The fundamental description of canopy geometry includes the inclination, azimuth, surface area, and location of individual plant parts. Data-gathering requirements can be eased by applying some reasonable assumptions. Azimuthal angle distributions of stems and leaves can be assumed to be symmetric, which is usually the case for most non-heliotropic plant species. Further, the location of individual canopy elements can be assumed to be random, usually in a horizontal monolayer. These are reasonable assumptions for many herbaceous canopies of nearly full cover (Norman 1979) so that the remaining parameter, inclination angle, is all that need be documented.
Further refinements are needed for canopies having widely spaced plants with nonhomogeneous horizontal or vertical dispersion patterns. Agricultural examples include orchard trees with dense crowns or some widely spaced row crops, such as grapes. In natural communities, individual plants may be aggregated due to microsite differences or to competitive interactions. For these complex cases, higher dimension shapes, such as ellipsoids (Norman and Welles 1983), have been used to decompose canopies into subunits. Ellipsoids may represent individual plants within the canopy or may depict a cylinder of biomass as might occur along a row of closely spaced plants. Canopy elements are usually assumed to be randomly located within ellipsoids, although aggregation can be introduced if more information on the geometric structure of individual plants is available.
The location of canopy elements is obviously non-random in canopies
of some large plants, for example, trees and some shrubs, even though inclination
and azimuth angles may be random. Smaller stems are completely dependent
upon larger stems with respect to location. Because branching angle can
be genetically fixed in a species, the inclination and azimuth angles of
smaller stems are also dependent to some degree upon those of larger stems.
Leaves, in turn, are usually attached only to the smaller stems and are
dependent upon them for location. However, because of phyllotaxy or twisting
of petioles, among other reasons, leaf angular distributions can be relatively
independent of the stem angular distributions (Fisher 1986). Because of
these location dependencies, statistical sampling of canopy geometry for
extrapolation to the stand or field level can be difficult.
The simplest one-dimensional models of radiative exchange in vegetation canopies, e.g. Verhoef (1984), assume that leaves are randomly located Lambertian scatterers, symmetrically distributed about the azimuth and inclined to the horizontal with some reasonable distribution. The essential information required for input to such models is leaf spectral properties, leaf area index (LAI), and leaf inclination distribution (LID). The LAI can be measured by a number of direct and indirect techniques (Norman and Campbell 1989). The LID can be characterized by a two-parameter beta distribution (Goel and Strebel 1984) or a single parameter ellipsoidal distribution (Campbell 1986).
The one-dimensional model of Suits (1972) which assumed random leaf positioning, a symmetric azimuthal distribution and leaves inclined in only vertical or horizontal directions, was the first to predict canopy bidirectional reflectance. Verhoef (1984) generalized Suits' approach to include any leaf inclination distribution with azimuthal symmetry. Several newer models have been proposed that are based on Lambertian deaf spectral properties, random leaf positioning, azimuthal symmetry, and any leaf inclination angle distribution (e.g. Cooper et al. 1982, Camillo1987, Choudhury 1987). Hapke (1984) published a similar model for soil surfaces. Norman et al. (1985) describe a numerical model of canopy bidirectional reflectance similar in assumptions but which specifically considers the soil bidirectional reflectance and non-Lambertian leaf characteristics.
A slight variation on the random leaf-positioning concept was proposed by Nilson (1971) to accommodate clumping or regular leaf-spacing tendencies with empirical coefficients. However, obtaining the necessary empirical coefficients depends more on fitting the modified quasirandom model to radiation penetration measurements than on appropriate canopy structural measurements. A different concept of clumping was proposed by Norman and Jarvis (1975) for spruce trees' and the radiation penetration model was linked to measurements of projected needle area of shoots and the organization of shoots onto branches, with the model including the woody portions of the canopy. This might be referred to as a weighted-random approach. Other clumping models have been proposed for predicting light penetration in agricultural crops and some have been reviewed by Norman (1975).
