Agricultural and Forest Meteorology 114 (2003) 197–211
Comparing common methods for assessing understory light
availability in shaded-perennial agroforestry systems夽
J.G. Bellow∗ , P.K.R. Nair
School of Forest Resources and Conservation, University of Florida, Gainesville, FL 32611, USA
Received 6 August 2001; received in revised form 3 September 2002; accepted 4 September 2002
Abstract
Regulating the shade provided by overstory trees is important in the management of shaded-perennial agroforestry systems.
In order to compare the merits of commonly used light-assessment techniques that could potentially be useful to farmers and
extensionists and to quantify the extent of shading in multistrata agroforestry systems, understory photosynthetically active
radiation (PAR) was measured beneath 28 single-species and four mixed-species stands of trees in Costa Rica. Stand age
varied from 1.5 to 20 years, with uniform age trees within stands. Canopy gap fraction was estimated by three methods in each
stand: densiometer, visual index, and hemispherical photography. The gap fractions so derived were compared as estimators of
mid-day PAR transmission. Canopy architectural parameters such as crown height, crown diameter, canopy coverage, and stand
density were measured and compared in regression models for their ability to predict PAR transmission. As expected, stand
characteristics alone did not accurately predict PAR transmission. Of the techniques, gap fractions using densiometers were
the most predictive, except under conditions of low stand density (<500 trees per hectare) and open canopies, where estimates
from hemispherical photograph were better. Shade assessment using densiometers may provide an adequate, dependable guide
for overstory management in multistrata systems and could be useful to farmers willing to adjust their management techniques.
© 2002 Elsevier Science B.V. All rights reserved.
Keywords: Agroforestry; Densiometer; Gap fraction; Hemispherical photography; Leaf area index
1. Introduction
Agroforestry systems involving integration of trees
with field or plantation crops is a common type of
land-use system in the tropics. The presence of overstory trees may result in reduced radiation availability
and buffered temperatures in the understory, improved
fertility status, and altered plant water relations (Nair,
1993). Plants that develop under reduced levels of pho夽 Florida Agricultural Experiment Station Journal Series Number
R-09053.
∗ Corresponding author. Tel.: +1-352-846-0888;
fax: +1-352-846-1277.
E-mail address: [email protected] (J.G. Bellow).
tosynthetically active radiation (PAR, 400–700 nm),
grow and develop differently than those in full sun, although the nature and extent of adaptation vary greatly.
Because of these differential plant responses to reduced light, it is unclear what levels of understory
PAR levels will optimize yields of understory species
under shaded conditions.
It is well established that, in general, where soil
nutrients, water, and temperature are not limiting and
losses from pests and diseases can be avoided, crop
growth and yield are dependent on the total solar radiation intercepted during the growing season (Monteith,
1978). Therefore, yields of crops grown in the understory are likely to be reduced. However, shade-grown
crops such as Coffea arabica L., Elettaria cardamo-
0168-1923/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 1 9 2 3 ( 0 2 ) 0 0 1 7 3 - 9
198
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
mum L., Piper nigrum L., Theobroma cacao L., and
Zingiber officinale Roscoe may produce more marketable yields when grown under varying levels of
shade than in full sun (Beer et al., 1997). The so-called
shade tolerance of these species has traditionally been
exploited by growing them beneath an overstory of
trees. The limited research that has been conducted
indicates that shading in the range of 40–60% may
enhance both yield quantity and quality in crops such
as coffee (Muschler, 1998). In such conditions, farmers may manipulate shade levels and seasonality by
species selection, stand establishment, and thinning.
To optimize anticipated benefits of shade management,
farmers must balance the intensity and spectral distribution of PAR required by crops with reduced transmission levels that may ameliorate stress. Accurate
determination of light levels is thus an important issue
to resource-limited farmers and plantation managers
in tropical and subtropical multistrata systems.
Because of the importance of appropriate shade
management, farmers and extensionists need access
to field assessment methods for PAR levels that are
simple, inexpensive, and readily available. While PAR
levels are most simply and easily measured with quantum sensors or sensor arrays, the necessary training
and equipment put this approach to shade assessment
beyond the reach of most practitioners. A different approach that holds promise to meet the appropriate technology needs of field-based practitioners is to integrate
measures of available light at plot or field levels, which
have been related to growth and dry matter production
of understory crops (Lawlor, 1995; Monteith, 1978;
Palmer, 1988; Ramakrishna and Ong, 1994; Rao et al.,
1998). Of the available measurement techniques, densiometers, hemispherical photography, visual estimation, and empirical assessments based on stand density
and tree species relationships show promise of usefulness under tropical field conditions. Of these, visual
estimates are currently most widely used by farmers
and hemispherical photography potentially the most
unbiased while also least available.
The objective of this study was to evaluate three
techniques for quantifying canopy openness within
stands of tropical trees with diverse canopy architectures and to compare the usefulness of canopy openness or gap fraction thus measured as a predictor of
measured mid-day transmission of PAR. It was hypothesized that an effective method should be able
to indicate that a managed canopy is transmitting between 40 and 60% PAR as currently indicated as optimal for shade-tolerant crops under most conditions
(Beer et al., 1997).
2. Materials and methods
Thirty-two plots were used in this study; 20 of them
were located near Centro Agronómico Tropical de Investigación y Enseñanza (CATIE) in Turrialba, Costa
Rica (600 m above sea level at 9◦ 53 N, 83◦ 38 W),
and 12 were at the La Selva Biological Station (Organization of Tropical Studies, OTS/OET in Spanish)
in Puerto Viejo de Sarapiqui, Costa Rica (35–150 m
above sea level at 10◦ 26 North, 83◦ 59 West). Nine
species were selected because of their range of crown
architectures and crown optical densities and because
of their potential as overstory species in shaded production systems. This broad range of attributes was
expected to increase the robustness of the findings.
