AGRICULTURAL
AND
FOREST
METEOROLOGY
Agricultural and Forest Meteorology85 (1997) 33-49
ELSEVIER
Optics of vegetation: implications for the radiation balance and
photosynthetic performance
Oleg Anisimov, Leonid Fukshansky
*
Biological Institute II, University of Freiburg, Sch2inzlestrasse 1, 79104 Freiburg i.B., Germany
Received 23 October 1995; revised 3 June 1996; accepted30 July 1996
Abstract
This paper considers light propagation in vegetation stands using an analysis of transmitted, absorbed and reflected
visible and near-infrared radiation, light gradients and photosynthetic performance. Optical theories of different complexity,
including the most sophisticated novel extension of the radiative transfer theory to fluctuating media, have been compared.
Whereas for the global radiation balance even the simple models are acceptable, calculation of absorption of the light and
light spectra necessary for the analysis of the photosynthetic performance requires more advanced radiation transfer theories.
It was shown that the stochastic heterogeneity of a canopy caused by clustering and clumping of the phytoelements affects
absorption and photosynthesis. In particular, heterogeneous canopies can absorb up to 15% less radiation and can have up to
15% higher efficiency of photosynthesis than a macrohomogeneous canopy with the same biomass. The state of the
phytochrome, the main pigment for the developmental control of light, has been calculated at different depths in the canopy.
The calculated phytoctwome profile is distorted when simple radiation transfer models are used. This profile is also strongly
affected by the degree of stochastic heterogeneity. © 1997 Elsevier Science B.V.
1. Introduction
The quantitative description of light-vegetation interactions is an important issue in photobiology and
environmental sciences. On a tissue level, it is required to correct in vivo absorption and action spectra
(Fukshansky, 1991; Richter and Fukshansky, 1994) and for the structural analysis of leaf photosynthesis and
photosynthetic adaptation (Fnkshansky and Martinez von Remisowsky, 1992). On a canopy level, it is a central
step in many environmental studies which include: (1) calculation of the transmitted, reflected and absorbed
photosynthetically active radiation (PAR, 400-700 nm), and near-infrared (NIR) radiation (700-13 500 nm) in a
vegetation canopy fbr application in global climatological, geobotanical and hydrological studies (Dickinson,
1983); (2) calculation of the light profiles and spectra at different heights in structural analysis of photosynthetic
production and photomorphogenetic activity as well as of photodamage in a canopy (Mooney and Field, 1989).
* Corresponding author.
0168-1923/97/$17.00 ~) 1997 Elsevier Science B,V. All rights reserved.
PII S0168-1923(96)02392-1
O. Anisimov, 1~ Fukshansky / Agricultural and Forest Meteorology 85 (1997) 33-49
34
Light propagation in foliage is dominated by two processes: absorption and multiple scattering. Therefore, all
descriptions are within the scope of the radiative transfer approach (Chandrasekhar, 1960), although the various
models range from the most simple Lambert-Beer's law neglecting scattering to the general equation of
radiative transfer (a comprehensive review has been given by Myneni and Ross (1991)). The use of radiation
transfer models operating with spatially constant absorption and scattering coefficients evoked criticism because
vegetation is a macroheterogeneous random optical medium (Menzhulin and Anisimov, 1991). Owing to
clustering of the phytoelements around branches of different order and single trees, the leaf area density and,
consequently, the absorption and scattering properties become fluctuating variables in space. Furthermore,
spatial fluctuations are superimposed on random temporal variations of leaves' positions. Considered in this
way, random spatial pattern of absorption results in the so-called distributional error (sieve effect). This effect is
not accounted for in the standard radiation transfer theory. It can be dealt with the theory of absorption statistics
(Fukshansky, 1987), which predicts an increased transmission in a heterogeneous sample as compared with the
same amount of uniformly spaced absorber.
Characteristics of both absorption and scattering appear not as fixed values ascribed to a unit volume but as
sums of the mean value and a fluctuating term. The recently developed extension of the radiative transfer
approach to fluctuating media (Anisimov and Fukshansky, 1992) considers optical parameters as random
variables characterized by mean values, variances and higher statistical moments. Accordingly, this theory
yields statistical characteristics of the radiation fields: mean values and higher moments of the radiances and
fluxes. The conventional theory of radiative transfer appears as a limiting case of the stochastic theory in which
the fluctuations are reduced to zero.
Thus we have a set of optical models of vegetation applicable to numerous ecological problems subdivided
into two groups. The aim of this paper is to show how far the radiative field calculations can be improved by
use of the more advanced models, and whether new problems can be stated or new methods developed on their
basis. On the other hand, we can estimate errors owing to the optical approximations, set limits for the use of
simplified models and prevent overinterpretations.
After an introductory review of the theoretical framework of the different models (Section 2), we perform
comparative calculations for the basic problems in the areas of radiation balance, propagation of PAR and NIR
radiation (Section 3.1), and analysis of photosynthesis and photomorphogenesis within a canopy (Section 3.2).
On the basis of a detailed discussion of these results (Section 4), we make some general conclusions and outline
plans for future developments.
2. Methods
2.1. Theoretical framework of different models
2.1.1. Exponential law
The simplest model is the modified variant of the exponential formula for the extinction of the downwelling
light in the vegetation canopy suggested byMonsi and Saeki (1953):
I(L,/x) = l(0,/x), exp( - K . L)
(1)
where I is the direct beam intensity, L is the leaf area index, K is the extinction coefficient of the vegetation
canopy and /z is the directional cosine of the beam. Extinction coefficient K can be expressed through the
geometrical parameters of the canopy as
G(L,~)
~(L,~) = - /z
where G is the angular distribution of leaves (Ross, 1981).
(2)
O. Anisimov, L. Fukshansky /Agricultural and Forest Meteorology 85 (1997) 33-49
35
Eq. (1) does not take into account the light scattered by the phytoelements. Goudriaan (1977) found that for
small values of the leaf scattering coefficient, to < 0.2, i.e. over the whole photosynthetically active radiation
band, Eq. (1) can be fitted to real data by an empirical adjustment of the extinction coefficient:
K ( L , I z ) = G(L'Ix-----~)-(1 - to),/2
/z
(3)
Thus it is possible to estimate the vertical profile of the total downwelling radiation flux by substituting Eq. (3)
into Eq. (1) and integrating over different directions of incident light.
