# Sensitivity Analysis of Multi-Temporal Sentinel-1 SAR Parameters to Crop Height and Canopy Coverage
## 2 Materials and Methods
### SAR Backscatter

Table 2: Specifications of acquired Sentinel-1 datasets over Konya basin, Turkey. \[=\left[ \begin{array}{ccc}\left|S_{HH}\right|^{2}&\sqrt{2}S_{HH}S_{HV} \;^{*}&S_{HH}S_{VV}\;^{*}\\ \sqrt{2}S_{HV}S_{HH}\;^{*}&2\left|S_{HV}\right|^{2}&\sqrt{2}S_{HV}S_{VV}\;^{*}\\ S_{VV}S_{HH}\;^{*}&2S_{HV}(S_{HV}-S_{VV})\;^{*}&\left|S_{VV}\right|^{2}\end{array}  \right], \tag{3}\]  
where ensemble averaging is shown by the \(\mid\mid\) represents the modulus, the \({}^{*}\) indicates complex conjugation and the complex conjugate transpose shown by superscript H. For natural targets, in case of monocratic radar, \(S_{\rm{HV}}\approx S_{\rm{VH}}\) when \(\rm{Str}\) indicates the complex scattering amplitude for received and transmitted polarization (\(\rm{r},\rm{t}\in\{h,v\}\)) for horizontal and vertical polarization and the scattering matrix is defined by three-element complex target vector, \(\rm{K_{C}}=\left[S_{HH}\sqrt{2}S_{HV}S_{VV}\right]^{T}\), where superscript \(\rm{T}\) indicates the matrix transpose [29; 30]. In the covariance matrix, diagonal elements (\(\rm{C_{11}}=\sigma^{0}_{\rm{HH}}\), \(\rm{C_{22}}=\sigma^{0}_{\rm{HV}}\), and \(\rm{C_{33}}=\sigma^{0}_{\rm{VV}}\)) define backscattering coefficients and the upper or lower triangular components represent complex numbers. The backscattering coefficients have correlation with the structural characteristics of the features [17; 31]. In comparison to the quad polarization, dual polarimetric SAR sensors collect a fraction of total (precisely half of the scattering matrix components) polarimetric information involved in fully polarimetric imagery [27]. It means that each resolution cell at each time point is defined by a \(2\times 2\) covariance matrix (\(\rm{C_{2}}\)) that is obtained from \(\rm{C_{3}}\). The resulting covariance matrix which is for dual polarization (e.g., Sentinel-1) is represented by Equation (4). \[\rm{C_{2}}=\left[ \begin{array}{cc}C_{11}&C_{12}\\ C_{21}&C_{22}\end{array} \right],\]  
\[\langle C\rangle_{dual}=\left[ \begin{array}{cc}\langle S_{VV}S^{*}_{VV} \rangle&\langle S_{VV}S^{*}_{VH}\rangle\\ \langle S_{VH}S^{*}_{VV}\rangle&\langle S_{VH}S^{*}_{VH}\rangle\end{array}  \right], \tag{4}\]  
Since dual polarization has only diagonal elements, the matrix with off-diagonal components are set to zero and do not follow a complex Wishart distribution; however, the two diagonal blocks (1 by 1) do [30; 32]. Polarimetric Synthetic Aperture Radar (PolSAR) technique has resulted many different investigations and improvements in crop growth monitoring, yield estimation, crop disaster prediction and prevention and in more general terms providing accurate information for precision farming. PolSAR products, such as Entropy (H), Alpha (\(\alpha\)) and Anisotropy (A) decompositions are calculated from the covariance matrix. The H-\(\alpha\)-A decompositions are used to extract average parameters from experimental data suggested by [PERSON] and [PERSON] [33]. This approach is based on second-order statistics using a smoothing algorithm [34]. Natural measure of the inherent reversibility of the backscattering data is defined by entropy (H), and indicates the randomness of the scatter, while the underlying average scattering mechanisms, scattering type (surface, double-bounce and volume scattering) can be identified using Alpha parameters. The relative power the second and third eigenvectors is described by Anisotropy (A), which represents being of different properties in different directions when measured along different axes [33; 35]. The Entropy (H) decomposition parameter has more sensitivity to the crop parameters and the density and randomness of some vegetation canopy than Alpha and Anisotropy [28; 36]. In agricultural radar monitoring, Radar Vegetation Index (RVI) is a method for observation of the level of the vegetation growth in time series data analysis as an alternative to NDVI (Normalized Difference Vegetation Index) method used in optical image processing studies [37].