The species were Cedrella odorata L., Cordia alliodora Ruiz. & Pav., Erythrina poeppigiana Walp.,
Eucalyptus deglupta Blume, Eucalyptus saligna Sm.,
Hieronyma alchorneoides Allemao, Musa sapientum L., Pouteria sapota Jacq. and Psidium guajava
L. The species were all evaluated in single-species,
even-aged plots except for four mixed-species plots
consisting of Cordia alliodora, and Erythrina poeppigiana in one and Eucalyptus deglupta, and Erythrina
poeppigiana in the other. Hereafter, plots are referred
to by their abbreviated species code and the individual stand characteristics in this study are shown
in Table 1.
2.1. Species descriptions
Cedrela odorata (Meliaceae) reaches 40 m and develops a pyramidal to elliptical crown volume. Leaves
are alternate and paripinnate and displayed in a single plane. New branches appear at regular intervals
along the main stem and a complete rotation is made
with five nodes. In La Selva, growth was observed
to be 0.9 m per year (Butterfield, 1995). Measurements taken in the Huertos stands at La Selva indicate
mean growth rates of 2.7–2.8 m per year for trees up
to 3 years old and 2.0–2.1 m per year for 7-year-old
stands. C. odorata has strong but variable dry season
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
199
Table 1
Species, stand age, mean crown diameter, mean crown height, stocking density, and plot codes for the 32 plots of overstory species studied
in Costa Rica
Plot code
Species
Age
(years)
Crown
diameter (m)
Crown
height (m)
Trees
per hectare
LAI
CV
k
CV
ceodo1
ceodo2
ceody1
ceody2
coalo1
coalo2
coaly1
coaly2
coer1o
coer2o
cord1
cord2
cordy1
cordy2
eryth1
eryth2
eude1o
eude2o
eusa1
eusa2
eusaer1
eusaer2
hyalo1
hyalo2
hyaly1
hyaly2
musa1
musa2
pout1
pout2
psid1
psid2
C. odorata
C. odorata
C. odorata
C. odorata
C. alliodora
C. alliodora
C. alliodora
C. alliodora
C. alliodora, E. poeppigiana
C. alliodora, E. poeppigiana
C. alliodora
C. alliodora
C. alliodora
C. alliodora
E. poeppigiana
E. poeppigiana
E. deglupta
E. deglupta
E. saligna
E. saligna
E. saligna, E. poeppigiana
E. saligna, E. poeppigiana
H. alchorneoides
H. alchorneoides
H. alchorneoides
H. alchorneoides
M. sapientum
M. sapientum
P. sapote
P. sapote
P. guajava
P. guajava
7–8
7–8
3–4
3–4
7–8
7–8
3–4
3–4
8–9
8–9
8–9
8–9
4
4
7–8
7–8
7
7
8
8
8
8
7–8
7–8
3–4
3–4
1–1.5
1–1.5
8–10
8–10
10–20
10–20
4.7
4.4
3.2
3.0
4.0
3.9
3.1
2.8
3.7
3.3
6.8
7.2
3.1
3.0
2.4
2.3
4.3
5.8
5.6
5.6
4.2
4.1
4.8
4.4
3.5
2.9
3.2
2.9
5.2
4.6
7.1
6.2
14.3
15.0
8.3
8.7
15.6
16.0
10.5
10.0
6.9
7.1
14.0
14.9
6.1
6.4
4.0
3.9
20.2
26.7
14.0
14.6
10.0
10.3
19.3
18.0
9.5
9.5
4.1
4.4
6.5
6.0
7.7
6.6
1080
1320
2410
2540
1180
1070
1810
1770
370
400
90
110
35
35
310
260
550
250
104
110
170
160
1130
1010
2050
2120
790
1100
190
160
480
430
1.4
1.5
1.4
1.6
1.8
1.6
2.1
2.4
0.9
1.0
0.5
0.6
0.1
0.1
0.3
0.2
1.7
2.2
0.9
0.9
0.8
1.2
2.7
2.1
2.5
3.4
0.9
0.8
0.6
0.8
2.0
2.1
0.22
0.25
0.34
0.20
0.15
0.21
0.13
0.23
0.40
0.47
0.26
0.19
0.51
0.55
0.78
0.98
0.08
0.11
0.31
0.28
0.34
0.22
0.13
0.14
0.13
0.16
0.50
0.47
1.13
1.00
0.19
0.18
0.06
0.05
0.20
0.18
0.32
0.72
0.49
0.72
0.94
0.85
0.85
0.79
1.66
1.33
0.50
0.87
0.64
0.53
0.53
0.67
0.93
0.62
0.85
0.91
1.79
0.96
0.56
0.47
0.59
0.54
0.99
0.82
0.81
0.74
0.34
0.42
0.18
0.24
0.17
0.25
1.38
0.74
1.94
1.70
0.33
0.42
0.60
0.62
0.20
0.15
0.70
0.66
0.11
0.23
0.18
0.14
0.14
0.15
0.52
0.61
1.00
0.63
0.33
0.29
Mean leaf area indices and extinction coefficients as calculated using Winphot analysis software and hemispherical photographs with the
coefficients of variance. Extinction coefficients calculated using Beer–Lambert equation of exponential extinction and measured transmittance
values.
deciduousness. In La Selva, variations in phenology
between older and younger trees (7 years versus 3
years) and between large and small trees of the same
age within a single site were observed. Leaf abscission was more pronounced and had an earlier onset in
both taller and older trees.
