## 2 H\({}_{2}\)O Collisional Broadening Measurements
### Setup for H\({}_{2}\)O Self-Broadening and Temperature Dependence at 1.37 \(\mu m\)
#### 2.1.2 Temperature Dependence of H\({}_{2}\)O Self-Broadening  
The temperature of the water bath (and thus the gas cell as measured by the PT100 in Figure 1) was varied from 296-348 K, while the preparation chamber (with the water sample) was connected to the gas cell (V\({}_{4}\) opened). As the temperature of the gas cell and the H\({}_{2}\)O gas increased, the H\({}_{2}\)O pressure correspondingly increased from 26 hPa to 230 hPa and was recorded by the pressure sensor. Figure 4a depicts spectra (derived similarly as for Figure 2a) measured at the different temperatures and pressures, and showing the increased self-broadening of the H\({}_{2}\)O absorption line. A Voigt profile was fitted (in the same manner as in Figure 2a) to the data in Figure 4a in order to derive the Lorentzian FWHM. The bottom panel of Figure 4a depicts the residuals from a Voigt fit. Using the peak absorbance of 0.07 and 1\(\sigma_{\text{total}}\) = 1\(\times\)10\({}^{-3}\), a signal to noise (S/N) ratio of 70 was found for the data in Figure 4a. Employing 1\(\sigma_{\text{Local}}\) = 5 \(\times\) 10\({}^{-4}\) from the bottom panel of Figure 4a, an optimum S/N of 140 could be reached for the measurements.  
Figure 4: H\({}_{2}\)O self-broadening measurements. (**a**) Plot of the measured absorbance data at different temperatures and pressures as a function of wavenumber. Voigt profiles (solid lines with different colors) are fitted to the measured data. Bottom panel: residuals from the different Voigt fits. (**b**) A GLR applied to \(ln(\Delta v_{L}/(2\cdot\gamma_{\text{H2O}}\cdot p_{H2})\) versus \(ln(T_{0}/T)\) to determine the temperature dependence exponent of self-broadening \(n_{\text{H2O}}\). Root mean square of the error (RMS error): 1.12 \(\times\) 10\({}^{-16}\). Top panel: measured gas temperature at the respective points.  
Figure 3: Measured Lorentzian FWHM of H\({}_{2}\)O versus measured water vapor pressure (\(p_{\text{H2O}}\)). A generalized linear regression (GLR, solid blue line) was applied to the data. The bottom panel depicts the residuals from the GLR fit.  
Considering the first term of Equation (1), the temperature dependence exponent \(n_{\rm H2O}\) can be derived from the following expression:  
\[ln\left(\frac{\Delta v_{L}}{2\cdot\gamma_{\rm H2O}\cdot p_{\rm H2O}}\right)=n_{ \rm H2O}\cdot ln\left(\frac{T_{0}}{T}\right) \tag{3}\]  
Figure 4b shows a plot of \(ln(\Delta v_{L}/(2\cdot\gamma_{\rm H2O}\cdot p_{\rm H2O}))\) as a function of \(ln(T_{0}/T)\). The uncertainties on both axes were estimated using the respective uncertainties of \(\Delta v_{L}\), \(\gamma_{\rm H2O}\), \(p_{\rm H2O}\) and \(T\), i.e., 1.5 %, 2.8 %, 1.2 % at 28.6 hPa and 0.5 % relative, respectively. A GLR was applied to the data in Figure 4b, resulting in a slope value of \(n_{\rm s}=n_{\rm H2O}\) of 0.692 \(\pm\) 0.011, \(k=1\), for the H\({}_{2}\)O absorption line at 7299.43 cm\({}^{-1}\). The uncertainty of 0.017 corresponds to 1.6% relative. The bottom panel of Figure 4b depicts the residuals from the GLR and the top panel the measured gas temperature at the respective measurement points.