The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. To take into account the clustered structures with the radiative transfer theory, the scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. Subsequently, the resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including the multi-scale structures, namely, trunks, primary and secondary branches, as well as needles, we interpret and simulate the polarimetric radar responses from pine forest for different frequencies and looking angles. The preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment

Beaudoin, A.

Han, H. C.

Hsu, C. C.

Kong, Jin AU

Letoan, T.

Shin, Robert T.

English

NASA Technical Reports Server

t 4
N9.3-13085
RADIATIVE TRANSFER THEORY FOR POLAR/METRIC REMOTE SENSING 01" PINE FOREST
C. C. Hsu, H. C. Hen, R. T. Shin, 3. A. Kong
Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
A. Bcaudoin, and T. Le "loan
Centre d'Etude Spatiale des Rayonnements, Toulouse, France
Abstract- In this paper, the radiative transfer theory is ap-
plied to interpret polarimetric radar backscatter from pln¢ for-
est with clustered vegetation structures. To take into account
the clustered structures with the radiative transfer theory, the
scattering function of each duster is calculated by incorporat-
ing the phase interference of scattered fields from each com-
ponent. Subsequently, the resulting phase matrix is used in
the radiative transfer equations to evaluate the polarimetric
backscattering coefficients from random medium layers embed-
dad with vegetation dusters. Upon including the multi.scale
structures, namely, trunks, primary and secondary branches,
as well as needles, we interpret and simulate the polarimetric
radar responses from pine forest for different frequencies and
looking angles. The preliminary results ate shown to be in
good agreement with the measured back_cattering coefficients
at the Landes maritime pine forest during the MAESTRO-1
experiment.
I. Introduction
In recent years, the application of radar polarimet r):for ac-
Live remote sensing of the earth terrain has inspired extensive
interests. A v_riety of theories have been used for electro-
magnetic modeling of geophysic_ terrain, such as snow, ice,
and vegetation canopy [1]. Among these studies, the radia- izations is defined as
tire transfer (RT) theory has been commonly used to calculate
radar hackscattering coefficients from layered geophysical me-
dia and to interpret the experimental measurements.
The radiative transfer theory consists of the radiative
transfer equations which govern the electromagnetic energy
propagation through scattering media. Various models have
been developed based on this theory [2-4]. In general, the
conventional R.T theory ignores the relative phase information
associated with structured scatterers, which may play an
important role in the overall scattering behavior [5]. In forest,
vegetation consists of structures of many different scale length
- the trunk, primary branches, secondary branches, and needle
leaves, etc. Vegetation elements of each scale are connected
to elements of other scales in a fashion statistically described
by the unique architecture pertaining to each tree species.
For the microwave remote sensing of forest, the vegetation
structures not only give rise to the separation of scattering
centers for different polarizations, but also provide partially
coherent scattering by different scatterers with statistically
prescribed relative positions.
In this paper, a four-layer RT modal is presented fer
the modeling of the pine forest in the Landes area, France-
1129
; - PRECEDING PAGE BLANK N0i" FILMED
We make use of the newly developed branching model for
vegetation [7] to account for the scattering properties of
structured pine trees. The modal thus constructed has a wide
validity range in frequency spectrum.
IL Radiative Transfer Theory
Consider an electromagnetic wave incident upon a multi-
layered random medium with the inddent angle 0o as shown
in Fig. 1. The scattering regions 1 to 3 are layers of
thickness ha (n = 1,2,3), where discrete scatterers embedded
in homogeneous background. The bottom boundary between
region 4 and region t can be either a flat surface or a rough
surface described by a Gaussian random process.
The vector radiative transfer equation for the spedfic
intensity in each scattering region is of the form
coss _(0, _, _) = _ _(s, _, _). 7(6,_,_)
,_ (z)
+ _ de?_(e, ¢;a',¢')- ?(o',¢',,)
where the Stokes vector 7 containing information regarding
field intensity and phase relation of the two orthogonal polar-
) [ (IEal:) '_
\2 Im<E, Eh) /"
(2)
In (2), the subscripts h and v represent the horizontal and verti-
cal polarizations, respectively. The angular bracket ( ) denotes
ensemble average over the size and orientation distributions
of scatterers; and 17 = _ is the free-space characteristic
impedance.
The extinction matrix _e represents the attenuation due
to both the scattering and absorption, and can be obtained
through the optical theorem in terms of forward scattering
functions. The phase matrix _(0,_;0r,_ ') characterizes the
