The geometry of the canopy of a dipterocarp rain forest in Sumatra

ELSEVIER

AGRICULTURAL AND FOREST M ETEO ROLOGY Agricultural and Forest Meteorology 85 (1997) 99-115

The geometry of the canopy of a dipterocarp rain forest in Sumatra Jean-Michel N. Walter *, Emmanuel F. Torquebiau 1 BIOTROP, P.O. Box 17, Bogor 16001, Indonesia Received 9 November 1995; accepted 3 June 1996

Abstract

A study was conducted in a lowland dipterocarp rain forest in Sumatra to assess the structure and dynamics of the forest canopy. The canopy structure was analysed at different scales, including a previous mapping of a 5 ha forest mosaic and an interpretation of the canopy architecture, along a horizontal gradient between the high forest and a 320 m 2 treefall. Canopy geometry was ascertained by analysis of digitized zenithal hemispherical photographs sampled at 25 near-ground sites. Gap size, morphology and dispersion varied continuously from the high forest to the treefall. An asymmetric pattern of gaps about the zenith was characteristic of almost all forest sites. The spatial dispersion of gaps was random in the high forest. It tended to be dumped in the forest border and in the treefall. Plant area indices ranged from 6.5 in the high forest to 2.9 in the treefaU. These values reflect a reduced leaf area during a severe dry spell, at the time of measurements. Inclination angles of canopy elements were highly correlated with gap dispersion and canopy openness, as observed from the high forest to the treefall. Implications of canopy heterogeneity on the distribution of light were analysed. The importance of lateral light penetrating from the forest border into the high forest is stressed. The canopy gradient of architecture and geometry from the high forest to the treefall and the very diverse structure of the high forest are emphasized. © 1997 Elsevier Science B.V.

1. Introduction

The structure and dynamics of forests have been of major concern in ecological research for a number of years, with particular interest in gap phase dynamics and forest regeneration (e.g. Oldeman, 1983; Brokaw, 1985; Hubbell and Foster, 1986; Denslow,

* Correspondence address: Centre d'I~tudes et de Recherches F~co-Gfographiques, URA 95 CNRS, 67083 Strasbourg Cedex, France. 1 Present address: Centre International pour la Recherche Agricole Orient~e vers le Dfveloppement (ICRA), Agropolis International, Avenue Agropolis, 34394 Montpellier CX 5, France.

1987; Platt and Strong, 1989; Oldeman, 1990). The amazing diversity and the immense complexity of canopy structures have been emphasized by several workers. As pointed out by Whitmore (1990), some workers reserve the term canopy for the roof of the forest (e.g. Mitchell, 1986; Van der Meer et al., 1994), which would be better named the canopy top. We use 'canopy' to denote the whole aerial part of the forest. A complete analysis of the structure or a detailed description of forest canopies is a formidable task, if not impossible, particularly in tropical rain forests (Hall6 and Pascal, 1993). Although the meaning is apparently obvious, the concept of canopy structure is diversely understood,

0168-1923/97/$17.00 ~ 1997 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 1 9 2 3 ( 9 6 ) 0 2 4 1 9 - 7

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J.-M.N. Walter, E.F. Torquebiau/ Agricultural and ForestMeteorology85 (1997) 99-115

depending on scale problems and study purposes. What is generally meant by 'structure' is the spatial and temporal arrangement of forest components or canopy elements. Structure is fundamentally expressed in terms of heterogeneity and variability on diverse space and time scales (Brunig, 1983). Two approaches to canopy structure, based on the concepts of architecture and geometry, have significantly contributed, in recent times, to a renewed understanding of forest dynamics and functioning. On the one hand, the architectural approach tries to integrate different hierarchical levels. It rests on the growth dynamics of individual trees, emphasized by the spatial arrangement of the axes bearing photosynthetic and reproductive organs, as well as their distribution within the patchy network of development phases, building the forest mosaic (Hall6 et al., 1978). Architecture may be interpreted as a 'spatiotemporal structure linked to a well-defined hierarchical level' (Oldeman, 1990). On the other hand, the geometric approach seeks to quantify the area, pattern and orientation of organs such as leaves, trunks, flowers and fruits, and the size, morphology and dispersion of gaps which separate them. These properties are related to the physics of matter and energy transfer. Their statistical analyses lead to an important reduction of data. Only a few synthetic geometrical descriptors are extracted, e.g. leaf area index, mean leaf inclination angle, canopy openness, and the related light distribution. Such key variables are increasingly used for driving functional biogeochemical and hydrological models of ecosystems and for explaining plant and animal responses to space and light resources. Analyses of canopy geometry attempt to link the scale of the phytoelements to the scale of the forest. However, spatial and temporal heterogeneity of canopy variables are still poorly documented. Scaling of ecological and ecophysiological processes are both theoretical and practical challenges (e.g. Ehleringer and Field, 1993). Spatialization of canopy variables and their calibration for scene models of remote sensing are greatly needed (Graetz, 1990; Laumonier et al., 1994). Methods and theories that may be appropriate for these estimates are becoming available (Goel and Norman, 1990). The objective of this paper is to try to link these two approaches, in describing the canopy geometry

of a primary dipterocarp rain forest in Sumatra in a hierarchic architectural context. Little is known about geometric variation along the architectural gradient from treefall to high forest--for instance, is the couple treefall vs. high forest interior as contrasted as is commonly stated? To achieve this goal, we analysed: (1) the size, morphology and spatial dispersion of canopy gaps; (2) the areal extension and the angular distribution of canopy elements; (3) the light distribution at various scales; (4) the relationships among these parameters and the overall architecture of the forest.

2. Methods 2.1. Study area

The study was conducted in a lowland welldrained dipterocarp rain forest at Pasir Mayang, near Hari river, Muarabungo, in Sumatra's Jambi Province (1°5'S, 102°10'E, altitude 100m above sea-level (a.s.l.)). The climatic conditions for the site are those of a very humid bioclimate, i.e. the mean temperature of the coldest month is above 20°C, the annual rainfall is between 2000 and 2500 mm, and there is no month with less than l o o m m of rain. Soils in the area are poor kaolinitic ferralitic soils, developed on sedimentary parent materials. The topography is regularly undulating and the drainage is good. The forest vegetation is the tropical lowland evergreen formation of Whitmore (1975) with a canopy of about 50m in height (Blasco et al., 1983; Laumonier, 1991) and with the following conspicuous tree species: Dipterocarpus crinitus, D. lowii, Shorea acuminata, S. macroptera (Dipterocarpaceae), Scorodocarpus borneensis (Olacaceae), Dialium platysepalum, Koompassia malaccensis (Leguminosae), Dyera costulata (Apocynaceae). The study site was a primary forest located on a small ridge with gentle slopes (up to 12°). In the same area as represented on a 5 ha forest mosaic map published elsewhere (Fig. 5 of Torquebiau (1986)), but on another site, a 90 m × 20 m plot was selected and drawn to scale as a detailed profile diagram (Fig. 2 of Torquebiau (1988)), following the method of Hall6 et al. (1978). The plot encompasses an eeologi-

