## 4 Validation
### Validation Datasets
#### 4.1.1 IGBP Stable Samples and Simulated Changes  
We acquired the reference land-cover labels for 402 pixels in MODIS tile h11v05 from the Land Cover and Surface Climate Group at Boston University. All pixels represent stable land cover from 2000 to 2012. The reference dataset were derived from and systematically maintained by manual interpretation of Landsat Thematic Mapper (TM) data, Landsat 7 data, orthorectified Geocover 2000 imagery, augmented by ancillary map data and Google Earth\({}^{\copyright\copyright\) imagery [29,30]. The dataset includes six IGBP land-cover classes (Table 1).  
Based on the six stable land-cover classes, we simulated land-cover changes by combining truncated time series that represent stable land cover. Specifically, let \(\boldsymbol{w}=\left\{w_{j}\left|j=1,...,C\right.\right\}\) denote the set of land-cover classes and \(\left(Y_{1}^{w_{j}},Y_{2}^{w_{j}},...,Y_{n}^{w_{j}}\right.)\) denote a time series of class \(w_{j}\) with n observations in a time period of T. A change from class \(w_{1}\) to class \(w_{2}\) may be simulated as  
\[\left(Y_{1}^{w_{1}},...,Y_{n-1}^{w_{1}},Y_{n}^{w_{2}},Y_{n+1}^{w_{2}},...,Y_{n }^{w_{2}}\right), \tag{6}\]  
where \(t^{*}\in\left\{1,2,...,n\right\}\) is the index of the change date. The index \(t^{*}\) can be simulated by drawing a random number from \(\left\{1,2,...,n\right\}.\) In addition, the simulated land-cover changes were assumed to obey the rules of a logical transition as defined in [PERSON] _et al._[31]. For instance, the simulated time series represent land-cover changes such as forest disturbance (e.g., forest \(\rightarrow\) grassland) or human activities (e.g., grassland \(\rightarrow\) cropland). We have simulated six types of land-cover changes containing one change, four types containing two changes, and one type containing three changes within the same time period of the real NDVI time series. Totally, 1200 time series were simulated for each change intensity level. The stable time series used to simulate changes were randomly selected in each simulation process from the pool of time series of corresponding land-cover classes out of the four grouped classes (Figure 4).  
\begin{table}
\begin{tabular}{c c c} \hline
**Index** & **IGBP Land-Cover Class** & **Definition** \\ \hline
1 & Deciduous broadleaf forest &
\begin{tabular}{c} Lands dominated by woody vegetation with a percent cover \(>\)60\% and height exceeding 2 m. \\ \end{tabular} \\ \hline
2 & Mixed forest &
\begin{tabular}{c} Lands dominated by trees with a percent cover \(>\)60\% and height exceeding 2 m. \\ \end{tabular} \\ \hline
3 & Woody savannas &
\begin{tabular}{c} Lands with herbaceous and other understory systems, and with forest canopy cover between 30\% and 60\%. The forest cover height exceeds 2 m. \\ \end{tabular} \\ \hline
4 & Permanent wetlands &
\begin{tabular}{c} Lands with a permanent mixture of water and herbaceous or woody vegetation. The vegetation can be present either in salt, brackish, or fresh water. \\ \end{tabular} \\ \hline
5 & Croplands &
\begin{tabular}{c} Lands covered with temporary crops followed by harvest and a bare soil period (e.g., single and multiple cropping systems). Note that perennial woody crops will be classified as the appropriate forest or shrub land-cover type. \\ \end{tabular} \\ \hline
6 & Croplands/natural vegetation &
\begin{tabular}{c} Lands with a mosaic of croplands, forests, shrubland, and grasslands in which no one component comprises more than 60\% of the landscape. \\ \end{tabular} \\ \hline \end{tabular}
\end{table}
Table 1: IGBP (International Geosphere–Biosphere Program) land-cover classes and definitions (modified from [30]).  
The stable IGBP time series were stratified for the six land-cover classes and randomly partitioned into two halves, one for algorithm training and the other for accuracy assessment. Similarly, the simulated time series were randomly partitioned into two halves with stratification for the three change intensities and corresponding change types.