2.1.2. Conventional radiation transfer equation (CRT)
Better accuracy is provided by the modified radiation transfer equation (Ross, 1981):
bl( L,r)
ix" O---T - - =
- G ( L,r) . I( L,r)
+ far( L,r,r') . l( L,r')dg2'
(4)
where F is the volumetric scattering phase function of the vegetation canopy per unit leaf area. The way for the
radiative transfer approach in phytoactinometry was paved by Ross's pioneering derivation of the relationships
between the measured quantities--optics and spatial distribution of the phytoelements--on one hand, and the
volumetric optical parameters on the other hand (Ross, 1981). The function F can be expressed through the
scattering phase function of a single phytoelement 7 and leaf normal distribution function g as
r(L,r,,") = f.r- lcos(,.i ,,.')I os(rL,r)ldaL
(5)
Here r and r' are the directions of scattered and incident beams, rt., is the leaf orientation, and /21 is the upper
hemisphere. Orientational functions G and g are related by the expression (Ross, 1981)
=
f,o, ±2~r • g( L,rL)lCos(r L ,r) Idg2L
(6)
Eq. (4) with the boundary conditions for the incident light and light reflected from the soil can be used to
calculate the intensities and radiation fluxes in a spatially homogeneous vegetation canopy. Even in the
one-dimensional version of Eq. (4) the equation of radiative transfer has no general analytical solution, and
many numerical methods have been developed for the different parameter ranges (Van de Hulst, 1980).
2.1.3. Two-stream approximation
In many practical cases the continuous radiation transfer description of the type Eq. (4) can be replaced by
the so-called multi-,~tream approximation (Mudgett and Richards, 1971). The simplest case is the two-stream
model, which in addition to the direct radiation considers only two hemispheric scattered fluxes: the downward
and upward diffuse light. In this model the diffuse radiances in different directions within a hemisphere are not
distinguished. The phenomenologieal absorption and scattering coefficients of the two-stream theory are not
equivalent to those of the radiation transfer equation; being quantities averaged over all angular components of
light, they are dependent on the angular distribution, which generally changes with depth. Therefore, these
coefficients are unknown functions of the depth coordinate. They also depend on the thickness of the sample,
phase function, absorption of the medium and on the angular distribution of the incident radiation, i.e. in the
case of a canopy on the Sun's elevation angle. Calculations illustrating these conclusions have been given, for
example, by Niklasson (1987). Therefore, the constant coefficients of a two-stream model are not physical
quantities but rather fitting parameters which should be varied until the fluxes calculated with this model agree
with those found by a more exact theory or experiment.
36
O. Anisimov, L. Fukshansky/ Agricultural and Forest Meteorology 85 (1997) 33-49
The use of the two-stream models for canopies seems to be not very relevant, first because of the
macroheterogeneity; second because here the optical parameters can be directly measured and by means of a
known procedure (Eqs. (2) and (5) and Eq. (6)) inserted in the better radiation transfer model (Eq. (4)).
Nevertheless, we will include this model in the subsequent tests because it has been suggested (Dickinson,
1983) and used (Sellers, 1985; Choudhury, 1987; Sellers et al., 1992) in canopy optics (however, by Sellers
(1985) only for calculations of the radiation balance, not of light profiles, where Goudriaan's formula (3) was
applied). Dickinson's model is based on a comprehensive study of the two-stream approximations applicable to
radiation transfer in planetary atmospheres by Meador and Weaver (1980), who derived the general form for a
family of two-stream models. Dickinson (1983) suggested and Sellers (1985) adopted for canopy calculations
one of them, the so-called constant hemispheric model. This was by no means the best choice because the model
originally developed by Coakley and Chylek (1975) as a case converging to the rigorous theory in the thin
atmosphere limit is not expected to be a good approximation for thick canopies, i.e. those with large leaf area
index (LAI). Even more unfavourable is that two errors crept in when representing the model in terms of canopy
characteristics. First, the terms for the direct flux (right-hand side of Eqs. (2.8) and (2.9) of Dickinson (1983)
and Eqs. (1) and (2) of Sellers (1985)) contain the superfluous factor K. Second, the boundary conditions for the
upward diffuse flux lack the factor/~ (in Eq. (9) of Sellers (1985)). Our calculations show that these errors can
result in albedos exceeding unity for some solar elevation angles. Therefore, in the calculations we apply the
corrected form of Dickinson's model:
-~"
~.
OJ-(L)
0----'~+ [1 - (1 - f l ) o o ] l + ( L ) - r.o/3I-(L) = wTz/3o • e x p ( - K . L)
OF(L)
O------E---+[1-(1--/3)~]I+(L)--o.~/3I-(L)=oJ~(1-/3o).exp(-K.L)
(7)
where I- and I + are the propagation ratios for the hemispheric downwards and upwards fluxes of radiation,
scattered by phytoelements, to incident radiation flux, o~ is the volumetric scattering coefficient, /3 and /3o are
the fractions of backscattering for the diffuse and direct beams, and /z is the average inverse optical depth for
the diffuse radiation per unit leaf area, defined as
t
rl
/-~
r
~ = J0 G - - ~ d/z
(8)
The boundary conditions for Eq. (7) have the following form:
I + (0) = 0
(9)
I - ( Lo) = As[ Is( Lo)l,Xs + Id( Lo) + l+(Lo) ]
where A s is the soil albedo, Is and Id are the propagation ratios (relative to incident light components) of the
direct sunlight and diffuse sky radiation, respectively, and Izs is the cosine of the Sun's zenith angle. The
attenuation of the direct components of the radiation field (direct solar and diffuse sky radiation) is calculated
using the exponential Eq. (1).
