IEEE Geoscience and Remote Sensing Magazine - June 2020 - 86

vegetation has flowers at later growth stages, the final level
consists of flowers grown from stems or terminal branches.
The structural model requires specification of the number of each type of component and their relative orientations. Different levels of vegetation detail can be achieved
by setting different levels of
complexity for the structural
mode l spec if ic at ion. The
TO ADDRESS THE NEED FOR
simplest model involves vegMODELING AND
etation consisting of sameSIMULATION OF
size cylinders [28]. Yueh et al.
INTERFEROMETRIC SAR,
implemented a two-scale
branching model for soybean
COHERENT SCATTERING
with its internal structure
MODELS HAVE BEEN
[29]. Their results indicate
DEVELOPED IN RECENT
that the architecture of vegeYEARS.
tation plays an important role
in coherent scattering. Huang
et al. eliminated the overlapping effects of branches in the former branching models
by introducing a conditional probability function into the
scattering model [30]. The retrieval performances are significantly improved using the proposed coherent model.
Liao et al. further considered the curvature of the
leaves and lodging characteristics of the vegetation [31].
Hsu modeled the pine forest with multiple-scale cylinders
[32] where two structure effects are studied: 1) the clustering structure of branches, which has smaller-scale scatterers attached to larger-scale scatterers, such as branches
attached to the trunk, and 2) the clustering effect of scatterers close to each other that form a larger-scale scatterer
with different shapes, such as leaves and twigs enveloped
into a crown.
Chiu presented an electromagnetic scattering model
based on the structure for short branching vegetation and
verified using polarimetric radar backscatter measurements of a soybean field obtained from the Jet Propulsion
Laboratory's airborne SAR [33]. The interaction between
the main stems and underlying rough surface is incorporated into this model, which is shown to be important only at low frequencies (L band) and for the crosspolarized backscattering coefficient. In terms of multiple
scattering effects modeling, Picard and Toan developed a
coherent vegetation multiple scattering model where only
branches are considered [34]. Studies have shown that
the first-order coherence model has an overestimation
of attenuation.
The growth-rule-based model, another method used
to characterize vegetation structure, is especially useful
in modeling trees, which are structurally more complex.
Lindenmayer introduced a string rewriting system for cellular interaction commonly called the L-system [35], [36].
This was later applied to plants and trees and is extensively
described in his book with Prusinkiewicz [37], which describes the system with a few extensions, such as allowing
for context sensitivity and random variations. L-systems
86

uses the rule of rewriting, that is, modeling a complex tree
by successively generating and replacing branches using a
set of production rules. Trees generated by L-systems are
quite realistic in appearance; for this reason, L-systems are
utilized to fully capture the architecture of trees and describe their growth.
Another approach of the growth rule-based approach
to tree modeling is fractals, which have been used to simulate trees since the early 1980s [38]-[40]. Mandelbrot used
the "pipe model," in which trees are described as bundles
of nonbranching vessels of fixed diameters connecting
roots to leaves [38]. The basic idea behind fractal geometry
is self-similarity, which is a well-known feature of certain
plant structures. Lin and Sarabandi use fractal theory to
model tree structure based on the Monte Carlo calculation method and establish a coherent scattering model of
a forest, which considers the scatterer phase correlation
within a single tree structure, although the phase correlation of scattered fields between two adjacent trees is not
considered [41].
Liu et al. developed a 3D forest coherent scattering
model, based on the real 3D structure of vegetation [42];
it was used to simulate the InSAR signals of trees, and the
heights of scattering-phase centers were estimated from the
simulated InSAR data. Weber and Penn presented a model
based on the recursive, rule-based, and growth algorithms
to create and render trees [43]. Liao combined these trees
models and along-track interferometry [44], [45] for a moving-target-indication simulation study [46]. The accuracy of
the analytic solver is assessed by comparing its results with
those of the full-wave solver [47].
Despite its ability to accurately simulate the coherent
phase, the current coherent scattering model could be further improved in the following aspects.
◗ The tree models employed are still much simpler than
the real scenario of forest canopy.
◗ These models are based on the Foldy approximation
[48]-[50], which assumes that the vertical distribution
of the vegetation canopy is not even and the horizontal distribution is uniform. It is applicable only to the
relatively uniform and continuous conditions of the
vegetation canopy but is obviously inappropriate for
real scenarios, such as trees in natural forests.
◗ Most coherent scattering models consider only the virtual 3D structure of a single tree, not the 3D structure
of a forest.
COHERENT SCATTERING CALCULATION
To have a simulation tool for PolInSAR system analysis, we
developed a coherent scattering model of vegetation, the
technical details of which are briefly introduced here [51].
First, the leaves, twigs, and trunks as a scattering object are
simplified: leaves are modeled as needles and disks with
general Rayleigh-Gans approximation [52], and twigs and
trunks are modeled as finite-length cylinders [53]. The original and simplified models are shown in Figure 2, where
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020

IEEE Geoscience and Remote Sensing Magazine - June 2020

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