Electromagnetic scattering from a corn canopy at L and C bands

The ability to retrieve and monitor soil moisture and vegetation water content (VWC) is of great importance. Yet accurate retrieval of such information from microwave observations presents a big challenge, which calls for the development of high fidelity scattering models. In the literature, a ”discrete scatter” approach was usually deployed, which attempted to determine first the scattering behavior of the individual constituent of the canopy, then that of canopy as a whole by summing up either incoherently [1] [?] or coherently [2]-[3]. To simplify the problem, constituents of the canopy are modeled as canonical geometrical objects. For corn canopy, the stalks are modeled as dielectric circular cylinders with finite length, and the leaves are represented as thin dielectric disks with elliptic cross section. Since scattering from each of the canonical object serves as the base for further ”assembling”, it is expected to be accurately determined. However, mush is still desired in this regard. For a dielectric cylinder of finite length, in studying its scattering behavior the generalized Rayleigh-Gans approximation (GRGA) [4] is usually applied, which approximates the induced current in a finite cylinder by assuming infinite length. This method is valid for a needle shaped scatterer with radius much smaller than the wavelength. Yet caution must be taken even at L band when EM scattering from the stalk of a corn plant is to be evaluated using GRGA. It is also well known that GRGA fails to satisfy the reciprocity theorem [2]. In the evaluation of scattering amplitude of leaves, the GRGA method is usually used. However, caution must be taken here. At C band the wavelength is 5.6 cm, which is comparable to the length of minor axis of corn leaves, which presents an unfavorable condition in applying GRGA and thus appreciable error is expected in the predicted scattering amplitude. When corn canopy is at its early stage of growth, or when the incidence angle is not large, contribution from the underlying ground is appreciable and thus its accurate prediction is important. Yet this roughness effect has not been adequately addressed in canopy scattering models, where what is typically applied is conventional analytical method such as Kirchhoff approximation (KA), or the small perturbation method (SPM) [5], or the more advanced yet still improvement-needed integral equation method (IEM) [6]. In this study, we choose to apply a more rigorous treatment of the rough surface contribution using the recently advanced EAIEM model by the authors [7]. With the advancement of several scattering models of dielectric cylinder and disks and of rough surfaces, it is the aim of this paper to investigate if a coherent combination of these constituent models can improve predictive power of the resultant canopy scattering model. To be more specific, in analyzing electromagnetic scattering from a dielectric cylinder of finite length, we use the new approach that we have recently proposed [8], where a long cylinder is divided into a cluster of N identical sub-cylinder by using N - 1 hypothetic surfaces, for each the T matrix can be calculated stably in the numerical sense. The boundary conditions at the hypothetic interface are treated carefully. A system of equations is set up for each sub-cylinder, and the overall system of equations is coupled and linear, thus can be solved by appropriate iterative method. Moreover, the VPM method is found to be applicable to dielectric cylinders of arbitrary length as long as the T matrix is attainable for the elementary sub-cylinder. The applicable relative dielectric constant can go up to 70 (real part), which is normally the upper bound for corn stalks at C band. The radius of the cylinder can be as high as 5 wavelengths, a feature of the model that is expected to be useful for forest applications [9]. Scattering from rough surface is treated using the EAIEM model [7], which is a unifing model recently developed by us for electromagnetic scattering from a Gaussian rough surface with small to moderate heights. It is based on the integral equation formulation where the spectral representations of the Greens function and its gradient are in complete forms, a general approach similar to those used in the advanced integral equation model (AIEM) [10]. Yet this new model can be regarded as an extension to these two models on two accounts: first it has made fewer and less restrictive assumptions in evaluating the complementary scattering coefficient for single scattering, and second it contains a more rigorous analysis by the inclusion of the error function related terms for the cross - and complementary scattering coefficients, which stems from the absolute phase term in the spectral representation of the Greens function. The proposed coherent scattering model will be validated at both L and C bands. At C band we acquired some RADARSAT-2 data of several test fields of corn canopy in Jiangsu province, China, in 2009, and carried out simultaneous measurement campaigns to collect the in situ ground truth. At L band high quality AIRSAR measurement data are available along with detailed ground truth in the literature [1] and will be used in the current work.