# Satellite and Ground Based Thermal Observation of the 2014 Effusive Eruption at Stromboli Volcano
## 3 TET-1 Data Processing Chain
### Time Averaged Lava Discharge Rate  
Observations of the time averaged lava discharge rate (_TADR_) are crucial for the monitoring of on-going eruptions as well as for all studies that model lava flow and magma system dynamics. _TADR_ considers volume fluxes averaged over a given time period [23]. In Section 4, this is aggregated to the mean output rate, which equals the final volume of erupted lava divided by the total duration of the eruption [23].  
The methodology for obtaining _TADR_ from thermal imagery is based on the work of [PERSON] [59], [PERSON] [60], and [PERSON] _et al._[54]. It assumes a simple heat budget for an active lava flow. Heat is supplied to the flow by advection (\(Q_{adv}\)) and crystallization (\(Q_{cryst}\)) while cooling from the eruption temperature to the solidus temperature at which the motion ceases. Heat is lost from the flow surface by radiation (_VRP_), convection (\(Q_{conv}\)), and heat loss conductively through the flow base (\(Q_{cond}\)).  
The loss of heat through radiation (_VRP_) was described in Section 3.3. In order to estimate the heat removed by the convective motion in the air above the flow we need to know the temperature of the lava flow (Equation (1)):  
\[Q_{conv}=A\cdot p\cdot h_{c}\cdot\left(T_{hot}-T_{amb}\right) \tag{3}\]  
\(A\) represents the pixel area (in m\({}^{2}\)), while \(p\) represents the fractional area (computed with Equation (1)); \(h_{c}\) is the convective heat transfer coefficient (see Section 4); \(T_{hot}\) is the lava flow temperature computed with Equation (1); and \(T_{amb}\) is the ambient air temperature. Although heat loss is dominated by the loss through the surface, we also need to consider the conductive heat loss at the base of the flow:  
\[Q_{cond}=A\cdot p\cdot k\cdot\left(T_{core}-T_{base}\right)/h \tag{4}\]  
Once again, \(A\) represents the area covered by lava; \(k\) represents lava thermal conductivity (see Section 4); \(T_{core}\) is the temperature of the lava core; \(T_{base}\) is the temperature at the base of the flow; and \(h\) is the thickness of the thermal boundary layer, where the temperature decreases from \(T_{core}\) to \(T_{base}\). The heat supply from the advected heat is defined as:  
\[Q_{adv}=TADR\cdot\rho\cdot c_{p}\cdot\Delta T \tag{5}\]  
where _TADR_ is the time averaged lava discharge rate; \(\rho\) is lava density (see Section 4); \(c_{p}\) is the lava specific heat capacity; and \(\Delta T\) is the temperature difference between the eruption and solidus temperature. The heat supply from crystallization is defined as:  
\[Q_{cryst}=TADR\cdot\rho\cdot f\cdot L \tag{6}\]  
where \(f\) is the mass fraction of the post eruption crystallization and \(L\) is the latent heat of the crystallization. Rearranging the heat budget (_VRP_ + \(Q_{conv}\) + \(Q_{cond}\) = \(Q_{adv}\) + \(Q_{cryst}\)_) makes it possible to compute _TADR_ per pixel:  
\[TADR=\frac{k_{inst}\cdot\left[\left(L_{hot}-L_{bkg}\right)\right]+A\cdot p \cdot\left[h_{c}\cdot\left(T_{hot}-T_{amb}\right)+k\cdot\left(T_{core}-T_{ base}\right)/h\right]}{\rho\cdot\left(c_{p}\cdot\Delta T+f\cdot L\right)} \tag{7}\]  
Finally, the sum of values from all pixels covering the lava flow results in the total _TADR_. An alternative estimate of _TADR_ proposed by [PERSON] _et al._[61] is based on the radiant density \(c_{rad}\) (Equation (8)), a parameter related to the silica content (see also Section 5.2). We followed this approach in our analysis of MODVOLC data. However, we fitted the radiant density based on the TET-1 values of _VRP_ and _TADR_ (Section 4.2).  
\[c_{rad}=\frac{VRP}{TADR} \tag{8}\]