As one can see, the parameters of Eq. (7) are not fired, and should be derived somehow from the properties
of the phytoelements. Obviously, no rigorous procedure for this purpose (like Ross's procedure for the proper
radiation transfer model) exists on the level of the two-stream model. Different approximate relationships
proposed so far can produce shifts of the parameter values which are not related to any real properties of a
canopy. To exclude this source of uncertainty we use in our tests at this stage the simplest case of uniformly
oriented phytoelements with isotropic scattering, where any approximation and even direct use of the leaf
parameters instead of the volumetric properties will result in the same parameter values.
O. Anisimov, L Fukshansky/ Agricultural and Forest Meteorology 85 (1997) 33-49
37
2.1.4. Stochastic theory of the radiation transfer (SRT)
A more realistic approach to account for the spatial and temporal inhomogeneity of the leaf distribution and
orientation is based on the stochastic radiation transfer equations, which consider both the vegetation and the
radiation field parameters as random functions. Such a method has been developed for the general case of a
random macroheterogeneous optical medium (Anisimov and Fukshansky, 1992), and was further adapted to
describe the radiation field in the vegetation canopy with varying geometry and fluctuating optical parameters
(Anisimov and Fukshansky, 1993).
The stochastic radiation transfer equations are derived from the basic light transfer Eq. (4) using the
procedure of statistical averaging over the random fluctuations of optical and radiation field parameters. The
system for the mean value of the light intensity has the form (Anisimov and Fukshansky, 1993)
7+
-7
l f4 F(r,r,)K( rl) . l( rl,Z)dg21 - --~
1 F( r,r)K'( r) I'( r,z)
_ ~ z [-gWj := ( ~,)2.7 + ~-7' .~+ ( K')21 '
1 1,(r,r)[K,E(r).~+K,(r)i,(r,z).K(r)+K,2(r)l,(r,z)
47r
-I~-~z[(K'lZI']=K'3.7+K'ZI'.~,+
]
2. (K')2.~-Q 7
1
4rrF(r,r)[K'3(r)"l(r,z) + K'2(r)l'(r,z).K(r)
(lO)
+ 2.K'2(r).K'(rll'(r,z)]
In these equations the vertical coordinate z is considered as the independent variable, and the horizontal
inhomogeneity of the leaf area index is included in the random fluctuations of the volumetric optical parameters.
A horizontal bar designates statistical averaging; K' and I' are the random fluctuations of the volumetric
extinction coefficient and light intensity. For the details of derivation of Eq. (10) as well as corresponding
equations for the higher statistical moments of radiance the reader is referred to the original paper cited above.
Variation of the w~getation optical parameters was described through the variance and asymmetry coefficients
of K:
K' 3
C~=
--
K
,-,k
¢~a - - -
-
(11)
(K,2) 3/2
The boundary conditions for Eq. (10) are, for the downward radiation on upper boundary:
I(r,z*)=Io(r,z* ) K'l'(r,z')=K'2I'(r,z*)=O
(12)
and, for the upward radiation on the lower boundary:
Z(r,0)
=asf l(rl,0)dg21
Ol
K'I'(r,O) =K'2I'(r,O)
= 0
(13)
where I ( r , z * ) is the radiation incident on the vegetation canopy.
The last step ensuring the application of the stochastic theory was to derive the higher statistical moments of
the volumetric optical parameters on the basis of the fluctuations of the geometrical and optical parameters of
the phytoelements. This is an extension of Ross's procedure, which solved the same problem for the mean
values (see Eq. (5) and Eq. (6)). This derivation was given previously (Anisimov and Fukshansky, 1993).
38
O. Anisimov, L Fukshansky/ Agricultural and ForestMeteorology 85 (1997) 33-49
2.2. Input data
Fig. l(a) and Fig. l(b) show the typical spectral composition of the incident solar and diffuse sky PAR used
in the calculations, as well as the spectral scattering coefficient of PAR for a green leaf. Scattering coefficient
for NIR radiation was assumed to be a constant value equal to 0.85. Most of the calculations were performed for
a vegetation canopy with a total LAI of five, a random leaf normal distribution, G = 0.5, and a uniform leaf
scattering phase function. In this case, the volumetric scattering cross-section can be replaced by the spectral
leaf scattering coefficient to E. Mean values of the leaf scattering coefficient and soil reflectance were
respectively 0.20 and 0.15 for PAR, and 0.85 and 0.30 for NIR radiation.
Variance and asymmetry coefficients of K can be estimated using the raw data on the leaf area density and
leaf angular distribution; normally in a canopy without large visible gaps Cvk does not exceed 0.5, whereas Cak
ranges from - 1 . 0 to 1.0. At first glance, the stochastic theory seems to require more measured data than is
needed for CRT calculations, but this is not the case. Any sample of measured magnitudes U(p), G(r,p), F ( p )
(where p is a random space point), which provide reliable mean values of volumetric optical parameters, must
contain enough information to permit calculating their higher statistical moments.
1o
a
O8
0
0
0
//"\
04
//
Ils
\\
/
.,\
0,2
00
400
s~o
800
l
760
~o
wave length, nm
0.0
wave length, nm
Fig. 1. (a) Spectral scatteringcoefficientof the phytoelements(after Ross (1981)). (b) Typicaldaylight spectra for diffuse sky radiation (0)
and direct sunlight ( O ) (after Smith and Morgan (1981)).
O. Anisimov, L. Fukshanskyl Agricultural and ForestMeteorology85 (1997)33-49
39
Most forests are characterized by a negative asymmetry of the extinction coefficient, this effect resulting
primarily from the pyramidal shape of the trees, with relatively low and highly variable leaf area density in the
upper layers. In different calculations the variance coefficient of K was set equal to 0, 0.25 and 0.50, to
correspond to a homogeneous, slightly inhomogeneous and noticeably macroheterogeneous vegetation canopy;
the asymmetry coefficient was set equal to - 0 . 8 , 0, and 1.0. With this choice we introduce the first rather
coarse classification of canopies with respect to the random macroheterogeneity.
2.3. Comparison of models with the experimental data
All the models considered in this paper were used to calculate the radiation field parameters in different
vegetation canopies. The comparison of model results with experimental data has been discussed in several
studies (Goudriaan, 1977; Ross, 1980, Ross, 1981; Sellers, 1985; Anisimov, 1988, Menzhulin and Anisimov,
1991, Anisimov and Fukshansky, 1993), and can be summarized as follows.
