## 2 Materials and Methods
### The BRIDGE DIAL Data Analysis Technique
#### 2.2.1 Preliminary Steps  
Generally, raw data are: (i) normalized by dividing the lidar signal by the laser energy; and (ii) background-noise subtracted [44]. Background noise here is measured by averaging the farthest part of the lidar echo (see Figure 2a(1)). To simplify, during its travel to distance R, the pulse energy decreases: (i) exponentially, due to air extinction; and as 1/R\({}^{2}\), simply because the detected photons are directly proportional to A/R\({}^{2}\) (i.e., the solid angle of the telescope), where A is its effective area. To compensate for this effect, the lidar signal P(R) (where P is the received power as a function of range R) is commonly transformed into the range-corrected signal (RCS). This is performed by multiplying the signal P(R) by R\({}^{2}\)[44] (see Figure 2a(2)). Finally, to further improve the SNR (Signal-to-noise Ratio), up to 100 laser shots have been averaged for every lidar return and a Savitzky-Golay filter [46] algorithm with 13 points was used (see Figure 2a(2)). 2.2 Conversion of RCS (Range Corrected Signal) Profiles Into Range-Resolved Profiles of in-Plume Excess CO\({}_{2}\) Concentrations  
The core of the BRIDGE DIAL technique consists of the following steps [21; 37; 38; 39; 40; 41; 42]:  
* Evaluation of CO\({}_{2}\) concentration in the natural background atmosphere (C\({}_{0}\)) outside the plume [39]. * Evaluation of the average excess CO\({}_{2}\) concentration (\(\Delta\)C) in the volcanic plume cross-section (e.g., between two rockfaces as shown in Figure 1[39]) encountered along the laser optical path in the examined region with respect to C\({}_{0}\). * Calculation of the range-resolved excess of in-plume CO\({}_{2}\) concentration, corresponding to each i-th ADC channel of the lidar profile from (see Figure 2b): \[\text{C}_{\text{CO${}_{2}$i}}=\text{ k\cdot RCS}_{\text{i}}\] (1) \[\text{k}=\frac{\Delta\text{C}(\text{R}_{1}-\text{R}_{2})}{\Delta\text{R}\sum _{i}\text{RCS}_{\text{i}}}\] (2)where k is the multiplication factor; \(\Delta\)C--as we mentioned--is the average excess carbon dioxide concentration measured between the two rockfaces and is inferred from the ratio of the corresponding two lidar echoes; R\({}_{1}\) and R\({}_{2}\) indicate the ranges of the two rockfaces; \(\Delta\)R is the range interval corresponding to an ADC channel; and RCS is the range corrected signal. It should be noted that, during the in-field preliminary setup, the system was optimized to perform measurements in selected directions, where one or more topographic targets were partially inside the lidar FOV (Field of View). This allowed us to retrieve some useful parameters (see C\({}_{0}\), \(\Delta\)C, and k) for the initialization of the data analysis technique. Once the multiplication factor is known, it is possible to perform sequential measurements multiplying each range-corrected lidar profile by this factor, within the limits of the expected dispersal area of volcanic plume. * Drawing CO\({}_{2}\) dispersion maps by scanning the selected region and arranging subsequent concentration profiles (acquired at different scanning angles and relative to the same scan) in chronological order. Figure 2: **(a)** Example of a lidar profile acquired during the Stromboli volcano field campaign on 26 June 2015. (1) Data profiles in the form of signal intensity (arbitrary units, a.u.) vs. range (in meters) cleaned by the noise. (2) Detail of the experimental RCS (Range Corrected Signal) and filtering of the OFF channel using a Savitzky–Golay filter algorithm with 13 points in which the plume peak is visible between two rockfaces in the range interval between 1800 and 2900 m. The laboratory peak in (1) provides the start time of the pulse emission and is due to the reflection of some laser radiation inside the mobile laboratory. The two rockface peaks (2), as their name indicates, are due to pulse backscattering by the rockfaces of Stromboli. Finally, the peaks from 2200 to 2700 m are linked to the backscattering of the laser pulse from the plume.