# Satellite and Ground Based Thermal Observation of the 2014 Effusive Eruption at Stromboli Volcano
## 3 TET-1 Data Processing Chain
### Area, Temperature and Volcanic Radiant Power of Lava Flow  
The visual analysis of TET-1 data showed that a static threshold (MIR radiance larger than 1 W/m\({}^{2}\)/sr/\(\upmu\)m) can be used to separate active lava flows on Stromboli from its background. This sort of threshold is not as sophisticated as common hotspot detection methods [43], but in our case it provided reliable results. Therefore, once the data are pre-processed, we estimated the temperature and the area covered by lava using the dual band method [20, 44]. The dual band method assumes that the pixel contains two components with different temperatures. Assuming that we know the temperature of one component, this method estimates the temperature of the second component and the partial area of both components. The assumption that merely two components cover the pixel is often unrealistic [45, 46, 47, 48, 49, 50]. A better solution is the method proposed by [PERSON] which assumes three components in a pixel [45]. However, as TET-1 provides only two suitable channels, we are left with the dual band method. In order to provide more robust results, we estimate the fractional area and the effective temperature of the lava (this is the integrated temperature of the lava crust and the lava core visible through cracks in the crust) for the entire cluster of lava pixels. Temperatures and fractions are calculated from [20, 44]:  
\[\begin{split} L_{MIR}&=p\cdot R\left(\lambda_{MIR},T _{hot}\right)+\left(1-p\right)\cdot R\left(\lambda_{MIR},T_{bckg}\right)\\ L_{TIR}&=p\cdot R\left(\lambda_{TIR},T_{hot} \right)+\left(1-p\right)\cdot R\left(\lambda_{TIR},T_{bckg}\right)\end{split} \tag{1}\]  
with the use of the Levenberg-Marquardt method [51, 52]. \(L_{MIR}\) and \(L_{TIR}\) are mean radiances of the lava flow in MIR and TIR bands corrected for the atmospheric effects and emissivity; \(p\) is the fractional area of a pixel covered by lava; \(R\) is Planck's function of a given wavelength \(\lambda\) and temperature of the lava flow \(T_{hot}\) or the background temperature \(T_{bckg}\). The background temperature is estimated from the TIR channel based on the pixels around the active lava flow.  
Volcanic radiant power is the most robust quantification of a thermal anomaly that can be compared among various instruments [53]. Volcanic radiant power (\(VRP\)) is also one of the parameters necessary to estimate time averaged lava discharge rates (Section 3.4) and magma flux rates in active lava lakes [54, 55]. \(VRP\) can be estimated from [PERSON]'s law [53], from a semi-empirical method based on the relationship between \(VRP\) and brightness temperature in the MIR spectrum [56], or using the spectral library approach [57]. [PERSON] _et al._[58] further showed that it is possible to estimate \(VRP\) with an accuracy of over 30% directly from unsaturated radiances in the MIR spectrum if the temperatures are above 600 K. Considering the robustness, we decided to isolate \(VRP\) of the lava flow from its background by adapting [PERSON]'s method [58] (Equation (2)):  
\[VRP=k_{inst}\cdot\left(L_{hot}-L_{bckg}\right) \tag{2}\]where \(k_{inst}\) is the coefficient unique to each instrument in nadir, and \(L_{hot}\) and \(L_{bkg}\) are the spectral radiances of the detected thermal anomaly and the background in the MIR band, respectively. For MODIS \(k_{inst}\) in nadir was estimated at \(1.89\times 10^{7}\) m\({}^{2}\). \(\upmu\)m\(\cdot\)sr [58], for TET-1 it was estimated with the same methodology to \(1.13\times 10^{5}\) m\({}^{2}\). \(\upmu\)m\(\cdot\)sr for a pixel at 40 m spatial resolution, and for observations from a boat (Section 4.1) at a distance of 2200 m the results showed a value of 33.3 m\({}^{2}\). \(\upmu\)m\(\cdot\)sr.