  We consider the inverse problem of fitting atmospheric dispersion parameters
based on time-resolved back-scattered differential absorption Lidar (DIAL)
measurements. The obvious advantage of light-based remote sensing modalities is
their extended spatial range which makes them less sensitive to strictly local
perturbations/modelling errors or the distance to the plume source. In contrast
to other state-of-the-art DIAL methods, we do not make a single scattering
assumption but rather propose a new type modality which includes the collection
of multiply scattered photons from wider/multiple fields-of-view and argue that
this data, paired with a time dependent radiative transfer model, is beneficial
for the reconstruction of certain image features. The resulting inverse problem
is solved by means of a semi-parametric approach in which the image is reduced
to a small number of dispersion related parameters and high-dimensional but
computationally convenient nuisance component. This not only allows us to
effectively avoid a high-dimensional inverse problem but simultaneously
provides a natural regularisation mechanism along with parameters which are
directly related to the dispersion model. These can be associated with
meaningful physical units while spatial concentration profiles can be obtained
by means of forward evaluation of the dispersion process.
