## 2 H\({}_{2}\)O Collisional Broadening Measurements
### Setup for H\({}_{2}\)O Self-Broadening and Temperature Dependence at 1.37 \(\mu m\)
#### 2.1.1 H\({}_{2}\)O Self-Broadening at 1.37 um  
Typical spectra measured with the setup in Figure 1 are shown in Figure 2a. The absorbance data in Figure 2a were derived using measured H\({}_{2}\)O signals and a background 3 rd order polynomial similar to [4; 38]. It should be noted here that, for this work, we worked with a single path setup, i.e., there was no monitor detector recording the background signal. The background was reconstructed from the fit to the measured signal. This avoided the typical differential offsets in dual channel setups. The linear absolute wavenumber axis was restored via the dynamic tuning coefficients derived by means of signals measured with an air-spaced etalon similar to [4; 18; 22; 38; 39] and the H\({}_{2}\)O line position (-7299.432 cm\({}^{-1}\)) as an absolute wavelength reference point. The wavenumber axis was derived with a long-term repeatability uncertainty of 1% and a significantly higher precision, with this small deviation showing a good linearity. The retrieved FWHM of the fitted absorption line was influenced by the uncertainty of the wavenumber axis coefficient of 1% that was one part of the total uncertainty attributed to the Lorentzian FWHM. A Voigt profile was fitted to the data in order to derive the FWHM of the H\({}_{2}\)O line at 7299.43 cm\({}^{-1}\). The fitting was performed with the line area kept free and a fixed Doppler width calculated using the measured gas temperature. It should be noted here that the flat residual structures (e.g., in Figure 2a) in this work show that the Voigt profile was appropriate to fit all data, and indicate that there was no need to use higher order line profiles like Galatry or Hartmann-Tran [40; 41; 42]. The peak absorbance for the data in Figure 2a was 0.06. For the data in Figure 2a, we calculated a standard deviation noise level from the residuals as \(\sigma_{\mathrm{total}}=7\times 10^{-4}\) (see bottom panel of Figure 2a), corresponding to a signal to noise ratio of 85. Employing the \(\sigma_{\mathrm{local}}=5\times 10^{-4}\) value, an optimal signal to noise ratio of 120 was reached for the H\({}_{2}\)O self-broadening measurements. From Equation (1), and for self-broadening exclusively, there is no foreign molecule in the H\({}_{2}\)O sample, and the Lorentzian FWHM at the gas temperature \(T=296\) K can be expressed as  
\[\Delta v_{L}=2\cdot p_{\mathrm{H2O}}\cdot\gamma_{\mathrm{H2O}} \tag{2}\]  
The bottom panel of Figure 2b depicts a plot of the Lorentzian FWHM (y-axis, left), derived from consecutive measurements similar to the data in Figure 2a as the gas pressure in the cell was varied (the gas temperature maintained at 296 K) by means of the valve V\({}_{4}\) (filling the gas cell in steps by slowly opening the valve) in Figure 1, as a function of the  
Figure 1: Schematic of the setup used for self-broadening measurements and temperature dependence. Det: detector. measurement number. The top panel of Figure 2b shows the measured gas temperature (the gas temperature was kept constant at 296 K (1\(\sigma\) = 32 mK)) across all measurements. The right y-axis of Figure 2b shows the gas pressure measured at different values of the FWHM. As indicated by the dotted red boxes, 50 consecutive measurements were used to determine the repeatability (calculated as the standard deviation of the mean) of the measured Lorentzian width of 5.66 \(\times\) 10\({}^{-5}\) cm\({}^{-1}\), i.e., 0.46% at, e.g., the FWHM of 0.012391 cm\({}^{-1}\). We note here that the relative uncertainty from fitting to derive the Lorentzian FWHM was estimated to be 1.1%. This value was calculated from the statistical uncertainty (repeatability: 0.46%) and the uncertainty of 1% (estimated here based on our experiences [9; 18]) due to lack of knowledge on the accuracy of the Voigt profile to fit H\({}_{2}\)O spectra as observed in [43]. This uncertainty component (1.1%) combined with the uncertainty of the wavenumber axis (1%, similar to [18]) was used to evaluate the combined uncertainty of the retrieved Lorentzian FWHM of 1.5% (relative).