# Advances in High-Precision NO2 Measurement by Quantum Cascade Laser Absorption Spectroscopy
## 3 Results and Discussion  
### Calibrations of the NO\({}_{2}\) Instruments  
Figure 7a shows the results of all three different calibration methods performed prior to the ambient air measurement period (23 January-2 February 2020). The original calibration factors of the four instruments are based on different sources. The NO\({}_{2}\) amount fraction reported by the QCL-Empa instrument was calculated solely based on the spectroscopic parameters using the HITRAN database and physical parameters (temperature, pressure and OPL). The CAPS and QCL-MIRO calibration parameters were preset by the instruments suppliers. The CLD calibration factors were based on calibration by a GPT unit similar to the one described in Section 2.2.2.  
The calibration factors were obtained by a linear fit to these data using a least square method. The intercept of the linear regression is left to vary for all instruments, because they use different zeroing methods. The intercept and slope values determined from the regression analysis are shown on Figure 7b. The error bars represent the 2 \(\sigma\) uncertainties of the fit. The width of the colored area represents the total uncertainty on the slope. It combines the uncertainty of the fit and that of the set span NO\({}_{2}\) concentration (k = 2). The latter is estimated for each case separately: (i) for CDC, it takes into account the uncertainty of the MFCs flow and the NO\({}_{2}\) cylinder concentration (\(\approx\)4%); (ii) for GPT, the uncertainty is a combination of the NO measurement uncertainty of the CLD and the uncertainty on the NO cylinder concentration (\(\approx\)2%); and (iii) the uncertainty on the ReGas method is a combination of the uncertainties of the permeation tube calibration and the MFC flows and considers environmental and temporal factors affecting the permeation rate [47]. The data in Figure 7 reveal a very good agreement (in terms of both the intercept and slope) between the NO\({}_{2}\) instruments (within the uncertainties) despite their different 'factory' calibration factors (based on either previous calibrations or purely spectroscopic data, such as for the QCL-Empa). On the other hand, significant discrepancies between the different calibration methods are observed. The average slopes (over the four instruments) for the CDC, GPT and ReGaS calibration are: 1.09, 1.01 and 0.92, respectively.  
The higher slope values obtained with the CDC method compared to the established GPT method indicate an overestimation of the span NO\({}_{2}\) concentration. This could be attributed to the long-term degradation of NO\({}_{2}\) via gas phase reaction with water residuals or wall surfaces effect in the gas cylinder or to losses of NO\({}_{2}\) on the internal surfaces of the pressure regulator of the cylinder. On the opposite side, calibration with the ReGaS instrument yields slopes values significantly lower than the GPT method. This implies an underestimation of the calculated set concentration (using the GPT as a reference). The latter is a function of the permeation rate (T and P dependent) and internal dilution factors. Potential errors in the calculation of the dilution factors alone are unlikely to explain the observed discrepancies with the established GPT method since they are based on mass flow readings with very low uncertainties [47]. The most probable source of error concerns the temporal gap between the permeation tube calibration and the inter-comparison campaign (9 months), the temperature readings in the permeation oven and the permeation tube purity indicated by the manufacturer. Another possible explanation for the lower slope values of the ReGaS calibration compared to the GPT and the CDC methods is that the latter two are subject to over-estimations of the set span concentration, for example due to losses of NO\({}_{2}\), or, for the GPT, to an over-estimation of the conversion efficiency of NO.