Efficient numerical estimation of transport parameters with image processing and modeling

The aim of the project is to design a novel method for estimating system parameters by image sequences as input data for a broad variety of interdisciplinary applications.

In order to fix ideas, the focus will be on an environmental problem, which consists in estimating transport fields, sinks and sources of airborne dust in desert regions (especially the Sahara desert). Environmental scientists are interested in such information for several reasons. On the one hand, sand has positive effects as a fertilizer (e.g. Amazonas region). On the other hand, airborne dust can transport causative organisms and pollutants, which can be harmful for the human health. Furthermore it is an open question whether sand plumes have an positive or negative impact on the global warming. The method might then be useful as a tool for these sciences.

Nothern Africa. Magenta: Dust plumes. Black: Water clouds.

The method will combine techniques from different scientific areas. Spectral pictures (see figure) of the Sahara desert from a geosynchronous satellite will be used as input data. The velocity field of a dust plume can be estimated by minimizing a functional which measures the brightness change in the whole image sequence. This is at first not a well-posed mathematical problem, so the optimization problem must be regularized. Therefore a model for the airborne dust transport will be used.

The foregoing procedure raises some fundamental problems:

  • during a long time period the illumination of the images is changing (altitude of the sun), so that the optimization functional must be modified
  • water clouds cover the dust plumes (see figure), so that the dataset must be recovered by image processing techniques
  • the dataset is very large and the model is highly nonlinear and unsteady, so that 'goal-oriented' adaptivity (mesh refining and coarsening) has to be applied in order to reduce the computational effort and to guarantee accuracy of the results

This work is part of an interdisciplinary collaboration with Christoph Garbe, IPM, University of Heidelberg and Ina Tegen, IFT, Leipzig.