2.2.1. Phenology Extraction

Due to cloud, atmosphere and snow contamination, we used Savitzky–Golay filtering to smooth the time series of GOSIF and MODIS EVI. Then, a double logistic function was fitted based on the smoothed time series to generate continuous curves. The double logistic is a flexible model for monitoring seasonal and inter-annual land surface dynamics based on satellite data, which has been widely used for various vegetation types at global or regional scales [30,31]. The double logistic function can be written as follows:

$$V(t) = V\_{\min} + (V\_{\max} - V\_{\min}) \times \left(\frac{1}{1 + e^{-mS \times (t - S)}} + \frac{1}{1 + e^{mA \times (t - A)}} - 1\right) \tag{1}$$

where *V*(*t*) is the value of vegetation proxies (i.e., GOSIF or MODIS EVI) at day of the year (DOY) *t*, *V*max is the maximum vegetation proxies in the year, *V*min is the minimum vegetation proxies in the year, *mS* and *mA* are the maximum slope of the curve in green up and in senescence, respectively, *S* and *A* are their corresponding DOYs. Finally, the SOS and EOS were estimated as follows [32]:

$$SOS = \frac{2\ln(\sqrt{3} - \sqrt{2})}{mS} + S \tag{2}$$

$$EOS = \frac{2\ln(\sqrt{3} - \sqrt{2})}{mA} + A \tag{3}$$

#### 2.2.2. Determination of Climate-Limited Area

We used long-term monthly average climate data to develop scaling factors (0–1) (refer to the climatic limitation index) [24]. The temperature limitation index, radiation limitation index and water limitation index were calculated using the criteria proposed by Nemani et al. [24] as follows:

$$IT = \begin{cases} \begin{array}{c} 1 - \frac{T\_{\text{min}} - TM\_{\text{min}}}{TM\_{\text{max}} - TM\_{\text{min}}}, TM\_{\text{min}} < T\_{\text{min}} < TM\_{\text{max}}\\ \begin{array}{c} 1, T\_{\text{min}} < TM\_{\text{min}}\\ 0, T\_{\text{min}} > TM\_{\text{max}} \end{array} \end{array} \tag{4}$$

where *iT* is the temperature limitation index, *T*min is the daily minimum temperature, *TM*min and *TM*max are the thresholds of the daily minimum temperature, which were set as −5 ◦C and 5 ◦C in this study, respectively.

$$R = \begin{cases} 1 - \frac{K\_{\text{max}} - RM\_{\text{min}}}{RM\_{\text{max}} - RM\_{\text{min}}}, RM\_{\text{min}} < R\_{\text{max}} < RM\_{\text{max}}\\ 1, R\_{\text{mean}} < RM\_{\text{min}}\\ 0, R\_{\text{mean}} > RM\_{\text{max}} \end{cases} \tag{5}$$

where *iR* is the radiation limitation index, *R*mean is the daily mean PAR, *RM*min and *RM*max are the thresholds of the daily mean PAR, which were set as 75 W and 150 W, respectively. In addition, we used the ratio of precipitation to potential evapotranspiration (*P*/*PET*) as an indicator of water-limited conditions, as below:

$$
\delta \mathcal{W} = \begin{cases}
1 - \frac{P}{\sqrt{P^\* \ast P \ast T} \cdot \frac{P}{P \ast T}} < 0.75 \\
0, \frac{P}{P \ast T} \ge 0.75
\end{cases}
\tag{6}
$$

The spatial patterns of the three climatic limitation indices are shown in Figure 1a. For classification, we define the pixels as the dominant temperature-limited area if: (1) *iT* is higher than *iR* and *iW*, and (2) *iT* is larger than 0.25. Radiation-limited areas and water-limited areas were determined by the same criteria. We determined the pixels as having no climatic limitation where *iT*, *iR* and *iW* are all lower than 0.25 (Figure 1b).

**Figure 1.** Spatial pattern of climatic limitations in China (**a**) and dominant climatic limitations (**b**).

#### 2.2.3. Relationship of Phenology Derived from SIF and EVI and Climatic Limitations

We randomly sampled 5000 pixels for each climate-limited area and adopted linear correlation regression analysis to explore the relationship between phenology generated using SIF and EVI and the dominant climatic limiting factors. Furthermore, we adopted the *C*-index proposed by Garonna et al. [33] to quantify the relative contributions of phenology derived from SIF and EVI to their differences with climatic limitation indices [34], which were calculated as follows:

$$\mathcal{C} = \frac{|\mathcal{S}\_{\rm SIF}| - |\mathcal{S}\_{\rm EVI}|}{|\mathcal{S}\_{\rm SIF}| + |\mathcal{S}\_{\rm EVI}|} \tag{7}$$

where *S*SIF or *S*EVI is the gradient (i.e., slope) of linear regression relationships between SOS/EOS generated using SIF or EVI and climatic limitation indices. As the *C*-index is unitless, ranging from −1 to 1, the contribution ratio based on the *C*-index (*Cr*) can be calculated as Equation (8). If the *Cr* of phenology from SIF or EVI is larger than 50%, this means that this factor is mostly attributable to the difference of phenology between SIF and EVI under climatic limitations.

$$\mathcal{C}\_{I} = \frac{1+\mathcal{C}}{2} \times 100\% \tag{8}$$