scattering of the Stokes vector from (Ol,_ I) direction into
(0, _) direction. The phase matrix can be formulated in terms
of scattering functions of the randomly distributed discrete
scatterers. Along with the'boundary conditions, we can solve
the radiative transfer equations iterativdy for the polarimetric
hackscattering coemdents [1].
"91-728I0/9!S03.00© (EF.E1992
https://ntrs.nasa.gov/search.jsp?R=19930003897 2020-03-17T10:30:34+00:00Z
• r .... k Ll_ L_p_
ZCrown Layer
region ! vertical cylinder dusters
Trunk Layerregion 2
vertical cylinders
region 3 Understory Layer
randomly oriented cylinders
region 4 Crass Layer
region t Cround
z=O
hz
xaB .-d i
h2
zm -d_,
h_
Z Ill _d 3
figure I. Configuration
°
600 "
N
figure 2. Cylinder Cluster
• .,_ J
- ._.;_ ._
III. Scattering Punction for Clustered Structure IV. Comparison with Experimental Data
In order to take into account the partially coherent effect
due to clustered vegetation structures, we formulate the phase
matrix based on the branching model for vegetation. In pine
forest, most of the scatterers are of cylindrical shapes. Hence
in this study, the main subject is cylinder dusters. For the
cylinder cluster that has one center cylinder and N branching
cylinders, the total backscattering function fa,8 is
N
nml
where f0a_ is the afl-th element of the scattering matrix for
the center cyllnder, and fna/_ is a_-th clement of the scattering
matrix for the n-th branching cylinder, a,_,7,6 represent
horizontal or vertical polarization.
Assuming all the-branching cylinders are identlcaland
independent of each other, the corrdation of f is ""
(/o_/_6) = (/0°_/_76) + _ (/-°M_76)
+
+ .N'(:N"-- 1)(fma_)(f;76)
• (4)
The relative phase of the n-th branch with respect to the center
cylinder is defined as
where r-i and k_ are the incident and scattered wave vectors,
respectively. _n is the location of the n-th branching cylinder
relative to the center cylinder.
In (4), the third and fourth terms are the coherent terms. It
can be seen that the incoherent approximation is valid when the
average of the random phase factor (eiC_J) is so small that the
coherent terms are negligible as compared with the incoherent
terms• However, this is not true for vegetation structure with
scale length comparable with wavdength.
For the calculation of scattered fields of different duster
dements, dielectric cylinders can be used to model trunks,
branches and coniferous leaves [6,7]. Leaves of deciduous tree •
can be modelled as disks [6,8]. The truncated infinite cylinder
approximation [9] is employed in this_study tq calculate
scattered fields from cylinders.
:_ 1130
The experiment is conducted by the Centre d'Etude Spa-
tlale des Rayonnements (CESR) at the Landes forest, in south-
west France, using the NASA/JPL Synthetic Aperture Radar
(SAR) during the MAESTRO-I campaign in August 1989. A
strong correlation between P-band backscatterlng toe'dents
and pine forest parameters has been observed in the measure-
ment data [10].
To modal the plne forest, the RT model described in
previous sections is adopted as depicted in Fig. 1..The top.
layer (region 1) consists of vertically orientated three-scale
didectrlc cylinder dusters characterin8 the trunks and the
attached smaller scale branching dusters. These smaller scale
branching dusters include primary and secondary brafiches, as
wall as needles. However, at P-band, only the primary and
secondary branches are important. In the three-scale too.dr,
all the smaller scale cylinders are uniformly distributed along
a larger scale center cylinder with 60 ° angle relative to the
orientation of the center cylinder, as show in Fig. 2. Region
2 contains vertically oriented dielectric cylinders representing
tree trunks. In region 3, vertical cyl;nders and randomly
oriented thin cylinders coexist characterizing a mixture of the
tree trunks and the short vegetation in the fores_ understory.
The underlying grass/ground consists of the attenuating grass
layer and the ground•
With this model, we calculate backscattering coe_dents
for six pine stands of different ages. The ages of the" forest
under investigation are 6, 14, 20, 30, 38, and 46 years old. It
is observed that as forest becomes aged, the average radius
of tree trunk grows bigger and the average tree height also
becomes taller. The primary and secondary branches grow
bigger as wall. In general, the above-ground blomass incre_es
despite the decrease in the number of trees per unit area
as forest ages. Since the ground truth indicates that the
surface is very smooth t'o_robservation at P-band, we modal the
ground as a planar surface. The grass layer above the ground
is considered as an homogeneous attenuating layer of 0.2m
height and characterized by a dielectric constant (1.05 + i0.5).
The calculated results for P-band are shown in Fig. 3. The
discrete points are the data collected by SAR; the curves are
the theoretical results. It is found from the simulations, the
main contribution for HH backscattering coeflldent is from
trunk-ground interaction and scattering ` from branches. As
for the W and HV, the branches are the dominate scattere_.

