The Annals of Applied Statistics

Bayesian motion estimation for dust aerosols

Fabian E. Bachl, Alex Lenkoski, Thordis L. Thorarinsdottir, and Christoph S. Garbe

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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.

Article information

Ann. Appl. Stat., Volume 9, Number 3 (2015), 1298-1327.

Received: August 2013
Revised: March 2015
First available in Project Euclid: 2 November 2015

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Zentralblatt MATH identifier

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


Bachl, Fabian E.; Lenkoski, Alex; Thorarinsdottir, Thordis L.; Garbe, Christoph S. Bayesian motion estimation for dust aerosols. Ann. Appl. Stat. 9 (2015), no. 3, 1298--1327. doi:10.1214/15-AOAS835.

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  • Aberg, S., Lindgren, F., Malmberg, A., Holst, J. and Holst, U. (2005). An image warping approach to spatio-temporal modelling. Environmetrics 16 833–848.
  • Alonso-Pérez, S., Cuevas, E., Querol, X., Guerra, J. C. and Pérez, C. (2012). African dust source regions for observed dust outbreaks over the subtropical eastern North atlantic region, above 25B0N. Journal of Arid Environments 78 100–109.
  • Ashpole, I. and Washington, R. (2012). An automated dust detection using SEVIRI: A multiyear climatology of summertime dustiness in the central and western Sahara. Journal of Geophysical Research: Atmospheres 117 D08202.
  • Bachl, F. E., Fieguth, P. and Garbe, C. S. (2012). A Bayesian approach to spaceborn hyperspectral optical flow estimation on dust aerosols. In Proceedings of the International Geoscience and Remote Sensing Symposium 2012 256–259. IEEE, New York.
  • Bachl, F. E., Fieguth, P. and Garbe, C. S. (2013). Bayesian inference on integrated continuity fluid flows and their application to dust aerosols. In Proceedings of the International Geoscience and Remote Sensing Symposium 2013 2246–2249. IEEE, New York.
  • Bachl, F. E. and Garbe, C. S. (2012). Classifying and tracking dust plumes from passive remote sensing. In Proceedings of the ESA, SOLAS & EGU Joint Conference “Earth Observation for Ocean–Atmosphere Interaction Science” (L. Ouwehand, ed.). ESA Special Publication 703 S1–S3. European Space Agency. European Space Agency Communications, Frascati, Italy.
  • Bachl, F. E., Lenkoski, A., Thorarinsdottir, T. L. and Garbe, C. S. (2015). Supplement to “Bayesian motion estimation for dust aerosols.” DOI:10.1214/15-AOAS835SUPP.
  • Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B. Stat. Methodol. 36 192–236.
  • Brindley, H., Knippertz, P., Ryder, C. and Ashpole, I. (2012). A critical evaluation of the ability of the Spinning Enhanced Visible and Infrared Imager (SEVIRI) thermal infrared red–green–blue rendering to identify dust events: Theoretical analysis. Journal of Geophysical Research: Atmospheres 117 D07201.
  • Corpetti, T., Memin, E. and Perez, P. (2002). Dense estimation of fluid flows. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 365–380.
  • Eissa, Y., Ghedira, H., Ouarda, T. B. M. J. and Chiesa, M. (2012). Dust detection over bright surfaces using high-resolution visible SEVIRI images. In Proceedings of the International Geoscience and Remote Sensing Symposium 2012 3674–3677. IEEE, New York.
  • Gilleland, E., Lindström, J. and Lindgren, F. (2010). Analyzing the image warp forecast verification method on precipitation fields from the ICP. Weather and Forecasting 25 1249–1262.
  • Glasbey, C. A. and Mardia, K. V. (1998). A review of image-warping methods. J. Appl. Stat. 25 155–171.
  • Gneiting, T. and Raftery, A. E. (2005). Atmospheric science. Weather forecasting with ensemble methods. Science 310 248–249.
  • Heitz, D., Mémin, E. and Schnörr, C. (2010). Variational fluid flow measurements from image sequences: Synopsis and perspectives. Experiments in Fluids 48 369–393.
  • Horn, B. K. P. and Schunck, B. G. (1981). Determining optical flow. Artificial Intelligence 17 185–203.
  • Jickells, T. D., An, Z. S., Andersen, K. K., Baker, A. R., Bergametti, G., Brooks, N., Cao, J. J., Boyd, P. W., Duce, R. A., Hunter, K. A., Kawahata, H., Kubilay, N., laRoche, J., Liss, P. S., Mahowald, N., Prospero, J. M., Ridgwell, A. J., Tegen, I. and Torres, R. (2005). Global iron connections between desert dust, ocean biogeochemistry, and climate. Science 308 67–71.
