This paper discusses the results from a series of field experiments using ground-based L-band microwave active/passive sensors. Three independent approaches are employed to the microwave data to determine vegetation opacity of coniferous trees. First, a zero-order radiative transfer model is fitted to multi-angular microwave emissivity data in a least-square sense to provide "effective" vegetation optical depth. Second, a ratio between radar backscatter measurements with the corner reflector under trees and in an open area is calculated to obtain "measured" tree propagation characteristics. Finally, the "theoretical" propagation constant is determined by forward scattering theorem using detailed measurements of size/angle distributions and dielectric constants of the tree constituents (trunk, branches, and needles). The results indicate that "effective" values underestimate attenuation values compared to both "theoretical" and "measured" values

Cosh, Michael H.

Jackson, Thomas J.

Joseph, Alicia T.

Kurum, Mehmet

Lang, Roger H.

O'Neill, Peggy

NASA Technical Reports Server

CHRACTERIZATION OF FOREST OPACITY USING MULTI-ANGULAR EMSSION AND 
BACKSCATTER DATA 
 
Mehmet Kurum (1), Peggy E. O’Neill (1), Roger H. Lang (2), Alicia T. Joseph (1), 
Michael H. Cosh (3), and Thomas J. Jackson (3) 
 
(1) Hydrological Sciences Branch / Code 614.3 NASA Goddard Space Flight Center, 
Greenbelt, MD 20771 USA, Mehmet.Kurum@nasa.gov 
 
(2) The George Washington University, Dept. of Elect. & Computer Engineering, 
Washington, DC, 20052 USA 
 
(3) Hydrology & Remote Sensing Laboratory, USDA ARS, Beltsville, MD 20705 USA 
 
 
ABSTRACT 
 
This paper discusses the results from a series of field 
experiments using ground-based L-band microwave 
active/passive sensors.  Three independent approaches are 
employed to the microwave data to determine vegetation 
opacity of coniferous trees.  First, a zero-order radiative 
transfer model is fitted to multi-angular microwave 
emissivity data in a least-square sense to provide “effective” 
vegetation optical depth.  Second, a ratio between radar 
backscatter measurements with the corner reflector under 
trees and in an open area is calculated to obtain “measured” 
tree propagation characteristics.  Finally, the “theoretical” 
propagation constant is determined by forward scattering 
theorem using detailed measurements of size/angle 
distributions and dielectric constants of the tree constituents 
(trunk, branches, and needles).  The results indicate that 
“effective” values underestimate attenuation values 
compared to both “theoretical” and “measured” values. 
 
Index Terms— Microwave, radar, radiometer, forest, 
attenuation. 
 
1. INTRODUCTION 
 
Soil moisture is recognized as an important component 
of the water, energy, and carbon cycles at the interface 
between the Earth’s surface and atmosphere.  Several 
planned microwave space missions, most notably ESA's 
Soil Moisture Ocean Salinity (SMOS) mission (launched 
November 2009) and NASA's Soil Moisture Active Passive 
(SMAP) mission (to be launched 2014/15), are focusing on 
obtaining accurate soil moisture information over as much 
of the Earth's land surface as possible [1, 2].  Current 
baseline retrieval algorithms for SMOS and candidate 
retrieval algorithms for SMAP are based on the tau-omega 
model [3], a zero-order radiative transfer approach where 
scattering is largely ignored and vegetation canopies are 
generally treated as a bulk attenuating layer.  In this 
approach, vegetation effects are parameterized by tau and 
omega, the microwave vegetation opacity and single 
scattering albedo, respectively.  This model has been 
validated over grasslands, agricultural crops, and generally 
light to moderate vegetation.  Its applicability to areas with a 
significant tree fraction is unknown, especially with respect 
to specific tree types, anisotropic canopy structure, and 
presence of leaves and/or understory. 
Although not really suitable to forests, Ferrazzoli et al. 
[4] proposed that a zero-order tau-omega model might be 
applied to such vegetation canopies with large scatterers, but 
that equivalent or effective parameters would have to be 
used.  They determined these effective parameters by 
minimizing a cost function computed from the difference 
between measured multi-angular dual-polarized emissivity 
and modeled data (tau-omega model).  
This paper compares the effective vegetation parameters 
computed from multi-angular pine tree microwave 
emissivity data with the results of two independent 
approaches which provide “theoretical” and “measured” 
vegetation characteristics.  These two techniques are based 
on forward scattering theory [5] and radar corner reflector 
measurements [6], respectively.  The results demonstrate 
that “effective” vegetation optical depths are lower than 
“theoretical” and “measured” ones.  
 