Eqs. (1)-(3) can provide reasonably good fit to the measured values of the downward radiation flux, as the
extinction coefficient K is empirically adjusted to a particular canopy type (Goudriaan, 1977). For the same
reason, this semiempirical method is not suited for the general analysis and in principle cannot be used to study
the canopy reflectance, as the upward radiation flux is not considered.
1.00
0.80
•
;_~t ~
O
O0
, ..,/,
0.60-
////"/
// //
";~
/
"~ o.4o-
0.20 0.0
0.00
0.00
0.5
0.125
e k, = 0.25
-
0.25
0.50
0.75
1 . 0t 0
P r o p a g a t i o n ratio
Fig. 2. Verticalprofilesof the propagationratio for the direct light in a reed stand calculatedby the SRT model, with different values of the
variance of the extinction coefficient: I1, Cv
k = 0; r3 ckv= 0.125; o, Ck = 0.250; V, Ckv= 0.500. O, Measured values. (After Anisimov
(1988).)
O. Anisimov, L Fukshansky /Agricultural and Forest Meteorology 85 (1997) 33-49
40
The accuracy of the two-stream approach was tested by Sellers (1985), who found that the calculated canopy
albedo for the short-wave radiation agreed closely with the measured data for a wide range of Sun elevation
angles (Fig. 1 of Sellers (1985)). He also found that there were noticeable divergences between the calculated
and measured values of light absorption and transmittance along the pathways through a canopy with high
optical thickness (Figs. 2 and 3 of Sellers (1985)). Both these statements, however, can be questioned, because
the two-stream calculations applied there were based on an erroneous formula (see Section 2.1).
Ross (1980, Ross, 1981) considered the general case of conventional radiation transfer theory and a number
of particular models for vegetation canopies, which were compared with the data obtained from the field
measurements. The conclusions of such a comparison were the following. The conventional radiation transfer
theory and the models based on the radiation transfer equations (including the two-stream models) provide
reasonably good accuracy in estimating the albedo and the penetration function of the diffuse short-wave
radiation in dense and spatially homogeneous vegetation; even in case of the homogeneous vegetation the
y
1.00
0.80
¢:uO
~.~ 0.60 / ~
1.00
,.C:
~
.~
a
.~
.
/
b ~ y "
0.80
.,,-a
060
--g
0.40
0 20
040
0 2O
O 00
025
0.00
050
0
5
0 O0
0.00
1 O0
Downward fluxes under
diffuse radiation
1.00
I O0
C"
.,~
,.C
0 80
0.60
•
"~
0.60
0.40
'
•"~
040
0.20
-
0.00
"~'
.
.
o.oo
.
.
.
,
o.~5
o.;o
o.~6
Downward fluxes under
direct solar radiation
0 10
Upward fluxes under
diffuse radiation
-
080 ~
0.05
l.bo
0.20
-
d
•
-
/
2
0.00
0.00
0.05
O.'IO
Upward fluxes under
direct solar radiation
Fig. 3. Light profiles through the vegetation canopy with a total LAI = 5: II, Goudriaan's model; o, two-stream model; rq, radiation
transfer equation; v , stochastic model with c~k = 0.5 and c ak = --0.8. Upper panel (a,b), diffuse skylight (uniform sky); lower panel (c,d),
sunlight, Sun elevation 45 °.
O. Anisimov, L. Fukshansky/ Agricultural and ForestMeteorology 85 (1997) 33-49
41
propagation of the direct solar radiation is underestimated. The theory and subsequent models provide rather
poor accuracy for all components of the radiation field except the canopy albedo, when macroheterogeneous
canopies are considered: the calculated short-wave light extinction is overestimated.
The stochastic properties of the radiation field in inhomogeneous vegetation, which are explicitly taken into
account within the f:ramework of the SRT approach, were studied experimentally (Anisimov, 1988), and
numerically through Monte-Carlo simulations of light attenuation through a canopy with known statistical
parameters of the extinction coefficient (Menzhulin and Anisimov, 1991). Both of these studies considered only
the direct component of the radiation field, neglecting the light scattered by the phytoelements. Anisimov and
Fukshansky (1993) gave several examples of SRT calculations of the total radiation field in vegetation with
different geometrical structure and statistical moments of the extinction coefficient.
In the experimental study of Anisimov (1988), the method of hemispheric photographs was used to calculate
the penetration of the direct solar and diffuse sky radiation into a reed stand. The photographs of the upper
hemisphere were taken at different heights at several training sites, and the relative density of gaps, which is in
this case an adequate index for the penetration ratio, was calculated for different directions of incident light. The
measurements of the geometrical parameters of the vegetation were performed immediately after taking the
photographs, and included: (1) number of plants and average distance between them; (2) height of plants; (3)
number of leaves and their area; (4) vertical distribution of leaves; (5) angular distribution of leaves.
The penetration of the direct solar and diffuse sky light in the reed stand with the same geometrical structure
was modelled using the Monte-Carlo method and the SRT approach. The measured profile of the penetration
ratio and the results of the SRT calculations for different values of the variance of the extinction coefficient are
shown in Fig. 2. As can be seen, the results calculated using the value of 0.25 for the variance coefficient of K
are in close agreement with the mean profile of the penetration ratio obtained with the help of hemispheric
photographs except a~t the highest level.
In more detail, the statistical moments of the extinction coefficient and effect on the radiation field were
addressed in the subsequent papers of Menzhulin and Anisimov (1991) and Anisimov and Fukshansky (1992).
The first of these papers contains figures contrasting the results obtained using two different modelling
strategies: the Monte-Carlo simulations (Figs. 2(a)-2(d), and 3(a) and 3(b)) and the SRT theory (Fig. 6(c)).
Although they were presented in different form (probability density of the penetration ratio at different depths in
the case of Monte-Carlo models, and vertical profiles of the mean penetration ratio in the case of the SRT
model), the values of the penetration ratios are very close in both types of curves, showing the increased light
penetration in the heterogeneous canopy with varying extinction coefficient. Thus it could be concluded that
when applied to a vegetation canopy with variable geometrical structure and optical properties, the SRT
approach provides higher accuracy than do any of the other radiation transfer theories and methods discussed
here.