J.-M.N. Walter, E.F. Torquebiau/ Agricultural and Forest Meteorology 85 (1997) 99-115

cal (architectural) gradient from the mature high forest through a transition zone to a 320 m 2 treefall. 2.2. Hemispherical photography

Twenty-five hemispherical photographs were taken near ground level at five microclimatic measuring sites (Torquebian and Walter, 1987) and 10m intervals in the plot (centre of 18 contiguous subplots), plus two photosites outside the plot. A 10 m m OP-Nikkor 'fish-eye' lens was mounted on a F2 Nikon camera. The le,ns had an orthographic projection and 180 ° field of view. The camera was about 3 0 c m above the ground on a tripod, levelled and

[]

101

oriented, looking upwards through the canopy. No correction was needed to obtain true north, as magnetic declination D was negligible in the area. Photographs were taken near sunrise, under overcast sky and still air. Exposures were determined by measuring the sky light at zenith through a nearby canopy hole, by means of an independent light meter (Gossen Polysix), allowing spot reading (field of view 10°). Opening one stop makes the sky black on the negative. Additional photographs were taken at the same site with two different exposures bracketing the reference value. A high-contrast Kodak Microfile (ASA 60) film was used to enhance the contrast between the sky and the canopy elements and to

o

Fig. 1. Near-ground hemispherical photographs. (a) High forest (Photosite 3), canopy openness 0.02; (b) high forest (Photosite 20, outside the plot), canopy openness 0.09; (c) transition zone (Photosite 7), canopy openness 0.14; (d) treefalt area, distal part (Photosite GD), canopy openness 0.20. Solar tracks for solstices: June (upper curve), December (lower curve). The orthographicprojection of the lens expands the zenith region of the canopy, compresses the zones near the horizon and reduces the curvature of the solar tracks.

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J.-M.N. Walter, E.F. Torquebiau / Agricultural and Forest Meteorology 85 (1997) 99-115

reduce the halo effect. The negatives were carefully processed with a Kodak PL2 developer. The photographs were digitized into a 512 × 5 1 2 matrix, using a Burle video camera connected to a computer equipped with a Cyclope graphical board, and a special program developed by Baret et al. (described by Varlet-Grancher et al. (1993)). Typical photographs are shown in Fig. l(a)Fig, l(b)Fig, l(c)Fig. l(d). The term 'gap', as used here, denotes an 'opening', whatever its form, size and origin, including a treefall, i.e. the canopy hole through which light penetrates unintercepted to the point of observation. 'Gap fraction' is the portion of sky (range 0-1) showing through the canopy within a given solid angle from a particular direction of the hemisphere. Data consisted of the 'gap fraction' in sectors of solid angle 5 ° zenith X 15° azimuth over the whole hemisphere. These data were used as input to CIMES, a package of programs to analyse hemispherical photographs (Walter, 1994). It is the development of these computer programs and of the theory of canopy geometry (see, for example, Norman and Campbell (1989), Myneni and Ross (1991) and Varlet-Grancher et al. (1993), for recent reviews) which has made it possible to put into a new perspective in the present paper field data initially collected in 1984 and already discussed in various publications (Torquebiau, 1986; Torquebiau and Walter, 1987; Torquebiau, 1988).

3. Results

3.1. Size, morphology and spatial dispersion of canopy gaps Canopy openness (CO) is the fraction, or per cent, of gap over the whole hemisphere, the total amount of gap projected onto the horizontal plane. Canopy openness is a good indicator of the basic canopy geometry and the potential penetration of solar radiation. It will be used for ranking all other canopy variables. In the present study, CO values ranged from 1% in the deep shade of the high forest to 31% in the proximal part of the treefall (i.e. the area around the base of uprooted and broken trees, as opposed to the distal part, the area struck by the

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Fig. 2. Typical patterns of gap distribution about zenith. Points are gap fraction values linearly averaged over azimuth, for each zenith

angle. Curves representgap distributionsexpectedby the Poisson model. Goodness-of-fit(G-test): (a) P = 0.661; (b) P = 0.324; (c) P = 0.038; (d) P = 0.021. Photosites are given in parentheses. GD, Treefallarea, distal part. falling tree crowns, with greatest destruction of the understorey vegetation). Gap fractions linearly averaged over azimuth were plotted against zenith angles from 0 ° to 70 ° (Fig. 2(a)Fig. 2(b)Fig. 2(c)Fig. 2(d)). To test canopies for randomness at each photosite, these measured gap fractions g' were compared with gap fractions g expected by the Poisson distribution, for each zenith angle. Poisson parameters used to generate g and the curves in Fig. 2 have been given by, for example, Bonhomme and Chattier (1972). For a random dispersion of gaps g' = g, whereas for a clumped dispersion g ' > g. A likelihood ratio test (Sokal and Rohlf, 1981) was used for goodness-of-fit in 25 sites. Results are summarized in Table 1. Thus, 16 sites corresponded to 'random canopies' (12 in high forest, four in transition zone) and nine sites displayed 'clumped canopies' (three in high forest, four in transition zone, two in treefall). No 'uniform canopies' were found ( g ' < g). Fisher's exact test (one tail) yielded P = 0.026 for high forest vs. transition zone, P = 0.0 for high forest vs. treefall, and P = 0.133 for transition zone vs. treefall. Clumping obviously characterizes the treefall and its borders, whereas randomness is a common feature in the high forest, at least as v~wed from ~ forest floor, at the spatial scale provided by the hemispherical photographs. The distribution of gaps about the zenith showed a pattern along the ecological gradient of the plot.

J.-M.N. Walter, E.F. Torquebiau /Agricultural and Forest Meteorology 85 (1997) 99-115 Table 1 Spatial dispersion of gaps: test for randomness Site a

CO%

G t,

P ~

Type d

hf hf hf hf hf hf hf hf hf hf hf hf hf hf hf tz tz tz tz tz tz tz tz tf tf

1.1 1.4 1.5 2.1 2.4 3.0 3.4 3.6 3.7 3.8 4.0 4.0 4.0 4.9 5.9 7.8 8.7 9.7 10.2 10.9 13.2 13.6 14.1 19.7 31.4

13.99 9.65 17.11 6.45 32.68 15.84 1:l.32 13.65 19.42 36.82 16.23 18.40 22.44 46.19 2:2.60 '9.12 16.84 20.13 30.17 12.70 45.42 19.89 23.34 23.86 111.54

0.234 0.788 0.194 0.928 0.002 0.324 0.661 0.324 0.150 < 0.001 0.237 0.143 0.070 << 0.001 0.047 0.824 0.207 0.024 0.007 0.550 << 0.001 0.098 0.038 0.021 << 0.001

R R R R C R R R R C R R R C R R R C C R C R C C C

a Sites at 10m intervals me ranked according to canopy openness (CO): hf, high forest; tz, transition zone; tf, treefall. b G-Statistics for goodnes,;-of-fit. 3 p = Q(X2), probability of accepting Ho: g' = g, where g' are measured gaps and g are gaps predicted by the Poisson model. 4 Type: R, random canopy; C, clumped canopy, a = 0.05.

