Volume Scattering Model over Agricultural Fields

To invert the surface parameters under vegetation cover, the key issue is to remove the effects of the scattering caused by vegetation canopy, which is called the volume scattering with its scattering process shown in Figure 1-4. However, until now this has been a challenging task to construct the volume scattering for accurate crop variable extraction due to the complex nature of the crop structure (Hajnsek et al., 2009). Many volume scattering models have been developed recently, but they can only characterize certain crop types (Huang et al., 2014). The extensively used method is to model the vegetation canopy scattering through integrating the scattering matrix of small-size scatterer with its orientation angle with respect to the line of sight (LOS) of radar satisfying a certain PDF. The small-size scatterers can be treated as needle-like dipole, spheroids, or disk-like plate depending on the size of the object compared with the radar wavelength. For long wavelength radar systems, they are often treated as needle-like dipoles; whereas for short wavelength radar systems, they are treated as spheroids or disk-like plate as shown in Figure 1-4.

Figure 1-4. Volume scattering in different radar frequencies.

Long Wavelength

Cloud of Dipole

Cloud of Spheroid Short Wavelength

Freeman and Durden (1998) developed the first volume scattering model based on the dipole assumption using the uniform probability density function. Yamaguchi et al. (2005) found that most of the vegetation areas were either horizontal or vertical dipoles, so they added the vertical and horizontal volume scattering models to extend the Freeman-Durden volume scattering model by making use of the first order sine probability density function. The von Mises distribution is in the class of circular probability distributions with the desirable characteristic of its PDF smoothly going down to zero, which has been proposed by Neumann et al. (2009) to characterize vegetation for polarimetric interferometry SAR (PolInSAR) applications. Arii et al. (2010) developed a

general scattering model based on a 𝑛𝑡ℎ power cosine square function, but the

randomness and orientation angle that are both unknown variables must be calculated simultaneously, which makes it very time-consuming. These volume scattering models are primarily developed to characterize forest canopy, but to directly apply them to agricultural areas is still limited as forest canopy always shows much higher randomness caused by the randomly distributed branches than crops that show certain orientations. To circumvent this issue, recently, a simplified adaptive volume scattering model based on

the 𝑛th-power sine and cosine functions were proposed by Huang et al. (2015) attempting

to describe the change of crops over time at different growing stages to sensor the C- Band RADARSAT-2 polarimetric data. Different from these above volume scattering models that use amplitude information to characterize the vegetation scattering, a novel volume scattering model based on the single-look phase distributions was developed by Lee et al. (2014) to characterize the statistics of phase difference of two polarization returns with circular Gaussian distribution, and it can better describe the distributions of the orientation angle due to the fact that orientation angles can be estimated by the phase difference between the left-left and right-right polarizations.

In summary, most of the abovementioned volume scattering models are still limited to only a few types of vegetation and cannot characterize crop development change over season. Additionally, most of these volume scattering models are based on needle-like dipoles as the elementary unit, which are valid only when the size of the objects is much smaller compared with the wavelength. Hence, for high frequency PolSAR systems such

as RADARSAT-2 in C band (5.4 cm) and TerraSAR-X in X band (3 cm), the needle-like dipole assumption is not likely satisfied. Being different from the above methods, An et al. (2010) assumed that it was only the vegetation canopy that causes scattering randomness. Based on this, they proposed a maximum entropy volume scattering model. However, Antropov et al. (2011) noted that the maximum entropy volume scattering model may require more experiments to be validated, and they proposed a generalized volume scattering model that can adapt to the sensitivity between the HH and VV co- polarizations for different types of vegetation. Additionally, the volume scattering is always related to the physical parameters of vegetation, hence, a finite-length slim cylinder is often adopted and the Rayleigh-Gans approximation method is used to model the stalk, branches or twiags of the crop (Jin & Xu, 2013). Finally, several empirical relationships were developed between polarization and/or dual frequency ratios and the physical parameters of crop fields. For instance, the radar vegetation index (RVI) computed at the L-band has been used to evaluate the biomass level of a corn crop (Kim et al., 2014). Other significant correlations have also been reported between: 1) HV/VV and soybean water content obtained in L-band (Roo et al., 2001), and 2) VV/HV and maize crop height and biomass at the S- and C-bands (Vecchia et al., 2008). As well, the HV/HH ratio at the C-band has been used to estimate the leaf area index (LAI) of sugarcane (Lin et al., 2009). Although these cross polarization ratios are almost insensitive to soil moisture, the application of these relationships is limited because they are only useful for specific crop types.