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Quantification of structure

The technical capabilities to observe and to measure the heterogeneous structure of terrestrial systems are improving steadily: from microtomography of soil porous structure through NMR and geophysical tools to remote sensing techniques.

A challenging problem is a suitable quantification, in the sense of sticking a limited set of meaningful numbers to the observed complexity. This is a prerequisite to relate structural and functional properties.

We develope scale-invariant tools for structure analysis which can be applied to structures of different dimensionality. It is based on integrals over the boundaries of the structure (Minkowski functionsals, top figure), coupled with mathematical morphology. This allows for a comprehensive description of geometries including size, spatial distribution and spatial connectivity of natural structures. It is applicable at any spatial scale and for 2D as well as 3D images. Examples are the 3D soil porous structure and the distribution of landscape patterns (figure) .

The developed tools will help to model structural properties and to evaluate their impact on processes within terrestrial systems.

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Distribution of savanna in a watershed
(Landsat, height 75km)

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Bio-pores in a Terra Fusca
(X-ray CT, height 0.5m)

Selected publications

Schlüter, S.,Weller, U., and Vogel, H.-J., 2011: Soil structure development including
seasonal dynamics in a long-term fertilization experiment, J. Plant Nutr. Soil Sci.,
doi: 10.1002/jpln.201000103.

Vogel, H.-J., Weller, U., and Schlüter, S. 2010: Quantification of soil structure based
onMinkowski functions, Computers & Geosciences, 36, 1236-1245, doi: 10.1016/j.cageo.2010.03.007

Schlüter, S., Weller, U., and Vogel, H.-J., 2010: Thresholding of X-ray microtomography
images of soil using gradient masks, Computers & Geosciences, 36, 1246-1251,
doi: 10.1016/j.cageo.2010.02.007

Vogel, H.-J., Tölke, J., Schulz, V. P., Krafczyk, M., and Roth, K. 2005: Comparison of a Lattice-Boltzmann model, a full-morphology model, and a pore network model for determining capillary pressure-saturation relationships, Vadoze Zone Journal, 4, 380-388

Vogel, H.-J., Hoffmann, H., and Roth, K. 2005a: Dynamics of crack formation in clay: Experiments and morphological quantification. Geoderma, 125, 203-211.

Vogel, H.-J. 2002: Topological characterization of porous media. In: Morphology and Condensed Matter - Physics and Geometry of Spatially Complex Systems. Mecke, K., and Stoyan, D. (eds.), Lecture Notes in Physics, 600, 75-92.

Vogel, H.-J., Cousin, I. and Roth, K., 2002: Quantification of pore structure and gas diffusion as a function of scale. Europ. J. Soil Sci., 53, 465-473.