## Materials and Methods
### Experimental Design  
For crop growth monitoring, the temporal evolutions of all polarimetric observables for each crop type used as input feature layers for classification were derived. First, the locations of the fields for each crop type were extracted from the ground truth set. Afterwards, the average values of polarimetric observables from all the ground truth fields for each crop type were produced on each RADARSAT-2 acquisition date. The analysis of temporal evolutions of polarimetric observables were more focused on the three major crops (corn, soybean, and winter wheat). For crop classification, 27 polarimetric observables for each SAR image were obtained and combined differently as the input feature layers according to ten groups defined in Table 3. As a result, 10 combinations of input layers were constructed. The detailed descriptions of the combinations of polarimetric observables are presented in Table 4. The frequently used Random Forest (RF) algorithm was applied to each combination in this study due to its good performance, and demonstrated advantages in crop classification [39; 54; 55; 56]. In addition, a beneficial property of RF is that it can quantify variable importance for classification [57; 58]. Previous studies have shown that accuracy of crop classification with RF nearly reaches stable values as the number of decision trees increases above 50 [39; 41; 56]. Finally, 100 decision trees were used in RF algorithm for all classification tests in this study. In total, ten groups of polarimetric observables were used as input features in classification. The combination of all types of polarimetric observables is usually adopted for crop classification and commonly generates better results than using single types of polarimetric observables alone. However, contributions from different features to crop classification accuracy may vary dramatically. Therefore, it is interesting to determine an optimal combination of features that could obtain the best classification accuracy. Moreover, in past studies with multitemporal SAR data, comparable, or even better crop classification accuracies, were sometimes obtained by combining a few images acquired at certain \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Source** & **Polarimetric Observables** & **Number of Images** & **Number of Layers** \\ \hline LP & HH (C11), HV (C22), VV (C33) & 7 & 21 \\ Pauli & HH + VV (T11), HH-VV (T22) & 7 & 14 \\ Span & Span & 7 & 7 \\ Ra & HH/VV, HV/HH, HV/VV & 7 & 21 \\ Ro & \(\rho_{HHVV,\,\rho_{HVV},\rho_{HHHV,\,\rho_{HH}+VV,HH-VV}}\) & 7 & 28 \\ Pha & \(\phi_{HHVV,\,\phi_{HVV},\phi_{HHHV,\,\phi_{HH}+VV,HH-VV}}\) & 7 & 28 \\ FD & \(\beta_{s},P_{d},P_{v}\) & 7 & 21 \\ CP & H, A, \(\alpha\) & 7 & 21 \\ ND & \(|\delta|,\phi_{s},\tau\) & 7 & 21 \\ RVI & RVI & 7 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The detailed descriptions of the combinations of input polarimetric observables. Note that abbreviations are explained in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Group** & **Polarimetric Observable** & **Description** & **Abbreviation** \\ \hline
7 & \(P_{s},P_{d},P_{v}\) &
\begin{tabular}{c} Scattering power from different scattering \\ mechanisms derived from Freeman-Durden \\ decomposition \\ \end{tabular} & FD \\
8 & \(\text{H,A,\alpha}\) &
\begin{tabular}{c} Entropy, anisotropy, alpha angle from \\ Cloude-Potitier decomposition \\ Magnitude and phase of the particle scattering \\ anisotropy, the degree of orientation randomness \\ derived from Neumann decomposition \\ Radar Vegetation Index \\ \end{tabular} & CP \\
9 & \(|\delta|,\phi_{s},\tau\) &
\begin{tabular}{c} Magnitude and phase of the particle scattering \\ anisotropy, the degree of orientation randomness \\ derived from Neumann decomposition \\ Radar Vegetation Index \\ \end{tabular} & ND \\
10 & RVI & Radar Vegetation Index & RVI \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._critical phenology stages [7; 10; 24; 26].