## 2 Materials and Methods
### Data Preprocessing
#### 2.3.1 Points Sampling and Quality Control  
The six kinds of datasets were processed using the following two steps. First, setting a mask for time series data with the quality control band provides the pixel quality status of each point in the time series. Second, to comprehensively analyze the reconstruction effects on the specific landcover types, the stable land cover type was defined as the land cover which has not been changed from 2001 to 2005, and eight stable land cover types were extracted from the MCD12Q1.006 [42] product for the period 2001-2005: evergreen needleleaf forests (ENF), evergreen broadleaf forests (EBF), deciduous needleleaf forests (DBF), deciduous broadleaf forests (DBF), mixed forests (MF), shrublands, savannas, grasslands, and croplands. Then, we selected 100 sampling points for each of the ENF, EBF, DBF, and MF datasets and 200 sampling points for each of the shrubland, savanna, grassland, and cropland datasets. The distribution of the sampling points and the stable land cover types are shown in Figure 2. The seasons in the northern hemisphere were defined as: winter, 1 December-28 February; spring, 1 March-31 May; summer, 1 June-31 August; and autumn, 1 September-30 November. Southern hemisphere seasons are exactly the opposite. For each sampling point in the different land cover types, five-year time series (2001-2005) were obtained according to these seasonal periods. Figure 2: Distribution of sampling points and stable land cover types. 13 kinds of stable land cover types from 2001 to 2005 are extracted from the MCD12Q1.006 product. For 9 kinds of vegetation land cover types, 100 sampling points for each of the ENF, EBF, DBF, and MF datasets and 200 sampling points for each of the shrubland, savanna, grassland, and cropland datasets are obtained. Noises in the time series can be reduced by methods, such as the maximum composite method (choosing the highest-quality pixel in a time interval [15]) and the typical time-series filter [36; 41; 43]. However, there were still spurious points that remained. Since outliers can deviate obviously from a gradually changing time series and always exhibit sudden increases or decreases, a series of algorithms were provided to recognize the spurious points in the time series. An outlier is defined based on two criteria. The first is that its value is greater/lower than the mean of its moving window plus/minus the cutoff (cutoff is twice the standard deviation of the points in the moving window [43]. In Equation (1), sigma (\(y(t-c)\), \(y(t-c+1)\),..., \(y(t)\), \(y(t+1)\),..., \(y(t+c)\)) is the standard deviation of the point values in the moving window). It is the serial number of time series points, where \(y(t)\) is the value of the \(t\)th time series point, \(c\) is half of the moving window size, and \(2c+1\) is the size of the moving window. \[ \begin{array}{l}y(t)<mean(y(t-c),y(t-c+1),\ldots,y(t),y(t+1),\ldots,y(t+c ))-cutoff\\ y(t)>mean(y(t-c),y(t-c+1),\ldots,y(t),y(t+1),\ldots,y(t+c))+cutoff\\ cutoff=2*sigma(y(t-c),y(t-c+1),\ldots,y(t),y(t+1),\ldots,y(t+c))\end{array}  \tag{1}\]  
In Equation (2), \(N_{K}\) is the value of the kth point; \(dN_{K-1}N_{K}\) is the inclining or declining slope from the \((k-1)\)th point \(N_{K-1}\) to the kth point \(N_{K}\); \(dN_{K}N_{K+1}\) is the inclining or declining slope from the \((k-1)\)th point \(N_{K}\) to the kth point \(N_{K+1}\); \(K\) is the serial number of the time series point; and \(ndt\) is the threshold of the time series points whose interval is \(n\)-day, which is defined as \(30\%/16\times n\) and equal to \(30\%\) when the temporal resolution is \(16\) days. The second criterion is that both \(dN_{K-1}N_{K}\) and \(dN_{K}N_{K+1}\) are larger than \(ndt\) or lower than \(-ndt\). \[ \begin{array}{l}dN_{K-1}N_{K}=\frac{N_{K-1}-N_{K}}{N_{K}}\times 100\%\\ dN_{K}N_{K+1}=\frac{N_{K+1}-N_{K}}{N_{K}}\times 100\%\\ ndt=30\%/16\times n\end{array}  \tag{2}\]  
If one of the above criteria is met, the point in the time series is defined as an outlier.