1. Stand Structure in Terrestrial Ecosystems
leaves (e.g., Monsi and Saeiki 1953; Hom 1971)
and branching patterns (Halle et al. 1978; Honda et
al. 1981).
Radiative transfer models based on foliage
amount and leaf angle distributions (LADs) are
commonly used to estimate properties such as canopy cover and leaf area index (LAI) from integrated
light measurements from quantum light sensors or
upward-looking, hemispherical photographs. An
example of such measurements is provided in Figure 1.1, which contrasts light profiles for late seral
Douglas fir-hemlock forest and a plantation forest
of broad-leaved Populus. Of special significance is
the use of simple radiative transfer models to derive
LA! from measured canopy "gap fraction," that is,
the fraction of a field of view through a canopy that
is not blocked by the canopy. One approach to derive LA! from gap fraction data uses the BeerLambert law of exponential extinction of light
though a canopy as a function of that canopy's extinction coefficient (e.g., Marshall and Waring
1986). A second related approach inverts a onedimensional model that is based on exponential extinction of light as a function of zenith angle, foliar
density, and LAD (Norman and Campbell 1989;
Welles 1990). Instruments and methods for gap
fraction analysis are discussed in more detail later
in this chapter.
Branch models by Honda et al. (1981) have been
used to simulate growth patterns in tropical trees.
More recent efforts have focused on fractal descriptions of branching patterns as a means of describing canopy architecture and modeling threedimensional radiative transfer (Myneni et al. 1990;
Chen et al. 1994). Fractal models of trees are attractive because complex branching patterns can be
described by a few simple equations and still generate remarkably realistic architectures (Zeide
1991, 1993).
Canopy-to-stand scale models have primarily
focused on the use of geometrical optical models
and crown shadows (Li and Strahler 1985). Geometrical optical models generally assume canopies
can be described as simple geometrical shapes,
such as cones, spheroids, and ellipsoids, and focus
on modeling the reflected light as consisting of
illuminated and shadowed ground and sunlit and
shadowed canopy. Early models disallowed mutual shadowing and were thus most applicable to
open forests and shrublands (e.g., Pech et al. 1986;
9
Franklin and Strahler 1988). More recent models
account for mutual shadowing (Li and Strahler
1992).
Understanding of the interaction between microwaves and vegetated surfaces has been advanced
by theoretical canopy backscatter models. One
class of models treats vegetation as a continuous
random medium above a reflecting soil surface
(e.g., Bush and Ulaby 1976; Attema and Ulaby
1978). A second class represents vegetation as an
aggregation of individual scatterers, such as leaves
and stems, over a continuous soil surface and uses
estimated probabilities of microwaves passing
though canopy gaps or intersecting crowns and
stems to calculate backscatter and attenuation
(e.g., Lang and Sidhu 1983). Most current forest
backscatter models are based on realistic forest
geometry, specified by size, shape, orientation,
density, and dielectric constant of cylindrical or
disk-shaped scattering elements. These models
compute microwave scattering from multiple
sources (trunk, ground, crown, trunk-ground
double-bounce, etc.) and evaluate net forest backscatter using a radiative transfer approach. Such
physically based models have been formulated for
use with both continuous and discontinuous canopies. Continuous models treat the canopy as a
randomly organized layer of scatterers (Richards
et al. 1987; Ulaby et al. 1990), whereas discontinuous models treat it as separate crowns, in which
the scatterers are aggregated into crown-shaped
volumes (Sun et al. 1991; McDonald and Ulaby
1993). The discontinuous models use estimated
probabilities of microwaves intersecting crowns
and stems or passing through canopy gaps to calculate backscatter and attenuation. More recently,
Sun and Ranson (1995) have introduced a threedimensional forest backscatter model that also
accounts for the size distribution and spatial arrangement of trees within a modeled pixel. Canopy backscatter models have helped elucidate the
mechanisms of microwave scattering in forests
(e.g., McDonald et al. 1990; Wang et al. 1993;
Imhoff 1995). However, the complexity of
surface-microwave interaction is such that current
physically based models can only be inverted under very restrictive assumptions about vegetation
structure and ground conditions (e.g., Polatin et al.
