  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.
