of incidence angles is image-dependent. (See section 4 for a more complete discussion of the incidence angle 
distribution.) However, the magnitudes of the signals and the approximate cluster shapes are encouraging. 
The L-band results given in Figure 4 are even more encouraging and allow a similar 
interpretation to those at C-band. The important feature is the increased penetration depth into the canopy, 
leading to lower amplitude returns (due to extinction) and slightly different polarisation properties. As as C- 
band, the variations in leaf properties are of importance in determining the cluster spreading, particularly 
uncertainties in leaf size. The P-band results are just as encouraging as those at L-band thought the potato 
cluster is much more tightly confined than the observational data. We note that the effect of the soil properties 
(roughness and moisture) are limited to a possible change of 2-3 dB for wheat but that they do not contribute 
significantly to the cluster spreading for either potatoes or sugar beet. 
As well as predicting the incoherent returns, the model also allows prediction of the complex 
HH-to-VV correlation, (¡>(HHVV*). This is parameterised in terms of the phase and amplitude of the correlation 
coefficient. In Figures 5 and 6 we show the observed and theoretical clustering diagrams for the phase of the 
HH-to-VV correlation in C-band against the C-HH signal and in Figures 7 and 8, equivalent data for L-band. At 
C-band there is a well-defined difference between the broad-leaved crops (which on average have a small, positive 
value for the phase) whilst the wheat varies over a reasonably large negative range. Again it is likely that these 
are explained by the highly random orientations of the scatterers in the broad-leaved canopies and the structure 
associated with the wheat. The predicted amplitude of the HH-to-VV correlation tends to be greater than that 
which is observed, which is probably due to the fact that the leaf scatterers are modelled as being planar. 
4 - DISCUSSION 
The conventional approach to studies of theoretical models is to make predictions of mean backscatter levels and 
compare these with observational data. In this study we have adopted an alternative approach which includes 
predictions of the cluster shapes as well as the mean positions. The focus on cluster predictions rather than 
means is more challenging for experiment design and modelling. Given that the cluster shapes depend on the 
distribution functions for all of the ground data, it is encouraging that the predictions for the signals are at least 
approximately correct in magnitude and should be no surprise if in some instance the cluster shape does not 
match observations. An example of this is the predicted form of the wheat cluster in the space C-VV versus C- 
HH (Figure 2). In this case, the cluster has a much larger spread in the HH direction than is observed. 
One of the most important input parameters in determining the cluster characteristics (both 
position and shape / size) is the incidence angle. For example, the returns from the broad-leaved crops decreased 
continuously as the incidence angle was increased. In the figures given in this report, we have made use of a 
uniform distribution of incidence angles in the range 30° to 60° though it would be more realistic to accurately 
model the distribution of incidence angles for each crop type in the appropriate image. We note that the 
dependence on incidence angle demonstrated in the Section 3 indicates that it is possible that the forms of the 
clustering diagrams could depend carefully on (a) whether the images are taken from an airborne SAR (which 
covers a range of incidence angles) or a satellite-bome SAR (for which the images are at a fixed incidence angle) 
and (b) the specific incidence angle of the satellite-bome SAR under consideration. 
As an example of this, we show in Figure 9 a simulation of the C-VV versus C-HH plane for 
wheat, sugar beet and potatoes at a fixed incidence angle of 23°, and in Figure 10 the equivalent graph for 39°. 
The former of these is intended to represent a near-range swath of the ASAR and the latter corresponds to the 
approximate incidence angle for Feltwell observations during the SIR-C mission. The diagrams show clearly 
that the increase in incidence angle leads to a decrease in the signals from the broad-leaved crops but that they 
still remain merged. This may not necessarily remain the case for other crop types (which could separate at 
different incidence angles) and may also depend carefully on the structure that is assumed for the crops. 
5 - CONCLUSIONS 
The aim of this paper has been to report on validation and use of a theoretical model for investigating the 
properties of SAR imagery of crops. The model has had some success in predicting the differences between 
crops and appears to work well in all three wavebands, P, L and C. We have identified incidence angle as one of 
the most important factors in determining the spread of clusters. Cluster separability tests conducted on multi- 
mcidence angle imagery are likely to give very different results to single incidence angle images (such as those 
which will be obtained from the SIR-C mission). It is likely that single incidence angle images would be of