3. Results
3.1. Light gradients and balance of PAR and NIR radiation
In this section we consider the light profiles and transmitted, reflected, and absorbed by vegetation canopy
PAR and NIR radiation. Fig. 3 shows the light profiles for downward and upward sunlight and diffuse sky
radiation integrated over the spectral range 400-13500nm, the Sun's elevation being equal to 45 ° and total
LAI = 5. For downward fluxes the same homogeneous canopy is represented by three different curves,
produced by the CRT, two-stream and Goudriaan models. The SRT model applied to this canopy will give the
same curve as the CRT model. The fourth curve represents the light flux in a macroheterogeneous canopy with
the same average LAI and higher statistical moments c vk = 0.5, c ak = - 0.8. If applied to this canopy, three other
models (CRT, two-stream and Goudriaan's) will produce the same curves as for the homogeneous canopy. The
O. Anisimov, L Fukshansky /Agricultural and Forest Meteorology 85 (1997) 33-49
42
i .00 -
1.00
J
0.80 -
,.~
0.60 0.40
-
/ /
0.80
"~
0.60
"--
0.40
(D
0.20
000L0.00
o~o
o~5
Downward fluxes. PAR
0.25
0.00
000
i bo
0.20 0.00
0.00
i
0.02
0.()4
f l u x e s , PAR
1.00
c
.j
...."~¢ /
0.60 0.40 -
/-~-
GJ .j,
,/o
' "I
Upward
1.00 080 -
b
U
0.25
0.50
..~
0.00
"~
r.
0.60
>
L
O.~t5
Downward fluxes, NIR
1.t)O
0.40
0.20
0.000 0 0
0.'25
0.50
Upward fluxes, NIR
Fig. 4. PAR and NIR light profiles through a vegetation canopy with a total LAI = 5 for diffuse skylight. Symbols are the same as in Fig. 3.
same statements are valid for the upward fluxes, with the addition that Goudriaan's model does not deal with the
idea of upward flux (therefore only three curves are presented).
One can see from Fig. 3 that the two-stream and even more so Goudriaan's model overestimate somewhat
the downward flux as compared with the results given by the CRT theory. This effect is more pronounced when
the Sun's incident flux instead of skylight was considered. The fluxes propagating deeply into the strongly
heterogeneous canopy (as calculated with the SRT) appear to be two to three times higher than those in a
homogeneous canopy (as calculated by radiative transfer model) with the same LAI. The upward fluxes on the
top of the canopy calculated with the two-stream model are higher than those calculated with the CRT, this
effect being more pronounced when the Sun is taken as the radiation source.
The difference in the spectral reflectivities of leaves and soil in the visible and NIR ranges produces dramatic
effect when PAR and NIR radiation components are considered separately. In our study we investigated how the
conclusions about the propagation of PAR and NIR radiation are affected by the choice of the optical model and
by the degree of random heterogeneity in a canopy.
The downward and upward light fluxes in the vegetation canopy with LAI = 5 under the condition of diffuse
sky irradiation calculated for PAR and NIR ranges, each taken separately, are presented in Fig. 4. (There is an
error in the study by Anisimov and Fukshansky (1993), where some results comparable with those in Fig. 4 are
presented; see p. 133 of this issue). It is seen that different models agree better in estimating the PAR, because
the leaf scattering coefficient for PAR is a factor of 4.5 lower than that for NIR radiation. Thus the errors owing
to the oversimplified description of light scattering are relatively small. The radiation fluxes calculated for the
macroheterogeneous canopy are distinctly different from those for the homogeneous vegetation if only the PAR
O. Anisimov, L Fukshansky /Agricultural and Forest Meteorology 85 (1997) 33-49
43
a
I.,AI= 1
LAI=3
LAI=5
LAI=7
NIR u n d e r d i f f u s e s k y r a d i a t i o n
b
LAI= 1
LAI=3
LAI=5
LAi=7
PAR u n d e r d i f f u s e s k y r a d i a t i o n
Fig. 5. Fractions of the transmitted, reflected and absorbed PAR and NIR radiation under diffuse sky radiation conditions. Columns 1-8 in
the histograms correspond to the following models: stochastic model (columns 1-6): 1-3, c k = 0.5; 4-6, c k ffi 0.25; asymmetry coefficient
of k = - 0 . 8 , 0, 1.0 (in columns 1, 2 and 3, respectively, and again in columns 4, 5 and 6, respectively). Column 7, radiation transfer
equation; column 8, two-stream model.
spectral range is considered, where scattering is small. This is a manifestation of the strong sieve effect, which
is not present in the NIR range, where the difference in the spatial pattern of absorption is smoothed by strong
scattering.
Fig. 5 presents the fractions of reflected, absorbed and transmitted by the canopy PAR (lower panel) and NIR
radiation (upper panel) calculated using different optical models and degrees of heterogeneity. The four boxes
represent four different LAI values (LAI = 1, 3, 5 and 7), each box being constructed in the following way.
Each single column corresponds to a definite canopy and a definite model, with the upper, middle and lower
part representing the reflected (hemispheric albedo), absorbed and transmitted fractions of the incident light,
respectively. The first six columns from the left correspond to macroheterogeneous canopies with different
combinations of Cvk and cak values (see figure legend) treated by the SRT model. The seventh and eighth
columns present a homogeneous canopy (with the same LAI) treated by the CRT and two-stream models,
respectively.
One can see that for LAI > 3 the PAR and NIR radiation spectral albedos do not change noticeably with the
total LAI; at least, these changes are very small compared with the differences between albedos calculated with
different models. Clearly, no information about the PAR and NIR fractions absorbed by the canopy or by the
soil can be gained directly from the hemispheric spectral albedos of the canopies with LAI > 3. Another
44
O. Anisimov, L. Fukshansky /Agricultural and Forest Meteorology 85 (1997) 33-49
consequence important for the photosynthetic studies is that the fraction of incident light absorbed by the
vegetation canopy strongly depends on the variance of the extinction coefficient, this effect being more
pronounced for PAR. Different models yield almost identical values of the absorbed fraction of PAR in a
homogeneous canopy over the whole range of LAI considered. In contrast, the introduction of a strong random
heterogeneity results in a significant decrease of the absorbed radiation.
