## 5 Results and Discussion
### IGBP Simulated Time Series  
Table 3 shows the results of applying SCD to the simulated time series, which represents 11 land-cover change types. The values of 0.075 for \(\alpha\) and 1.0 for \(\beta\) were selected with training process. For the time series with intensity at one change, the RMSE of detected change date ranged from 4.6 to 8.2 steps across the six change types, with an overall of 6.8 steps (equivalent to 156 days). The MSE of detected change date ranged from 0.4 to 3.8 steps with an overall of 1.9 steps, indicating slightly overestimated change dates (later than the actual change dates). The RMSE of the number of changes varied around 2 and MSE varied around 1, which means the number of detected changes was overestimated for all six change types. The overall ratio of omission error is 11.2, or 67 out of 600 time series equivalently. Among the six change types, the change from grassland to wetland is associated with the greatest RMSE of detected change date and the most omission errors. A possible reason is that grassland and wetland likely have similar phenological characteristics and similar NDVI values in our dataset (refer to supplementary file). In addition, the time series of grassland and wetland were more sensitive to noise than the other classes (refer to Section 5.3). The change from forest to cropland had the second largest omission errors, which is possibly due to the greater inter-annual variation in the time series for forest or cropland, which can be confused with land-cover change occasionally.  
For the time series with intensity at two changes, the RMSE of detected change date ranged from 7 to 9 steps across the four change types. The overall RMSE of detected change date is about 1 step greater than the overall RMSE for the time series with intensity at one change. The MSE of detected change date ranged from \(-1.9\) to \(3.0\) steps with an overall of 0.6 steps, indicating slightly overestimation about the actual change date. The RMSE from 1.5 to 1.8 with an overall of 1.6, and MSE of the number of change ranged from 0.4 to 0.9, which are more accurate when compared with the results for the intensity at one change. In addition, the overall ratio of omission error is also smaller than that for the time series with intensity at one change. The results are interesting because the four change types simulated for the intensity at two changes are actually four different combinations of the six change types simulated for the intensity at one change; and the accuracy values are in certain degree mimic the average of the accuracy values for the associated change types.  
\begin{table}
\begin{tabular}{c|c c|c c} \hline \multirow{2}{*}{**IGBP Land-Cover Class**} & \multicolumn{2}{c|}{**Sample Size**} & \multicolumn{2}{c}{**False Change (pixel)**} \\ \cline{2-5}  & **Train** & **Test** & **SCD** & **BFAST** \\ \hline Deciduous broadleaf forest & 30 & 29 & 2 & 22 \\ Mixed forest & 39 & 39 & 1 & 26 \\ Woody savannas & 11 & 10 & 0 & 1 \\ Permanent wetlands & 15 & 15 & 0 & 7 \\ Croplands & 103 & 103 & 1 & 48 \\ Croplands/natural vegetation mosaic & 4 & 4 & 0 & 0 \\ All & 202 & 200 & 4 & 104 \\ Overall accuracy & & & 98\% & 48\% \\ \hline \end{tabular} Notes: train = training samples; test = testing samples; SCD = the proposed sub-annual change detection method; Overall accuracy is calculated as the ration of the overall false changes to the total number of tested stable time series.  
\end{table}
Table 2: Summary of the results for the stable samples.  
One change type was simulated for time series with intensity at three changes. The values of the five indices are close to the overall values of the indices for the time series with intensity at two changes.