## 3 Methods
### Development of the MODIS Time-Share Two-Stage CI Product
#### 3.2.2 MODIS Time-Share Two-Stage CI Product  
The processing flow and algorithm framework of this MODIS time-share two-stage CI product are shown in Figure 2 and Table 1. The MODIS LSP and MODIS 8-day CI products are used as input data to retrieve the SOS and EOS of each year, based on the \"greenup\" and \"dormancy\" bands of the MODIS LSP product. All CI values and corresponding QAs of the MODIS 8-day CI product in LOS and LFS in turn and the QA with the highest occurrence frequency in the MODIS 8-day CI will be set as the QA of the MODIS time-share two-stage CI. If the QAs ranging from 32,765 to 36,767 (representing snow, barren or sparsely vegetated areas, and water bodies) occur most frequently and contain other QAs in the MODIS 8-day CI, then the QA of the MODIS time-share two-stage CI is set to 4. If all the QAs are 32,765-36,767 8-day MODIS CIs, then both the MODIS time-share two-stage CI and its corresponding QA are set to the fill value of 32,767. Additionally, two algorithms were designed for the MODIS time-share two-stage CI. The first algorithm averages only the 8-day CIs corresponding to the QA with the highest frequency. The second algorithm averages the 8-day CIs corresponding to the QAs with frequencies less than and equal to the highest QA frequency. Finally, the two algorithms were applied to produce the global MODIS time-share two-stage CI products for 2008 and 2018, which were statistically evaluated to identify the optimal algorithm, and the time-share two-stage CIs obtained from the optimal algorithm were validated against field-measured CIs, resulting in the final MODIS time-share two-stage CI product. Furthermore, time-share two-stage CIs for each of the two vegetation cycles were derived based on the MODIS LSP product's distinction between annual and biannual vegetation. As a result, the MODIS time-share two-stage CI product produced in this study consists of eight bands: the first to fourth bands represent the estimated time-share two-stage CIs for each phenological stage of the vegetation cycle, and the fifth to eighth bands correspond to the QA values for each stage. The band settings are provided in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Most Frequent QA in**} & \multirow{2}{*}{**Output QA**} & \multicolumn{2}{c}{**Output CI**} \\ \cline{3-4}  & & **The First Algorithm** & **The Second Algorithm** \\ \hline
0 & 0 & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}=0)\) & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}=0)\) \\
1 & 1 & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}=1)\) & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}\leq 1)\) \\
2 & 2 & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}=2)\) & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}\leq 2)\) \\
3 & 3 & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}=3)\) & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}\leq 3)\) \\
32,765–32,767 (partial) & 4 & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}\leq 3)\) & \(Cl_{t}=\frac{1}{n}\sum\limits_{i=1}^{n}Cl_{i}\), \((CI_{t}\_QA_{i}\leq 3)\) \\
32,765–32,767 (all) & 32,767 & 32,767 & 32,767 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Development algorithm and quality assurance (QA) system of the MODIS time-share two-stage CI product.  
Figure 3: Diagram of the phenometrics retrieved for a single hypothetical vegetation cycle of the MODIS LSP product (MCD12Q2, V061).