Models that incorporate clumping require some measurements of the horizontal distribution of foliage and these are difficult to obtain. The three-dimensional radiation penetration model of Norman and Welles (1983), which is similar to the models of Whitfield and Conners (1980) and Welles (1978), has attempted to simplify the measurement input requirements by requiring only the dimensions of an ellipsoidal envelope within which all the leaves are contained and assumed randomly distributed. Thus, for these envelope models, the only additional measurements beyond those required for a one-dimensional model are the overall crown dimensions of individual trees. The light penetration model of Norman and Welles (1983) has been recently extended to include the canopy bidirectional reflectance distribution function (BRDF) by Welles (1988).
Incorporating the three-dimensional structure of the canopy into radiation models permits closer approximation of the complexity of real canopies. The model of Kimes and Kirchner (1982), which considers the general three-dimensional distribution of elements, requires even more detailed spatial data on the distribution of canopy elements than envelope models. This is also true for the model of Wang (1988).
The most general three-dimensional canopy radiative transfer models are based on ray tracing (Myneni et al. 1987) and Monte Carlo techniques (Ross and Marshak 1985). An additional general method termed radiosity has been used in graphics applications (Greenberg et al. 1986) but no published literature is yet available for its application in canopy studies. In principle, these radiative transfer approaches can accommodate almost any architecture. The Monte Carlo model of Ross and Marshak (1985, 1988) is a good example of a model capable of predicting the canopy BRDF, including the 'hot spot', for generalized canopy architectural descriptions even though they considered a random canopy. The latter model inputs considerable canopy structural information, including the number of leaves per canopy and the distance between leaves—information which is not generally available.
The greatest obstacle to the application of three-dimensional radiative transfer models is that suitable canopy architectural information is scarce because of the difficulty in obtaining such measurements. Although recent advances in L-systems (Lindenmayer 1987) and fractal geometry (Mandelbrot 1982) can provide quantitative tools for representing some vegetation structures, detailed structural characteristics such as branching patterns, leaf size, leaf shape, and the distribution of flowers and fruits must still be measured directly.
The study described in this paper provides the essential information
required to characterize fully a three-dimensional canopy with L-systems
or fractals. That task will be the subject of another paper. Here we describe
the methodology for obtaining the essential information and summarize the
results of the fundamental distribution of canopy elements from row-spaced
trees with complex crown architecture. The canopy geometry of walnut trees
which had received irrigation treatments of 100 and 33 percent of calculated
evapotranspiration (ET) for two years was measured. The angular and spatial
distributions of stems were sampled in a manner that allowed a verifiable
three-dimensional reconstruction of the canopy stem components. Combined
with other data (e.g. leaf angular distributions; tallies of branches,
leaves and fruits; wood and leaf specific weights) we can provide estimates
of important canopy architectural characteristics such as LAI and biomass.
For each segment we measured length, diameter, zenith angle (from vertical) and azimuth. Figure 1 presents a diagram of the stem and leaf angles measured. Lengths were measured to the nearest centimetre. Zenith angle (q b, figure 1(a)) was measured by placing a draughtsmen's protractor with a plumb-bob along the segment. Zenith angle is the angle between a vertical line and the line the branch segment forms when its base intersects the vertical line. A branch pointing straight up would have a zenith of 0°; horizontally, 90°; straight down, 180°. Zenith angles were translated to elevation angles (0° = horizontal, 90° = vertical) for use in the beta distribution calculations described below. Azimuth angles (q a , figure 1 (a)) were measured with a magnetic compass and later corrected to true north, or estimated with the protractor (using the true north-south row direction for orientation) where accurate magnetic readings were precluded. All angles were recorded to the nearest 5°.
Data for each segment were stored in a doubly linked list, i.e. the segment number from which the current segment came was recorded as well as the numbers of the segments into which the current segment branched. A doubly linked list was used, even though a singly linked list would suffice, to safeguard against errors which would break the linkage. This data structure allowed us to examine the relations among the segments and permitted the three-dimensional reconstruction of the data set.
Orchard-level sampling
Eight trees in a two-tree by four-tree block, were sampled for each
irrigation treatment (33 and 100 percent ET). For the orchard-level sampling,
the critical size class was Class 4, so that only segments greater than
4 cm diameter (229 in all) were measured on all 16 trees. All segments
greater than 4 cm diameter are referred to collectively as Class 5 segments.
All segments of size Classes 1-4 which branched directly from the Class
5 segments were tallied. There were no leaves or fruits directly attached
to any of the Class 5 segments.