Several morphologic types were recognized, with: (1) tiny and few gaps irregularly dispersed over the hemisphere (high forest); (2) more conspicuous gaps forming a girdle at mid-elevation angles (high forest); (3) numerous conspicuous gaps increasing in size from horizon to zenith; (4) large gaps concentrated laterally (transition zone) or near the zenith (treefall). Fig. l(a)Fig, l(b)Fig, l(c)Fig, l ( d ) s h o w typical examples (note that orthographic projection increases apparent gap size towards the zenith). These gap patterns, grading into one another, can be quantified by means of spherical statistics. Spherical statistics deal with the distribution of gaps as a function of their location and dispersion in the hemisphere (see Jupp et al. (1980) and Appendix A). Indeed, each direction cosine of the hemisphere

103

is weighted by a gap fraction. These gap weighted vectors are used to define a spherical resultant whose direction (spherical mean) should be near the zenith. The spherical variance (SV) measures the concentration of gaps about that direction. In effect, SV varied from 0.277 in the high forest to 0.052 in the treefall. This translates into a shift from high gap dispersion to an increasing gap concentration, and is consistent with the distribution of gaps about the zenith. The symmetry of gap distribution was quantified by the moments of inertia of gaps in relation to a direction u. Moments of inertia minimize the sum of the squares of the perpendicular distances of the gaps to that direction. They are represented by the standardized eigenvalues s 1, s 2 and s 3 of the matrix of weighted sums of squares and products of the gap vectors. Thus, the direction of maximum gap inertia (first axis), corresponding to the first eigenvalue, will be a direction of maximum gap in the hemisphere. It should be identical to the direction of the resultant and should be near the zenith. If s 1 is large, and s 2 and s 3 are identical and both small, the distribution of the gaps is symmetric about the first axis and the canopy has a 'vertical' structure. The lower the value of s~, the more 'horizontal' the canopy structure. If s 2 and s 3 are very different, the canopy shows a high dispersion of the gaps or a strong asymmetry. Table 2 summarizes the interpretation of the eigenvalues and the relationships of gap morphology with light spectral properties (Section 4.3). Fig. 3(a) shows variation in moments of inertia of gap for a sequence of photosites, spatially arranged. In Fig. 3(b), direction of maximum gap and direction of gap resultant are related: the more they diverge from one another and from zenith, the higher the asymmetry in gaps. In conclusion, asymmetry in gap dispersion predominates along the transect. 3.2. Plant area index

Binary images with only sky and canopy elements do not distinguish between leaves and other elements. Let Lp be the plant area index, including leaves, flowers, fruit, twigs and branches. The plant area index of a canopy is half the total area of canopy elements per unit area of soil. Simplifying, as demonstrated by Lang (1991) on a theoretical basis, Lp----L 1nt- L w, where L 1 is the leaf area index and

Table 2 Classification of spherical gap distributions and relationships with light spectral properties Dimensions of eigenvalues a

s I large and s 2 and s 3 small s 2 ~-- s 3 s 2 >~ S3 s~ small a n d s 2 and s 3 large s 2 >> s 3 s 2 ~ s~ sl = s2 ~ s3

Typology of gap distribution

Dominant canopy feature

Other observations values ~

E x a m p l e s in forests

Light habitats b

Ranked ~"

unimodal

' vertical' canopy

symmetry rotation about the s j axis

treefall high forest forest edge ridges

large gap numerous gaps woodland shade

+ + + + + + + + + + +

slopes high forest high forest obstructed overhead high forest very dense

woodland shade small gaps small gaps forest shade forest shade

+ + + + + + + + + +

unimodal

high azimuthal asymmetry

2.

~, girdle

girdle subtended by the axes s 2, s 3

symmetric girdle uniform

symmetry rotation about the axis s i ,L 'horizontal' canopy

non-oriented axes

a The eigenvalues si, s 2 and s 3 of the gap orientation matrix satisfy the relation s I + s 2 + s 3 = 1. After Mardia (1972), cited by Jupp et al. (1980). b After Endler (1993). ¢ ~', the r e d / f a r - r e d ratio ( + , low; + + + + + , high). Typical values of ~', for sunny conditions, are: forest shade 0.16; woodland shade 0.51; small gaps 1.16; large gaps 1.44 (after Endler (1993), p. 14).

t..n

105

J.-M.N. Walter, E.F. Torquebiau/ Agricultural and Forest Meteorology 85 (1997) 99-115 .

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Fig. 3. Spatial dispersion of gaps. (a) Moments of inertia of gaps. Standardized eigenvalues :q, s2 and s3, for a sequence of photosites. The lower s I, the more dispersed the gaps. Asymmetry of gaps is indicated by s2 =.~s 3. (b) Direction of maximum gap (moments of inertia) vs. direction of gap resultant (spherical mean). Coordinates are zenith angles in degrees. Each circle is a photosite. The closer the circle to 0,0 coordinates and to line 1:1, the more symmetricare gaps about the zenith. For each photosite, n = 360 directions of the hemisphere.

L w is the wood (bark) area index. The leaf area index ( L l = LAD can be measured accurately only b y time-consuming direct methods, i.e. destructive sampling with specific leaf area measurements for converting mass to area, combined with litterfall collections and studies of leaf turnover rates (e.g. Ashton, 1978; Kira, 1978; Alexandre, 1981; Saldarriaga and Luxmoore, 1991). Poisson-model derived plant area indices were estimated by using the approach of Norman and Campbell (1989). Results are displayed in Fig. 4. Values of Lp in high forest ranged from 6.5 in sites with few inconspicuous gaps irregularly dispersed, or with obstructed zenith region ('horizontal' canopies: Fig. l(a)) to a minimum of 4.0 in sites with conspicuous gaps increasing in number and size from horizon to zenith ('vertical' canopies: Fig. l(b)). The lowest values for the ecological gradient were found in the treefall (proximal part), with Lp = 2.9. Using the T u k e y - K r a m e r method for multiple pairwise comparisons among means of unequal samples (Sokal and Rohlf, 1981), high forest (Lp = 5.1, n = 15), transition zone (Lp = 4.3, n = 8), and treefall (Lp = 3.0, n = 2), differed significantly (cz = 0.05). 3.3. Plant element inclination angles

