  The interaction between the flow above and below a permeable wall is a
central topic in the study of porous media. While previous investigations have
provided compelling evidence of the strong coupling between the two regions,
few studies have quantitatively measured the directionality, i.e.,
causal-and-effect relations, of this interaction. To shed light on the problem,
we use transfer entropy as a marker to evaluate the causal interaction between
the free turbulent flow and the porous media using interface-resolved direct
numerical simulation. Our results show that the porosity of the porous medium
has a profound impact on the intensity, time scale and spatial extent of
surface-subsurface interactions. For values of porosity equal to 0.5, top-down
and bottom-up interactions strongly are asymmetric, the former being mostly
influenced by small near-wall eddies. As the porosity increases, both top-down
and bottom-up interactions are dominated by shear-flow instabilities.