Tree-level sampling
Two trees in each of the two irrigation treatments were sampled. Each
Class 3 or Class 4 segment tallied in the orchard-level sampling was measured
down to and including Class 2 segments. Here, the critical size class was
Class 1, so no Class 1 segments were measured on these Class 3 or Class
4 segments except when a Class 1 segment terminated a long-shoot, or was
greater than 25 cm in length (a 'sucker' shoot). A total of 553 segments
were measured. The number of Class 1 segments occurring on each segment
measured were tallied. The number of leaves and fruits on the Class 1 segments
measured were tallied. Notice that this sampling scheme does not include
Class 2 segments which branch directly from Class 5 segments. A relatively
small number of these branches exist. Most of these Class 2 segments were
located in the interior of the canopy and, for the purposes of calculations
described below, are estimated to be the equivalent of three Class 1 branches.
Branch-level sampling
Five branches, each on a different tree, were sampled down to and including
all Class 1 segments. The diameters of the basal segment of these branches
were 1.9, 1.9, 2.0, 2.0 and 3.4 cm. They included upper, lower, east- and
west-side canopy positions. All leaves and fruits occurring on Class 1
segments were tallied. Of the 256 segments sampled, 126 were Class 1 segments
which contained 378 leaves and 209 fruits. These data are used here primarily
for establishing leaf and fruit numbers per Class 1 branch for extrapolations
to the whole tree level.
2.3.2 Leaves
The odd-pinnate compound leaves show a bilateral symmetry about a plane
along the rachis such that the elevation angle of the lateral leaflets
from this plane is about the same on both sides. The leaflets also show
a similar symmetry of laminar folding about the midrib of the leaflet (figure
1 (c)).
We measured 147 leaves on 20 vertical transects of 8 trees in the 100 percent ET treatment and 72 leaves on 10 vertical transects of 6 trees in the 33 percent ET treatment. The transect locations were randomly selected below the canopy and the leaf nearest the vertical transect at 0.5 m intervals from the ground was measured. Measurements were made to fully describe the leaf in three-dimensions. For each leaf we measured the height, number of leaflets, the length of the petiole plus rachis, and the zenith (q r) and azimuth (q a ) of the rachis (figure 1 (a)). The terminal and lateral leaflets were obviously different in several respects so we measured the terminal leaflet and the adjacent left-lateral leaflet for the following: midrib zenith (q 1) and azimuth angles, the azimuth of the normal to the leaflet lamina (or the zenith angle of the normal if necessary), and the width at the widest part of the leaflet lamina when naturally folded and when flattened with the ruler. The last two measurements allowed calculation of the folding angle of the leaflet lamina about the leaflet midrib (q m, figure 1 (c)).
2.3.3. Biomass measurement
Stem volumes for 110 stem segments were determined by displacement
of water and subsequently divided by the stem dry weight to determine the
wood density for stems in size Classes 1-4. Stems in Class 5 were assumed
to have the same density as those in Class 3. The dry weight of 100 fruits
in the 33 percent ET treatment and 80 fruits in the 100 percent ET treatment
was measured. Both dry weight and leaf area (LICOR LI-3000 Leaf Area Meter)
were measured on each of 50 freshly excised leaves to determine leaf specific
weight. Leaf area was measured for each leaflet on 100 leaves from each
irrigation treatment. These data were used in the calculation of the area-weighted
average of leaf zenith angles.
2.3.4. Plumb-line measurements
To verify the three-dimensional reconstruction based on the angle and
length measurements for stems, we hung plumb-lines at identified points
in each of the trees sampled for tree-level measurements. The measured
vertical heights and distances from the trunk of each of the 58 plumb-lines
were compared with calculated values from the reconstruction.
The three-dimensional reconstructions are subject to cumulative positional errors. These errors could be a function of the number of preceding segments (greater chance for errors) or a function of the length of the preceding segments (incorrect projection of segments due to errors in angle measurements). To evaluate the fidelity of the three-dimensional reconstructions, we compared the calculated positions in space of 58 points on the four trees used in the tree-level sampling with independent measurements of location determined by plumb-line. There is close agreement between the two datasets for both vertical height (figure 4) and horizontal distance from the trunk (figure 5). The regression equation in each case is highly significant (p<0.001). Intercepts are not significantly different from 0 and slopes are not significantly different from 1.0 (standard error of slope for each regression is 0.025). Examination of residuals shows no deviation from the linear model.
