## 2 Materials and Methods
### Data Curve Fitting and Phenology Extraction  
Common methods of vegetation growth curve fitting include the logistic function-fitting method, the asymmetric Gaussian function-fitting method, and polynomial fitting. Among them, the double logistic (D-L) method features automatic threshold establishment, is suitable for extracting different types of vegetation phenology, and is widely used in the simulation study of vegetation growth process. This study was based on a D-L model to fit the growing season trajectory of _P. tomettsoa_.  
\[g(t)=(m-W)\bigg{\{}\frac{1}{\left[1+\exp(-mSx(t-S))\right]}+\frac{1}{\left[1+ \exp(-mAx(t-A))\right]}\bigg{\}}-1+W \tag{2}\]  
where \(g(t)\) indicates the fitted value of the color index, \(t\) refers to the Day of Year (DOY), \(m\) means the minimum value of the year, and \(W\) represents the maximum value of the year. \(S\) and \(A\) represent the beginning of the season and the end inflection points (SOS, EOS), \(mSx\) and \(mAx\) are the rates at points \(S\) and \(A\), representing spring greening rate (RSP) and autumn senescence rate (RAU), respectively.  
The key phenological parameters were the SOS, end of growing season (EOS), length of growing season (LOS), and the maximum value of growing season, which are the key event points of the vegetation growth process, as well as parameters such as the greening rate and the decline rate. The maximum curvature method was selected to extract phenological parameters, and the rate of change of curvature reflects the node changes in the growth period and the withering period, as well as the speed of growth. The formula based on the maximum curvature method is as follows:  
\[P(t)=\left|\frac{g^{\prime\prime}(t)}{\left(1+g^{\prime}(t)^{2}\right)^{\frac{ 3}{2}}}\right| \tag{3}\]  
where _P(t)_ is the curvature, \(g(t)^{\prime}\) is the first-order derivative with respect to \(t\), and \(g(t)^{\prime\prime}\) is the second-order derivative with respect to \(t\).  
The following seasonal changes in vegetation were observed: in winter and early spring, there were only bare trunks and other natural phenomena, and at this time, the vegetation was in the dormant period, and the color of the image was primarily that of the trunks. As the external environment changed, notably with respect to temperature, _P. tomettsoa_ B301 showed leaf buds and gradually expanded [33] (Figure 5a), and vegetation began to grow (SOS). As the temperature increased, the digital image dominated by the trunk color was steadily replaced by sporadic leaf buds as they formed and elongated,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Color Index** & **Equation** & **Reference** \\ \hline Ratio greenness index & \(GGR=G/R\) & [28] \\ \hline Green chromatic coordinate & \(GCC=G/(R+G+B)\) & [29] \\ \hline Green excess index & \(GEI=2G-(R+B)\) & [29] \\ \hline Red chromatic coordinate & \(RCC=R/(R+G+B)\) & [30] \\ \hline Green red vegetation index & \(GRVI=(G-R)/(G+R)\) & [31] \\ \hline \multirow{4}{*}{Hue} & \(HUE=(B-R)/(I_{max}-I_{min})\times 60+120\) & \\  & \(G=I_{max}\) & \\ \cline{1-1}  & \(HUE=(B-R)/(I_{max}-I_{min})\times 60+240\) & \\ \cline{1-1}  & \(B=I_{max}\) & \\ \cline{  
which is known as the leaf bud opening stage (Figure 5b). When the light and temperature were adequate, _P. tomentosa_ B301 gradually spread its leaves and began to enter the vigorous growth period, and emerald green became the dominant tone of the image (Figure 5c). Over time, the leaf color in the image steadily changed from emerald green to dark green (Figure 5d), which is known as the leaf discoloration period. With the gradual yellowing and widening of leaves in autumn and winter, natural shedding occurred, and the tree entered the deciduous stage (Figure 5e), whereupon the digital images show the trunk color again until the end of the vegetation growing season (EOS).