Bayesian inference for sources of reactive gases in urban canyons based on the adjoint method

Although various methods have been proposed for source term estimation, they mainly focus on hazardous gases behaving as passive scalars. These methods will struggle in identifying unknown sources of reactive gases, which are common in complex urban environments. Focusing on one of the most severe atmospheric pollutions in urban areas, the NOx-O3 photochemical reactive gas dispersion, this research proposed a novel source term estimation method based on Bayesian inference and the adjoint method. Utilizing sparse measurements and background concentrations, this method can effectively identify and quantify the source terms of NO and NO2. To evaluate the performance of the proposed method, a case of an urban canyon in Paris was studied. The NOx gases were released from the traffic, which was a line source at the central bottom of the canyon, and the strength was measured on-site. The measurements of multiple sensors were synthesized by numerical simulations validated by on-site concentration measurements. First, deploying sensors in the target canyon, the proposed method was coupled with a super-Gaussian function to estimate the location, shape, and strength of NOx sources. Our method successfully estimated the length and width of sources by using 4 sensors located at roadsides and roofs. When sensors increased to 7, the strength estimation errors could be controlled within 5%. The heights of sources were found to be the most difficult term because sources were close to the bottom wall and flows were strongly circulated in the canyon, making the adjoint concentration simulation biased. Secondly, assuming the unknown sources are points, the proposed method was applied to estimate source terms in continuous urban street canyons based on sensors on each roof. It was found that our method can identify the exact canyon where sources were located and estimate their strength with about 10% errors. In addition, the conventional Bayesian approach for passive scalars has failed in both cases, demonstrating the necessity and advantages of our method.