Close inspection of the statistical patterns provides further support
for the validity of the reconstructions. Correlations of residuals from
regressions in figures 2 and 3 to the number of preceding segments, or
their summed length, were significant only for distance residuals versus
number of preceding segments (r=0.474, p=0.001). However,
when the number of preceding segments was included as a term in the regression
model for distance, the R2 increased only slightly from
0.9773 to 0.9801. Thus, the accumulation of measurement errors, leading
to large deviations from the expected measurements in height or distance,
was not found to be significant in the data set. Hence, this data set can
be used with some confidence for parameters which depend on the three-dimensional
location of canopy components.
The stem length distributions for the tree-level sampling (figure 7) are expressed for the two irrigation treatments (two trees per treatment). The data for Class 1 and Class 2 stems includes extrapolated values for the tallied Class 1 and Class 2 stems which occurred on the Class 5 stems. Extrapolations were based on the following assumptions. A mean Class 1 branch length of 6.72 cm (calculated from the branch-level sampling) was assumed for the tallied Class 1 branches. A further assumption was made for the Class 2 segments tallied on Class 5 segments. These small branches are mostly in the interior of the canopy. Examination of branch-level data most similar to them indicates that the Class 2 branches are equivalent in length to between three and six Class 1 segments. We assumed for our calculations that one Class 2 branch is equivalent to three Class 1 segments. An assumption at the upper extreme of six Class 1 segments per Class 2 would increase the summed length of Class 2 segments by 9.0 percent in the 100 percent ET treatment and 6.4 percent in the 33 percent ET treatment. The summed length of all stem size classes would increase 2.9 percent in the 100 percent ET treatment and 2.1 percent in the 33 percent ET treatment. Thus, the worst-case error indicates that the assumptions provide reasonable values for further modeling.
The results (figure 7) for the two irrigation treatments are very similar
for each size class category and similar in the summed length of all stem
size classes (27.5 and 27.0m in the 100 and 33 percent ET treatments, respectively).
This pattern is consistent with the maintenance of the carbon allocation
to smaller stems under water stress and contrasts with the observed pattern
of reduced allocation to larger stems.
The zenith angle of the four stem size classes for both treatments is
shown in figure 9. Stem zenith angles range from 0 (vertical) to 90°
(horizontal) to 180° (stem pointing downward). Our definition of zenith
angle for stems differs from the conventional because the angle is expressed
in reference to the origin of the stem and therefore extends over a 180°
arc. There is a clear trend for larger stems to be more upright as shown
by the rapid rise of the curve for the Class 5 (>4.0 cm diameter) branches
in the 0 to 90° region. In contrast, the Class 2 stems are nearly uniformly
distributed throughout the 180° range.
The zenith angles of the four leaflet types are shown in figure 11. Zenith angles are expressed relative to the origin of the petiole and the top surface of the leaf. Leaf zenith angles may exceed 180° in cases of extreme petiole twisting. Terminal leaflets are more steeply angled than lateral leaflets within a treatment. The mean angles for the 100 percent ET leaves are 151.4° and 131.0°, terminal and lateral leaflets, respectively, and 156.4° and 139.8° for the 33 percent ET treatment. The leaflets of the 100 percent treatment are more horizontal than the same type of leaflet in the 33 percent treatment, as shown by the shift to lower zenith angles in figure 11 for the 100 percent ET treatment leaflets.
The area-weighted average leaflet zenith angle was calculated for each
treatment. The 100 percent ET treatment leaves have 6.77 leaflets, and
the 33 percent ET treatment leaves have 6.49 leaflets per leaf. Average
terminal leaflet area is 83.0 and 77.8cm2, lateral leaflet area
is 36.3 and 36.2cm2, for 100 and 33 percent ET treatments. Therefore,
the area-weighted average leaflet angle for the 100 percent ET treatment
is 136.8° from vertical, and is 144.5° for the 33 percent ET treatment.