Cordia alliodora grows to 30 m in height and
develops an elliptical crown volume and a straight
single-stemmed bole. C. alliodora conforms closely
to the Fagerlind architectural model (Halle et al.,
1978) with a distinctive branching pattern from the
center of a whorl of plagiotropic shoots at each new
branch order. Leaves are simple and alternately displayed in clusters at the whorls. Growth rates for
C. alliodora range from 0.9 m per year (Butterfield,
1995) to 1.4–1.5 m per year in 3-year-old stands
and 2.2–2.3 m per year in 7-year-old stands at La
Selva. Leaf abscission occurs during the mid- to
late-dry season and variation in onset is present between individuals at the same location and of the
same age with deciduousness being delayed and less
pronounced in younger trees. Both old and young
200
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
stands were evaluated before any indication of phenological changes in the earliest part of the dry
season.
Erythrina poeppigiana (Papilionoideae group of
Fabaceae) has distinctive alternate, trifoliate leaves
and spines on the trunk and branches. E. poeppigiana
must be considered to have two distinct habits due to
management practices that frequently occur in multistrata systems. Unmanaged, it grows taller than 30 m
with an elliptical to spheroid crown volume. Under
management, it is short-statured, and is maintained at
less than 6.0 m. Management involves pollarding all
branches every 4–6 months and leads to the formation of a short bole up to 2.5 m tall with new shoots
that develop from the callus zone and creating a conical to spherical crown volume. At La Selva, growth
rates in young trees were 1.0 m per year (Butterfield,
1995). In Turrialba, older established trees subject to
pollarding had mean increases in crown heights at
rates between 3.6 and 5.8 m per year. E. poeppigiana
has both juvenile and mature phenology. Pollarded
trees usually remain in a juvenile phase and exhibit
neither deciduousness or flowering. In trees not subjected to pollarding, flowering and leaf abscission
occur in the dry season. Trees in this study were
evaluated at their maximum size before pollarding.
Eucalyptus deglupta (Myrtaceae) is a large tree
reaching 35–70 m with an open pyramidal crown and
straight bole. The lanceolate leaves are simple and
alternate or opposite when very young. Branching
patterns produce numerous and well distributed intracrown gaps. Growth rates of 3.2–5 m per year have
been reported (Webb et al., 1984). Growth at La Selva
was 3.2 m per year (Butterfield, 1995). Leaf loss was
observed in the Turrialba area to occur in the latedry season, but at no point was foliage reduced below
50%.
Eucalyptus saligna (Myrtaceae) is a medium size
tree reaching 35–45 m at maturity with a pyramidal
volume and a visual porosity less than E. deglupta. It
has simple, alternate lanceolate leaves. Mean growth
rates of 2.4–5.0 m per year are reported for this species.
A mean rate of 2.4 m per year was recorded at La
Selva (Butterfield, 1995). E. saligna had some foliage
loss in the later part of the dry season in the Turrialba
area (April).
Hieronyma alchorneoides (Euphorbiaceae) reaches
mature heights of 50 m with a visually dense, ellip-
tical crown. Large leaves are simple and alternate.
Mean growth rates were 1.8 m per year (Butterfield,
1995) to 2.8 m per year within 7-year-old stands and
3.2 m per year in 3-year-old stands. This species replaces foliage in the early dry season (January and
February in La Selva) and lower foliage elements
(within plantation stands) are shed resulting in an
increase in canopy height greater than the increase in
foliated canopy depth.
Pouteria sapota (Sapotaceae) is a small tree growing to 15–20 m at maturity. It has a single straight
stem and it develops a branching pattern leading to an open crown with a pyramidal to elliptical volume. The single entire leaves are displayed
in distinctive upright whorls with dense foliage
clumping at branch ends. P. sapota had a mean
growth of 0.7–0.8 m per year in Finca La Cabiria
at CATIE. In La Selva Pouteria sp. grew at 0.56 m
per year (Butterfield, 1995). Deciduousness was
not observed during the dry season in Turrialba.
Flushing of new foliage was observed but the visual porosity of the crown volume remained constant.
Psidium guajava (Myrtaceae) is a short, multi-trunk
tree rapidly growing up to 8 m tall with a spreading
and thin crown resulting in an umbrella or flattened
lozenge shape. The leaves, simple and opposite, are
displayed evenly throughout the crown resulting in
small well distributed intra-crown gaps. The tree also
responds well to pruning by producing rapid flushes
of new growth. P. guajava does not show strong
dry season phenology. Optical density of the crown
was constant from December through April in the
Turrialba area.
Musa sapientum (Musaceae) is a tropical rhizomatous perennial commonly called banana. Plantains,
M. paradisiaca, are expected to have similar shading properties as banana as both possess identical
architecture. The aerial portion of the plant is a false
stem of overlapping leaves. Variation in height is
large with some dwarf varieties reaching anthesis at
2 m, while others grow to 4–9 m. Individual banana
shoots do not show phenological patterns in the classic sense. Leaves emerge, become worn and tattered,
and eventually senesce after approximately 100 days
(Stover, 1974). The plots in the study were variable in
shoot age and height as is common in stands shading
understory crops.
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
2.2. Crown architecture measurements
With the exception of Cedrella odorata plots, measures were taken during periods of full foliation with
the assumption that during periods of deciduousness or
following pruning, shading would be reduced. All light
transmission measurements and gap fraction measurements were taken at the end of the wet season or the
early dry season. Thirty-two plots were established
in 16 separate stands. Sampling was conducted on a
6.0 m × 6.0 m grid located randomly within the plot.
The sampling grid did not parallel the planting grid
and systematic relations were avoided to the extent
possible. The plots were located on level terrain.
All trees taller than 1.7 m within the plots were
measured, with two outer rows of trees excluded as
borders. Crown heights, crown base heights, crown
diameters, and plot stem density were recorded as
measures of stand structure within the 32 plots.
Additionally, foliated canopy depth (the difference
between crown height and crown base height) and
canopy coverage (the sum of horizontal crown area
divided by plot area) were calculated. A clinometer
was used to estimate the height to the lowest foliated
branch and the height of the highest foliated branch.