3.2. Canopy photosynthesis and photomorphogenesis
So far, we have compared different models and canopy types with respect to the radiation field parameters.
In this section, the comparison is extended to the description of radiation as a driving force of photosynthesis.
For this purpose, a simple semi-empirical model of net leaf photosynthesis P as a function of absorbed PAR,
assuming no limitations from other environmental factors, is suitable:
P = PMAX" [1 -- exp(-ap-FpAR/PMAx)
]
(14)
Here PMAX is leaf photosynthesis under saturating light conditions (photosynthetic capacity), and Ap is the
apparent quantum efficiency. (The magnitudes P and PMAX are in IxmolCO2 m-2 s -1, Ap is in mol - l
photons mol CO2), and FpAR is in ixmolphotonsm -2 s-1.) The empirical constants PMAX and Ap acquire the
values
PMAX = 26.2 ixmolCO 2 m -2 s -1,
Ap = 0.273mol -1 photonsmolC02
(15)
from fitting a typical curve of C 3 photosynthesis under normal 02 and CO 2 partial pressure (see Fig. 11.1 of
Lawlor (1987)). These values correspond to 95% saturation of leaf CO z assimilation when the absorbed flux
reaches 2000 ixmol photons m -2 s-1 (incident flux is approximately 2350 Ixmol photons m -2 s-l).
On the basis of this model we can now scale leaf photosynthesis to the canopy level using descriptions of
light environment derived with different models and for different canopy types. Fig. 6(a) shows the photosynthesis of a canopy with LAI = 5 and uniform leaf orientation as a function of diffuse sky irradiance (the
lower curve represents single-leaf photosynthesis). The photosynthetic capacity is assumed constant over the
canopy height with the value given by Eq. (15). Different treatments give the same CO 2 assimilation for a
homogeneous canopy. Remarkably, the introduction of a strong heterogeneity results in only a 4% reduction of
the photosynthetic rate, even though, as shown in Fig. 5(b), the corresponding reduction of the absorbed PAR is
four times as much. This is obviously a consequence of better light penetration and redistribution of the
photosynthetic performance between upper (overilluminated) and lower (shaded) levels.
Fig. 6(b) shows the CO 2 assimilation rates of a vegetation canopy with different total LAI under conditions
of low, medium and high irradiation. As all of the radiation models provide very close estimates of the
photosynthesis in the homogeneous canopy, only two models--the radiation transfer equation and the stochastic
model--were used to calculate the curves contrasting tile results for homogeneous and macroheterogeneous
canopies. Again, we can see--this time over the whole range of LAI values--that although 10-15% less
radiation is absorbed in a strongly heterogeneous canopy (compared with that in a homogeneous one with equal
LAD, this is compensated by a more efficient spatial pattern of photosynthetic performance. This compensation
is larger for high incident fluxes.
This finding has the following consequence. For two canopies with the same absorbed fraction of PAR the
photosynthetic rates can diverge up to 20%, and information on the degree of random heterogeneity is necessary
to estimate the photosynthesis more accurately.
Light is not only the driving force of photosynthesis but one of the most important environmental factors
controlling plant growth and development. This action of light is mediated by the photochromic pigment
phytochrome and some other less investigated receptors absorbing in the blue and UV spectral range (Mohr,
1972; Kendrick and Kronenberg, 1994). Concerted action of all photomorphogenetic receptors provides the
adjustment of the genetically programmed growth and development to the light quantity and light quality of the
O. Anisimov, L Fukshansky /Agricultural and Forest Meteorology 85 (1997) 33-49
45
90
T
(13
8O
E
70-
E
6050-
O
c~
40'
,0
30. ,.d
~O
~q
20
C
10
L)
0
0
~
400
200
~
600
~
BOO
10~00
PAR, /zmc, I phot,Drls m--~s '
b
_
'
110
~'
100
E
E
j _ _ _ ~ y
2ooo
120 t
• iJ "~
90
8o
70
0
60
o~
50-
~
40-
m
30-
.J'
20-
C
r..)
500
10o
too
o
Total Leaf Area Index
Fig. 6. (a) Calculated CO:: assimilation of the canopy with LAI = 5 and of a single leaf under different PAR: *, single leaf photosynthesis;
other curves correspond to models with the same designations as in Fig. 3. (b) Photosynthesis of canopies with different LAI under different
PAR calculated using the CRT model and SRT model with c~k = 0.5 and Cak = - 0.8. Open symbols, SRT model; closed symbols, CRT
model. PAR irradiance: [3, 100 p, m o l p h o t o n s m -2 s - l ; zx, 5001zmolphotonsm -2 s - l ; ,7, 2000txmolphotonsm -2 s -1.
local environment. In this way, an appropriate spatial distribution of individual species in a plant community is
formed and stabilized. The phytochrome state affecting growth and many developmental steps in a way specific
for a particular plant or plant organ is itself a function of the spectral composition of light at a given location.
Hence, in calculating light spectra at different heights of a canopy, one can determine the phytochrome state
(which is a general problem because the phytochrome phototransformations obey the same rules in all plants)
and estimate the effect on growth (which is a specific problem because the same phytochrome state affects
O. Anisimov, L Fukshansky / Agricultural and Forest Meteorology 85 (1997) 33-49
46
0.8.
a
0.6-
/
0
.,..~
0.40
09
<
0.2
0.0
400.
500.
76o.
600.
8oo.
Wave length (nm)
Pfr/(Pfr+Pr) ratio
0.35
0.40
0.45
0.55
0.50
m
J
b
"0
~D
k,
.<
,--1
Fig. 7. (a) P h y t o c h r o m e Pr ( o ) a n d Pfr ( [ ] ) absorption spectra. (b) Gradients o f the p h y t o c h r o m e photoequilibria t h r o u g h the c a n o p y with
v, SRT
L A I = 5 obtained with different models, o, T w o - s t r e a m model; [ ] , C R T model; × , S R T m o d e l with c kv = 0.25 a n d c ak _- _ 0 . 8 ;
model with cv~ = 0.5 a n d c ak -_ - 0 . 8 .