The beta distribution parameters for the five size classes of branches are plotted in figure 12 for each treatment. The smallest diameter branches in both treatments show a uniform distribution tending slightly towards planophilic (most angles horizontal). With increasing diameter, the distribution shifts past uniform toward spherical or spherical erectophilic (most angles vertical). Branches of Classes 3 and 4 in the 33 percent ET treatment tend to be more towards plagiotropic (most angles about 45°) than the corresponding 100 percent ET treatment branches. Class 5 branches of both treatments tend toward the erectophilic distribution but the 33 percent ET branches show a lower variance.
Leaflet angle beta distributions are plotted in figure 13. Terminal
leaflets in both treatments have an approximately spherical distribution
of elevation angles. The distribution of lateral leaflets differs between
the treatments. The 33 percent ET lateral leaflets have a plagiotropic
distribution. The 100 percent ET lateral leaflets have a distribution between
uniform and plagiotropic due to a greater variance (x=41.0°, s2
= 381.2) than the 33 percent ET lateral leaflets (x=48.7°, s2=259.8).
The tendency for the 33 percent ET leaflets to be more erect than the 100
percent ET leaflets is indicated by their position more towards the erectophile
point than the uniform-plagiotropic line.
The zenith angle of the leaflet midrib showed a significant increase with height for lateral leaflets in both treatments but only weakly for terminal leaflets in the 100 percent ET treatment. The zenith angle of the rachis, to which the leaflets are attached, is significantly negatively correlated with height only in the 33 percent ET treatment. The angle becomes more horizontal toward the top of the canopy.
The width of the terminal leaflets is negatively correlated with height for both treatments. Lateral leaflets show a significant negative correlation with height only in the 100 percent ET treatment. The number of leaflets per leaf significantly increases with height in both treatments.
Despite the statistically significant correlations of some leaf geometry
parameters with height, it is important to note that the R2
values are generally low and the slopes are often small.
Class 5 stems were assumed to have the same wood density as Class 4 stems. Individual fruit weight was 11.10 and 8.29g for the 100 ET and 33 percent ET treatments, respectively. Leaf area per leaf was measured at 297.04 cm2 in the 100 percent ET treatment, and 285.43 cm2 for the 33 percent ET treatment.
The average height of the 100 percent ET trees is greater than for the 33 percent ET trees, but there is near overlap in values. However, the maximum height of the Class 5 branches shows significant separation of the two types, with the 100 percent ET trees taller than the 33 percent ET trees. This is consistent with the results for Class 5 segments on all 16 trees measured at the orchard-level where the 100 percent ET trees have a maximum height of 411 cm which is significantly greater than the 335 cm height of the 33 percent ET trees (t = 5.245, p = 0.0001). The 33 percent ET trees may reach maximum heights as great as the 100 percent ET trees but have fewer large diameter branches in the upper canopy. The reduced irrigation treatment appears to have decreased radial growth of stems more than extension growth.
The total biomass of the 100 percent ET trees is greater than the 33 percent ET trees which are about 86 percent of the biomass of the 100 percent ET trees. The apportionment of biomass among organs, however, seems to be about the same between the treatments except for fruits. Notably, the 33 percent ET trees are 89 percent of the stem weight and 94 percent of the leaf weight, but they have only 76 percent of the fruit weight of the 100 percent ET trees.
Stem areas were calculated as the summation of length times diameter
for all stems. Stem areas and leaf areas are greater for the 100 percent
ET trees. LAI (m2 leaf area per m2 ground area) averages
3.40 for the two 100 percent ET trees and 3.18 for the two 33 percent ET
trees presented in table 2. However, projected LAI exhibits a greater difference
between the treatments because of the steeper leaflet angles of the 33
percent ET trees. The number of sucker shoots is greater on the 100 percent
ET trees (7 and 9 shoots) compared to the 33 percent ET trees (0 and 4
shoots) which contributes to the dissimilar appearances of the trees in
the field. The projected surface outline of the upper tree canopy is the
primary visual difference between the treatments and leads to this perception.
Our data sets provides a good picture of the consequences of two years
reduced irrigation on walnut tree morphology: less biomass of stems, fruits
and leaves, lower LAI, less allocation to large stems, fewer sucker shoots,
and more vertically inclined leaf angles. These data can be used to test
and validate canopy photosynthesis and carbon gain models.
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