## 2 Data and Method
### Method
#### 2.3.2 Modeling of Vegetation Recovery  
Fire disturbances cause abrupt changes in the trend and seasonality of vegetation growth trajectories. Several studies concerning the regeneration of vegetation have proven that the NDVI is particularly useful for monitoring plant regrowth after fire disturbances [23, 24, 25]. To ascertain how long it takes burnt vegetation stands to return to their pre-fire average NDVI conditions, a relationship between pre- and post-fire NDVI values for a control scenario is necessary. The post-fire recovery also relies on the so-called healthy state [26]. Here, the healthy state is considered the theoretical potential vegetation attainable (\(\mathit{NDVI}_{\mathit{potential}}\)) by an ideal healthy state without any disturbance. Therefore, we define the stand regrowth index (SRI) at time \(t\) after the fire as  
\[\mathit{SRI}_{t}=\frac{\mathit{NDVI}_{\mathit{post},t}}{\mathit{NDVI}_{ \mathit{potential}}}\times\mathrm{100\%} \tag{2}\]  
where \(t\) is the elapsed year since the fire and \(\mathit{NDVI}_{\mathit{post},t}\) is the stand average annual NDVI at time \(t\). Moreover, \(\mathit{NDVI}_{\mathit{potential}}\) is the NDVI value of the healthy state, which is defined by the maximum NDVI value of the pre-fire period (1984-1986). Actually, it is very difficult or even impossible for all post-fire pixels to reach the healthy state. Therefore, stand regrowth index approaches 100% as time progresses following a fire disturbance. However, the rate never attains this value. Therefore, the growth rate can be used as a proxy for the vegetation recovery trend.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Year** & **Date** & **Sensor** & **Path/Row** \\ \hline
1986 & 5 June & TM & 121/23 \\
1987 & 24 June & TM & 121/23 \\
1987 & 15 June & TM & 121/22 \\
2000 & 19 June & ETM+ & 121/23 \\
2004 & 22 June & TM & 121/23 \\ \hline \end{tabular}
\end{table}
Table 1: Landsat TM and ETM+ scenes used in this analysis.  
Furthermore, inter-annual NDVI signals are also greatly influenced by climate changes, e.g., temperature and precipitation anomalies. With the goal of separating the inter-annual variations caused by climate from changes in NDVI and highlighting fire-induced effects on vegetation, another similar index using a control stand NDVI instead of the pre-fire NDVI has been used in numerous fire recovery studies [9, 27, 28]. This relative regrowth index (RRI) at time \(t\) can be expressed as follows:  
\[RRI_{t}= NDVI_{B,t}-NDVI_{C,t} \tag{3}\]  
where \(NDVI_{B,t}\) and \(NDVI_{C,t}\) are the average NDVI values of the burned area and unburned control plot, respectively, derived from the GIMMS NDVI.  
The advantage of using SRI to evaluate post-fire recovery is that it relates all post-fire NDVI values to the actual situation in the stand before the fire. However, pre-fire vegetation is specific to antecedent environmental conditions affecting vegetation growth. Hence, by utilizing an adjacent unburned control stand NDVI to derive the RRI, changes in environmental conditions are potentially captured by the NDVI signals throughout the analysis period [27]. It is very important for the calculation of the RRI that the selected control area has similar properties (e.g., vegetation type or climate) to the burnt area. The control area was required to have a long history without fire or other disturbances to ensure that it was not undergoing changes associated with vegetation recovery. To minimize differences in temperature and precipitation characteristics, the selected control area should have a similar elevation range to the burned area. In considering these premises, an adjacent area to the fire scar was chosen as the unburned control area (Figure 1).