O. Anisimov, L Fukshansky/Agricultural and Forest Meteorology 85 (1997) 33-49
47
different plants and organs in different ways). We consider now the downward gradient of the phytochrome
state based on the spectral composition of light calculated with different optical models and for different degree
of macroheterogeneity in a canopy with LAI = 5.
Basically two stable forms of phytochrome, Pr and Pfr, interconvert in a green leaf into another in the
photochemical reactions Pr--* Pfr, Pfr--* Pr, with rate constants trr and trfr, respectively. Each of the
wavelength-dependent cross-sections, ~ and trfr, is a product of the corresponding absorbance (shown as a
function of wavelength in Fig. 7(a)) and the quantum yield (which is known for both reactions and is constant
over the spectrum). ()wing to overlapping of Pr and Pfr absorption curves, monochromatic light can drive both
reactions with the rate constants proportional to the absorbances. As only the Pfr form is physiologically active,
a complete description of the phytochrome state can be given by the value of the Pfr fraction, ~o= Pfr/(Pr + Pfr),
at the photoequilibrium established after a few minutes of illumination. For polychromatic irradiation with
spectrum I(A) the phytochrome state is calculated as
ar
~o= - -
Ar + Agr
(16)
with A r - - f/(A)~(h)dA, Afr = f/(A)o'fr(A)dA, these being the so-called light action function with respect to
the phytochrome forms. The derivation of Eq. (16) has been given by Holmes and Fukshansky (1979), who
applied this approach to calculations of the phytochrome state across a leaf. For general background, the reader
is referred to the study by Fukshansky and Schaefer (1983).
Fig. 7(b) shows the downward gradient of the phytochrome state in a canopy with LAI = 5 under diffuse
skylight found as described above using the spectral compositions I(A) calculated at different optical heights
with the two-stream model and CRT for the homogeneous canopies and with the SRT model for heterogeneous
canopies. The spectra are not shown; for examples of the spectra at different depths calculated with the SRT
model, the reader is. referred to the study by Anisimov and Fukshansky (1993). As seen in Fig. 7(b), the
phytochrome states calculated with different models and for different degrees of heterogeneity show strong
differences at the lower layers of a canopy. At the ground level the two-stream model underestimates ~p for a
homogeneous canopy by about 30% as compared with the CRT and SRT models, which are similar in this
case). Introduction of macroheterogeneity strongly enhances the ¢p value and makes q~ distribution with depth
much more uniform. Remarkably, the strong heterogeneity with negative asymmetry ensures almost constant
phytochrome activity over the entire canopy.
4. Discussion
In this paper we rigorously limit the subject to comparing models, contrasting statistically homogeneous vs.
heterogeneous canopies, at the price of omitting some important features of the advanced theories merely
because they have nothing to compare with their simpler counterparts. A few comments on these features will
be made in this section.
As seen from the calculations of radiation regime for a homogeneous canopy, the two-stream model
underestimates the fraction of light absorbed by the canopy and overestimates that absorbed by the soil. These
errors are moderate for diffuse skylight but increase for direct solar radiation. The calculations show that CRT
gives a good prediction only for a homogeneous canopy and for a canopy with moderately random heterogeneity. However, for global meteorological calculations, both these approximations can be acceptable, especially
when the estimates are averaged over the day (and, therefore, over different solar elevation angles). We expect
that these conclusi(ms will remain valid after a detailed sensitivity analysis (variations of leaf angular
distribution and soil reflectance), which is in progress.
48
O. Anisimov, L. Fukshansky / Agricultural and Forest Meteorology 85 (1997) 33-49
The stochastic effects of random heterogeneity have important consequences for the analysis of the
photosynthetic performance, particularly the results, showing that a heterogeneous canopy has a 15% higher
photosynthetic efficiency and a correspondingly higher photosynthetic rate when absorbing the same amount of
PAR. This is similar to the higher performance of canopies with erectofile leaves as compared with those with
planofile leaves found by Choudhury (1987), as well as earlier findings by Monteith (1965) and Duncan (1971).
Also, studies concerned with the hypothesized optimization of canopy photosynthesis by adjusting the vertical
profile of the photosynthetic capacity (nitrogen profile) to the light gradient (Mooney and Gulmon, 1979; Field,
1983; Hirose and Werger, 1987; Mooney and Field, 1989) may be affected by this phenomenon. Hirose and
Werger (1987) estimated the photosynthetic performance under the actual nitrogen distribution in the studied
canopy as being 4.7% lower than the theoretical optimum and 21% higher than it would be under uniform
nitrogen distribution. Field (1983) found smaller differences between these cases. Now we can conclude that the
changes in photosynthetic efficiency owing to alterations in the random heterogeneity may be of the same order
of magnitude.
In this paper only a uniform nitrate profile was used and no gradients of the photosynthetic performance were
evaluated. In future considerations, we will also analyse variable nitrogen allocation and calculate the
photosynthetic spatial structure on the basis of light spectra at different depths and photosynthetic action spectra.
Furthermore, an evaluation of the photomorphogenetic activity at different depths will be attempted. Fig. 7
shows the first step in this direction: a gradient of the phytochrome state calculated with different models and
for different heterogeneities of a canopy. It is hoped that on the basis of the phytochrome state-response curves
and fluence-response curves for the blue light receptors the gradient of light mediated growth control can be
modelled. Combining both photosynthetic and photomorphogenetic models, we may arrive at an appropriate
tool to study the interactive structure of the coexistence of species within a vegetative community, its
development and its stability. Whether an optimizing principle can be seen behind such a structure remains
open; in any case, it is a product of a long lasting evolutionary pressure.
Acknowledgements
We are grateful to Dr. R. Cassada for a critical reading of the manuscript. O.A. Anisimov is a Fellow of the
Alexander von Humboldt Foundation, on leave from the State Hydrological Institute, Second Line V.O., 23, St.
Petersburg, Russia.
References
Anisimov, O., 1988. A comprehensive method of calculating the radiation regime of a nonuniform plant cover. Sov. Meteorol. Hydrol., 1:
48-55.
