The geometry of pore space in soil is considered to be the key in understanding transport of water, gas and solute. However, a quantitative and explicit characterization, by means of a physical interpretation, is difficult because of the geometric complexity of soil structure.

Pores larger than 40 μm within two soil horizons have been analysed morphologically on 3-dimensional digital representations of the pore space obtained by serial sections through impregnated specimens. The Euler-Poincaré characteristic has been determined as an index of connectivity in three dimensions. The pore connectivity is quantified as a function of the minimum pore diameter considered leading to a connectivity function of the pore space. Different pore size classes were distinguished using 3-dimensional erosion and dilation. The connectivity function turned out to differentiate between two soil materials. The pore space in an upper Ah horizon is intensely connected through pores between 40 and 100 μm, in contrast to the pore space in the AhBv beneath it. The morphological pore-size distributions were compared to the pore-size distribution obtained by water retention measurements. The discrepancy between these different methods corresponds to the expectation due to pore connectivity.