Recovery of sparse urban greenhouse gas emissions

To localize and quantify greenhouse gas emissions from cities, gas concentrations are typically measured at a small number of sites and then linked to emission fluxes using atmospheric transport models. Solving this inverse problem is challenging because the system of equations often has no unique solution and the solution can be sensitive to noise. A common top-down approach for solving this problem is Bayesian inversion with the assumption of a multivariate Gaussian distribution as the prior emission field. However, such an assumption has drawbacks when the assumed spatial emissions are incorrect or not Gaussian distributed. In our work, we investigate sparse reconstruction (SR), an alternative reconstruction method that can achieve reasonable estimations without using a prior emission field by making the assumption that the emission field is sparse. We show that this assumption is generally true for the cities we investigated and that the use of the discrete wavelet transform helps to make the urban emission field even more sparse. To evaluate the performance of SR, we created concentration data by applying an atmospheric forward transport model to CO2 emission inventories of several major European cities. We used SR to locate and quantify the emission sources by applying compressed sensing theory and compared the results to regularized least squares (LSs) methods. Our results show that SR requires fewer measurements than LS methods and that SR is better at localizing and quantifying unknown emitters.