Electromagnetic Scattering from Foliage and Vegetation:
Modelling and applications in Active Microwave Remote Sensing
H.T. Chuah
Faculty of Engineering
Universiti of Engineering
Jalan Ayer Keroh lama
75450 Melaka
Tel: +606-2523456; FaxL +606-2316552
E-mail: htchuah@unitele.com.my
Abstract
This paper aims to review some theoretical models for electromagnetic wave-matter scattering and propagation in foliage and vegetation that have been developed for the past ten years or so. These include models using the Renormalization Technique (a field approach); the Radiative Transfer Theory (an energy/intensity approach) and models using the Monte Carlo technique (a statistical method). Various examples are given to illustrate the potentials of these methods: study of propagation of wave in a vegetation canopy to calculate the effective attenuation coefficient, and radar backscatter from a vegetation field/forest stand. The simulated results are compared with experimental data wherever possible to validata the models.
Introduction
Electromagnetic scattering and propagation in foliage and vegetation is a complex vector problem because of the multiple scattering between a mixture of randomly distributed components of the medium, including the ground surface. The task of modeling a complete vegetation medium must include all the interactions between the separate components of the vegetation, including the soil. Various volume and scattering theories have been developed for modeling the scattering and propagation in such random media [1]. Basically, there are three main approaches: the field approach, the energy/intensity approach and the statistical approach. In the past ten years, some research work has been done in Malaysia to develop models based on such formulation. This paper aims to give an overview of those models developed, together with some results and comparisons with experimental data.
2. High-order Renormalization Method (HRM)
In this field approach, the vegetation medium is characterized by a complex permittivity function:
e(r) -
ea +
ef (r) ...(1)
where
ea and
ef are the average and fluctuations of the complex permittivity of the random medium. The vector wave equation for the electric field E in the medium is then written as:
(Ñ*Ñ*-ko2ea)E=LE=
ko2ef
=xE ……………….(2)
By separating the electric field E into the mean field Em and the fluctuating field Es, and assuming center-valued Gaussian statistics for the fluctuations in the random medium, we obtain:
(L-(xL-1x))Em
=-(xL-1xEs)
and LEs
=xEm
+[xEs - (xEs)] ..(3a)and(3b)
To solve for the mean field Eq. (3) is iterated starting with
E
m=E
om and E
s=0. After some manipulation, for second order iteration, we have:
(L- (xL-1x))E2m
=0 and LE2s
= x))Eom
+ xL-1xEom
- (xL-1x)Eom ..(4a)and(4b)
The basic approach is to find a good approximation for the mean field E
m from which the scattered field is then determined from Eq. (4b). The mean field is governed by theDyson equation, which can be conveniently respreseted by Feynman Diagram:
where
represents the mean field,
the half space Green's dyadic and the mass operator
represents an infinite series of strongly connected terms,
in which
represents the correalation between r and r' as given by the product (
x(r)
x (r')).
By only selecting the first three terms of the mass operator, we are able to solve the Dyson equation of the form:
Eq. (7) gives a mean field improved by the two additional infinite series compared to bilocal approximation where only the first term of the mass operator is considered. Using the improved mean field, the second order scattered field
E
2s and the radar backscatter coefficient can be calculated. Figure 1 compares the results of the calculations using both the mean field based on bilocal approximation and the HRM. We note that the results from HRM give a much slower drop at large incident angles, a trend that agrees with data from experiments. Figure 2 shows a typical comparison with experimental data for soyabean at 7.1 GHz.
Fig. 1: Comparison between bilocal and HRM mean field Renormalization Method
Fig.2: Comparison between HRM and experimental data for soyabean at 7.1 GHz
