
data in a large number of contrasting canopies, e.g. grass–legume mixtures Sinoquet et al., 1990; Fau-
rie et al., 1996, row canopies Sinoquet and Bon- homme, 1992; Andrieu and Sinoquet, 1993; Mabrouk
et al., 1997, alley-cropping Tournebize and Sinoquet, 1995. SIRASCA was run using LAI and mean leaf
inclination of each plant species in each canopy layer, as well as leaf scattering coefficient of each species.
Incident radiation was assumed to be an overcast sky obeying the SOC luminance distribution Moon and
Spencer, 1942.
ERIN was run with some modifications to the orig- inal version proposed by Wallace 1997. The original
extinction coefficients were replaced by those given by Eq. 6 i.e. as a function of mean leaf inclina-
tion, and they were weighed by √
1 − σ in order to account for leaf scattering as proposed by Goudri-
aan, 1977. Such changes were aimed at harmonising the models for the calculation of the extinction coeffi-
cients, in order to compare the models only with regard to their ability in computing light partitioning. In the
case of the monolayer canopy, the two-species were assumed to have the same height, while plant height
was entered as described earlier for the multilayer canopies. ERIN was not applied to the four-component
canopy.
With regard to the KM model proposed in this work, only the simplified equations as described in Section
2.3 were used, even in the case of the monolayer canopy.
4. Results
