## 4 Rice Monitoring Results and Discussion
### H/\(\bar{\kappa}\) Decomposition  
The entropy and \(\bar{\kappa}\) values for the FCP, DCP, and DLP modes are plotted in Figure 7. Note that the \(\bar{\kappa}\) for the DCP mode was treated with the condition \(\bar{\kappa}^{\prime}\) = 90\({}^{\circ}\)\(-\)\(\bar{\kappa}\) for comparison purposes as discussed in Section 2.2.1. The entropy values shown in Figure 7a exhibit relatively lower values at stage 1, because of the non-planted soil condition which produces highly deterministic scattering. Right after vegetation starts to grow, other scattering mechanisms such as double-bounce and volume scattering make entropy higher. Except for stage 1, entropy values fluctuate within the ranges 0.95-1 for FCP, 0.8-0.9 for DCP, and 0.4-0.6 for the DLP mode. It can also be noted that the entropy values for FCP and DCP represent a similar progressive trend and around 0.12 discrepancy between them. On the other hand, entropy for DLP ranges between 0.4 and 0.6 which is comparably lower than those of FCP and DCP. Furthermore, an abrupt decrease at DoY 203 is also observed in the DLP mode, which is not the case in the FCP and DCP modes. The \(\bar{\kappa}\) characteristic is shown in Figure 7b. FCP and DCP patterns are approximately identical except for non-rice and DoY 159 observations which differ by about \(\sim\)5\({}^{\circ}\). Despite this, each pattern shows an increasing trend, indicating a progression from surface scattering to dipole-like scattering. Figure 6: Backscattering coefficients of LL, RL, and RR polarization. On the contrary, \(\bar{\alpha}\) of DLP reveals a notably different result. Stage 1 measured a high \(\bar{\alpha}\) of \(\sim\)78\({}^{\circ}\), which is regarded as multiple scattering. The value then stabilizes to around \(\sim\)75\({}^{\circ}\) on average. To gain a deeper understanding of the scattering mechanisms contained in FCP and DCP data, the independent components of the \(H/\bar{\alpha}\) decomposition are investigated separately. Firstly, the appearance probabilities \(P_{i}\) for each scattering type defined by the associated eigenvector are calculated (see (6) and (8) for the DCP case) to interpret the entropy plots in Figure 7a. Note that the decomposition of FCP and DCP data produces three and two eigenvectors/probabilities, respectively. Also, the probability values are constrained by the expressions, \(P_{1}+P_{2}+P_{3}=1\) and \(P_{1}\geq P_{2}\geq P_{3}\) for FCP, and similarly for DCP. The variation of these probabilities as a function of DoY are displayed in Figure 8. The probability \(P_{1}\) for DCP data shows a similar trend to that of FCP over the whole observation period but experiences slightly higher value (\(\sim\)10%) for stages 3 and 4. From Figure 8a, an almost constant and relatively large \(P_{3}\) (recessive scattering) (\(\sim\)10%) is observed for FCP data. This is the case when more than three scattering mechanism components contribute to the receiving signals. Usually, complex targets such as forested areas give rise to this type of multi-scattering. If the third eigenvalue corresponding to \(P_{3}\) strongly affects the receiving signal, the difference between the entropy values between FCP and DCP becomes higher because entropy is formulated by summation of each independent scattering contribution which corresponds to scattering probability. As [PERSON] et al. pointed out in [20], compact mode systems typically produce higher entropy compared to the FP system. Secondly, \(\bar{\alpha}\) results given in Figure 7b are investigated in terms of their components. For each eigenvector \(u_{i}\), the corresponding \(\alpha_{i}\) is extracted by using \(\alpha_{i}=\arccos(\,\mid u_{1i}\,\mid)\) where \(\mid u_{1i}\,\mid\) is the absolute value of the first element of the eigenvector. From the results given in Figure 9, we notice that \(\alpha_{1}\) and \(\alpha_{2}\) for DCP indicate different trends and values from FCP values.