The diameter (maximum extension) of the crown in
two directions was used to calculate the mean crown
diameter for each tree.
Crown cover was calculated as the sum of the
elliptical crown area based on two crown diameter
measures of all trees within the plot divided by plot
area. The crown coverage index was closely related to
qualitative assessments of canopy closure within the
plots. Values less than 1.0 indicated that the canopy
had not reached closure and that there was substantial
inter-crown gap. Values greater than 1.0 indicated that
there was some inter-crown competition for space and
that more canopy gaps existed as intra-crown gaps.
2.3. Shade measurements
Shading is a poorly defined but commonly used
concept. For this study, shading is defined as the fraction of incident PAR transmitted to a height of 1.0 m
in the understory. Light transmission measures provided the definitive estimate of stand shade characteristics and were used as the shade standard to compare
potential assessment techniques. Light transmission
201
measurements were made using a Li-cor 190SA
quantum sensor, mounted on a 3 m pole and leveled
in an open area outside the stand for incident light
and a Sunfleck ceptometer (Model CEP-40, Decagon
Devices, Pullman, WA, USA) for the transmitted fraction of both direct and indirect PAR. Total incident
and below-canopy PAR were measured simultaneously for each point of the plot grid. Below-canopy
PAR was measured in eight directions radial to the
sample point and the mean of 320 individual sensor
readings was used as a spatial average. A regression
equation was developed (R 2 = 0.998) to standardize
the ceptometer measures to the quantum sensor and
it was used to calculate a percentage referred to as
percent transmission of PAR (Eq. (1)):
Ca = 0.95C + 0.23
(1)
where C is the measured value and Ca the adjusted
value. All light measures were performed between
10:00 a.m. and 2:00 p.m. local time.
2.4. Canopy gap fraction measurements
Three methods were used within each plot to independently estimate the canopy gap fraction. Gap
fraction of the canopy is the fraction of the sky vault
without canopy leaves, branches, or other plant material between the sky and the point of observation.
This measure ranges from 0% (no portion of the sky
is visible) to 100% (no plant material obscures the
sky). This is similar to the definitions of Ackerly and
Bazzaz (1995), Brokaw (1982), Popma et al. (1988),
and Runkle (1982). As defined by Bunnel et al.
(1985), this includes gaps occurring both within and
between crowns. The three methods were consistently
employed in the order of visual estimate, followed by
hemispherical densiometer, followed by hemispherical photographs. In most cases all three methods
were measured in the same day for an individual plot.
When windy or non-overcast conditions prevented
the photographic assessments, that measure was made
the following day at dawn or dusk. In all cases, light
transmission measures were made at mid-day immediately following gap fraction estimates and occurred
within 2 days following initiation of visual estimates.
The first gap estimate in each plot was made using an index (Table 2) referred throughout as the visual estimate or visual gap fraction. This estimate was
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J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
Table 2
Categories of gap fraction classes on a 0–5 scale based on visual
estimates of gap fraction range (or % openness) for the overstory
canopies of 32 agroforestry shade tree stands in Costa Rica
Gap fraction class
Gap fraction range (% openness)
0
1
2
3
4
5
5–15
16–30
31–45
45–60
61–75
75–95
Sample points were assigned to gap fraction classes based on
perceived overstory canopy gap fraction range.
made by observing the canopy directly overhead at
each sample point. Observations were limited to an
area with an approximate radius of 6.0 m. Within this
region, the openness of the canopy was estimated and
placed in one of the six ranges (Table 2) following the
approach of Daubenmire (1959). No analysis of observer differences was made in this study. Using a binomial scale for visual estimation of canopy coverage,
Vales and Bunnell (1988) found no observer effects on
the estimates of canopy openness. Vora (1988) concluded that visual estimation was as reliable as hemispherical densiometer depending on vegetation type,
and was superior when foliage was close to the ground.
A second estimation was made using a spherical
densiometer using a modification of Lemmon’s (1956)
method. He suggested estimating forest cover using
a multiplier of 1.04 to standardize the 24 squares to
100%. For this study the method was modified so the
count was made in quarter square units (possible count
of 96). The estimation process was repeated facing
in four directions at each point and the simple mean
was taken as the densiometer gap fraction. Lemmon
(1956) found no effects due to observer. In contrast,
Vales and Bunnell (1988) found that observer effects
increased with complexity of the estimation technique
and that there were differences due to observers using
a spherical densiometer.
A third estimation was made using hemispherical
photographs of the canopy at each point. The photos
were made during windless weather when conditions
approximated a uniform overcast sky (Monsi and
Saeki, 1953). A 7.8 mm fisheye lens was used with
a remote shutter release at f 5.8 with ISO 100 film.
Plots with insufficient contrast were re-photographed
within 2 days. Digitized images were analyzed twice
using Winphot software (ter Steege, 1993). First, gap
fraction was estimated for the entire image constituting a 180◦ field of view. A second analysis of gap
fraction was performed constraining the analysis to a
cone of 108◦ of arc at the center of the image. This
effectively removed information from close to the
horizon from consideration. It was expected that the
constrained analysis would more closely reflect what
was observed in visual and densiometer estimations.
Both analyses were subsequently compared.
2.5. Leaf area estimation
The leaf area index (LAI) above each sample point
was calculated using the unconstrained analysis (180◦
field of view) of each hemispherical photographs by
Winphot analysis software (ter Steege, 1993). The
technique is similar to that described by Welles and
Norman (1991) and used by the Li-cor LAI-2000
plant canopy analyzer (Li-cor Instruments, Lincoln,
NE, USA).
