# An Object- and Shapelet-Based Method for Mapping Planted Forest Dynamics from Landsat Time Series
## 2 Materials and Methods
### Methods
#### 2.2.4 Mood Median Test  
After implementing the detection algorithm, the best time-series shapelets were extracted for each forest object. Subsequently, a time-series object was identified as a planted forest if there was a significant difference between the shapelet and non-shapelet, or else it was classified as a natural forest. Here, the Mood median test (m-test) [55] was adopted to evaluate whether there was a significant difference in the NDVI medians for the two segments, which offered the benefit of being insensitive to outliers over the widely used Student's test [56]. More specifically, a contingency table was employed to record the numbers in each group (shapelet or non-shapelet) below and above the median value of the NDVI time series [57], and the m-test statistic chi-square (\(\chi^{2}\)) derived from the contingency table acted as a measurement for the discrepancy between the normal status and variations. For a given time-series shapelet \(\mathrm{S_{(p,l)}^{*}}\) of a forest object, its statistic \(\chi^{2}\) was calculated using the following formula:  
\[\chi^{2}=\sum_{k=1}^{T}\left(\frac{\left(\mathrm{A_{k}}-\mathrm{n_{k}}/2 \right)^{2}}{\mathrm{n_{k}}/2}+\frac{\left(\mathrm{B_{k}}-\mathrm{n_{k}}/2 \right)^{2}}{\mathrm{n_{k}}/2}\right) \tag{5}\]  
where r represents the number of groups, which is 2 in this study. \(\mathrm{A_{k}}\) and \(\mathrm{B_{k}}\) are the number of NDVI values in group k that are above or below the median of the entire time series, respectively; \(\mathrm{n_{k}}\) is the stand sample size in each group. The greater the value of the statistic \(\chi^{2}\), the more significant the difference. Referring to the historical high-resolution images from Google Earth and the NHAR forestry expert advice, five typical cases were used to illustrate how the m-test differentiated the planted forests from the natural forests. The shapelet segments are highlighted by the blue rectangles. Figure 5a shows that the difference between the shapelets and non-shapelets is not significant (\(\chi^{2}=2.59\)) because there are fewer outliers during the NDVI trajectory of the intact natural forest. For the time series of the natural forests affected by cloud noise (Figure 5b), its shapelet consists of a noise point and the points with higher NDVI values on both sides of the noise. Owing to the insensitivity of the m-test to the abrupt change-point in the time series, its statistical value (\(\chi^{2}=2.84\)) was relatively low. Impeded by harsh environmental conditions, only those subjected to relatively mild disturbances can recover in the short term (within one to four years), whereas others damaged by severe destruction have little chance to survive. Thus, we depict a quickly recovered natural forest object from disturbances (e.g., logging, and irregular rainfall) in Figure 5c, whose discrepancy (\(\chi^{2}=4.91\)) between the two segments is marginally larger. A planted forest object converted from grassland or cropland with a high statistical value (\(\chi^{2}=11.07\)) is shown in Figure 5d. Its shapelet, composed of low NDVI values caused by the site preparation, the adaptation period after seedling transplantation, and a low canopy density stage, is considerably different from the non-shapelet representing high vegetation cover. Figure 5e illustrates an example of the significant differences (\(\chi^{2}=14.72\)) between the shapelet and non-shapelet of the planted forests converted from bare land, corresponding to the low-vegetation-cover period before forest maturity and the latter period of high vegetation cover. Essentially, the difference between the two segments induced by planting events is larger than that induced by image noises and most of the disturbances, so that the statistic \(\chi^{2}\) of the planted forests is larger than that of the natural forests.