elements (where 0 ° is horizontal and 90 ° is vertical); (2) the angular distribution of plant area fractions. It is important to note that these two types of angular information, derived from the inversion of gap fraction data or measurement of sunflecks, do not describe specifically the angular distribution of leaves or trunks, but take into account the whole canopy geometry, from leaves, clusters, crownlets and crowns, to boles and trees, at each nested scale. Mean inclination angles were computed, following the Lang (1986) method. Values of Ap are shown in Fig. 4 and Fig. 5(a)Fig. 5(b). They ranged from approximately 10° in the densest part of the high forest to approximately 80 ° in the treefall. High forest ( .4p = 27 °, n = 15), and transition zone ( .4p = 63 °, n = 8), differed significantly ( a = 0.05). Transition zone and treefall (Ap = 81 °, n = 2) were not significantly different (oL = 0.05), using the T u k e y Kramer method. Fig. 5(a) shows a linear relationship between arcsine transformed SV and Ap values. ThUS, Ap is directly related to gap concentration, i.e. the change in Ap is the result of nonrandomness of canopies near large gaps. Similarly, Ap increases non-linearly with CO (Fig. 5(b)). The whole canopy area can be subdivided in plant area fractions for each angle class, ranging from 0 ° to 90 °. For example, if the plant elements are uniformly distributed, each angle class of, say, 10° interval, contains the same amount of foliage area. Non-uniform distributions of plant area are the most common situations. The plant area fraction of all photosites was distributed in ten classes of inclination angles (Norman and Campbell, 1989). The most typical photosites are represented in Fig. 5(c).

High Forest

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Fig. 4. Plant area indices Lp and mean tilt angles Ap of canopy elements. Bars, Lp vNues, ranked according to canopy openness; • , mean tilt angles Ap.

106

J.-M.N. Walter, E.F. Torquebiau /Agricultural and Forest Meteorology 85 (1997) 99-115 40

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inclination angles of plant elements was derived from sunfleck measurements carried out by Alexandre (1982) in the Ta'i forest of Ivory Coast (Fig. 5(d)). The average area in sunflecks was 10%, somewhat overestimated, owing to penumbral effects. However, their distribution and relative amount for February and March 1978 agreed well with the planophile structure of the canopy interior, suggesting that the planophile geometries identified in our plot are not mere chance.

,

30 6O 90 Plant Elemem Tilt Angles, Degrees

30 60 .90 Plant Element Tilt Angle~, Degrees

Fig. 5. Spherical variance (SV), canopy openness and angle distribution of canopy elements. (a) Correlation between SV (values arcsin ~ transformed) of gaps and mean tilt angles Ap ( r = -0.84). Equation of the first principal axis (continuous line): arcsin S ¢ ~ - = 30.8-0.223Ap. Arrow indicates outlier (Photosite 5) with dense canopy and one conspicuous lateral gap. (b) Relationship between canopy openness and Ap; empirical equation for the curve of best fit: Y = 5 . 6 3 - 0 . 4 5 X + 0 . 0 2 2 X 2 - 3 . 8 7 2 e 4X 3 + 2 . 8 e - 6 X 4 ( r 2 =0.95). (c) Area fraction ( × 10) for ten inclination classes. Characteristic patterns of planophile ('horizontal'), plagiophile, extremophile and erectophile ('vertical') canopies. Curves represent Photosites 3, 5, 12 (high forest) and 13 (transition zone), respectively. (d) Area fraction ( × 10) for ten inclination classes, computed after sunfleck distributions in Ta'i forest, Ivory Coast (Alexandre, 1982). Data consisted of 906 records per hour along transects, for I day in February and 1 day in March 1978. Horizontal reference line indicates uniform distribution of plant area fractions ( × 10).

'Planophile' ('horizontal') canopies were found only in the high forest (four sites), whereas 'erectophile' (' vertical') canopies characterized the transition zone (eight sites) and the treefall (two sites) but were also present in the high forest (two sites). Both 'plagiophile' and 'extremophile' canopies were found in the high forest (six and three sites, respectively). Thus, the angular distribution of plant elements followed the sequence planophile -o plagiophile extremophile ~ erectophile. It fits well the ecological gradient of the plot, emphasizing particularly the geometric diversity of the high forest. For comparison with independent data, a plot of area fraction vs.

Light transmittance ~- (range 0-1) is the ratio of light measured beneath the canopy to light incident above the canopy (visible light and photosynthetically active radiation (PAR), waveband 400700nm). Calculated for cloudy days with only diffuse radiation, ~'soc relies on the standard overcast sky radiance distribution (SOC), which at zenith is three times that at the horizon. This approximation seems realistic in the tropics (e.g. Whitmore et al., 1993). For sunny conditions, ~'DIR accounts for direct sunlight and 0-toT for direct plus diffuse blue sky light. In addition, ~'xox incorporates radiation scattered (reflected and transmitted) by leaves, as a diffuse component. Transmittance values were derived by using analytical equations describing the distribution of direct and diffuse light for clear and overcast days above and beneath the canopy. A numerical method, based on radiative flux discretization, was applied to derive the potential light transmission. This approach reduces the number of simplifying assumptions and translates best the interfering Earth-Sun geometry with heterogeneities in canopy structure. Scattered light was estimated by an iterative technique (Walter and Gr6goire Himmler, 1996). For canopy openness, the sky radiance distribution is assumed to be isotropic. The standard overcast sky in rso c implies a radiance distribution with symmetry about the zenith and cosine corrections. TDIR depends upon the Sun's position and "/'TOT combines the apparent course of the Sun with a heterogeneous blue sky radiance distribution. ZTOT adds a supplementary weight in the form of light scattered by leaves. This weight increases with

J.-M.N. Walter, E.F. Torquebiau/ Agricultural and Forest Meteorology 85 (1997) 99-115 Table 3 Pearson's correlation coefficients r for canopy openness (CO), transmittance of diffuse (TSOC), direct (TmR) and total (TToT) light and daily sunfleck duration in minutes (FLK) a

TSOc TDIR TTOr FLK

CO

TSOC

0.981 0.963 0.968 0.943

0.986 0.991 0.980

TDIR

"/'TOT

0.999 0.944

0.995

a For TDIR and "/'TOT,averages from June to December (fifth, 15th and 25th of each month, i.e. 21 days) were used, assuming constancy of canopy structure, n = 25 photosites, P << 0.001.

canopy closure. Therefore, within a given area and for the same forest type, ~'TOT is most likely to predict the light microclimate. Solar tracks are represented in Fig. l(a)Fig. l(b)Fig, l(c)Fig, l(d). The quasi-straight lines for solar tracks in the orthographic projection of the photographs emphasize the ' verticality' of the apparent course of the Sun near the Equator, as perceived by an observer. TDIR and ~'TOT were computed for the fifth, 15th and 25th of each month, from December to June at each site, assuming constancy of the basic canopy morphology. Canopy openness, light transmittance and daily sunfleck duration in minutes were strongly correlated, as expected near the Equator (Table 3 and, e.g. Smith et al. (1992)). In Fig. 6(a)Fig. 6(b), sites are ranked according to CO, from the high forest interior to the treefall. ~'soc values are often lower than O.5

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Fig. 6. Canopy openness (CO) and light transmittance. Values ranked according to CO. (a) CO and transmittance of diffuse light, TSOC; (b) transmittance of direct, TDm, and total light, TTOT; each point is the mean of 21 chiys (fifth, 15th and 25th, from June to December); outlier in the transition zone (Photosite 13) receives approximately 30% of total incident light from June to August and only approximately 3% from October to December. Constancy of canopy structure is assumed.

