## 2 Materials and Methods
### Construction of Optimal Identifying Feature
\(Hv\) refers to the high valley value of the backward scattering coefficients of the 14 May, 26 May, and 7 June data for the six polarizations and their combinations:  
\[Hv=\frac{Ma_{14}+Ju_{07}}{2}-Ma_{26} \tag{4}\]  
where \(Ma_{14}\) is the backscatter coefficient for the 14 May data, and \(Ju_{07}\) and \(Ma_{26}\) represent the backscatter coefficients for the 7 June and 26 May, respectively. Figure 2: Separability of orchards, cropland, and other forest and vegetation: (**a**) separability of orchards, cropland, and other forest and vegetation in 3D feature space; (**b**) distance box plot of each vegetation type to the optimal threshold plane; (**c**) scatter plot of divisibility of orchards and other forest and vegetation species; (**d**) knowledge model diagram of optimal identification features of orchards and other forest and vegetation. Sentinel-1 (S-1) data were used to make divisions among orchards, cropland, and other forest and vegetation. \(C\_D\) represents the difference in backscattering coefficient between the 13 June data and the 25 June data; \(Hv\) refers to the high valley value of the backward scattering coefficients of the 14 May, 26 May, and 7 June data for the six polarizations and their combinations; \(Tb\) represents the difference between the backscattering coefficient of the data of 7 June and those of 14 January. \(Tb\) represents the difference in the backscattering coefficients of the data of 7 June and those of 14 January. In January, lithchi was in the spring period, when the vegetation information was weak and the backscattering value was low. Therefore, the difference between the two periods of data is an important growth stage feature:  
\[Tb=Ju_{07}-Ja_{14} \tag{5}\]  
where \(Ju_{07}\) is the backscattering coefficient of the 7 June data; \(Ja_{14}\) is the backscattering coefficient of the 14 January data. \(C_{-}D\) represents the difference in backscattering coefficients between the 13 July data and the 25 July data. July is the crop harvesting and planting season, and there is a difference in the backscattering coefficients of the two data, which can accurately distinguish cropland from other features:  
\[C_{-}D=Jl_{13}-Jl_{25} \tag{6}\]  
In the above equation, \(Jl_{13}\) is the backscatter coefficient for the 13 July data, and \(Jl_{25}\) is the backscatter coefficient for the 25 July data. \(Lo\) and \(Cr\) indicate that the backward scattering coefficients of longan and mandarin orange are high in the trough of the ripening stage:  
\[Lo=\frac{Jl_{13}+Au_{06}}{2}-Jl_{25} \tag{7}\]  
\[Cr=\frac{Se_{23}+No_{11}}{2}-Oc_{17} \tag{8}\]  
In the above equation, \(Jl_{13}\), \(Jl_{25}\), \(Au_{06}\), \(Se_{23}\), \(Oc_{17}\), \(No_{11}\) are the backscatter coefficients for the 13 July, 25 July, 6 August, 23 September, 17 October, and \(11\) November data, respectively. The growth stages of mature lithchi fruit trees typically exhibit the following features: as lithchi trees are categorized under broadleaved evergreen forests, their vegetation remains fairly stable throughout the year; during the first half of the year, lithchi undergoes the flowering and fruit growth stage, resulting in noticeable shifts in the spectral properties of lithchi fruit trees. This is partly attributable to the unique growth of the lithchi fruit, where the shell develops initially, followed by the flesh. During April and May, the lithchi fruit undergoes growth and expansion. By June, the shell loses its green color, transitioning from lime green to a shade of red. Along with the fruit's expansion, the shading effects of the leaves on the lithchi fruit trees also gradually increase. As the picking period approaches, the spectral effects of the fruit's shading on the canopy of the lithchi trees weaken steadily.