124 
Y =y +x .Y 
'total 'veg eq soil 
(12f) 
a =o +t .0 ., 
total veg eq soil 
And when a corner reflector is present 
a' =a +t .0 .,+x .a 
total veg eq soil eq corner 
Since 0 ' _ , and 0 ,. can be measured and 0 
(9a) 
(9b) 
(10) 
eq 
. , total total 11 ^ corner 
is known, t can be calculated. The corner reflector 
eq 
experiment aims at assessing a good estimation of T 
in L- and X-band for several incidence angles and 
polarizations for both coniferous and deciduous tree 
types. 
The parameter T e q is of direct importance when the 
influence of the soil, soil moisture content, stan 
ding water or undergrowth under a forest canopy has 
to be modelled. This may be done using the cloud 
model as illustrated above or using other (more 
elaborate) models. 
4. THE ANALYSIS OF FOREST SCATTEROMETER DATA USING 
A MULTI-LEVEL MODEL 
When solving the radar equation for airborne radar 
data backscattering is assumed to originate from a 
certain plane or surface. Due to relevant height 
differences of scatterers in a forest volume this 
assumption is easily violated. Operating at relative 
ly low altitudes and with small beam widths in range 
direction, as is the case for DUTSCAT, height diffe 
rences of scatterers in a forest have to be taken 
into account to avoid major errors. 
This phenomenon can be studied by calculating the 
actual pulse shape and delay time of the radar return 
from a homogeneous isotropically scattering flat sur 
face and analysing the effect of height deviations 
on the pulse returned. 
For a transmitted pulse with shape P t (t) and an 
tenna pattern with shape G(0,<j>) the equation for the 
received pulse follows from the radar equation and 
integration over the illuminated area (Ulaby et al. 
1982); 
.(t) =Jf 
Pt(t-T) . G 2 (9,(fr) 
(4tt) 
dx. dy (11) 
illuminated 
area 
with T = delay time, 
t = time, 
X = wavelength 
and r = distance. 
The antenna gain may be separated into components 
in the 0 (across-track) and cf> (along-track) direc 
tions ; 
G(0,<j>) = G 0 .g Q (0) •g ( f ) ( ( t ) ) 
(12a) 
where gg (0) and g (<}>) are pattern factors with maxi 
mum value unity aha G 0 is the maximum gain. For the 
DUTSCAT it can be shown that as a result of the nar 
row beams for all six frequencies the along-track 
differential distance dx can be approximated by 
dx = Rd<j> ( 12b) 
With r=cT/2 and y-\/r 2 -h 2 (fig. 1) it follows 
dy=rdr/ v /^T^2 = dr/sin0 =cdT/2sin0 (12c) 
With 
0° = y.cos0, (12d) 
P t(t) = Ptm-P^) > (12e) 
where P tm is the maximum value of the transmitted 
power and 
0 = 0(T) = arccos(h/r) = arccos(2h/cT) 
equation 11 by substituting eqs. 12a-12f can be re 
written as; 
p r (t) • P tm ♦ Go 2 . Jg| (<1>) d({>. j P (fc ~ T) l 8 &i d ( ? } :. Y . dT 
T 3 .tan(0(T)) 
c 7T 
(13) 
The factors before the convolution integral are con 
stants for each band, the factors in the convolution 
integral determine the actual shape of the radar 
return signal. The factor p(t) may be approximated 
for the DUTSCAT by the Gaussian function 
p(t) = exp (-ln(2) -) 
ÜT) 2 
(14a) 
and the factor gg(9) ma Y be approximated for the 
DUTSCATby the Gaussian function 
(0 -0 ) 2 
ggiQ-jO = exp(-ln(2) : ) 
(14b) 
OB) ; 
where T 
0 t 
B 
B 
B 
is 100 ns, 
is the antenna tilt angle, 
is the two-way across track beam width, 
is 2.4 degrees in the C-band with HH- 
polarization and 
is 13.0 degrees in the L-band with HH- 
polarization. 
For a homogeneous isotropically scattering surface the 
return signal is calculated with equations 13 and 14 
and shown as a function of range distance in 
figure 3. The big arrow indicates the position of the 
centre of the beam, the small arrows the +/- 3 
degrees and +/- 6 degrees beside centre points. The 
differences in distance to the radar within the 
illuminated spot causes the strongest returns to 
arise from an area just before the position of the 
centre of the beam on the surface. 
Actual measurements of a grass field approximate 
the simulated return very well (fig. 4a). A stand 
of poplars situated next to the grass field, mea 
sured in the same run, at the same incidence angle 
and altitude, yielded a significant different return. 
The received signal was wider and delay time was less 
as is apparant from figure 4b. (All signals are 
scaled to the same level.) 
To analyse the return of the forest stand a simple 
model is introduced. The scatterers of the forest are 
assumed to be concentrated in horizontal planes 
equally distanced. Figure 5 shows how a stand of po 
plars with a tree height of 27 m is modelled as a 
collection of 4 scatter planes at 9 meter intervals. 
In figure 6 the individual radar returns from each 
of these planes is drawn. The return signal of level 
3 (closest to the radar) is the strongest, the 
narrowest and has the shortest delay time, the return 
from level 0 is the weakest, the widest and has the 
longest delay time and is the same as the one drawn 
in figure 3. 
In figure 7a simulated returns are drawn for a 
different frequency 
and a different incidence angle and are compared 
with (fig. 7b) the return of the grass field and 
(fig. 7c) the return of the poplar stand. As expec 
ted the return of the grass field closely matches the 
return of level 0 from the model. The poplar return 
shows a second peak matching the level 2 return from 
the model. Apparently there are contributions from 
the ground as well as from scatterers near the 18 
m level. Near the 27 m and 9 m levels the returns 
are clearly weaker. In this case contributions of 
scatterers from several layers can be separated at