## 2 Experimental
From the Allan plot in Figure 3b, an optimal precision of 825 nmol/mol (detection limit) is evaluated (conservatively, as there is no minimum visible) for the instrument at a time resolution of 86 s.  
Repeated measurements were performed at different amount fraction levels (switching from about 100 to 1000 umol/mol as shown on Figure 4a) to study the behavior, response and linearity of the instrument. The gas mixture used for the measurements at the lowest amount fraction level of 100 umol/mol was a primary gas mixture (SI traceable, prepared using gravimetry by a national metrology institute). At 300 umol/mol we used a commercial gas mixture (secondary: SI-traceable, with a Deutscher Kalibrierdienst-DKD certificate [50]) and that at 1000 umol/mol was a commercial gas mixture from the same manufacturer (internally assigned, with no SI-traceability information provided). The \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & \begin{tabular}{c} **Relative Standard** \\ **Uncertainty (\(k=1\))/\%** \\ \end{tabular} & \
\begin{tabular}{c} **Index (\% Individual** \\ **Contribution)** \\ \end{tabular} \\ \hline Pressure & 108.5 hPa & 0.20 & 0.10 \\ \hline Temperature & 294.3 K & 0.10 & \(\leq\)0.05 \\ \hline Path length & 77.4 cm & 0.13 & \(\leq\)0.05 \\ \hline Line strength (HITRAN value [40]) & 5.425\(\cdot\)10\({}^{-21}\) & 5.00 & 96.00 \\ \hline Line area & 0.0010999414 cm\({}^{-1}\) & 1.00 & 3.80 \\ \hline NO2 concentration (\(x_{\text{NO2}}\)) result & 982 μmol/mol &
\begin{tabular}{c} 5.10 (combined \\ uncertainty) \\ \end{tabular} & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Uncertainty budget of the NO2 amount fraction results. Figure 3: (**a**) Repeated NO2 measurements: plot of NO2 OGS amount fraction results vs. measurement number; (**b**) Allan deviation: plot of the \(x_{\text{NO2}}\) Allan deviation as a function of time. standard uncertainty reported for the NO\({}_{2}\) amount fractions in these gas mixtures are all 1% (k = 1), corresponding to expanded uncertainties of 2% (k = 2). As presented, the sampling lines and the gas cell were all coated by Silconert, resulting in a fast response time of 0.5 s for the NO\({}_{2}\) measurements in Figure 4a. It could be noted here that this response time of 0.5 s does not also include the cylinder switching time and the time of manually opening valves to introduce the NO\({}_{2}\) gas sample into the gas cell. The repeatability (calculated as the standard deviation of the mean) at the lowest NO\({}_{2}\) results at the 100 \(\upmu\)mol/mol level is 0.5 \(\upmu\)mol/mol (0.5% relative). At the respective amount fraction levels, 1\(\sigma\) (standard deviation) values were evaluated, demonstrating the short-term reproducibility (<10 \(\upmu\)mol/mol at 1\(\sigma\)) for the NO\({}_{2}\) OGS results. Using the respective 1\(\sigma\) values, an SNR from 18 at 100 \(\upmu\)mol/mol to 106 at 1000 \(\upmu\)mol/mol levels, at a time resolution of 86 s, were evaluated for the measurements in Figure 4a. Figure 4b shows a plot of the NO\({}_{2}\) amount fraction results as a function of the certified values reported for the probed gas mixtures. A generalized linear regression (GLR) was applied to the data in Figure 4b, resulting in a slope of 0.984 \(\pm\) 0.095 (_k_ = 2) and an intercept value of (10.25 \(\pm\) 16.10) \(\upmu\)mol/mol, respectively. The slope value of 0.984 shows the good accuracy of the dTDLAS instrument, while the small deviation from the linear fit shows good linearity. The intercept value is consistent with zero, indicating an offset free measurement. The relative residuals from the linear model in the bottom panel of Figure 4b are all within the 1% range and thus well within the expanded uncertainty of the dTDLAS results of 5.1%, \(k\) = 1), which shows good agreement (compare well; validation step) with the certified values associated with the gas mixtures.