Tomographic DOAS retrieval of NO2 distributions in an urban setup

We present a new Bayesian retrieval algorithm for tomographic reconstruction of nitrogen dioxide (NO₂) distributions in urban environments using scanning LP-DOAS instruments. The approach utilizes crossing light paths from multiple DOAS instruments scanning different retroreflectors, enabling the retrieval of three-dimensional trace gas fields in an urban setting. Rather than directly inverting measurements to obtain a single concentration field, the method formulates the problem probabilistically and estimates the full posterior distribution of the NO₂ concentration field given the observations. Bayesian inference is employed to combine measurement information with prior knowledge on spatial structures. The posterior probability is derived from a likelihood function describing the statistical properties of the DOAS measurements and a prior probability encoding assumptions about spatial correlations, using Bayes’ theorem.

Prior knowledge on the NO₂ field is parameterized through correlation lengths represented in Fourier space by a power-law power spectrum. The field realizations are generated from latent Gaussian variables and transformed into real space via inverse Fourier transform, ensuring physically plausible spatial smoothness while retaining flexibility to resolve sharp gradients typical for urban pollution sources. The forward model links these concentration fields to line-integrated DOAS observations along the intersecting measurement paths.