2.6. Analyses
Correlation analysis was performed between all of
the measures of crown structure to assure independence of variables. All measures of crown structure
were analyzed for correlation with PAR transmission as well. Linear models of crown height, foliated
crown depth, crown base height, and crown diameter
were examined in relation to PAR transmission on
a point (n = 936) and plot mean (n = 32) basis.
Arcsin transformations were made for gap fraction
by densiometer, both analyses of hemi-photos, and
PAR transmission to account for binomial data. The
performance of simple linear models of PAR transmission using gap fraction from each technique were
compared under different conditions. Each model’s
R2 -value, a measure of the method’s ability to explain
variations in PAR transmission, were assessed and
compared for all points and plot means for subsamples of stands with contrasting characteristics.
Using the Beer–Lambert model of light transmission (Eq. (2)), where IU is PAR transmitted into
the understory and IO is incident PAR above the
canopy, an extinction coefficient (k) was calculated
at each point for all plots using measured PAR
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
transmission and LAI values calculated from unconstrained hemispherical photograph analysis. Because all measurements were taken around mid-day,
the cosine correction of Beer–Lambert was not
done:
IU
= e−Lk
(2)
IO
3. Results
3.1. PAR transmission
3.1.1. Crown height, foliated canopy depth, and
crown diameter
Canopy heights and foliated canopy depths did not
differ among plot pairs except for Eucalyptus deglupta
(Table 1). Eude1 was significantly shorter (P < 0.05)
than eude2 (Tukey–Kramer, α = 0.05). Overall,
crown heights had poor negative correlation with PAR
transmission (r = −0.31, n = 32). However, where
mean crown height was <10.5 m, correlation was
greater (r = −0.61, n = 20). Likewise, with mean
heights >14.0 m (r = −0.63, n = 12), greater corre-
203
lation was also observed. Canopy depth was poorly
correlated with PAR transmission (r = 0.25, n = 32).
Foliated canopy depth did not significantly affect PAR
transmission. Crown diameters and PAR transmission
were also poorly correlated (r = −0.11, n = 32).
Correlation of crown heights and crown diameters for
single trees was weak (r = 0.53, n = 2841).
3.1.2. Stand density and crown cover
Stand density and mean crown diameter were poorly
correlated (r = −0.42, n = 32), but separate examination of height classes showed differences. The short
class, <10.5 m (r = −0.31, n = 20), was less correlated than the tall >14.0 m (r = −0.82, n = 12).
Crown cover was weakly negatively correlated with
PAR transmission (r = −0.42, n = 32).
3.1.3. Structural model of PAR transmission
Several different model formulations incorporating
stand density, crown height, foliated crown depth,
crown base height, crown diameter, crown coverage, and additional stand structure variables were
examined in relation to PAR transmission. When C.
odorata was included, none of the models examined
Fig. 1. Relationship between stand density and PAR transmission in 32 plots in Costa Rica. Cedrella odorata plots are circled.
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was that of square of stand density (R 2 = 0.41, n =
28, P < 0.05). Without C. odorata, crown cover was
strongly negatively correlated (r = −0.85, n = 28)
with PAR transmission and significant (R 2 = 0.73,
P < 0.05) as an effect in a linear regression model
of PAR transmission.
using these parameters in various combinations was
significant.
3.1.4. Exclusion of Cedrella odorata
In examining the relationships between stand structure components and PAR transmission, plots containing C. odorata were found to have a different
relationship than the other 28 plots (Fig. 1). Possible
reasons for this are presented in the discussion and
additional analyses were made with them excluded.
With C. odorata excluded, mean canopy height had
a significant effect in PAR transmission (R 2 = 0.16,
n = 28, P < 0.05), similarly, effect of stand density
was significant (R 2 = 0.48, n = 28, P < 0.05) as
3.2. Canopy gap fractions
The first assessment made in each plot was the
visual estimate of canopy gap fraction and was the
most rapid of the three techniques. The second gap
fraction estimates using a hemispherical densiometer
differed from those estimated using visual estimation
Table 3
Plot means and coefficients of variation for transmittance of PAR through overstory canopies of 32 plots in Costa Rica
Plot code
n
Percent PAR
transmitted
CV
Visual
openness
Densiometer
gap fraction
Hemispherical photo
gap fraction (180◦ )
Hemispherical photo
gap fraction (108◦ )
ceodo1
ceodo2
ceody1
ceody2
coalo1
coalo2
coaly1
coaly2
coer1o
coer2o
cord1
cord2
cordy1
cordy2
eryth1
eryth2
eude1o
eude2o
eusa1
eusa2
eusaer1
eusaer2
hyalo1
hyalo2
hyaly1
hyaly2
musa1
musa2
pout1
pout2
psid1
psid2
24
24
18
18
24
30
18
18
35
35
35
35
35
35
35
35
32
32
35
35
35
35
24
30
18
18
24
24
35
35
35
35
92.2
92.8
76.2
75.8
56.5
32.6
35.7
20.1
61.6
53.0
78.5
76.4
86.5
88.6
84.9
87.0
35.3
32.3
66.8
60.3
47.3
50.2
10.3
14.9
1.3
4.3
61.9
70.2
74.6
70.0
18.5
20.8
0.06
0.06
0.09
0.14
0.10
0.12
0.09
0.16
0.62
0.47
0.44
0.44
0.05
0.05
0.16
0.17
0.20
0.11
0.29
0.35
0.19
0.20
0.15
0.11
0.51
0.31
0.38
0.28
0.42
0.42
0.88
0.55
4.5
4.0
3.7
2.7
2.5
2.0
2.3
1.4
3.2
3.2
3.4
3.0
4.9
4.8
4.6
4.7
2.2
2.1
3.5
3.4
3.9
3.8
1.1
1.7
0.4
0.3
3.8
3.9
4.0
3.4
0.9
1.7
0.85
0.79
0.71
0.66
0.43
0.26
0.28
0.18
0.71
0.67
0.79
0.74
0.98
0.98
0.89
0.93
0.40
0.34
0.72
0.74
0.76
0.75
0.16
0.20
0.09
0.13
0.71
0.72
0.82
0.71
0.14
0.30
0.30
0.25
0.25
0.22
0.18
0.21
0.13
0.13
0.38
0.38
0.51
0.50
0.76
0.74
0.63
0.70
0.21
0.14
0.40
0.40
0.41
0.34
0.08
0.13
0.10
0.05
0.39
0.43
0.54
0.48
0.17
0.16
0.57
0.47
0.43
0.40
0.33
0.33
0.22
0.21
0.60
0.57
0.75
0.70
0.97
0.97
0.85
0.92
0.29
0.19
0.67
0.65
0.66
0.64
0.12
0.17
0.13
0.07
0.62
0.64
0.78
0.68
0.19
0.20
Measures of gap fraction class (visual estimate) and canopy gap fraction for spherical densiometer and hemispherical photography using
two analysis methods.