V. Conclusions
Radiative transfer theory is applied to the modeling of
polarimetric radar backscatter for vegetation canopy. The
phase matrix is derived with the coherent effects due to
the clustered structures. With this model, we simulate
runlet-frequency and multi-_ingular backscatterlng coef_dents
at different radar polarizations. Theoretical results _re in good
agreement with the measurement data collected by NASA/JPL
SAIL This paper presents the comparison performed at P-Band
&equency.
Acknowledgments
This work was supported by the NASA Grant No. NAGW-
1617, the NASA Contract No. 9.58461, the ESA Contract No.
AO/1-2413/90/NL/PB, and the ONR Contract No. N00014-
89-J-1107.
References
[1] Tsa_ng, L., J. A. Kong, and IL T. Shin, Theory of Mi.
c_o_ave Remote Serving, Wiley-Intersclence, New York,
1985.
[2] Han, H. C., S. V. Nghlem, and J. A. Kong, "Analytical so-
lution of vector ra_at_ve tra.nsfet equation whh rough sur-
face boundary condition," preg_ in Elec_romagneticJ
Re_earc_ S_mposium, Cambridge, Massachusetts, 1991.
[3] Slain, IL T., and 3. A. Kong, "Radiative transfer theory
for active remote sensing of. two-layer random medium, _
Progre_J in Electromagnetic Re,earth, Vol. 1, Chapter 4,
ed. by 3. A. Kong, Elsevier, New York, 1989.
[4] Tsang, L., J. A. Kong, and IL T. Shin, =Radiative transfer
theory for active remote sensing of a layer of nonspherlcal
particles," Redio Science, VoL 19, 629-642, 1984.
[5] Yueh, S. H.,'3. A. Kong, J. K. Jao, R. T. Shin, and T.
Le Toan, "Branching model for vegetatlon," IE£E Tranj.
Geo,ci. Remote Sensing, Vol. CE-30, No. 2, 1992.
[6] Karam, M. A., A. If.. Funs, and Y. M. M. Antar,
=Electromagnetic wave scattering from some vegetation
samples," IEEE Trans. Geosci. Remote Sensing, Vol. GE-
26, No. 6, 799-808, 1988.
[7] Durden, S. L., 2.3. van 2yl, and H. A. Zebker, "Modeling
and observation of the radar polarization signature of
forested areas," IEEE Tranj. Geo_ci. Remote Sensing,
Vol. GE-27, No. 3, 290-301, 1959.
[8j Lang, 1_. H., and H. A. Saleh, "Microwave inversion of leaf
area and inclination angle distribution from backscattered
data," IEEE Trans. Geo,ci. Remote Sending, Vo]. GE-23,
No. 5, 68,5-694, 1985.
[9] van de Hulst, H. C., Li£]_t Scatterin.g by Sm_ll PGrficles,
Dover, New York, 1981.
[10] Le 'roan, T., A. Beaudoin, J. _om, and D. Guyon
,Relating forest blomass to SAR data," IEEE T_ns.
Geosci. Remote SenJing, Vol. GE-30, No. 2, 1992.
1131
-5
a3
-c7
v
"_ -I0
,3
_ -'15
m
-20
-25
0
O ' | |
Simulation HH
-- -- Simulation W
.... Simulation HV
V X X ..''_X"
X
X
/
X /"
7
/"
X/-
X Is.-"
/ x
I = I
2O -4O
Age (,veor)
Figure _. Backsc_ttering for P-band



Radiative transfer theory for polarimetric remote sensing of pine forest

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server