# Unraveling the Scale Dependency of SIF-Based Phenology: Amplified Trends and Climate Responses
## 2 Data and Methods
### Methodology
#### 2.3.1. Phenology Extraction  
To accurately capture the trend of SIF during the vegetation growth cycle, the SIF data were smoothed using--Savitzky-Golay (S-G) filtering. S-G filtering filters out environmental noise from remotely sensed data, preserving the trend and periodicity characteristics of the data by selecting multiple data points within a neighborhood of the data points and replacing their values using polynomial fitting [53]. Next, we used a cubic smoothing spline model to fit the SIF time series and predict the SIF values for each day of the year [54]. This method can flexibly model the seasonal variation pattern of vegetation while maintaining the smoothness of the curve and effectively reconstructing the seasonal trajectory.  
\[\mathrm{S_{i}(x)=a_{i}+b_{i}(x--x_{i})+c_{i}(x-x_{i})^{2}+d_{i}(x-x_{i})^{3}} \tag{1}\]  
In this equation, \(x\) and \(x_{i}\) are the two neighboring points (with a step size of eight days for the SIF data), and \(a_{i}\), \(b_{i}\), \(c_{i}\), and \(d_{i}\) are the fit coefficients of the equation. The value of SIF between each pair of neighboring points is calculated using several cubic polynomials \(S_{i}\).  
In this study, vegetation phenology was estimated using the dynamic threshold method, focusing on two primary metrics: the Start of Growing Season (SOS) and the End of Growing Season (EOS). The SOS marks the transition when the plant changes from a dormant or slowed-down state to an active state of growth, while the EOS signifies the shift in plant growth from an active phase to a dormant stage. The determination of SOS and EOS is based on dynamic thresholds, specifically the ratio of the difference between the observed value and the annual minimum to the difference between the annual maximum and the annual minimum [55]. The corresponding dates are recognized as SOS and EOS when this ratio reaches 0.3 and 0.5, respectively [56].  
\[\mathrm{f_{ratio}(t)=\frac{y(t)-y(t)_{min}}{y(t)_{max}-y(t)_{min}}} \tag{2}\]  
Figure 2: Technology roadmap.  
In this equation, t represents the time at which the SIF time series is reconstructed, y(t) denotes the SIF value at time t, and y(t)\({}_{\text{min}}\) and y(t)\({}_{\text{max}}\) correspond to the minimum and maximum annual SIF values, respectively.  
Figure 3 illustrates a schematic representation of the dynamic threshold method. In this method, the time corresponding to a certain percentage (\(n\)) between the lowest point (SIF\({}_{\text{min}}\)) and the peak value (SIF\({}_{\text{max}}\)) on either side of the SIF fitting curve is labeled as the critical period of the phenology. During the ascending phase of the curve, the time at which the SIF reaches a value corresponding to a set percentage n is defined as the Start of Growing Season (SOS). In contrast, during the descending phase, the point where the SIF value aligns with the same percentage indicates the End of Growing Season (EOS), with the corresponding time marking this transition.  
SOS: Start of Growing Season; EOS: End of Growing Season; SIF\({}_{\text{max}}\): maximum value of Solar-Induced chlorophyll Fluorescence (SIF); SIF\({}_{\text{min}}\): minimum value of Solar-Induced chlorophyll Fluorescence.