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
205
Fig. 2. Gap fraction estimates by hemispherical densiometer compared to estimates from hemispherical photographic analysis and a modified
analysis constraining the image to the central 108◦ . The straight line indicates perfect fit with densiometer measures.
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Table 4
Linear correlation (Pearson’s r) between estimation techniques of canopy gap fractions of 32 overstory agroforestry species in Costa Rica
Visual estimate
Densiometer
Hemi-photo 180E
Hemi-photo 108E
Visual estimate
Densiometer
Hemi-photo 180◦
Hemi-photo 108◦
1.0
0.89
0.79
0.84
1.0
0.90
0.95
1.0
0.97
1.0
Data was transformed using an arcsin transformation to account for the binomial nature of the variables.
(Table 3). This technique also took the greatest
amount of time per sample point in the field. Gap
fractions estimated from hemispherical images, using
Winphot software for 180◦ of the image (Table 3)
gave systematically lower gap values than densiometer values (Fig. 2). Constraining the analysis to a cone
of 108◦ of arc (Table 3) produced stronger concordance with densiometer readings (Fig. 2), however,
hemispherical photo-derived gap fraction remained
systematically lower with the constrained analysis
as well.
fraction were fitted to a simple linear model of PAR
transmission (Eq. (3)) and compared under different
canopy characteristics:
YP = b1 × (G) + E
(3)
where YP is the percentage transmitted and G is the
gap fraction estimated by one of the four techniques.
The explanatory power of the model combined with
the estimation technique was measured as the R2 -value
of the model. The predictive ability of hemispherical
densiometer-derived gap fractions was greater under
most conditions. When canopy coverage was low,
constrained hemispherical photographs provided a
marginally better predictions at the single point scale.
At whole plot scales, visual estimates were better
predictors in mixed-species stands and hemispherical photo-estimates were better when stocking levels
were low (Table 5).
3.3. PAR transmission predicted by gap fraction
The linear correlation between the four estimates of
gap fraction was strongly positive. The highest relationship was between the two analyses of hemispherical photographs (Table 4). The four estimates of gap
Table 5
The coefficient of determination (R2 ), values of linear prediction model of PAR transmission from single point (P) and whole plot means
(M) of gap fraction estimates of overstory canopies of agroforestry tree species under contrasting conditions in Costa Rica
Method (point and means)
Whole data set (n = P − 930, M − 32)
Single-species plots (n = P − 790, M − 28)
Mixed-species plots (n = P − 140, M − 4)
Direct light (n = P − 598, M − 18)
Indirect light (n = P − 332, M − 14)
Open canopy (n = P − 608, M − 18)
Closed canopy (n = P − 322, M − 14)
High stocking (n = P − 440, M − 18)
Low stocking (n = P − 490, M − 14)
Tall crowns (n = P − 354, M − 12)
Short crowns (n = P − 576, M − 21)
Densiometer
Visual estimate
Hemi-photo 180◦
Hemi-photo 108◦
P
M
P
M
P
M
P
M
0.73
0.81
0.22
0.67
0.76
0.56
0.88
0.86
0.45
0.68
0.77
0.89
0.94
0.31
0.95
0.83
0.78
0.96
0.95
0.62
0.92
0.89
0.59
0.69
0.01
0.53
0.61
0.39
0.66
0.64
0.30
0.50
0.65
0.85
0.90
0.68
0.87
0.80
0.63
0.91
0.89
0.37
0.91
0.87
0.55
0.59
0.13
0.60
0.37
0.53
0.55
0.50
0.44
0.40
0.67
0.62
0.63
0.01
0.90
0.47
0.88
0.83
0.61
0.82
0.51
0.72
0.64
0.71
0.16
0.67
0.49
0.58
0.71
0.67
0.49
0.55
0.72
0.73
0.77
0.44
0.96
0.58
0.85
0.93
0.78
0.75
0.69
0.79
The model used is: YP = b1 (G) + for each method. The four estimation methods are from single point measures (P) and plot means
(M) of canopy gap fraction and PAR transmission.
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
3.4. Leaf area index
The LAIs were calculated by unconstrained analysis of hemispherical photographs (Table 1). Plots with
higher stocking or greater canopy closure had the highest LAIs. The largest coefficients of variance for LAI
occurred in plots with the lowest canopy coverage and
the highest gap fractions. Calculated LAI had a strong
negative linear relationship with transmitted PAR (r =
−0.75, n = 936). For comparison, the gap fraction
(hemispherical densiometer) model had R 2 = 0.73
when fitted to PAR transmission (Table 5).
