## 2 Materials and Methods
### Methods
#### 2.5.3 Phenological Transition Characterization  
With the phenological time-series curve smoothed and modelled as described in the previous sections, the focus now shifts to extracting critical transition points from the phenological curve for estimating crop physiological growth stages such as the jointing, tasseling, and silking stages. This study employs four widely recognized phenological characterization methods: threshold-based (TR), derivative-based (DB), curvature-based (CU) and Gu-based (GU), to identify these transition points. The transition points and corresponding lines for these methods are illustrated in Figure 2.  
The threshold-based (TR) method estimates three transition points in the phenological development curve by defining specific thresholds [41]. The thresholds can be defined as absolute values or relative values of the growing-season maximum value (amplitude of the curve) [74]. Relative studies have examined the performance of different thresholds settings in phenological monitoring [5, 74, 75, 76]. Because the SIF and EVI data adopted in this study range differently in growing-season phenological observation, with EVI data ranges from 0 to approximately 1 and the value of SIF data could exceed 1 or even 1.2, an absolute value as the threshold for both SIF and EVI data is not appropriate for further comparation. So, this study chose the 50% of the amplitude of the growing-season phenological curve as the threshold. Start of season (SOS) and end of season (EOS) are defined as the time when the threshold being reached at the upward and downward direction of the phenological curve, respectively, while peak of season (POS) is at the peak of the curve. The derivative-based (DB) method identifies the SOS, POS and EOS by examining local extremes in the first derivative of the phenological time-series curve. Specifically, as it is shown in Figure 2, the SOS and EOS of the DB method correspond to the absolute maximum and minimum points, respectively, of the first derivative curve of the model-fitted curve. And POS of DB method is defined as the zero point of the first derivative curve between the SOS and EOS. From the definition, it is obvious that the POS in the DB method aligns with the POS in the TR method. The curvature-based (CU) method characterizes crop phenophases based on local extremes in the rate of change (the second derivative) of the curvature of the phenological curve [31, 33]. As it is presented in Figure 2, this method extracts four transition points: greenup (GU), maturity (MT), senescence (SN) and dormancy (DM). GU and MT correspond to the two local maxima points in the second derivative curve of the first-half growing season, while SN and DM are defined as the two local minima points in the second derivative curve of the second-half growing season. If the maxima or minima cannot be reached, the CU method will keep on tracking the extreme points until reaching the boundary of the time range. In this study, the rotation points were recognized to divide the phenological observation of the whole year into two growing seasons of winter wheat and maize, which could cause a rapid change at the rotation points as it is illustrated in Figure 2. For winter wheat, some mis-recognitions of DM may occur due to the rapid change at the rotation points dividing the phenological observation of the entire year into two growing seasons. The Gu-based (GU) method is the most complex of the four, capturing four transition points: upturn (UD), stabilization (SD), downturn (DD), and recession (RD). It achieves this through a combination of local extremes in the first derivative curve and the boundary lines [73]. The boundary lines consist of a baseline and a plateau line, marking the minimum and maximum of the phenological curve, respectively. Additionally, this method models the trajectory of the growing-season phenological curve with a recovery line in the first-half growing season and a senescence line in the second-half.