On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales

We study the scale dependence of the saturated hydraulic conductivity Ks through the effective porosity ne by means of a newly developed power-law model (PLM) which allows to use simultaneously measurements at different scales. The model is expressed as product between a single PLM (capturing the impact of the dominating scale) and a characteristic function κ⋆ accounting for the correction because of the other scale(s). The simple (closed form) expression of the κ⋆-function enables one to easily identify the scales which are relevant for Ks. The proposed model is then applied to a set of real data taken at the experimental site of Montalto Uffugo (Italy), and we show that in this case two (i.e. laboratory and field) scales appear to be the main ones. The implications toward an important application (solute transport) in Hydrology are finally discussed.