4. Discussion
4.1. Light transmission to understory in relation to
overstory characteristics
As expected and reported in literature (Clark et al.,
1985; Johnson and Lakso, 1991; Rich et al., 1993),
there was an increase in correlation between mean tree
height and PAR transmission. Crown diameter was, in
general, negatively correlated with PAR transmission,
especially when variation in height was reduced (by
analyzing tall and short plots separately). The low
but negative relationship (r = −0.42) between crown
diameter and stand density is not surprising, because
only small crown diameters are possible at high stocking rates. The positive correlation (r = 0.52) between
crown depth and crown diameter may support the
idea that both are limited concurrently when canopy
closure is reached.
Stand density was more negatively correlated with
transmission rates in the taller-height class (>14.0 m)
than in the shorter-height class (<10 m). Again, this is
expected, because beneath a shorter canopy, the horizontal influence of neighboring trees is less compared
to the situation in taller canopies, where cumulative
effects of many crowns may affect the transmission
of light even at high solar elevations. In combination
with the crown diameter squared, stand density influenced PAR transmission; the low value of R2 suggests,
however, that other aspects of canopy architecture are
also important in influencing PAR transmission.
Crown cover and stand density had a strong linear relationship. If the transition of crown covers
from <1.0 to >1.0 indicates crown closure, a sharp
207
distinction between open and closed stands is evident.
When segregated, the correlation of crown coverage
and stand density dropped from r = 0.79 to r = 0.13
in closed stands, but remained at r = 0.74 in open
stands. Since crown coverage measures inter-crown
gap area to crown area, this suggests that inter-crown
gap area is not well related to stand density at higher
stocking values.
When Cedrella odorata was excluded, the mean
gap fraction estimated by densiometer was well correlated (r = −0.93, n = 28) to crown cover. A possible
implication is that gap fraction in dense stands occurs
primarily within crowns and is more independent
of stand density after canopy closure. This idea is
further supported by the low linear correlation value
between gap fraction and stand density (r = 0.33).
In less densely stocked plots or open canopies, gap
fraction remains highly correlated with crown cover
(r = −0.87). In low-density stands, gap fraction
seems related to the extent of crown coverage mediated by crown diameter and stocking rate, whereas,
in high-density stands, gap fraction is principally an
intra-crown characteristic only weakly influenced by
crown diameter or stocking rate.
The predictive model based on stand canopy parameters performed better when C. odorata was excluded. One possible explanation involves variability
in the phenology of C. odorata at the site studied. For
all plots, light transmission measures were taken when
trees were assumed to be fully foliated. It was noted
in C. odorata that some individual trees rapidly lost
all their foliage, while neighboring trees of the same
age and size showed no signs of foliar replacement or
loss during a 4-month dry season. It is possible that
the assumption of full foliation may have inadvertently
been violated within C. odorata plots. If some individuals had lost part of their foliage, the differences in
within-plot optical density may have resulted in higher
transmission rates than expected for the stand density
as seen in Fig. 1. Gap fraction-based models may require similar phenological stages for comparison.
Shade levels in plots composed of species commonly associated with agroforestry systems were
highly variable, both between species and plots as
well as within plots. Variability in shade levels was
minimized under high and low shade levels. The
predictive models using stand density, tree size, and
crown coverage failed to perform adequately under
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the conditions studied, suggesting that these parameters cannot be used as indicators of below-canopy
PAR levels. This brings into question the validity of
making shading management recommendations in
agroforestry systems based on trees per hectare and
suggests that findings for one species may not be
readily transferable to other species. At best, this approach will need to be validated empirically for each
new species.
4.2. Canopy gap fractions and understory light
availability
Canopy gaps have been related to differences in
understory light several studies (Ackerly and Bazzaz,
1995; Canham et al., 1990; Chazdon and Fetcher,
1984). All the three methods of estimating gap fraction examined in this study were well correlated with
the measured PAR transmission (Table 4). PAR transmission measures were limited to mid-day (10:00 a.m.
to 2:00 p.m.). However, transmission during this range
may not be indicative of the overall shading conditions
within a plot, either on a daily or seasonal basis. It was
not possible to take additional measures of PAR transmission to establish the relationship between instantaneous assessments and integrated daily or seasonal
patterns beneath the studied stands. For this reason,
generalization of these results is limited to management for specific mid-day understory light regimes.
4.3. Comparison of gap fraction estimation
techniques
In comparing the prediction value of a visual
technique against the hemispherical densiometer estimates, the densiometer technique was more precise
for single measures (Table 5). For plot means, this
distinction was greatly reduced and visual estimates
were frequently the second-best technique. Visual estimates were poor for comparisons between open and
closed stands. This is similar to Vora (1988), who,
while studying Pinus ponderosa (Douglas ex Lawson) in California found no significant differences
between the densiometer and ocular measures in assessing percent forest cover (1.0 − gap fraction). The
gap fraction classes used with the visual technique
(Table 2) most likely reduced precision excessively
for point measures, while conserving its usefulness
for plot scale estimates. While visual estimations are
the techniques used most commonly by limited resource farmers in assessing shade, densiometer-based
techniques have potential to increase accuracy in assessment at a reasonable cost. Further investigation is
needed to determine whether shade management and
pruning by farmers aided by densiometer measures, is
an improvement over visual estimates when measured
by crop responses to management.
In the point-by-point analysis, densiometer gap fractions were consistently superior in explaining variation in transmitted PAR, except in low stocking plots
(n = 490) and beneath open canopies (n = 608). In
these situations, gap fraction estimated with the constrained analysis of hemispherical photos was better.
Densiometer estimates were superior to both the standard as well as the constrained analysis of hemispherical photographs for predicting mid-day PAR transmission. Densiometer estimates were less reliable at the
plot scale, but the loss of predictive power was less
(3% loss in explained variation) than for hemi-photos
(15% loss).
