## 5 Results and Discussion
### Independent Random Samples  
Results for the random samples extracted from the sub-area are shown in Table 4. The values of the two parameters used in the simulated time series (refer to Section 4.3) were utilized to generate results for the random samples. Within the 244 samples, 77 time series represent changed land cover and 167 represent stable land cover. The SCD had greater omission errors than BFAST for changed land cover. cover, but fewer false changes for stable land cover. Such results indicate the SCD is more conservative compared to BFAST and tends to detect real change instead of false change with some degree of omissions. For the changed time series, SCD has a MSE of 0.06 for the number of detected changes and BFAST a MSE of 0.22, which is consistent with the characteristics indicated by omission errors. SCD generated a RMSE of 0.84 for the number of detected changes, which is very close to the RMSE for BFAST. The SCD was more accurate in determining the time of detected change compared to BFAST. SCD generated a RMSE of 4 steps, or the equivalent of about two months from the actual change time, whereas the BFAST had a RMSE of six steps, which is equivalent to more than three months. According to the MSE, the time of detected change estimated by both methods was later than the actual time in most cases, though SCD generated smaller bias than BFAST. Figure 7 shows the examples of changes detected in the time series for three pixels. The time series in Figure 7a recorded the changes from forest to bare soil earlier in the period (_i.e._, the forest had been cleared for industrial mining) and a return of grassland years later. According to visual inspection of the Landsat time series data, the two changes occurred in April 2003 and October 2006. SCD detected four changes, two of which matched the time of the actual changes identified from the time series of Landsat images. The other two also corresponded to observable shifts in NDVI values, though they may not have been associated with land-cover changes, or at least the changes were not recorded by the Landsat images. In contrast, BFAST only detected one change, the time of which was close to the second observed change in October 2006. Figure 7b shows a time series with similar land-cover trajectories, from forest to bare soil and then to grassland, as the time series in Figure 7a. SCD detected both change dates and they are close to the reference dates, which is more accurate than the result of BFAST for this time series. The time series shown in Figure 7c recorded a change from bare soil to grassland, where the change date detected by SCD is less accurate than the first change date detected by BFAST. The examples illustrate how SCD can be used to detect land-cover changes in a time series. The computation time required for the two methods is also reported in Table 4. The proposed SCD method cost much less time for processing 244 time series compared to the BFAST algorithm. Computation time may be a critical issue when large number of time series need to be analyzed, such as with global datasets. \begin{table}
\begin{tabular}{c c|c|c c|c c|c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c|}{**Stable (167)**} & \multicolumn{4}{c|}{**Changed (77)**} & \multirow{2}{*}{**Computational Time (Second)**} \\ \cline{2-2} \cline{4-7}  & **False Change** & **Omission Error** & & **Time Step** & \multicolumn{2}{c|}{**Number**} \\ \cline{3-7}  & **(pixel)** & **(pixel)** & **RMSE** & **MSE** & **RMSE** & **MSE** \\ \hline SCD & 21 & 15 & 4.05 & \(-\)0.26 & 0.93 & 0.10 & 16 \\ BFAST & 49 & 6 & 6.02 & 0.25 & 0.86 & 0.20 & 635 \\ \hline \hline \end{tabular} Note: in the first row, stable represents stable land-cover samples, and changed represents changed land-cover samples, and the number in the parenthesis is the number of samples; time step stands for the time of detected changes in the unit of step (16 days), and number stands for the number of detected changes.  
\end{table} 
Table 4: Summary of the results for the random samples in the sub-area.