100-1 50-~

High Forest

(3)

o/ ~

100- rash ~ Fo~ (z0) 500 15010050-

107

105~

[ . [ ] ~ HighFor~ (3)

0

,,

''r,,~

.... ,

10 "fiamitionZone 35

350.E : ~ dZ50200-

-~

Treefall(GD)

1(305ll-

)i

0~

I

I

I

J

J

A

I

I

I

(GP)

I

O N D

S Month

2 ~5 a ° l " l 1

J J AS

O N D

Month

Fig. 7. Light distribution for a sequence of photosites with increasing canopy openness. (a) Daily sunfleck duration (in min); (b) daily amount of potential transmitted light (in mol m - 2 ); clear sky (bars) and overcast sky (SOC: continuous lines). Values for the fifth, 15th and 25th, from June to December, assuming constancy of canopy structure. Photosites are given in parentheses. GD, Treefall area, distal part; GP, treefall area, proximal part.

those of CO (Fig. 6(a)), owing to the frequent obstruction of the zenith region of the canopy, even in the treefall (protruding trees: Fig. l(d)). Most ~'DIR values are below TTOr values in the high forest. This trend reverses in the transition zone and the treefall area, where direct sunlight penetrates more easily (Fig. 6(b)). The relative beam radiation enrichment of the canopy characterizes the small treefalls in the tropics (see solar tracks, Fig. l(d)) in contrast to higher latitudes, where the diffuse component dominates. Explanation and details of calculations are given in Appendix B, The spatial and temporal variations of daily sunfleck duration and potential amount of light under clear and overcast sky are shown for some typical sites in Fig. 7(a)Fig. 7(b) (for comparison with actual amount of light, see Torquebiau (1988)). They emphasize the interference of gap pattern and the changing Sun's path with time. For example, in the high forest (Photosite 3, Fig. l(a)) from August to September, when the Sun is near the zenith, no

108

J.-M.N. Walter, E.F. Torquebiau /Agricultural and Forest Meteorology 85 (1997) 99-115

sunflecks appear on the forest floor. Only light scattered by leaves and bark, and from sky at low elevation angles, illuminates the forest floor. In June and December, more light is transmitted when the Sun is lowest, thus emphasizing lateral light. Conversely, in some high forest sites with gaps near the zenith (e.g. Photosite 20, Fig. l(b)), light transmission culminates around the equinoxes. The transition zone (Photosite 7, Fig. l(c)) shows a strongly asymmetric pattern under clear sky, without direct sunlight for 3 months. Only skylight is transmitted, more efficiently from overcast sky (Tsoc = 0.15) than from blue sky (~'TOT= 0.05). Afterwards, the light regime changes drastically, with the peak value in December. In the treefall, the distribution of light tends to be increasingly symmetric around the equinox (September) as one moves from the distal part (see Fig. l(d)) to the proximal part. The relationship between Lp and transmitted light may be written, by analogy with the Beer-Lambert law: r = exp(-KLp), where K is the light extinction coefficient and the other terms are as indicated above. Defining the light interceptance ~ = 1 - T, thUS omitting the canopy light reflectance p, and Lmax the value that ~ takes when Lp is infinite, the model takes the form: ~ = Lmax[1 - e x p ( - KLp)]. This model was empirically adjusted to values o f , and Lp, with

a non-linear weighted least-squares method, providing the best fit to our data. The two parameters of the fit, namely Lmax and K, were estimated separately for the whole plot and for the high forest, as shown in Table 4. I,max is close to unity, within the uncertainty limits of the estimates, whereas K varies according to rso C, TDIR, TTOT and the set of photosites. These parameters were derived from daily integrated light interception. For direct and total PAR, unless otherwise indicated, they were calculated for June-December, using the average light transmission of 21 days at 10 day intervals. In the high forest sites, values of K are very close for overcast sky (0.80) and clear sky (0.78 for direct and 0.78 for total). Where diffuse radiation predominates, as in the dense high forest, light variability under clear sky is smoothed out at the day level. Uncertainties about K are higher than for the whole plot. Values of r 2 are low, particularly for total light on individual days. Thus, on clear days a small sample of daily integrated light interception values is a poor predictor o f Lp, and vice versa. In spite of these limitations, values of K characterized well the closed forest. They compare with the daily average of K = 0.74, found by Saldarriaga and Luxmoore (1991) in a succession sequence of an Amazonian rain forest, and 0.72 for Pasoh Forest, West Malaysia

Table 4 P a r a m e t e r statistics for light interceptance Parameters a

SOC

Direct b

Total

T176 c

T265

T356

1.025 0.040 - 0.530 0.086 0.999 0.650

1.051 0.070 - 0.450 0.101 0.994 0.505

1.021 0.050 - 0.496 0.092 0,999 0.579

0.969 0.036 - 0,703 0.177 0.676 0.129

1.064 0.091 - 0.407 0.103 0.995 0.499

1.008 0.046 - 0.450 0.111 0.934 0.375

0.982 0.011 - 0.797 0.110 0.838 0.493

0.981 0.016 - 0.782 0.146 0.629 0.296

0.968 0.014 - 0.783 0.131 0.700 0.359

0.970 0.018 - 0.805 0.195 0.507 0.169

0.958 0.012 - 0.947 0.255 0.461 0.063

0.960 0.019 - 0.889 0.300 0.424 0.083

Whole plot (n = 25) I,max Uncertainty K Uncertainty P r2

High forest (n = 15) ~m~x Uncertainty K Uncertainty P r2

a Parameters are fitted to the m o d e l ~ = rmax(1 - e x p ( - KLp), using a w e i g h t e d least-squares m e t h o d ( L e v e n b e r g - M a r q u a r d t ) . r 2 b a s e d o n u n w e i g h t e d values. b Direct and total transmittance are m e a n s o f 21 days (fifth, 15th and 25th f r o m June to December), a s s u m i n g c a n o p y constancy. Three particular d a y s for total light illustrate the effect o f solar position about solstices (julian d a y s 176, 3 5 6 ) and equinox (julian d a y 265) o n the parameters.

