Bayesian motion estimation for dust aerosols

Dust storms in the earth's major desert regions significantly influence microphysical weather processes, the CO$_2$-cycle and the global climate in general. Recent increases in the spatio-temporal resolution of remote sensing instruments have created new opportunities to understand these phenomena. However, the scale of the data collected and the inherent stochasticity of the underlying process pose significant challenges, requiring a careful combination of image processing and statistical techniques. In particular, using satellite imagery data, we develop a statistical model of atmospheric transport that relies on a latent Gaussian Markov random field (GMRF) for inference. In doing so, we make a link between the optical flow method of Horn and Schunck and the formulation of the transport process as a latent field in a generalized linear model, which enables the use of the integrated nested Laplace approximation for inference. This framework is specified such that it satisfies the so-called integrated continuity equation, thereby intrinsically expressing the divergence of the field as a multiplicative factor covering air compressibility and satellite column projection. The importance of this step -- as well as treating the problem in a fully statistical manner -- is emphasized by a simulation study where inference based on this latent GMRF clearly reduces errors of the estimated flow field. We conclude with a study of the dynamics of dust storms formed over Saharan Africa and show that our methodology is able to accurately and coherently track the storm movement, a critical problem in this field.