Open Access
September 2015 Bayesian motion estimation for dust aerosols
Fabian E. Bachl, Alex Lenkoski, Thordis L. Thorarinsdottir, Christoph S. Garbe
Ann. Appl. Stat. 9(3): 1298-1327 (September 2015). DOI: 10.1214/15-AOAS835


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. 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. We critically extend this framework to satisfy the integrated continuity equation, thereby incorporating a flow field with nonzero divergence, and show that such an approach dramatically improves performance while remaining computationally feasible. Effects such as air compressibility and satellite column projection hence become intrinsic parts of this model. 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 storm movement, a critical problem in this field.


Download Citation

Fabian E. Bachl. Alex Lenkoski. Thordis L. Thorarinsdottir. Christoph S. Garbe. "Bayesian motion estimation for dust aerosols." Ann. Appl. Stat. 9 (3) 1298 - 1327, September 2015.


Received: 1 August 2013; Revised: 1 March 2015; Published: September 2015
First available in Project Euclid: 2 November 2015

zbMATH: 06525987
MathSciNet: MR3418724
Digital Object Identifier: 10.1214/15-AOAS835

Keywords: Gaussian Markov random field , Horn and Schunck model , integrated continuity equation , integrated nested Laplace approximation (INLA) , optical flow , remote sensing , Saharan dust storm , satellite data , storm tracking

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.9 • No. 3 • September 2015
Back to Top