109

J.-M.N. Walter, E.F. Torquebiau/Agricultural and Forest Meteorology 85 (1997) 99-115

(Kira, 1978). Thus, the apparent uniformity of daily light conditions on the forest floor betrays the influence of the rather uniform vertical distribution of canopy elements, characteristic of mature tropical rain forests, as compared with temperate forests (Kira, 1978; Shuttleworth, 1989; Kira and Yoda, 1989). Considering the whole plot, K values are lower than those of the high forest alone: 0.53 (diffuse), 0.45 (direct) and 0.50 (total). The analysis of residuals of the fit (not detailed here) shows the presence of outliers, corresponding to treefall and transition zone sites with clumped structure, which transmit more light than predicted by a random canopy. The incorporation of those microsites into the calculations strongly affects the values of K. As expected, single days present contrasting values of K for total light (Table 4), emphasizing the varying geometric relationship between the solar position and gap morphology. Thus, at the equinoxes, light interception is maximum in the high forest, when the Sun is overhead and the zenith is obstructed by foliage (Fig. l(a)). Light penetrates less to the forest floor. The value of K reaches 0.95. At the solstices, with the Sun at higher incidence angles, the penetration of lateral light is increased, and K is lower. For the whole plot, the situation reverses: at the equinoxes, there is a minimum of canopy interception in the treefall (Fig. l(d)), in some transition zones (Fig. l(c)) and in high forest sites (Fig. l(b)). The value of K drops to 0.41. Conversely, for those sites at the solstices, direct sunlight is intercepted by the dense transition zone and K increases to 0.70. The spatial variability of K is shown in Fig. 8(a) for diffuse light (SOC) and in Fig. 8(b) for direct and total light, along the ecological gradient. These values were calculated as: K = - l o g ( ¢ ) / L p . The frequent canopy obstruction near the zenith, particularly in the high forest, explains higher local values of K for SOC and for direct beam. The transmission of direct radiation increases strongly as gaps become larger. Lower local values of K for total light are the consequence of the contribution of the bright diffuse sky zone around the Sun, in addition to direct radiation, and of the scattered radiation component of the canopy, especially in the high forest. Calculated scattered light represented 4-34% of total transmitted light in the high forest, 2-18% in the transition

1.2

1.2 High For¢~

bc

1-

Trmmition Zone Treefa~

Di~

u

Transition Zon© Tt~f~

~

0.8

0.8-

._~ 0.6- °°°e°~J°o°oO°o°L

°o

•

ii ooo~o ~e

0.6

mow m m Total

~mma •

o.,mm •

(a) I Ranked Phot~it~

0.2

-i

S~

i'm i

0.4

0.40.2

High Fore~

,

' mmm~,~ •

Cb) I

Ranked Photosites

Fig. 8. Light extinction coefficients K. (a) K for diffuse light (overcast sky: SOC) ranked accordingto canopy openness (CO); (b) K for direct and total light ranked according to CO. Each point is a photosite. For direct and total light, each point is the mean of 21 days (fifth, 15th and 25th, from June to December). Constancyof canopy structureis assumed. zone and 1-11% in the treefall, depending on the day of the year. In spite of considerable variation between sites, calculation suggests that scattered PAR is far from being negligible on clear days, at least in those high forest sites with 'small light patches' (Torquebiau, 1988; Whitmore et al., 1993). Finally, K is highly variable in space and time. Departure from the value of 0.5, commonly used in light interception models, may not be negligible.

4. Discussion 4.1. Gap size, morphology and dispersion

There was a progressive change in size, distribution and spatial dispersion of gaps along the ecological gradient from the treefall to the high forest. The azimuthal anisotropy of gaps was present in almost all forest sites, but particularly emphasized in the transition zone. The spatial pattern of gaps is related to the dispersion of the phytoelements. Randomness was observed commonly only in the high forest. Unlike mature coniferous forests, where clustering of phytoelements is so conspicuous at several nested scales, albeit difficult to quantify, closed broad-leaved canopies tend to obscure this feature. Indeed, viewed from the bottom of the high forest, the perception of clumping is frequently blurred by the overlapping and imbrication of the plant elements, especially when the direction of view comes near the horizon. As one moves horizontally from the high forest to

110

J.-M.N. Walter, E.F. Torquebiau // Agricultural and Forest Meteorology 85 (1997) 99-115

the treefall, or vertically from the ground to the top of the canopy, clumping becomes more and more apparent. In thinned stands or in degrading ecological units, as the canopy becomes more discontinuous, clumping of gaps reappears. In fact, the dispersion of gaps and canopy elements is a question of scale. The fundamental grouping of canopy elements at all scales has been emphasized by numerous workers (e.g. Halls et al., 1978; Brunig, 1983; I~delin, 1984; Givnish, 1984): rosettes of leaves, modular construction of crowns, reiteration, metamorphosis, crownlets, crown shyness, individualization of single trees reaching the canopy top are all different expressions of this grouping. Clumping at the species population level is also commonly observed. Thus, clumping of canopy elements in a hierarchic way is a primary feature of tall forests. This feature is clearly shown on large-scale aerial photographs such as those obtained from a canopy raft (Hall6 and Pascal, 1993). 4.2. Plant area index and mean tilt angle

As long as the gap dispersion is close to random, reliable Poisson-model estimates of Lp can be derived. Otherwise, Lp values tend to be underestimated. When dealing with nonrandomness, one way of assigning the clumping factor is by fitting the gap frequency observations to direct measurements of LAI (A.R.G. Lang, personal communication, 1992). Another way is by dividing the canopy into smaller regions within which the elements are random, computing Lp for those regions, and then averaging the Lp values (Lang et al., 1991). None of these approaches was applied in the present analysis. The method of Norman and Campbell is robust with respect to nonrandomness. J-M.N. Walter (unpublished data, 1995) obtained reliable estimates of LAI in a uniform beech forest and in a heterogeneous hardwood alluvial forest as well, by calibrating those estimates against LAI values derived from litterfall measurements. So far as we know, Lp has barely been decomposed into its two components L t and L w, from direct measurements. Values of L w are rarely reported in the literature. Only scarce hard data come from temperate forests. Hutchison et al. (1986) gave L w = 0.6, or proportionally 10.9% of total Lp (5.5),