1994).
leaves (e.g., Monsi and Saeiki 1953; Hom 1971)
and branching patterns (Halle et al. 1978; Honda et
al. 1981).
Radiative transfer models based on foliage
amount and leaf angle distributions (LADs) are
commonly used to estimate properties such as canopy cover and leaf area index (LAI) from integrated
light measurements from quantum light sensors or
upward-looking, hemispherical photographs. An
example of such measurements is provided in Figure 1.1, which contrasts light profiles for late seral
Douglas fir-hemlock forest and a plantation forest
of broad-leaved Populus. Of special significance is
the use of simple radiative transfer models to derive
LA! from measured canopy "gap fraction," that is,
the fraction of a field of view through a canopy that
is not blocked by the canopy. One approach to derive LA! from gap fraction data uses the BeerLambert law of exponential extinction of light
though a canopy as a function of that canopy's extinction coefficient (e.g., Marshall and Waring
1986). A second related approach inverts a onedimensional model that is based on exponential extinction of light as a function of zenith angle, foliar
density, and LAD (Norman and Campbell 1989;
Welles 1990). Instruments and methods for gap
fraction analysis are discussed in more detail later
in this chapter.
Branch models by Honda et al. (1981) have been
used to simulate growth patterns in tropical trees.
More recent efforts have focused on fractal descriptions of branching patterns as a means of describing canopy architecture and modeling threedimensional radiative transfer (Myneni et al. 1990;
Chen et al. 1994). Fractal models of trees are attractive because complex branching patterns can be
described by a few simple equations and still generate remarkably realistic architectures (Zeide
1991, 1993).
Canopy-to-stand scale models have primarily
focused on the use of geometrical optical models
and crown shadows (Li and Strahler 1985). Geometrical optical models generally assume canopies
can be described as simple geometrical shapes,
such as cones, spheroids, and ellipsoids, and focus
on modeling the reflected light as consisting of
illuminated and shadowed ground and sunlit and
shadowed canopy. Early models disallowed mutual shadowing and were thus most applicable to
open forests and shrublands (e.g., Pech et al. 1986;
9
Franklin and Strahler 1988). More recent models
account for mutual shadowing (Li and Strahler
1992).
Understanding of the interaction between microwaves and vegetated surfaces has been advanced
by theoretical canopy backscatter models. One
class of models treats vegetation as a continuous
random medium above a reflecting soil surface
(e.g., Bush and Ulaby 1976; Attema and Ulaby
1978). A second class represents vegetation as an
aggregation of individual scatterers, such as leaves
and stems, over a continuous soil surface and uses
estimated probabilities of microwaves passing
though canopy gaps or intersecting crowns and
stems to calculate backscatter and attenuation
(e.g., Lang and Sidhu 1983). Most current forest
backscatter models are based on realistic forest
geometry, specified by size, shape, orientation,
density, and dielectric constant of cylindrical or
disk-shaped scattering elements. These models
compute microwave scattering from multiple
sources (trunk, ground, crown, trunk-ground
double-bounce, etc.) and evaluate net forest backscatter using a radiative transfer approach. Such
physically based models have been formulated for
use with both continuous and discontinuous canopies. Continuous models treat the canopy as a
randomly organized layer of scatterers (Richards
et al. 1987; Ulaby et al. 1990), whereas discontinuous models treat it as separate crowns, in which
the scatterers are aggregated into crown-shaped
volumes (Sun et al. 1991; McDonald and Ulaby
1993). The discontinuous models use estimated
probabilities of microwaves intersecting crowns
and stems or passing through canopy gaps to calculate backscatter and attenuation. More recently,
Sun and Ranson (1995) have introduced a threedimensional forest backscatter model that also
accounts for the size distribution and spatial arrangement of trees within a modeled pixel. Canopy backscatter models have helped elucidate the
mechanisms of microwave scattering in forests
(e.g., McDonald et al. 1990; Wang et al. 1993;
Imhoff 1995). However, the complexity of
surface-microwave interaction is such that current
physically based models can only be inverted under very restrictive assumptions about vegetation
structure and ground conditions (e.g., Polatin et al.
1994).