Agricultural and Forest Meteorology 101 2000 251–263
Comparison of models for daily light partitioning in multispecies canopies
H. Sinoquet
a,∗
, M. Rakocevic
b
, C. Varlet-Grancher
c
a
INRA-PIAF, Site de Crouelle, 234 avenue du Brézet, F-63039 Clermont-Ferrand Cedex 2, France
b
Faculty of Agriculture, University of Belgrade, 11080 Zemun, Yugoslavia
c
INRA-SEPF, Domaine des Verrines, F-86600 Lusignan, France Received 16 July 1999; received in revised form 3 December 1999; accepted 9 December 1999
Abstract
A simulation model of light partitioning in horizontally homogeneous multispecies canopies is proposed. The model is based on the Kubelka–Munk equations KM applied to a mixture of N vegetation components. Only two hemispherical fluxes, i.e.
downwards and upwards, are considered. The exact solution of KM equations was then simplified in such a way that the model can be easily extended to multispecies canopies including several vegetation layers. The simplified KM model KMS was
compared to two other light models dealing with mixed canopies: the more detailed model SIRASCA [Sinoquet, H., Moulia, B., Gastal, F., Bonhomme, R., Varlet-Grancher, C., 1990. Modeling the radiative balance of the components of a well-mixed
canopy: application to a white clover–tall fescue mixture. Acta Oecol. 11, 469–486], and the simpler model ERIN [Wallace, J.S., 1997. Evaporation and radiation interception by neighbouring plants. Q. J. R. Meteorol. Soc. 123, 1885–1905]. All three
models were applied to theoretical two-species monolayer canopies, and to actual mixed canopies, the geometry of which was retrieved from the literature. In the PAR waveband, the model KMS gave simulation results very similar to those of SIRASCA
in case of contrasted canopy structures. In conditions of high leaf and soil scattering, deviations between SIRASCA and KMS outputs were higher and reached maximum values of –0.08 for erectophile species. Comparison between SIRASCA and ERIN
outputs showed that ERIN largely underestimated light competition in a two-component canopy in several conditions, due to light partitioning only based on height differences between components. Simulations also showed the significant effect of the
vertical distribution of leaf area on light partitioning in the case of mixtures where components had equal or different heights. Finally it appears that the model KMS could be a candidate for inclusion in growth models for multispecies canopies, since all
KMS parameters have physical meaning and it is very easy to implement. ©2000 Elsevier Science B.V. All rights reserved.
Keywords: Radiation balance; PAR; Inter-cropping; Grass; Legume; Canopy structure
1. Introduction
Light partitioning is a crucial issue in multispecies canopies because light is involved in most plant re-
sponses e.g. photosynthesis, transpiration, morpho-
∗
Corresponding author. Tel.: +33-4-73-62-4361; fax: +33-4-73-62-4454.
E-mail address: sinoquetclermont.inra.fr H. Sinoquet.
genesis and the effects of light reduction on the dom- inated species may be either negative e.g. species
extinction, Caldwell, 1987 or positive e.g. shelter from water stress, Allen et al., 1976; improvement of
light use efficiency, Willey, 1979; Harris et al., 1987; Cruz, 1995. All process-based simulation models de-
voted to multispecies canopies treecrop, McMurtrie and Wolf, 1983; e.g. cropweeds, Kiniry et al., 1992;
cropcrop, Caldwell and Hansen, 1993; grasslegume,
0168-192300 – see front matter ©2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 9 9 0 0 1 7 2 - 0
252 H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263
Soussana et al., 2000 include a sub-model of light partitioning between species. Similarly growth analy-
sis methods for multispecies canopies are all based on the ones by Monteith 1972 where primary produc-
tion is regarded as the combined result of light capture and use. This requires the assessment of light sharing
between species. This is expressed in terms of light interception efficiency ε
i
of individual component i, namely the fraction of incident radiation which is ab-
sorbed by component i e.g. Azam-Ali et al., 1990; Cruz and Sinoquet, 1994.
