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THEORETICAL MODELLING OF MULTI-FREQUENCY 
POLARIMETRI RADAR IMAGERY OF CROPS 
PJ. SAICH 1 , P.A. WRIGHT 1 , R.A. CORDEY 1 & A. WIELOGORSKA 2 
'GEC-Marcom Research Centre, West Hanningfield Road, Gl Baddow, Chelmsford, 
Essex CM2 8HN, UK 
2 Hunting Technical Services Limited, Thamesfield House, Boundary Way, Hemel Hempstead, 
Herts. HP2 7SR, UK 
ABSTRACT: 
A first order solution of the vector radiative transfer equation has been used in conjunction with extensive 
(agricultural) ground data to make predictions for the polarimetrie backscatter from different crop types. The 
model predictions focus on the clustering patterns in the 15-dimensional space composed of the incoherent return 
(HH, VV and HV) along with the phase and amplitude of the HH-to-VV correlation coefficient in each of the 
three wavebands P, L and C. The results show that there is a fair quantitative agreement for the returns at all 
three wavelengths. The model is able to explain the generic differences that arise between different types of 
crops. Crop moisture is seen to be extremely important whereas soil properties and leaf number density are 
often unimportant, especially in the case of well-developed, dense crops such as potatoes and sugar beet, late in 
the growing season. The range of incidence angles is found to be one of the most important factors in 
determining the cluster spread for certain crops (potatoes and sugar beet) and is expected to lead to differences 
between airborne and spacebome S AR results. 
KEY WORDS: Active Microwaves, SAR, Polarimetrie, Agricultural, Crops, Theoretical Modelling 
1 - INTRODUCTION 
Crop monitoring is a potentially important application of satellite synthetic aperture radar (SAR). Currently, it 
is being investigated by programs of research with ESA’s ERS-1 satellite which exploit the multi-temporal 
coverage of this C-band VV-polarised radar (for example, the DRA Crop Monitoring Experiment, Bird et al 
1993, Wright et al 1994). Other radar frequencies and polarisations need to be assessed for potential use on 
future satellite missions and experiments with NASA’s multi-frequency polarimetric aircraft SAR (AIRSAR) 
and the forthcoming SIR-C / X-SAR Space Shuttle missions present opportunities to further this research. 
Feltwell has been chosen to be a SIR-C / X-SAR experiment site and work underway at the site includes 
calibration studies, validation of single pixel statistics against the multivariate complex gaussian model and 
empirical investigations into optimum SAR parameters for crop discrimination (Cordey et al 1993). This paper 
reports on theoretical modelling work conducted in support of these investigations using data from the JPL 
AIRSAR and a detailed database of in-situ measurements. In Section 2 a brief description of the theoretical 
model is given along with a discussion concerning the ground parameters measured and their relationship with 
the inputs required to drive the model. The modelling approach used in the remainder of the paper is also 
described at this stage. In Section 3 the results are given and direct comparisons with observations are made. 
Interpretation of the theoretical predictions is given wherever this is possible and illuminating. In Section 4, we 
discuss the results in the context of airborne and satellite-borne SAR systems. Final conclusions and 
recommendations are given in Section 5. 
2 - THE THEORETICAL MODEL AND INPUT DATA 
The model that has been used is based upon the first order solution to the vector radiative transfer equation 
(Tsang et al 1985) for either a single or two-layer medium over a rough surface. The scattering properties of the