Anisimov, O. and Fukshansky, L., 1992. Stochastic radiation transfer in macroheterogeneous random optical media. J. Quant. Spectrosc.
Radiat. Transfer, 2: 169-186.
Anisimov, O. and Fukshansky, L., 1993. Light-vegetation interaction: a new stochastic approach for description and classification. Agfic.
For. Meteorol., 66: 93-110.
Chandrasekhar, 1960. Radiative Transfer. Dover, New York.
Choudhury, B.J., 1987. Relationship between vegetation indices, radiation absorption and net photosynthesis evaluated by a sensitivity
analysis. Remote Sans. Environ., 22: 209-233.
Coakley, Jr., J.A. and Chylek, P., 1975. The two-stream approximation in radiative transfer: including the angle of the incident radiation. J.
Atmos. Sci., 32: 409-418.
Dickinson, R.E., 1983. Land surface processes and climate-surface albedos and energy balance. Adv. Geophys., 25: 305-353.
Duncan, W.G., 1971. Leaf angle, leaf area, and canopy photosynthesis. Crop Sci., 11: 482-485.
Field, C., 1983. Allocating leaf nitrogen for the maximization of carbon gain: leaf age as a control on the allocation program. Oecologia
(Berlin), 56: 341-347.
O. Anisimov, L Fukshansky / Agricultural and Forest Meteorology 85 (1997) 33-49
49
Fukshansky, L., 1987. Absorption statistics in turbid media. J. Quant. Spectrosc. Radiat. Transfer, 38: 389-406.
Fukshansky, L., 1991. Photon transport in leaf tissue: applications in plant physiology. In: R.B. Myneni and J.K. Ross (Editors).
Photon-Vegetation Interactions. Springer, Berlin, pp. 253-303.
Fukshansky, L. and Martinez von Remisowsky, A., 1992. A theoretical study of the light microenvironment in a leaf in relation to
photosynthesis. Plant Sci., 86: 167-182.
Fukshansky, L. and Schaefer, E., 1983. Models in photomorphogenesis. In: W. Shropshire, Jr. and H. Mohr (Editors), Encyclopedia of Plant
Physiology, Vol. 16. Photomorphogenesis. Springer, Berlin. pp. 69-95.
Goudriaan, J., 1977. Crop Micrometeorology: a Simulation Study. Wageningen Centre for Agricultural Publishing and Documentation,
Wageningen.
Hirose, T. and Werger, M.J.A., 1987. Maximizing daily canopy photosynthesis with respect to the leaf nitrogen allocation pattern in the
canopy. Oecologia (Berlin), 72: 520-526.
Holmes, M.G. and Fukshansky, L., 1979. Phytochrome photoequilibria in green leaves under polychromatic radiation: a theoretical
approach. Plant Cell Environ., 2: 59-65.
Kendrick, R.E. and Kronenberg, G.H.M. (Editors), 1994. Photomorphogenesis in Plant. Martinus Nijhoff, Dordrecht.
Lawlor, D.W., 1987. Photosynthesis: Metabolism, Control, and Physiology. Longman, Harlow, UK.
Meador, W.E. and Weaver, W.E., 1980. Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of
existing methods and a new improvement. J. Atmos. Sci., 37: 630-643.
Menzhulin, G.V. and Anisimov, O.A., 1991. Principles of statistical phytoactinometry. In: R.B. Myneni and J.K. Ross (Editors),
Photon-Vegetation Interactions. Springer, Berlin, pp. 111-137.
Mohr, H., 1972. Lectures on Photomorphogenesis. Springer, Berlin.
Monsi, M. and Saeki, T., 1953. Uber den Lichtfaktor in den Pflanzengeselischaft und seine Bedeutung fur die Stoffproduktion. Jpn. J. Bot.,
2: 22-52.
Monteith, J.L., 1965. Liglat distribution and photosynthesis in field crops. Ann. Bot., 20: 17-37.
Mooney, H.A. and Field, C.B., 1989. Photosynthesis and plant productivity--scaling to the biosphere. In: W. Briggs (Editor), Photosynthesis. Alan R. Liss, New York, pp. 19-44.
Mooney, H.A. and Gulmon, S.L., 1979. Environmental and evolutionary constraints on the photosynthetic characteristics of higher plants.
In: O.T. Solbrig, S. Jain, G.B. Johnson and P.H. Raven (Editors), Topics in Plant Population Biology. Columbia Univ. Press, New York,
pp. 316-337.
Mudgett, P.S. and Richards, L.W., 1971. Multiple scattering calculations for technology. Appl. Opt., 10: 1485-1501.
Myneni, R.B. and Ross, LK. (Editors), 1991. Photon-Vegetation Interaction. Springer, Berlin.
Niklasson, G.A., 1987. Comparison between four flux theory and multiple scattering theory. Appl. Opt., 26: 4034-4036.
Richter, T. and Fukshansky, L., 1994. Authentic in vivo absorption spectra for chlorophyll in leaves as derived from in situ and in vitro
measurements. Photochem. Photobiol., 59: 237-247.
Ross, J., 1980. Problems of phytoactinometry. In: Proc. Xlth Conf. on Actinometry. Part I. Plenary Meeting, Tallinn, Estonia, pp. 3-5.
Ross, J., 1981. The Radiation Regime and the Architecture of Plant Stands. Dr. W. Junk, The Netherlands.
Sellers, P.J., 1985. Canopy reflectance, photosynthesis and transpiration. Int. J. Remote Sens., 8: 1335-1372.
Sellers, P.J., Berry, J.A... Collatz, G.J., Field, C.B. and Hall, F.G., 1992. Canopy reflectance, photosynthesis, and transpiration. IIL A
reanalysis using improved leaf model and a new canopy integration scheme. Remote Sens. Environ., 42: 187-216.
Smith, H. and Morgan, D.C., 1981. The spectral characteristics of the visible radiation incident upon the surface of the Earth. In: H. Smith
(Editor), Plants and the Day Light Spectrum. Academic Press, New York, pp. 3-20.
Van de Hulst, H.G., 1980. Multiple Light Scattering. Academic Press, New York.