All simulation models devoted to light partition- ing between species are based on the turbid medium
analogy, i.e. the classical Beer’s law computing light transmission I as a negative exponential function of
the downward cumulated leaf area index LAI, L
I = I exp −KL
1 where I
is incident radiation and K is an extinction coefficient. Because it deals with light transmission
i.e. non-intercepted radiation, Beer’s law cannot be used by itself to estimate light sharing between
species, except if foliages occupy separated canopy spaces e.g. treegrass, McMurtrie and Wolf, 1983. In
other cases, assessment of light partitioning needs fur- ther development. From the basic assumptions used
to derive Beer’s law in vegetation canopies i.e. small leaf size, random leaf dispersion, several authors
e.g. Rimmington, 1984; Sinoquet and Bonhomme, 1991 showed that light interception efficiency ε
i
of species i in a mixture of N components can be written
ε
i
= K
i
L
i
P
N j =1
K
j
L
j
1 − exp
−
N
X
j =1
K
j
L
j
2 Eq. 2 shows that total light interception i.e. the term
in square brackets in the right member is partitioned between species according to their contribution to
total LAI L
i
weighted by their interception ability i.e. extinction coefficient K
i
. While several models are based on Eq. 2 Rimmington, 1984; Ryel et al.,
1990; Sinoquet et al., 1990; Wiles and Wilkerson, 1991, other models share light between species ac-
cording only to the contribution to total LAI Spitters and Aerts, 1983; Graf et al., 1990, i.e. differences in
extinction coefficient are not taken into account. Eq. 2 or similar relationships have been included in light
models by different ways. The canopy may be treated as a mono-layer Rimmington, 1984 or a multilayer
medium Spitters and Aerts, 1983; Rimmington, 1985; Graf et al., 1990. Most models applied Eq. 2
to a single hemispherical downward flux, but Ryel et al. 1990 and Sinoquet et al. 1990 distinguished a
set of directions in order to apply Eq. 2 to directional fluxes. Ryel et al. 1990 and Sinoquet et al. 1990
also included multiple scattering in their models.
In contrast to the previous approach, Wallace et al. 1991 proposed a rather different way to esti-
mate light sharing in two-species canopies: in the first step, light interception is computed from Beer’s
law applied to i a two-layer canopy where Species 1 overtops Species 2 ε
1 max
and ε
2 min
, and ii another one where Species 2 overtops Species 1
ε
1 min
and ε
2 max
. These two virtual situations corre- spond to cases of maximum dominance of one species
over the other, hence in the actual situation, ε
i
range between ε
i min
and ε
i max
. In the following step, ε
i
is thus written as a linear combination of ε
i min
and ε
i max
ε
i
= ε
min i
1 − f
i
+ ε
max i
f
i
3 where f is an empirical function of species heights h
1
and h
2
, e.g. Wallace, 1997 f
i
= h
i
h
1
+ h
2
4 Although light partitioning models are numerous,
candidates that could be included as sub-models in simulation models of multiple-species are scarce.
Detailed models e.g. Ryel et al., 1990; Sinoquet et al., 1990 include most knowledge about radiation
transfer within canopies, but they are too complex to be included in growth models. Simpler models
generally use parameters which are not explicitly related to canopy structure and leaf optical proper-
ties, i.e. the parameters involved in radiation transfer. This is especially true for the extinction coefficient
in all models dealing with a single downward flux. Last but not least, light sub-models should explic-
itly take into account the main determinants of light partitioning, i.e. vertical dominance and differences
in foliage inclination Sinoquet and Caldwell, 1995. While mono-layer models do not match this re-
quirement, multilayer models and that of Wallace 1997 explicitly deal with the vertical structure of
H. Sinoquet et al. Agricultural and Forest Meteorology 101 2000 251–263 253
multiple species canopies. Multilayer models, how- ever, need many more input parameters i.e. LAI
of each component in each layer than of Wallace 1997 i.e. total LAI and height of each compo-
nent.
The first objective of this paper was to propose a simple light partitioning model for horizontally homo-
geneous canopies, where parameters could be explic- itly related to canopy structure and optical properties
of the leaves and the soil surface. Such a model would be useful as a sub-model in growth simulation mod-
els. For this purpose, we derived the KM equations Kubelka and Munk, 1931 for the case of a mixture of
N vegetation components, and we simplified the solu- tion in order to obtain simple equations for light par-
titioning. As a test, we compared the simplified KM equations KMS to the detailed model of Sinoquet
et al. 1990 on contrasting canopy structures. The second objective was to assess the requirements in
structure parameters for an accurate estimation of light partitioning. For this, the detailed and simplified
models were run on mono and multilayer canopies, and compared with the model of Wallace 1997.
2. Kubelka–Munk equations for multispecies canopies
