Uncertainty Quantification in 3D Imaging of Atmospheric Dispersion Processes with Dial

We consider the problem of fitting atmospheric dispersion parameters from time-resolved back-scattered differential absorption Lidar (DIAL) measurements. A clear advan- tage of optical remote sensing modalities is an extended range which makes them less sensitive to strictly local mod- elling errors or the distance to a plume source. In contrast to other state-of-the-art DIAL methods, we dont make a single scattering assumption but propose the collection of multiply scattered photons from wider/multiple fields-of- view that can aid in the reconstruction of certain image features. The scattering of photons in heterogeneous media is modelled through the time dependent Radiative Transfer Equation (RTE) which drastically increases the computational complexity compared current DIAL based approaches. Motivated by environmental emergency response applications and the need to solve the problem in nearly real-time, we address this issue by reconstructing an image representation based on dispersion parameters which avoids a high-dimensional inverse problem and regularises the otherwise ill-posed problem. The obtained parameters are directly related to a dispersion model and any point estimate or UQ can be associated with meaningful physical units. This approach not only achieves a high degree of interpretability but has the potential to naturally incorporate the effect of uncertainties in the optical measurements as well as atmospheric quantities on the reconstructed gas concentration.