# Sensitivity Analysis of Multi-Temporal Sentinel-1 SAR Parameters to Crop Height and Canopy Coverage
## 2 Materials and Methods
### SAR Backscatter  
Several studies on the processing of radar data indicate that the phenological stages of the plant have an effect on the backscatter of the signal, and there is a significant correlation between the biophysical parameters of the plants, including height, leaf area index, vegetation mass, plant water content, and radar signal backscatter [15; 23; 24; 25]. Radar backscattering from vegetation is a function of both wavelengths polarization and frequency. Different frequencies and polarizations enable one to infer various and supplementary information from the single object. In agricultural radar applications, combination of polarizations (co-polarization and cross-polarization) allows analyst to extract extra information about crop characteristics. The polarization of backscattering microwaves indicates the target structural properties and visualizes scattering characteristics of observed features [1; 5]. A majority of the space borne radar systems often transmit only one polarization and receives both polarization giving rise to dual polarimetric SAR data (e.g., Sentinel-1 with VH and VV polarizations), while some collecting full polarimetric so-called quad polarization (HH, VV, HV, and VH) imagery (e.g., PALSAR, TerraSAR-X, and RADARSAT-2). Fully polarimetric SAR data is acquired using the H and V polarizations which extracted from SLC data and can be represented by a \(2\times 2\) scattering matrix S (Equation (1)) including polarimetric information for each individual resolution cell [26; 27; 28]. \[\text{S}=\left[ \begin{array}{cc}S_{HH}&S_{HV}\\ S_{VH}&S_{VV}\end{array} \right], \tag{1}\]  
Scattering matrix which depends on incident and the scattered field, has four components, each representing the received and transmitted polarizations [29; 30]. The scattering matrix consists of information on the nature and characteristic of the observed media and features. Full polarimetric SAR data set which is described as scattering matrix is foundation for several coherent polarimetric decomposition and analysis. For polarimetric analysis an alternative procedure is derived from a covariance matrix (C\({}_{3}\)) that represents the average polarimetric information extracted from a set of neighboring pixels to produce the mean polarimetric response. The covariance matrix C\({}_{3}\), (Equation (2)), is determined from the outer element of the vector form of the scattering matrix with its Hermitian conjugate, KC [17; 27]. The averaged target vector (covariance matrix) for fully polarimetric data is given by Equation (3). \[\text{C}_{3}=\text{K}_{\text{C}}.\text{K}_{\text{C}}\ ^{*\text{T}}=\left[ \begin{array}{ccc}C_{11}&C_{12}&C_{13}\\ C_{21}&C_{22}&C_{23}\\ C_{31}&C_{32}&C_{33}\end{array} \right],\]  
\[\left\langle\text{C}\right\rangle_{full}=\left\langle\text{S}(i)\text{S}\ (i)^{H}\right\rangle,\]  
\[=\left[ \begin{array}{ccc}\left\langle S_{HH}S^{*}_{\ \ HH}\right\rangle&\left\langle S_{HH}S^{*}_{\ \ HV}\right\rangle&\left\langle S_{HH}S^{*}_{\ \ VV}\right\rangle\\ \left\langle S_{VH}S^{*}_{\ HH}\right\rangle&\left\langle S_{HV}S^{*}_{\ \ HV} \right\rangle&\left\langle S_{VH}S^{*}_{\ \ VV}\right\rangle\\ \left\langle S_{VV}S^{*}_{\ \ HH}\right\rangle&\left\langle S_{VV}S^{*}_{\ \ HV} \right\rangle&\left\langle S_{VV}S^{*}_{\ \ VV}\right\rangle\end{array} \right], \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Acquisition Date**} & \multicolumn{2}{c}{**Incidence**} & \multirow{2}{*}{**Satellite**} & \multirow{2}{*}{**Polarization**} & \multicolumn{2}{c}{**Nominal**} & \multirow{2}{*}{**Orbit**} \\  & & & & & & **Resolution(m)** & \\ \cline{2-2} \cline{5-6}  & **Near** & & & & **Range** & **Azimuth** \\ \hline
13 June 2016 & 30.72 & 49.09 & Descending & VH and VV & 2.33 & 13.93 & 65 \\
07 July 2016 & 30.72 & 49.11 & Descending & VH and VV & 2.33 & 13.93 & 65 \\
31 July 2016 & 30.72 & 49.11 & Descending & VH and VV & 2.33 & 13.93 & 65 \\
24 August 2016 & 30.72 & 49.11 & Descending & VH and VV & 2.33 & 13.93 & 65 \\ \hline \hline \end{tabular}
\end{table}