Urban Atmospheric Inverse Modeling via Hybrid Reconstruction Methods based on Compressed Sensing

Abstract. Being able to trace and pinpoint greenhouse gas sources in urban environments in the face of climate change is more urgent than ever. Current atmospheric inversion approaches typically rely on Bayesian Inversion (BI) with Gaussian priors, which perform well for wide-range area sources but systematically smooth sharp emission peaks. This limits their ability to detect unknown point sources. An emerging method addressing this limitation is Sparse Reconstruction (SR), which enables the detection of localized emitters. However, they often fail to adequately represent spatially diffuse emissions.

In this paper, we combine these two complementary methods by introducing a novel hybrid atmospheric inversion framework based on the mathematical theory of compressed sensing. Our approach separates the recovery of concentrated point sources and dispersed area sources into two sequential steps. Using an observing system simulation experiment, we compare the performance of conventional BI and the proposed hybrid approach. The results demonstrate that the hybrid method significantly improves the recovery of mixed emission fields, mitigates over-smoothing of point sources, and enables inversions without a spatial prior in situations where BI using a Gaussian prior alone becomes infeasible. These findings highlight the potential of sparse and smooth hybrid inversion strategies for more reliable urban-scale greenhouse gas emission monitoring.