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The data given in Table 2 were measured for two fields of each of five different crop types (winter wheat, sugar 
beet, potatoes, beans and carrots). Note that the dielectric constants for both crop components and ground are 
estimated from the moisture contents of each of these. In the case of the crop components, the relationship 
given by Ulaby & El-Rayes (1987) is used, which requires the gravimetric moisture content of the crop along 
with the frequency and temperature. To calculate the ground dielectric the model would use the empirical 
relationship of Hallikainen et al (1985) which requires only the volumetric soil moisture and the frequency. 
However, this relationship does not extend to P-band and also requires the soil texture (the fractional 
composition in terms of sand, clay and silt) to have been measured. For the case of the peat soils at this 
Feltwell site, this has not been done. In order to circumvent these problems, values for the soil dielectric 
constant have been assumed. The other parameters that were not measured included the radii and mean and spread 
of the inclination angles of the crop stems and wheat ears. Values for these have been assumed following 
similar modelling work concerned with this site. Our work has concentrated on the wheat, sugar beet and potato 
data. 
Additionally, we note that the leaves are modelled as planar elliptical discs, which may not be 
an adequate description of some crop types. The measured ground data has attempted to quantify this by 
including the orientation angles of the leaves at the tip and near to the stem. A more accurate description for the 
leaves would include this curvature. In this work, we have attempted to incorporate the data only in so far as 
describing the sugar beet leaves as two disc segments, inclined according to the tip and stem angles previously 
mentioned. Questions regarding the structural description of plants clearly requires more careful analysis in the 
future. 
The approach that we have adopted in using the model differs from that which is usual in 
theoretical studies. Previous authors have chosen to examine the dependence of the mean backscatter on ground 
parameters by plotting the model predictions against, for example, incidence angle or soil moisture. However, 
the crop discrimination work that preceded this was based upon the identification of clustering properties in the 
15-dimensional parameter space made up of the HH, VV, HV returns and the amplitude and phase of the HH-to- 
VV correlation, for each of the wavebands, P, L and C. The clusters that appear in two-dimensional projections 
through this space are composed of individual fields from the polarimetric images. Therefore, we have chosen to 
make theoretical predictions for these clustering data. In order to do this, we have used one of the field examples 
of each crop type to derive a set of input parameters for the model and, importantly, have then estimated the 
field-to-field variation of each of the input parameters by using both field examples. It is hoped that the mean 
input parameter values lead to an accurate prediction for the mean position of the cluster, and that the input 
parameter variations will account for the cluster size and shape. It should be noted that in addition to the field- 
to-field variations in the ground parameters, the images also cover a range of incidence angles from 
approximately 30° to 60° and that therefore the incidence angles for the crop simulations should reflect this. 
3 - RESULTS 
In Figure 1 we show the observed clustering diagram for C-band VV versus HH returns, for each of the crop 
types wheat, sugar beet and potatoes and Figure 2 shows the theoretical predictions. Figures 3 and 4 show the 
equivalent data for L-band. Several features of Figures 1 and 2 are of especial interest. The observed clusters for 
the broad-leaved crops have a shape distinct from the wheat and appear to lie approximately on the line C-VV = 
C-HH. The theoretical predictions match this well and allow the interpretation that this is probably caused by 
the randomised orientations of the scatterers. The cluster spreading arises primarily because of variations in leaf 
density, moisture and the mean and spread of the inclination angle. Also, one of the most important model 
input parameters in determining the cluster shape and size for the broad-leaved crops is the incidence angle at 
which the field backscatter is calculated. For the broad-leaved crops, the increase in the incidence angle from 30° 
to 60° leads to a smooth decrease in the mean backscattered signal for both HH and VV returns (along the VV = 
HH line) as the canopy attenuation becomes more important For the case of the wheat fields, the relationship 
between the VV and HH signals is much less simple since the lower layer of the crop is characterised by the 
nearly vertical stems as well as the more randomly oriented leaves. This leads to dramatically different 
polarisation properties. Changing the incidence angle does not lead to a monotonic variation in the signals. It 
is also evident that the cluster size for the wheat is not as well-represented as the sugar beet and potato clusters 
but this could be accounted for by a number of reasons. Principal among these is that the question of the 
distributions for the model input parameter variations. It is most likely that the crop parameters would be drawn 
from skewed distributions of a strictly positive variable, such as lognormal or Rayleigh, whilst the distribution