## 2 H\({}_{2}\)O Collisional Broadening Measurements
### H\({}_{2}\)O Air Broadening and Temperature Dependence at 1.37 \(\mu m\)
#### 2.2.2 Temperature Dependence of H\({}_{2}\)O Air Broadening  
In order to derive the temperature dependence coefficient of air broadening, the 20 cm gas cell was replaced by a heatable 38 cm single-pass gas cell (SITEC) with the cell body temperature sensor and the static/no flow pressure sensor directly connected to the gas cell. Due to the design and position of the pressure sensor, and similarly as for other experiments in this work, it was assumed that there was no pressure drop between the sensor and the gas cell. The temperature stability and gradient across the gas cell were better than 0.5 K and about 2 K. For the temperature dependence measurements using this spectroscopic system and also probing the H\({}_{2}\)O line at 7299.43 cm\({}^{-1}\), a umol/mol-level H\({}_{2}\)O in air mixture was prepared by manometric mixing in the 38 cm gas cell and the temperature of the gas cell (and thus the gas temperature) was varied from 290-600 K.  
Figure 6a depicts typical absorbance data (derived similarly as for Figure 2a, measured at 293 K and 473 K, 100 averaged scans) for the temperature dependence measurements of air broadening. The data were fitted with a Voigt profile, similar to Figure 2a, to derive the Lorentzian FWHM (\(\Delta\
u_{L}\)). The bottom panel of Figure 6a shows the residuals from the Voigt fit with 1\(\sigma_{\text{total}}\) = 1.05 \(\times\) 10\({}^{-3}\) and 1\(\sigma_{\text{total}}\) = 1.11 \(\times\) 10\({}^{-3}\) for the data at 293 K and 473 K, respectively. Using the residuals from the fits and the respective peak absorbances of 0.55 (at 293 K) and 0.43 (at 473 K), S/N values of 523 and 387 were found, respectively. The residual structures in Figure 6a are observed to be a result of the possible systematic deficiencies of the Voigt profile to model higher order line shape contributions like the Hartmann-Tran profile [40; 41; 42]. This is accounted for by the uncertainty of 1% attributed to the use of this line profile.  
With the measured values of \(\gamma_{\text{H2O}}\) (at (296.00 \(\pm\) 1.00) K), \(n_{\text{H2O}}\) and \(\gamma_{\text{air}}\) (at (295.04 \(\pm\) 1.00) K, covering the temperature of 296 K), and utilizing Equation (1), the temperature dependence exponent \(n_{\text{air}}\) can be derived by means of Equation (5),  
\[ln\bigg{(}\frac{(\Delta\
u_{L}/2)-\gamma_{\text{H2O}}\cdot p_{\text{H2O}}\cdot \left(T_{0}/T\right)^{n_{\text{H2O}}}}{\gamma_{\text{air}}\cdot p_{\text{air} }}\bigg{)}=n_{\text{air}}\cdot ln\bigg{(}\frac{T_{0}}{T}\bigg{)} \tag{5}\]  
Figure 6b depicts a plot of measured \(ln(((\Delta\
u_{L}/2)-\gamma_{\text{H2O}}\cdot p_{\text{H2O}}\cdot\left(T_{0}/ T\right)^{n_{\text{H2O}}})/\gamma_{\text{air}}\cdot p_{\text{air}})\) as a function of \(ln(T_{0}/T)\). A GLR was applied to the data in Figure 6b, with the slope value of 0.761 \(\pm\) 0.017 taken as the temperature dependence coefficient of air broadening \(n_{\text{air}}\). The combined uncertainty of 0.017 corresponds to a relative uncertainty of 2.2%, \(k=1\).  
Figure 6: (**a**) Temperature dependence exponent of air broadening: absorbance data at 293 K and 473 K. (**b**) A GLR linear regression applied to measured data to determine the temperature dependence coefficient of air broadening. RMS error: 1.30 \(\times\) 10\({}^{-16}\).