  • Klüser, L. and Schepanski, K. (2009). Remote sensing of mineral dust over land with MSG infrared channels: A new bitemporal mineral dust index. Remote Sensing of Environment 113 1853–1867.
  • Krajsek, K. and Mester, R. (2006a). A maximum likelihood estimator for choosing the regularization parameters in global optical flow methods. In IEEE International Conference on Image Processing 1081–1084. IEEE, New York.
  • Krajsek, K. and Mester, R. (2006b). On the equivalence of variational and statistical differential motion estimation. In IEEE Southwest Symposium on Image Analysis and Interpretation 11–15. Denver, Colorado.
  • Lensky, I. and Rosenfeld, D. (2008). Clouds-aerosols-precipitation satellite analysis tool (CAPSAT). Atmospheric Chemistry and Physics 8 6739–6753.
  • Lindgren, F., Rue, H. and Lindström, J. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach. J. R. Stat. Soc. Ser. B. Stat. Methodol. 73 423–498.
  • Lucas, B. D. and Kanade, T. (1981). An iterative image registration technique with an application to stereo vision. In Proceedings of the 7th International Joint Conference on Artificial Intelligence 2 674–679. Morgan Kaufmann, San Francisco, CA.
  • Mahowald, N. M., Baker, A. R., Bergametti, G., Brooks, N., Duce, R. A., Jickells, T. D., Kubilay, N., Prospero, J. M. and Tegen, I. (2005). Atmospheric global dust cycle and iron inputs to the ocean. Global Biogeochemical Cycles 19 GB4025.
  • Marzban, C. and Sandgathe, S. (2010). Optical flow for verification. Weather and Forecasting 25 1479–1494.
  • Rivas-Perea, P., Rosiles, J. G. and Chacon, M. (2010). Traditional and neural probabilistic multispectral image processing for the dust aerosol detection problem. In IEEE Southwest Symposium on Image Analysis Interpretation (SSIAI), 2010 169–172. IEEE, New York.
  • Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. Monographs on Statistics and Applied Probability 104. Chapman & Hall/CRC, Boca Raton, FL.
  • Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. B. Stat. Methodol. 71 319–392.
  • Schefzik, R., Thorarinsdottir, T. L. and Gneiting, T. (2013). Uncertainty quantification in complex simulation models using ensemble copula coupling. Statist. Sci. 28 616–640.
  • Schepanski, K., Tegen, I. and Macke, A. (2012). Comparison of satellite based observations of Saharan dust source areas. Remote Sensing of Environment 123 90–97.
  • Schepanski, K., Tegen, I., Laurent, B., Heinold, B. and Macke, A. (2007). A new Saharan dust source activation frequency map derived from MSG-SEVIRI IR-channels. Geophysical Research Letters 34 L13401.
  • Schmetz, J., Pili, P., Tjemkes, S., Just, D., Kerkmann, J., Rota, S. and Ratier, A. (2002). An introduction to Meteosat Second Generation (MSG). Bulletin of the American Meteorological Society 83 977–992.
  • Schnörr, C. (1991). Determining optical flow for irregular domains by minimizing quadratic functionals of a certain class. Int. J. Comput. Vis. 6 25–38.
  • Seemann, S. W., Borbas, E. E., Knuteson, R. O., Stephenson, G. R. and Huang, H.-L. (2008). Development of a global infrared land surface emissivity database for application to clear sky sounding retrievals from multispectral satellite radiance measurements. Journal of Applied Meteorology and Climatology 47 108–123.
  • Simoncelli, E. P., Adelson, E. H. and Heeger, D. J. (1991). Probability distributions of optical flow. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition 310–315. IEEE, New York.
  • Simpson, D., Lindgren, F. and Rue, H. (2012). In order to make spatial statistics computationally feasible, we need to forget about the covariance function. Environmetrics 23 65–74.
  • Xu, K., Wikle, C. K. and Fox, N. I. (2005). A kernel-based spatio-temporal dynamical model for nowcasting weather radar reflectivities. J. Amer. Statist. Assoc. 100 1133–1144.

Supplemental materials

  • Software. All software related to this project is available as supplemental material provided in Bachl et al. (2015). For an up-to-date version check the corresponding author’s website,