2. ACTIVE/PASSIVE MICROWAVE EXERIMENTS 
OVER PINE TREES 
 
During 2008 and 2009, active/passive dual-polarized 
microwave measurements were acquired over a natural 
stand of Virginia pine coniferous trees at multiple incidence 
angles (from 15º to 55º with 10º increment) [7].  The 
supporting ground truth data were also collected.  
https://ntrs.nasa.gov/search.jsp?R=20110011770 2019-08-30T15:46:43+00:00Z
 The soils of the pine tree site were loamy sand, with 
textures varying from 57% sand, 13.6% clay to 87% sand, 
3.4% clay depending on location within the site.  Tree 
heights average about 12 m, with DBH (diameter at breast 
height) varying from 4 to 29 cm.  Surface roughness was 
very small, with an rms roughness height < 0.5 cm.  The 
forest floor had a surface layer of loose debris/needles and 
an organic transition layer above the soil. 
In addition to the regular active/passive data, a separate 
radar experiment with and without trihedral corner reflector 
(with 1.22 m front edge length) under trees was carried out 
in September 15, 2009 as shown in Fig. 1.  The goal of this 
experiment was to measure forest opacity directly by radar 
as an independent estimate.  The data were collected at a 45º 
incidence angle and at 19 different azimuth locations (from 
0º to 90º with 5º increment) to get an average estimate.  
The L-band microwave instrument system used in this 
study is called ComRAD for Combined Radar/Radiometer.  
The system is mounted on a 19-m hydraulic boom truck and 
has been developed jointly by NASA/GSFC and George 
Washington University.  It includes a dual-pol 1.4 GHz 
radiometer and a quad-pol 1.25 GHz FMCW radar sharing 
the same 1.22-m parabolic dish antenna with a 12° field of 
view. 
 
3. TECHNIQUES TO DETERMINE FOREST 
OPACITY 
 
In this section, the forest optical depths are calculated by 
three independent techniques.  Summary of these techniques 
are given below: 
 
3.1. Trihedral Corner Reflector Approach– “Measured” 
 
Trihedral corner reflectors are widely used for external 
radar calibration since they yield large backscattering radar 
cross sections over wide azimuth and elevation angular 
ranges [6].  This approach is based on the expected strong 
return from a corner reflector under trees.  It assumes that 
coupling between the corner reflector and the surrounding 
background and trees is small.  Basically, the ratio between 
co-polarized radar backscatter measurements with the corner 
reflector under trees and in an open area provides the loss in 
propagation through trees.  This retrieved forest opacity 
represents the “measured” opacity 𝜏𝑚, which is given by: 
 
𝜏𝑚 = − cos 𝜃2 ln𝜎𝑚20 − 𝜎𝑚10𝜎𝑚40 − 𝜎𝑚30  (1.a) 
 
where 
𝜎𝑚1
0 = 𝜎𝑑0 + 𝜎𝑑𝑟0  (1.b) 
 
𝜎𝑚2
0 = 𝜎𝑑0 + 𝜎𝑑𝑟0 + 𝑒−2𝜏𝑚 sec𝜃𝜎𝑐𝑟0  (1.c) 
 
𝜎𝑚3
0 = 𝜎𝑏𝑐𝑘𝑔𝑟𝑑0  (1.d) 
 
(a) 
 
 
(b) 
 
Figure 1 Pictures of the trihedral taken from (a) front 
and (b) behind during the radar measurements. 
 
 
 
 
 
Figure 2 “Measured” vegetation optical thicknesses 
from trihedral experiment at incidence angle of 45º on 
September 15, 2009. 
 
𝜎𝑚4
0 = 𝜎𝑐𝑟0 + 𝜎𝑏𝑐𝑘𝑔𝑟𝑑0  (1.e) 
 
The quantity 𝜎𝑚10  is measured backscattering coefficient 
from trees and it is composed of volume (𝜎𝑑0) and double 
interaction terms (𝜎𝑑𝑟0 ) [5].  The backscattering coefficient 
of the measurement with trihedral under tree is denoted by 
𝜎𝑚2
0  and it includes a return from the corner reflector (𝜎𝑐𝑟0 ) 
attenuated by the vegetation volume (𝑒−2𝜏𝑚 sec𝜃).  Radar 
measurement of background in an open field is represented 
by 𝜎𝑚30  and measurement of trihedral in an open area is 
denoted by 𝜎𝑚40 .  
Fig. 2 shows the “measured” vegetation opacity values 
obtained at angle of incidence 45º using the radar returns 
with and without trihedral corner reflector under trees at 
several azimuth locations.  The “measured” vegetation 
optical depth at h-polarized channel is 1.33 ±  0.39 while 
“measured” v-polarized one is 1.12 ±  0.38. 
 
