Quantification of pore structure and gas diffusion as a function of scale

The quantification of the spatial heterogeneity of soil structure is one of the main difficulties to overcome for an adequate understanding of soil processes. There are different competing concepts for the type of heterogeneity, including macroscopic homogeneity, discrete hierarchy or fractal. With respect to these different concepts we investigate the structure of the pore space in one single sample (4 x 10(3) mm(3)) by analysing basic geometric quantities of the pores > 0.3 mm within gradually increasing subsamples. To demonstrate the relation between geometrical and functional properties we simulate gas diffusion within the three-dimensional pore space of the different subsamples. An efficient tool to determine the geometric quantities is presented. As a result, no representative elementary volume (REV) is found in terms of pore-volume density which increases with sample size. The same is true for the simulated gas diffusion coefficient. This effect is explained by two different types of pores, i.e. big root channels and smaller pores, having different levels of organization. We discuss the different concepts of structural organization which may be appropriate models for the structure investigated. We argue that the discrete hierarchical approach is the most profitable in practice.