## 2 Materials and Methods
### Robust ASTER Thermal Anomaly System (RASTer)  
In this paper, we implemented the RST algorithm under GEE by analyzing the signal measured in the ASTER channel 13, which is centered at 10.6 \(\upmu\)m (see Table 1). The index in Equation (1) is then calculated pixel by pixel, according to the general RST prescriptions:  
\[\otimes_{TIR}(x,y,t)=\frac{BT_{10.6}(x,y,t)-\mu_{BT_{10.6}}(x,y)}{\sigma_{BT_{ 10.6}}(x,y)} \tag{2}\]  
In Equation (2), the role of the variable \(V(x,y,t)\) is played by the brightness temperature \(BT_{10.6}(x,y,t)\) measured at the Top of Atmosphere (TOA) at around 10.6 \(\upmu\)m (band 13), \(\mu_{BT_{10.6}}(x,y)\), and \(\sigma_{BT_{10.6}}(x,y)\) are the temporal mean and standard deviation computed for each location (\(x\),\(y\)) over 20 years (i.e., 2000-2020) of ASTER observations (e.g., a total of 635 ASTER images were analyzed to generate the spectral reference fields at Shinmoedake).  
\begin{table}
\begin{tabular}{c c c} \hline
**Name** & **Resolution** & **Wavelength** \\ \hline B01 & 15 m & 0.520–0.600 \(\upmu\)m \\ B02 & 15 m & 0.630–0.690 \(\upmu\)m \\ B3N & 15 m & 0.780–0.860 \(\upmu\)m \\ B04 * & 30 m & 1.600–1.700 \(\upmu\)m \\ B05 * & 30 m & 2.145–2.185 \(\upmu\)m \\ B06 * & 30 m & 2.185–2.225 \(\upmu\)m \\ B07 * & 30 m & 2.235–2.285 \(\upmu\)m \\ B08 * & 30 m & 2.295–2.365 \(\upmu\)m \\ B09 * & 30 m & 2.360–2.430 \(\upmu\)m \\ B10 & 90 m & 8.125–8.475 \(\upmu\)m \\ B11 & 90 m & 8.475–8.825 \(\upmu\)m \\ B12 & 90 m & 8.925–9.275 \(\upmu\)m \\ B13 & 90 m & 10.250–10.950 \(\upmu\)m \\ B14 & 90 m & 10.950–11.650 \(\upmu\)m \\ \hline \end{tabular} \({}^{*}\)Operational until April 2008.  
\end{table}
Table 1: Spatial and spectral resolutions of the ASTER bands.  
The \(\otimes_{TIR}(x,y,t)\) index is a standardized variable having a Gaussian behavior. Hence, pixels having values of \(\otimes_{TIR}(x,y,t)>3\) have a probability around 99.85% of being anomalous (e.g., [13]). As discussed in previous studies, the ALICE index is intrinsically protected against site effects (e.g., natural warming of volcanic rocks [2]). On the other hand, in this work, due to a dataset much less populated than other sensors (in average 25-35 ASTER daytime/nighttime images per month, spanning over twenty years of observations, are available), we used a normalized index in combination with that in Equation (1) to also detect subtle hotspots with a high confidence level of detection:  
\[ND_{B12-B13}(x,y,t)=\frac{BT_{9,1}(x,y,t)-BT_{10,6}(x,y,t)}{BT_{9,1}(x,y,t)+BT_ {10,6}(x,y,t)} \tag{3}\]  
In Equation (3), \(BT_{9.1}(x,y,t)\) and \(BT_{10.6}(x,y,t)\) are the brightness temperatures measured at \(\
eg 9.1\)\(\upmu\)m (i.e., band 12) and \(\
eg 10.6\)\(\upmu\)m (i.e., band 13). TOA (Top of Atmosphere) BT values were calculated from the radiance at sensor. High-temperature targets, emitting strongly at shorter rather than longer TIR wavelengths, should lead to positive values of the \(ND_{B12-B13}\) index. Hence, RASTer identifies thermal anomaly if at least one of the following conditions is satisfied:  
\[\left\{\begin{array}{c}\otimes_{TIR}(x,y,t)\geq 4\;(high\;intensity\; hot\;spots)\\ OR\\ \otimes_{TIR}(x,y,t)\geq 3\;AND\;ND_{B12-B13}(x,y,t)>0\\ (mid-low\;intensity\;hot\;spots)\end{array}\right. \tag{4}\]  
The first test enables the identification of high-temperature features such as lava flows, while the second one should favor the identification of less intense hotspots (e.g., those associated with a mid-low Strombolian activity), increasing the confidence level of detection by combining the two above defined indices (i.e., \(\otimes_{TIR}(x,y,t)\) and \(ND_{B12-B13}\)).