IEEE Geoscience and Remote Sensing Magazine - March 2013 - 27
the volume by using macroscopic statistical and/or symmetry derived scattering properties have been established
due to their flexibility and the (relative) small number of
parameters needed for parameterization. For vegetation
applications two layer statistical models, consisting of a
vertical distribution of scatterers f (z) that accounts for the
vegetation scattering contribution, and a Dirac-like comv ) d (z - z 0) that accounts for the scattering
ponent m G (w
contribution(s) with the underlying ground (i.e., direct
surface and dihedral vegetation-surface contributions)
have been proven to be sufficient in terms of robustness
and performance especially at lower frequencies [18], [35],
[109], [110]
v ) = f (z, w
v ) + m G (w
v ) d (z - z 0), (40)
F (z, w
polarizations. In forest applications random volumes have
been established so that a single polarimetric baseline
allows the inversion of the Random-Volume over Ground
(RVoG) model [18], [110]. Oriented volumes are more
expected to be important in agriculture applications where
the scatterers within the agricultural vegetation layer are
in many cases characterized by an orientation correlation
introducing anisotropic propagation effects and differential extinction [115]-[118].
2) The second approach to estimate F (z) or associated
structure parameters is to approximate F (z) by a (normalized) polynomial series or another orthogonal function
basis Pn (z) [35], [119], [120]
v ) = / a n (w
v ) Pn (z) (45)
F (z, w
n
where m G is the ground scattering amplitude. Substituting
(40) into (37) leads to
v ) = exp(i{ 0)
c Vol (k z, w
v)
cu V0 + m (w
v ) , (41)
1 + m (w
where
hV
#
cu V0 =
fV (zl ) exp(ik z zl ) dzl
0
, (42)
hV
#
v ) measurements to estimate the
and to use then c Vol (k z, w
coefficients a n of the individual components. The advantage of this approach is that there is no assumption on the
shape of F (z) required, allowing the reconstruction of arbitrary vertical scattering distributions. In its original proposed form [119], [120], F (z) was expressed in terms of the
Legendre polynomials PLn leading to
v ) = exp (ik z z 0) exp (ik V ) $
c Vol (k z, w
1
fV (zl ) dz
0
and
v) =
m (w
v)
m G (w
hV
#
(43)
fV (zl ) dzl
0
is the effective ground-to-volume amplitude ratio.
For modeling the vertical distribution of scatterers in the
vegetation layer f (z) different models can be used. A widely
and very successfully used model for f (z) is an exponential
distribution of scatterers [18], [109], [111]
fV (z) = exp (2vz/ cos (i i)), (44)
where v is a mean extinction value for the vegetation layer
that defines the "attenuation rate" of the profile. Besides
the exponential profile, that appears to fit better higher
frequencies, Gaussian [112], [113], [114], or linear scattering distributions have been proposed especially at lower
frequencies.
Equally important with the shape of the vertical distriv ) is its polarimetric characterizabution of scatterers F (z, w
tion. While the ground scattering component is strongly
polarized and therefore has to be assumed to be polarization dependent, the volume scattering component can be
both. In the case of oriented volumes, the vertical distribution of scatterers in the volume is polarization dependent, while in the case of random volumes, the vertical
distribution of scatterers in the volume is the same for all
march 2013
ieee Geoscience and remote sensing magazine
# 71 + / n a n (wv ) PLn (z N) exp (ik V )A dz N
-1
1
# 71 + / n a n PLn (z N)A dz N
(46)
-1
with k V = k z h V /2, where the height of the volume h V and
the interferometric phase related to the ground need to be
estimated a priori, e.g., using the first approach. According
to (46), the availability of multiple Pol-InSAR interferograms makes it possible to determine, in addition to forest
height and the underlying ground topography, the vertical
distribution of scatterers within the volume.
The Role of Frequency: With changing frequency, the
attenuation in the volume changes while at the same time
the effective scatterers in the volume - sized on the order of
the wavelength - may change, too. Both effects make F (z)
(and in consequence the interferometric volume coherence)
to vary with frequency [121], [122]. In addition, the maximum volume height/depth that can be assessed is limited
by the penetration depth that decreases with increasing
attenuation, i.e., frequency.
In the case of vegetation, with decreasing frequency
the volume attenuation (and scattering contribution)
decreases while the direct and dihedral contribution
of the underlying ground increases. The significance of
smaller scatterers (as leaves and branches) decreases and
larger scatterers are pronounced: As larger scatterers are
usually located at the lower vegetation parts, moving to
lower frequencies (P-band) may lead to an inversion of
the shape of F (z) [122].
27
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