Nitrogen dioxide source detection in satellite images, using inverse time integration methods

Abstract

To regulate pollution emission of $\text{NO}_2$ and greenhouse gasses like carbon dioxide and methane, satellite images of the TROPOspheric Monitoring Instrument (TROPOMI) are used to map the spread of air pollution. This instrument delivers near-daily 'snapshots' of the $\text{NO}_2$ concentration over the whole Earth. In this report, first, the spread of $\text{NO}_2$ pollution is modelled using a so called convection-diffusion equation. This equation is constructed from a convection term, which contributes to how much the wind transports matter, and a diffusion term which described the natural mixing of gases. Next, $\text{NO}_2$ pollution sources were reconstructed using the inverse of the time propagation of the model. Thus, known $\text{NO}_2$ concentrations are used to reconstruct temporal information. By finding out what is missing between data snapshots, sources can be reconstructed. The verification of the algorithm was first performed on artificial data, after which it was applied to experimental data.

The convection-diffusion equation that was used is a two dimensional equation, using longitude and latitude as Cartesian coordinates. The equation was solved by the method of lines, i.e. first a spatial discretisation was made using the Finite Volume Method, after which time integration methods were used to propagate the problem in time. In this report two time integration methods formed the basis for the time propagation and two source reconstruction algorithms. The algorithms take two $\text{NO}_2$ snapshots $\textbf{y}_n$ and $\textbf{y}_{n+m}$, with $m$ time steps in between. First the inverse form of Forward Euler is used, which performed well on artificial data on a small time scale. Afterwards the Backward Euler method is used to define the inverse problem of finding the source function. This algorithm performed well on artificial data with 24 hours between snapshots. The algorithms were found to be sensitive to noise and to be influenced greatly by the second $\text{NO}_2$ snapshot. After applying the algorithm to experimental data it was found that the algorithm is able to localise extended sources of emissions, but is not capable of pin-pointing individual point sources. In addition, sources with low emission rates were left undetected due to information being lost in the noise. Emission rates were not reconstructed accurately either, although it was able to find the main sources of emissions. The performance of the algorithm will take advantage from more frequent data. With this improvement, this method is a viable option for finding not only $\text{NO}_2$ sources, but can also be applied to other tropospheric gases.