in a temperate deciduous forest. In a tropical rain forest of French Guyana, Bonhomme et al. (1974) found a proportion of 7% of Lp = 5.0, by planimetry of bark surfaces in IR hemispherical photographs and telephotos. As a conjecture, applying a 7% proportion for L w to an Lp of 6.5 would give an L l (LAI) of 6.5-6.5 × 7//100 = 6.0 in the high forest. However, such an exercise needs to be considered in the light of the uncertainties inherent in indirect methods scarcely tested, if at all, against independent direct measurements in complex tropical rain forests. As indirect methods tend to underestimate true LAI (e.g. Lang, 1986, Lang, 1991), LAI can be reasonably equated with Lp. At first sight, Lp, and hence LAI, values seem surprisingly low for a tropical rain forest, when compared with those found in the literature. For example, Alexandre (1981) reported an average maximum LAI of 8.2 in mature rain forests at the global scale, with values up to 12. Laumonier et al. (1994) found Lp of 5-6.4 (range 3-7) in Campo forest (Cameroun), by means of a Li-Cor LAI-2000 plant canopy analyser (Li-Cor, Lincoln, NE, USA). It has long been stressed that the leaf area density (LAD (m 2 m-3), surface of leaves per unit of canopy volume) of tall forests is low, as compared with that of shrub and grass canopies (Kira, 1978; Kira and Yoda, 1989). In this respect, in one of the most elegant measurements of LAI and LAD ever carried out in the tropics, Ashton (1978) found at Pasoh Forest, West Malaysia, that individual trees had an LAI range of 0.8-5.3 m 2 m -2 and an LAD range of 0.02-3.85m 2 m -3. A profile of 5 m height in the primary forest gave a mean LAD of 0.1-0.8 from top to bottom and a mean LAI of 2.5. These values compare with a maximum LAD of 0.25 in the 2025m layer, a mean LAD of 0.14, a total LAI of 6.7 for the tree cover with stems greater than 4.5 cm dbh (diameter at breast height), and an LAI of about eight for a whole canopy at Pasoh Forest (Kira, 1978). These are among the scarce data available at present from direct measurement in an area not too far from Sumatra. Are West Malaysia values representative for Sumatra forests? Indeed, nothing demonstrates that LAI values in our plot should be actually so high. One may speculate about the long-term effects of the 1983 E1 Nifio Southern Oscillation drought, which is

J.-M.N. Walter, E.F. Torquebiau / Agricultural and Forest Meteorology 85 (1997) 99-115

known to have particularly affected the area. Did the canopy recover from such a dry period before our measurements? An exceptional dry spell occurred at the time of our observations, December 1984. Visually, the canopy seemed abnormally clear, and the soil was covered by a thick dry leaf litter, prone to fire. Therefore, we hypothesize that the effects of stress, which reduced the leaf area, explain the relatively low values of Lp found in our plot. Stress and disturbance will influence significantly the canopy geometry. Comparing two series of solar radiation measurements beneath a mature forest canopy at Barro Colorado Island (Panama), at 1 year interval, Becker and Smith (1990) showed that spatial autocorrelation was typically different: in the E1 Nifio year 1983, light penetration was abnormally high owing to drought-induced leaf fall in the dry season preceding me.asurements, which were positively autocorrelated from 2.5m to 12.5-22.5m, whereas in 1984, a more typical year, measurements were positively autocorrelated only between adjacent sites 2.5 m apart. Similarly, the effects of foliage recovery on light tra:asmission, thus increasing LAI values, after establishment of pioneer trees and growth, following hurricane Hugo in 1989, have been analysed in l~aerto Rico by Fernandez and Fetcher (1991) and in Guadeloupe by Labb6 (1994). L o values differentiated clearly the high forest, the transition zone and the treefall. However, this hides a still greater contrasting distribution of foliage, through vertical variations in LAD and horizontal variation in proportions of leaf and bark surfaces. In the treefall, foliage is concentrated in a dense layer near the ground, whereas in the forest interior it is split into several layers. As the forest becomes mature, the proportion of bark surfaces increases. Unfortunately, no quantitative vertical distributions of Lp were available, although the published profile diagram and light extinction profiles (Torquebiau and Walter, 1987; Torquebiau, 1988) give some insight into the vertical distribution of the crowns. The mean tilt angle Ap of canopy elements was strongly correlated with the concentration and amount of gaps. Comparisons of values of Ap with data from the literature can barely be made at the community level (Anderson, 1981; Hutchison et al., 1986) or at the individual level (Ashton, 1978). The derivation of Ap, albeit very sensitive to error, none the

111

less gave consistent information with respect to the prevailing geometric and ecological conditions of the plot, and seems not to be the consequence of a photographic artefact.

4.3. Light distribution Despite local discontinuities, canopy structure appears as a continuum at a more encompassing level. A property ascertained at one location may interfere with processes or functions some distances apart. For example, the influence of a treefall on the radiation regime is exerted far beyond its physical limits in the high forest. The asymmetry of treefall borders, receiving direct sunlight at limited periods of time or only skylight for the whole year, is striking. Lateral light is an essential feature of the understorey of heterogeneous forests, allowing the penetration of direct radiation, as sunflecks of varying duration, deep into the forest interior. This has an important beating on the ecophysiology of the undergrowth, the survival of seedlings and animal life, as emphasized in many recent publications (e.g. Raich, 1989; Canham, cited by Platt and Strong, 1989; Lawton, 1990; Turner, 1990; Chazdon and Pearcy, 1991; Smith et al., 1992; Brown, 1993; Endler, 1993; Labb6, 1994). Oldeman's generalization (Oldeman, 1990, Oldeman, 1992) of 'ecological interference' expresses pertinently the influence of canopy openings from different directions. It is tempting to relate Endler's 'light habitats' and 'environments' (Endler, 1993) to the structural features described above. Whereas light environments are described by spectral properties, mainly the ambient light colour, light habitats are primarily determined by canopy geometry, weather and time of day or year. Endler recognized four light habitats: 'forest shade' in canopy closed overhead, with only tiny or few gaps; 'small gap' in canopy, where direct sunbeams penetrate and with essentially no sky light; 'woodland shade' in more open canopy, where a significant fraction of incident light comes from the sky; 'large gap', where direct sun and diffuse sky light contribute most of the ambient light. All these light habitats determine the light environments, and are of high significance for animal behaviour and plant growth and development. In particular, the red/far-red ratio ff is highly correlated with canopy

112

J.-M.N. Walter, E.F. Torquebiau /Agricultural and Forest Meteorology 85 (1997) 99-115

geometry (Lee, 1987; Endler, 1993; Varlet-Grancher et al., 1993). The relationships between gap pattern, light habitat and light quality are summarized in Table 2. Predictions for sunny conditions (Fig. 7(a)Fig. 7(b)), for example in transition zone (7), suggest a 'woodland shade' regime in June-July, likely to be characterized by blue-grey ambient spectra from the blue sky and the leaves, without the interference of direct sunbeams. The treefall, distal part, would experience a shift from 'woodland shade' (June-July) to 'large gap' (August-December), with whitish ambient light typical of the open. The proximal part is in open conditions the year round. High forest (Photosite 3) would be under 'forest shade' (yellow-green) and 'small gap' (reddish ambient spectra) alternatively, whereas high forest (Photosite 20) is likely to shift continuously between 'forest shade', 'small gap' and ' woodland shade'.