Hemi-photo analyses were the poorest technique to
predict PAR transmission in 7 of 11 scenarios. Predictions were the poorest in plots with multiple species in
separate strata. Lasko (1980) reported strong relations
between gap fraction estimated by hemi-photos and
mid-day PAR transmission through Malus domestica
crowns, however this was within single trees. Results
in mixed-species plots were not significant in part due
to low sample number. It is known that gap fraction
information alone is not sufficient to characterize understory light climate; additional information describing the spatial distribution of gaps has been helpful
in other studies. For example, strong relationships
have been found between photosynthetic photon flux
densities and predictions of transmitted PAR using
hemispherical images and superimposed solar tracks
(Becker et al., 1989; Chazdon and Field, 1987) or by
introducing a site specific calibration into PPFD predictions from hemispherical photos (Rich et al., 1993).
Since light measures were limited to mid-day,
the assumption that gap information contained in
the outer portions of the photos would not improve
prediction seems reasonable. The exclusion of gap
information outside a central angle of 108◦ resulted
in improvements in correlation of densiometer and
the constrained photographical estimates (Fig. 2).
J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
Predictive power of the gap model based on photoderived gap fractions improved likewise (Table 5). A
fraction of the remaining differences can be attributed
to errors introduced in digitizing and conversion of
grayscale images. Parallel processing of two images
of each point has promise to resolve this issue. Using
the densiometer, there were no difficulties distinguishing plant material from sky.
4.4. Multiple species plots
Plots which contained two species in distinct strata
had the lowest potential for PAR transmittance to
be predicted by gap fraction estimates regardless of
technique. However, the gap fraction effect was not
significant due to low sample number. Where the plots
contained one tall overstory species and a second
significantly shorter overstory species (coer1, coer2,
eusaer1, eusaer2), no method of gap fraction-based
prediction was accurate. In single-species plots, the
gaps present are possibly more equal in their effects
on the overall gap fraction. When plots contain trees
of extremely different heights, it is possible that small
gaps in the lower strata contributed proportionally
more to the total than an equally large gap in the upper strata and thus may bias the results. Vora (1988)
noted that gap fraction using densiometer techniques
were less reliable when understory plants were an
appreciable part of the canopy cover being assessed
and likely to result in underestimation of gap fraction. Jenkins and Chambers (1989) studied the effects
of developing separate prediction models for light
transmission based on crown cover estimated by densiometer, crown cover here being 1.0 − gap fraction.
They concluded that, while different equations were
developed based on species differences in the mixed
stands, the differences (8%) were not large enough
to warrant the additional effort required. Multistrata
stands may not be reliably assessed by these gap
fraction methods when distinct strata occur.
Until this obstacle can be overcome, direct measures of PAR transmission for a species, and empirical
relationships with gap fraction seem to be the most
productive approach. Further investigation in this direction should attempt to establish a value or range of
values for transmission through the crowns of specific
species independent of stand architecture, essentially
establishing the effect of a species specific interaction
209
between leaf phenology and crown architecture (as
used by Halle et al., 1978). The use of optical porosity of the species (Vincent et al., 1999) may contribute
to progress and address the failure of the approach in
this study to perform in multi-species stands.
The gap fraction by constrained hemi-photo analysis had a superior predictive ability for mean PAR in
plots with open canopies and those with low stocking.
The four methods were not consistent in response
to different conditions. Densiometer estimates were
the highest predicting for closed canopied and highly
stocked plots. Hemispherical photo-estimates and
visual estimates were most frequently the poorest.
Densiometer estimates are the most useful of the
techniques investigated to predict mid-day PAR.
4.5. LAI
As expected, plots with high crown coverage also
had high LAI indices. Transmission rates in open
stands remained high even as LAI values increased.
The model of transmission proposed by Jackson
(1983) may account for this observation: within open
stands, understory PAR may be modeled as the sum
which passes through the tree crowns plus what passes
between them with between crown transmission contributing a greater fraction.
Extinction coefficients were calculated using the
Beer–Lambert exponential relationship between transmitted radiation and LAI. The assumptions for this
extinction model in canopies are: a horizontally uniform canopy so that the transmitted light is equal
at any point of a given horizontal plane, leaves that
are randomly distributed throughout the canopy volume rather than being preferentially displayed along
branches, and opaque leaves. While the assumptions
of the model are violated in most forestry applications,
many researchers have found it useful in estimating
canopy leaf areas (Cannell et al., 1987; Lang, 1987;
Pierce and Running, 1988).
There is little previous research on the use of
densiometers and visual estimates in estimating understory PAR in agroforestry systems. However, gap
fraction has repeatedly been correlated with plant
responses (Gerhardt, 1996; Kappel et al., 1983;
Lasko, 1980). These results suggest that beneath
closed canopies of monospecific shade stands, as frequently found in coffee and cacao plantations, visual
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J.G. Bellow, P.K.R. Nair / Agricultural and Forest Meteorology 114 (2003) 197–211
estimation techniques and densiometers have potential
for accurately estimating shade levels and developing optimal microclimatic conditions for understory
crops. The use of densiometers was the overall best
method in terms of accuracy over the range of conditions. The gap fraction techniques may be used to
manage overstory shade trees and deserves further
investigation to determine if farmers can adapt this
approach and improve their shade management and
to refine and validate the techniques for a wider range
of conditions. Further research should validate the
response of the understory crops to overstory management supported by densiometer evaluated shading
levels.
The levels of shading and variability recorded at
stand densities and within species commonly found as
components of shaded Coffea arabica systems and integrated over 1 m were only seldom within the range
indicated by previous research (Cannell, 1975; Fahl
et al., 1994; Guiscafre Arrilaga and Gomez, 1942;
Muschler, 1998) to provide physiological benefits even
though plot means frequently were. Useful research
foci for the future might address the actual mechanisms for observed yield effects within these shaded
plots. Relating canopy structure to the causal mechanism of yield responses may provide a more effective
and general approach to shade management.
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