Accurate monitoring of nitrogen dioxide (NO₂), a significant atmospheric pollutant, is essential for effective environmental management. Differential absorption lidar (DIAL) technology has emerged as a robust approach to address this challenge. However, the wavelength dependency of aerosol optical properties has a substantial impact on NO₂-DIAL measurements. Previous studies mostly focus on the narrow-band NO₂-DIAL technique without considering the spectral width of the emitted laser pulse. Therefore, the influence of aerosol optical properties on the retrieved NO₂ mass concentration of the broad-band DIAL technique remains unclear. We aim to investigate aerosol-induced NO₂ mass concentration errors under various atmospheric conditions through simulation studies and an approximation method for the broadband NO₂-DIAL technique. We hope that this research can offer valuable insights into comprehending the influence of aerosol optical properties on broadband NO₂-DIAL techniques.

We carry out research based on the broadband NO₂-DIAL technique (Fig. 1) employing the Scheimpflug principle. The broadband NO₂-DIAL system utilizes image sensors as detectors and high-power laser diodes as light sources (wavelength is 450 nm, power is 1.6 W), with an emission spectral typically ranging from 1-2 nm (full width at half maximum). Two different methods (the simulation method and the approximation method) have been adopted to elucidate the influence of atmospheric aerosols on the broadband NO₂-DIAL technique. The broadband DIAL equation has been established, based on which simulated atmospheric lidar signals can be obtained with measured laser spectra and different atmospheric parameters, e.g., aerosol extinction coefficient, backscattering coefficient and ?ngstr?m exponent (Fig. 5). Therefore, the NO₂ mass concentration containing the aerosol-induced retrieval errors can be acquired through segmented fitting for the simulated atmospheric lidar signals (Fig. 6). As a result, the NO₂ mass concentration errors introduced by the aerosol extinction effect and the aerosol backscattering effect under various atmospheric conditions can be obtained through numerical calculation. Besides, the aerosol-induced NO₂ mass concentration errors can also be mathematically derived based on spectral approximation—the approximation method. Meanwhile, cross-validations between the aerosol-induced NO₂ mass concentration errors obtained from these two methods have also been carried out.

Several conclusions can be drawn according to simulation studies. When the atmospheric condition is homogeneous, for an extinction coefficient of 0.3 km^-1 and an ?ngstr?m exponent of 3, the aerosol-induced retrieval error of the NO₂ mass concentration is 14.7 μg/m3, while the error introduced by the aerosol backscattering effect is only about 0.6 μg/m3 (Fig.7). Therefore, when atmospheric aerosols are homogeneously distributed, the inversion error of NO₂ mass concentration mainly depends on the aerosol extinction coefficient. The proportion of the NO₂ mass concentration inversion error generated by the backscattering effect is generally less than 5%, which can be ignored. Besides, if the ?ngstr?m exponent approaches 1, the NO₂ mass concentration error introduced by the aerosol extinction effect will decrease to 5 μg/m3 (Fig. 9). If aerosol plumes appear in a homogeneous atmosphere (0.3 km^-1), for the extinction coefficient of 0.66 km?¹ within the inhomogeneous range and an ?ngstr?m exponent of 3, the NO₂ mass concentration error resulted from the aerosol extinction coefficient in the inhomogeneous region is 18.9 μg/m3. However, the error introduced by the aerosol backscattering effect increases to 3.3 μg/m3 with a fitting distance of 500 m (Fig. 11). Under typical weather conditions with a relatively small ?ngstr?m exponent of 1, the NO₂ mass concentration error introduced by the aerosol backscattering effect will increase to 6.8 μg/m3 (Fig. 12). The simulation results indicate that the inversion error of aerosol backscattering effect on NO₂ mass concentration largely depends on the non-uniformity of atmospheric aerosol distribution, the fitting range, etc. Meanwhile, increasing the fitting range can greatly reduce the NO₂ mass concentration error introduced by the aerosol, especially for the backscattering effects. Comparison studies between the approximation method and the simulation method reveal that the NO₂ mass concentration retrieval error introduced by the extinction effect is almost the same, while the backscattering coefficient-induced errors may be quite different (Figs. 13 and 14).

We evaluate the measurement errors of NO₂ mass concentration caused by aerosol extinction and backscattering effects under various atmospheric conditions by two different methods (the simulation method and the approximation method) for the broadband NO₂-DIAL technique. In the case of a homogeneous atmosphere, the NO₂ mass concentration error is primarily determined by the aerosol extinction coefficient, while the contribution from aerosol backscattering effects can be neglected. However, if the atmosphere is inhomogeneous, the NO₂ mass concentration error caused by the aerosol backscattering effect is significantly influenced by the inhomogeneous distribution of aerosol. It should be mentioned that the backscattering coefficient-induced NO₂ mass concentration error is inversely proportional to the ?ngstr?m exponent in this case. In addition, we also derive an approximation model for NO₂ mass concentration inversion errors caused by the extinction and backscattering coefficients based on spectral approximation. The comparison between the approximation method and the simulation method shows that the NO₂ mass concentration inversion error generated by the extinction coefficients obtained by the two methods are generally in good agreement with small discrepancies. The inversion error caused by the aerosol backscattering coefficient may be affected by factors such as the computation method, the fitting range, and the spectral approximation. The approximation model provides an important tool for evaluating NO₂ mass concentration errors in practical DIAL measurements.