## 2 Materials and Methods
### The BILLI System
The specifications of the whole system are reported in Table 1, and more details are available in previous works [21; 37; 38; 39; 40; 41; 42]. From Table 1, it is possible to note that, with respect to the Pozzuoli Solfatara field campaign [21; 37; 38], the operative wavelengths were slightly changed during the campaign carried out at Stromboli and Mt. Etna [39; 40; 41; 42]. This was due to the different mode of operation of the system. In fact, in the first campaign, the line (2012.194 nm) was selected looking for low cross-sensitivity to water vapor and high absorption coefficient [37; 38] that was optimum for short-range measurements of CO\({}_{2}\) concentration, whereas, in the other cases, the main goal was to reach longer ranges. To do this, the differential absorption cross section of carbon dioxide (\(\Delta\sigma\)) was reduced and a different ON line (2009.537 nm) was chosen [39; 42]. For more details, see Table 2[21; 37; 38; 39; 40; 41; 42]. As will be shown in the following, it was observed that the measurement uncertainty was governed by instability in the wavelength set. For this reason, from the Stromboli campaign, a photo-acoustic cell--with CO\({}_{2}\) at atmospheric pressure and temperature--was mounted at the laser output, thus providing wavelength accuracy, repeatability, and stability, as has been shown in the laboratory [36; 37; 38; 39; 40; 41; 42]. \begin{table}
\begin{tabular}{c c c} \hline
**Transmitter** & Pulse energy & 25 mJ \\ \hline  & Pulse duration & 8 ns \\ \hline  & Repetition rate & 10 Hz \\ \hline  & Wavelengths & ON: 2009.537 nm, OFF: 2008.484 nm \\  & & _(Stromboli Volcano 2015, Mt. Etna 2016)_ \\ \hline  & & ON: 2012.194 nm, OFF: 2011.1 nm \\  & & _(Pozzuoli Solfatara 2014)_ \\ \hline  & Laser linewidth & 0.04 cm\({}^{-1}\) \\ \hline  & Beam divergence & 0.5 mrad \\ \hline
**Receiver** & Mirror coating & Al \\ \hline  & Clear aperture & 300 mm \\ \hline  & Focal length & 900 mm \\ \hline  & Field of View & 1 mrad \\ \hline
**Scanning elliptical mirrors** & Mirror coating & Al \\ \hline  & Clear aperture & 320 mm \(\times\) 451 mm \\ \hline
**Detector module** & Photodiode & InGaAs PIN \\ \hline  & Diameter & 1 mm \\ \hline  & Responsivity & 1.2 A\(\cdot W^{-1}\) \\ \hline  & Gain & 5.1:104 V\(\cdot\)A\({}^{-1}\) \\ \hline  & NEP & 10 pW\(\cdot\)Hz\({}^{-1/2}\) \\ \hline  & Bandwidth & 0–10 MHz \\ \hline
**Analog-to-digital converter** & Dynamic range & 14 bit \\ \cline{2-2} (ADC) & Sampling rate & 100 MS\(\cdot\)s\({}^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Main specifications of the BILLI system during the BRIDGE field campaigns. Moreover, a new version of the software was developed: the step motor that modifies the resonator cavity inside the dye laser now allows one to shift the emitted wavelength, and the photo-acoustic signal was measured, averaging for 1 s (i.e., for 10 laser shots). In this way, the wavelength shown by the laser monitor can be corrected for a small shift (0.12 cm\({}^{-1}\)) and the experiment and theory [45] agreed within the linewidth of the emitted pulse (0.04 cm\({}^{-1}\)). This leads to being able to control the wavelength with the photo-acoustic cell before every lidar measurement, so that the operator can fix the ON and OFF wavelengths with a smaller error than the emitted linewidth [39]. Therefore, a gradual refinement of the system performances was obtained in the last two in-field campaigns, thanks to the following measures:  
* an appropriate choice of CO\({}_{2}\) absorption cross section, which enabled both short- and long-range measurements;
* the implementation of the photo-acoustic cell, resulting in a containment of systematic uncertainty associated with measurements of CO\({}_{2}\) concentration (see Section 2.2.5); and
* the reduction of the laser beam divergence due to a better optical setting, resulting in an improvement in the signal-to-noise ratio (SNR). As will be shown in the following, this allowed us to detect CO\({}_{2}\) plume peaks beyond 4 km and to improve the accuracy of the CO\({}_{2}\) flux measurements.