5. The application of these methods for monitoring canopy geometry and light distribution, in response to phenology (Van Schaik et al., 1993), stress (Becker and Smith, 1990) and disturbance (Fern~indez and Fetcher, 1991; Labbr, 1994). Finally, in the scope of indirect methods, hemispherical photography remains a valuable alternative to other similar techniques, when sunshine is too scarce to allow work with the transmission of a direct beam and when the absence of a large clearing makes reference measurements of full sky radiation impracticable. This standardized technique has reached maturity for assessing light conditions in forest canopies, as testified by recent long-term measurements (Rich et al., 1993; Whitmore et al., 1993). However, much remains to be done with respect to canopy geometry in complex heterogeneous forests of the tropics, where calibrations of indirect against direct methods are still lacking.

4.4. Methodological remarks

5. Conclusion Extensions, improvements and applications of the methods used in the present study could include: 1. the analysis of the spatial structure of canopy variables by means of geostatistics, in intensively sampled transects or grids across different ecological units and gradients, for optimal sampling and mapping (Walter and Grrgoire Himmler, 1996). 2. The separation of the 'green foliage' (leaves) from the 'grey background' (trunks, soil, litter), for example, by image analysis of colour IR photographs of canopies (Bonhomme et al., 1974). This is indispensable if LAI data are to be used for interpretation of remote sensing spectral vegetation indices, or for driving functional models of ecosystems. 3. The calibration of gap distribution, or predictions of PAR transmission, against measured red/farred ratios ~ and other light habitat spectrum, as suggested in Table 2 (see Lee, 1987; Endler, 1993). 4. The use of hemispherical photography for assessing objectively the size, limits and morphology of treefalls, particularly in studies of gap creation and closure, of gap phase dynamics and turnover rates of forests (e.g. Whitmore et al., 1993; Van der Meer et al., 1994).

Canopy variables and ecological units are strongly related, yet Lp, and therefore LAI, appears as a 'smeared' variable, from the perspective of scene models of remote sensing (Graetz, 1990). This is true particularly in dense tropical forests, where the distinction between 'clump LAI' and 'whole canopy LAI' is impracticable. Canopy architecture grades from mature high forest to treefall. This variation is continuously reflected in geometric parameters. In spite of the characteristic gap distribution pattern, the uncertainties of contours in the transition zone make it difficult to draw limits around the treefall.

Acknowledgements The present work was supported by the French Cooperation Programme with the Regional Centre for Tropical Biology (BIOTROP) of the South East Asia Ministries of Education Organization (SEAMEO, Bogor, Indonesia). We gratefully acknowledge Dr. A.R.G. Lang for his careful review of an earlier draft. We wish to thank Dr. R. Bonhomme and Dr. Y. Laumonier for their valuable comments.

J.-M.N. Walter, E.F. Torquebiau / Agricultural and Forest Meteorology 85 (1997) 99-115

Appendix A. Equations used to compute the spherical variance of gap and the moments of inertia of the gap weighted vectors (from Jupp et al., 1980) A point on the upper hemisphere may be represented as a unit three-dimensional vector. In polar coordinates, this point takes the form

( l , m , n ) = (sin 0cos ~b,sin 0sin ~b,cos 0) where angle. Let of the zenith

(gl)

0 is the zenith angle and ~b is the azimuth

(lij,mij,nij) be the coordinates of the centre jth division of the ith ring of the azimuth × sampling grid. Let gij be the gap fraction in the i,jth division. Then the spherical mean is defined to be l, ~ , fi), where = ~_~ g i j l i j / / R

ij

~t = Y'. g i j m i j / R

(A2)

q

7t = ~_, gijnij/R q where e=

gijlij

~-

gijmij

dr

gijnij

;l

(A3)

The spherical variance SV is defined to be

SV = ( N - R ) / N

(A4)

where N = ~.i$ij. The moments of inertia of the gap weighted vectors may be calculated as follows. Let T be the 3 × 3 matrix of weighted sums of squares and products of the gap vectors E g21ijmij ij T=

Eg2jrnijlij q

Eg2nijlij ij

q

ij

2 2 E gijmij ij

2 E gijnijmij ij

E g2 lijnij Eg2mi)nij ij

/N

113

zenith (0 = 0). If the gap distribution is symmetrical about the first axis, then the other eigenvectors are not important. The eigenvalues of T, ( s p s 2 and s 3, which satisfy s 1 + s 2 + s 3 = 1) are interpreted in the text and in Table 2.

Appendix B. Calculation of PAR transmittance on clear days: an example from Fig. 6(b) Indices DIR, DIF and TOT refer to direct component, diffuse component and total PAR, respectively. The extreme right-hand value in Fig. 6(b) (treefall area, proximal part) shows TDIR > TTOT. Let Q be the amount of PAR, incident above the canopy: QDIR = 43.3, QDIF = 19.9 and QTOT = 63.2molm -2 day-1 (julian day 259). The amount of PAR Q, transmitted through the canopy is: QrDIR = 19.5, QrDIF = 4.3 and Q,TOT = 2 3 . 8 m o l m - 2 day -1. Following the definition of transmittance, ~'= Q , / Q . Thus, '/'DIR= 19.5/43.3 =0.450, '/'DIE= 4.3/19.9 = 0.216 and ~'TOT= 23.8/63.2 = 0.377. Eighteen out of 21 days give '/'DIR> "/'TOT' Average values (n = 21) are: ~'DIR = 0.314 _+ 0.026 (SE), ~'DIF = 0.210 5:0.006 and YTOT= 0.282 + 0.019. These values of ~'OIR and YTOT were plotted at the extreme right-hand side of Fig. 6(b). Another expression of the contribution of the direct component to the total light beneath the canopy is the ratio Q'rDIR/Q'rTOT (where both terms are in m o l m -2 day-1). From the previous example (julian day 259), Q~Dm/Q~ToT = 19.5/23.8 = 0.819. This ratio compares with the ratio from the open: QzDIR/QrToT = 43.3/63.2 = 0.685. Averaged over 21days, we find the ratio 0.760 _+ 0.017 (SE) beneath the canopy and ratio 0.707 + 0.004 for the open. These values, significantly different (paired t-test, n = 21, P = 0.0138), confh-m the previous estimate of relative beam radiation enrichment beneath the canopy in the treefall area.

(5)

2 2 E gijni) ij

The first eigenvector of T will be a direction on the sphere corresponding to the direction of maximum gap, which should be identical to the spherical mean, and in most plant canopies should be near the

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