## 3 Methods
### Iterative Algorithm to Detect Forest Disturbance  
The season-trend method is a linear regression model proposed by [PERSON] to account for seasonal and trend changes typically occurring within climate-driven biophysical indicators derived from satellite data [15; 16]. The model is an additive decomposition model, which is based on the characteristics of the periodic variation of remote sensing data from the vegetation-covered surface. It is assumed that the time series is mainly composed of seasons and trends; thus, the modeling results are obtained using the trends and seasons in the model sequence to be decomposed, as follows  
\[\mathrm{Y}_{t}=a_{1}+a_{2}t+\sum_{j=1}^{k}r_{j}\sin\biggl{(}\frac{2\pi jt}{f}+ \sigma_{j}\biggr{)}+\varepsilon_{t} \tag{1}\]  
where \(\mathrm{Y}_{t}\) is the time series observation at time \(t\), the intercept \(\alpha_{1}\), slope \(\alpha_{2}\), amplitudes \(\gamma_{j}\), and phases \(\delta_{j}\) are the unknown simulation parameters, \(k\) is the number of harmonic terms that should be specified manually, \(f\) is the frequency of the time series observations, and \(\varepsilon_{t}\) is the error term at time \(t\). We used three harmonic terms to robustly simulate phenological changes within GLASS LAI time series [34; 35]. The formula for LAI time series simulation can be expressed as follows  
\[Y(t)=a+b*t+c*sin\biggl{(}\frac{2\pi t}{f}+\sigma_{1}\biggr{)}+e*sin\biggl{(} \frac{4\pi t}{f}+\sigma_{2}\biggr{)}+g*sin\biggl{(}\frac{6\pi t}{f}+\sigma_{3} \biggr{)} \tag{2}\]  
Figure 2: Flow chart of the forest disturbance detection. LAI = leaf area index; DI = disturbance index; NBR = normalized burn ratio. In a large area of forest disturbance detection, the idea for monitoring techniques is simple. In this paper, the estimation of parameters was performed by iterating through the following steps until reaching the last value of the monitoring period or until a disturbance is detected:  
Step 1: Based on a given LAI time series (there are two parts of data: the mean phenological change of 1997-2001 and the year 2002, thus we call it background data), the Equation (2) was used to simulate the LAI time series, the initial simulation parameters (i.e., \(a\) and \(c\) in Equation (2)) were used as the reference parameters for detection. Step 2: The iterative procedure began with a simulation of Y (2003) of Equation (2) by using the season-trend method. The modeling data was a combination of background data and monitoring data. The first LAI data in 2003 was the starting point of the monitoring data for detection, and the parameters of the fitting model were calculated. Step 3: The size of the window was the same as the background data, the moving width of the window for monitoring data was equal to 1. When we add monitor LAI data to the end of the background data, the first of the background data is removed. The fitting model parameters obtained after adding the monitoring data were compared with the reference parameters to determine whether any change was detected. The mean LAI can represent the normal phenological pattern of forests. The LAI of the prior year shows whether forest growth has changed. Through the simulation of background data, the growth structure of the forest can be determined. It can be considered, as the phenology of the previous year occupied a higher weight in the simulation process. These time-stepping modeling processes were iterated until reaching the last value of the monitoring period or until disturbances are detected. Through analysis of the model parameters, the amplitude parameter was found to be the most sensitive to structural changes in the time series, as shown in Figure 3. For the detection of forest disturbances, we defined the DI\({}_{c}\) and DI\({}_{a}\) using the following formulas  
\[\left\{ \begin{array}{c}\mathrm{DI}_{c}=\frac{c_{n}-c_{0}}{c_{0}}<-0.1(c_{0} \
eq 0)\\ \mathrm{DI}_{a}=a_{n}-a_{0}>0.15\end{array} \right.