3.2. Multi-Angular Emissivity Approach – “Effective” 
 
The principle of this approach depends on exploiting 
multi-angular emissivity data in order to retrieve 
simultaneously geophysical products such as soil moisture 
and vegetation characteristics [8].  The algorithm uses an 
iterative approach, minimizing a cost function computed 
from the differences between measured and modeled 
brightness temperature data, for all available incidence 
angles.  It provides “effective” or equivalent vegetation 
parameters [4].  Recently, this approach was also tested by 
using L-band microwave measurements over a coniferous 
(pine) and deciduous forest [9]. 
The values of effective vegetation optical depth 𝜏𝑒𝑓𝑓  and 
single scattering albedo 𝜔𝑒𝑓𝑓  are calculated by minimizing 
the following merit function: 
 
min�� � �𝑒𝑝(0)�𝜏𝑒𝑓𝑓 ,𝜔𝑒𝑓𝑓 ,𝜃𝑖� − 𝑒𝑚𝑝(𝜃𝑖)�2
𝑝=h,v
𝑁
𝑖=1
 (2) 
 
where 𝜏𝑒𝑓𝑓  and 𝜔𝑒𝑓𝑓  act as free parameters and are defined 
as independent of polarization and angle, 𝜃𝑖 is the 
observation angle from the nadir, 𝑒𝑚𝑝 is measured 𝑝-
polarized emissivity, and 𝑒𝑝
(0) is modeled 𝑝-polarized zero-
order radiative transfer emissivity (tau-omega model [3]).  
The subscript 𝑝 denotes polarization and it can be horizontal 
(h) or vertical (v).  In this minimization, it is assumed that 
surface reflectivies are known a priori.  In this investigation, 
they are calculated by using a three-layer soil forest floor 
model that includes a litter layer (loose debris/needles), a 
transition layer (organic humus), and soil [7].   
In Fig. 3, the measured microwave emissivity collected 
on September 8, 2008 is plotted over the observation angles 
from 15º to 55º along with the results of the fitted zero-order 
tau-omega model to compare the model with data.  Fig. 4 
demonstrates “effective” opacities computed at different 
days over almost a year span (from August 1, 2008 to April 
23, 2009).  The “effective” vegetation optical depth for all 
measurements is found to be 0.91 ±  0.10.  
 
3.3. Forward Scattering Approach – “Theoretical” 
 
The vegetation propagation constant is determined by the 
forward scattering amplitudes of each of the tree 
constituents, averaged over all particle sizes and angle 
orientations [5].  Since the forward scattering amplitude of 
an arbitrary particle is a complex quantity, then this medium 
will attenuate the wave.  This technique requires detailed 
measurements of size/angle distributions and dielectric 
constants of the tree constituents (trunk, branches, and 
needles).  These data were obtained by destructive tree 
sampling.  The calculated forest parameters in this technique 
represent “theoretical” values. 
 
 
Figure 3 Radiometer angular response from Virginia 
pine forest and the fitted zero order model for data 
collected on September 08, 2008.  
 
 
 
Figure 4 “Effective” vegetation optical thicknesses 
from the multi-angular emissivity data. 
 
The vegetation opacity or optical thickness is given by 
𝜏𝑝(𝜃) = 𝜅𝑒𝑝(𝜃)𝑑, where 𝜃 is the observation angle from the 
nadir, 𝑑 is thickness of the vegetation layer, and the volume 
extinction coefficient is defined by: 
 
𝜅𝑒𝑝(𝜃) = 4𝜋𝑘0 �𝜌𝛼ℑ𝑚�〈𝑓𝑓𝑝𝑝(𝛼)〉�
𝛼
    𝑝 ∈ {h, v} (3) 
 
where the angular brackets denote ensemble average over 
the angular and size statistics of particles, the number 
density of the scatterer type α is given by 𝜌𝛼, and 𝑘0 is the 
wave number, 𝑘0 = 2𝜋𝑓0/𝑐 , where 𝑓0 is the frequency and 
𝑐 is the speed of light in free space.  Notice that in this 
formula  𝑓
𝑓𝑝𝑝
(𝛼)  is the forward scattering amplitude of the 𝛼𝑡ℎ 
type of scatterers and the scatterer type 𝛼 can be branch, 
leaf/needle, or trunk.  The subscript 𝑝 denotes polarization. 
In Fig. 5, angular and polarization dependences of 
“theoretical” vegetation optical depth are plotted. The figure 
also includes “measured” h- and v-polarized vegetation 
opacity at 45º and “effective” opacity for comparison 
purposes.  As seen from the plots, the followings can be 
concluded: (a) “effective” values are lower than both 
“measured” and “theoretical” values; (b) “theoretical” 
opacity depends weakly on angle and polarization. This 
result provides a basis to choose effective values as 
independent of polarization and angle in (2); (c) “measured” 
opacities are higher than the other results and are more 
polarization dependent than the “theoretical” result at 
incidence angle of 45º. 
 
4. CONCLUSION 
 
In this paper, vegetation opacity was characterized by 
three independent approaches based on multi-angular pine 
tree microwave emissivity data (“effective” opacity), radar 
corner reflector measurements (“measured” opacity), and 
forward scattering theory (“theoretical” opacity).  The 
results from these techniques are compared and they 
demonstrate that “effective” values are lower than both 
“measured” and “theoretical” values. 
 
 
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Figure 5 Vegetation optical thicknesses comparison.  


Characterization of Forest Opacity Using Multi-Angular Emission and Backscatter Data

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