## 2 Experimental  
Figure 1 depicts a schematic of the dTDLAS spectrometer for direct NO\({}_{2}\) measurements [43]. The instrument employs an interband cascade DFB laser (Nanolplus) emitting at 3.4 \(\upmu\)m, a 77 cm siliconert(r) coated stainless-steel single pass gas cell and a photovoltaic mid-infrared detector (Vigo system, detector diameter: 1 mm\({}^{2}\)). The sampling lines as well as the gas cell are coated to minimize the potential adsorption effects of NO\({}_{2}\) in the gas sample. For spectroscopic measurements, NO\({}_{2}\) gas samples flow (typical flow rate: 1.5 L/min) through the gas cell controlled by a mass flow controller (MFC, Bronkhorst) at the gas input and a valve at the output (connected to a pump) of the sampling lines as shown in Figure 1. The laser wavelength is swept at a frequency of 139.8 Hz (similar to [7; 8; 9; 10], and the collimated laser light is passed through the gas cell on to the detector. The signal from the detector, pre-amplified with a transimpedance amplifier (Femto DLPCA 200), is acquired using a data acquisition card (DAC, 18 bits, 625 KS/s NI PCI-6289) and is subsequently saved on a personal computer (PC) with a state-of-the-art operating system. Figure 2a depicts typical signals (with NO\({}_{2}\) absorption lines visible around 2919.6 cm\({}^{-1}\)) measured at 0.2 Hz (the measurement frequency for single scan measurements is 18 Hz, i.e., \(\sim\)0.056 s time resolution which is longer than the acquisition time of approximately 0.00352 s (2200 points on the up ramp at 625 KS/s) due to the extra time needed to save the data using our acquisition software and corresponds to a time resolution of about \(\sim\)5.6 s, i.e., \(\sim\)0.2 Hz measurement frequency for 100 averaged single scans) for a gas mixture with an NO\({}_{2}\) amount fraction of 979 \(\upmu\)mol/mol in the air. It could be noted here that the measurement frequency is different from the laser modulation frequency of 139 Hz. The absorbance data (Figure 2b derived using the data in Figure 2a, 100 averaged scans, 739 points in the fit window) are fitted by a set of 8 Voigt profiles [44] in order to derive the line areas (areas underneath the absorption lines), i.e., together with the NO\({}_{2}\) line at 2919.59 cm\({}^{-1}\), 7 other neighboring NO\({}_{2}\) lines (see right y axis and the lines in red: line strength [45] plot in Figure 2b) are fitted in the spectral window selected for data analysis. The fitting was performed with the line positions, the line areas and the Lorentzian line widths kept free. The Doppler line widths were calculated at the measured gas temperature. Figure 1: Schematic of the dTDLAS instrument for direct NO\({}_{2}\) measurements (Det: detector). The bottom panel of Figure 2b shows the residuals from the multiline Voigt fit with \(1\sigma_{\text{total}}=2.7\times 10^{-4}\). Using the \(1\sigma_{\text{total}}\) value and the peak absorbance value of 0.092, a signal-to-noise ratio of 341 was calculated for the data in Figure 2b. Due to the signal-to-noise ratio (SNR) around and below 100 and the complex multi-line structure of the NO\({}_{2}\) line used, higher order line shape profiles like Galatry or Hartmann-Tran profiles [46; 47; 48] were not found to be suitable and advised to fit the data in this work.