## 3 Results  
### Backscattering Coefficient Analysis and Decision Tree Development  
Distributions of backscattering coefficients of the training dataset, expressed in a logarithmic scale, and their combinations (calculated in linear scale then expressed in logarithmic scale) at each phase, are shown in boxplots (Figure 7). In the figure, VH/(2 VH+VV+HH) was also plotted because of its sensitivity to vegetation parameters [41]. In each subplot, four boxes were drawn to represent the distributions of four phases. The red line visually showed a feasible division value. For example, the VH backscattering coefficients increased in general from the transplanting phase to the maturity phase (Figure 7a). The red line near \(-20\) dB divided the transplanting phase from later phases with few data points crossing the division line. Ranges of the later phases, especially the vegetative and reproductive phase, severely overlapped with each other. Thus, VH data could not discriminate the vegetative phase from the reproductive phase. Figure 5: A simple decision tree of a variable, \(\lambda\). Three thresholds divide \(\lambda\) into four classes through two decision layers. Figure 6: Distributions of development phases vs. VH backscattering coefficients. The data are training data. At about \(-20\) dB, the transplanting phase is separated from other three phases. Figure 7: Boxplots of backscattering coefficients (training dataset, expressed in logarithmic scale) and their combinations (calculated in linear scale then expressed in logarithmic scale) at each phase, (**a**) VH, (**b**) VV, (**c**) HH, (**d**) HH/VV, (**e**) VV/VH, (**f**) HH/VH, (**g**) HH \(\times\) VV, (**h**) VV \(\times\) VH, (**i**) HH \(\times\) VH, (**j**) HH \(-\) VV, (**k**) VV \(-\) VH, (**l**) HH \(-\) VH, (**m**) HH \(+\) VV, (**n**) VV \(+\) VH, (**o**) HH \(+\) VH, (**p**) VH/(2 VH \(+\) VV \(+\) HH). Red lines represent possible division values to separate at least two interquartile ranges (grey part of boxes). As shown in Figure 7, there are varying degrees of overlaps between different phases and for different polarization data. The single polarized HH or VV data can hardly differentiate all phenological phases, but the joint use of several polarized data can achieve the needed separation. Taking subplot (d), (e), and (f) of Figure 7 as an example, one can use HH/VV data to divide the maturity phase from the vegetative and reproductive phases or the transplanting phase from the other three phases. The VV/VH parameter can be used to distinguish the transplanting phase from later phases. The HH/VH parameter can be used to differentiate the transplanting and vegetative phase from the reproductive and maturity phase. Thus, a combination of three polarized data can be used to distinguish four phenological phases. Then, a decision tree can be constructed (Figure 8). The backscattering properties of a rice paddy during the transplanting period were mainly affected by water since the plant was small and the plan coverage was sparse. Thus, backscattering at this phase was quite different from that during the later three phases. As a result, backscattering coefficients of the transplanting phase were more distinctive by many polarized data (Figure 7). This was attributed to the high level of the determination accuracy (table 4). On the other hand, most of the misclassification occurred in the vegetative and reproductive phases because the water was very shallow or the field was dry. The rice canopy almost covered the fields continuously. Backscattering coefficients exhibited no distinctive changes from the vegetative phase to the reproductive phase for most polarized data (Figure 7). This was especially true during days of phase transition in which the plant height and water content of the plants changed slowly. The backscattering was mainly influenced by the plant density because rice plants in some fields had similar growth statuses (e.g., the number, size, orientation and water content of stems, leaves and young heads).