Estimation of Intrinsic Length Scales of Flow in Unsaturated Porous Media

Characteristic lengths govern processes related to flow in unsaturated porous media, e.g., during drainage or evaporation. One can estimate these lengths, i.e., air-entry pressure head and critical capillary head, from either a water retention curve (WRC) or a hydraulic conductivity function (HCF). We provide new analytical expressions for the characteristic lengths based on a linearized analysis of the WRC and HCF curves. These are then used to investigate the impact of model selection on length-scale estimates, to assess their sensitivity to model parameters, and to provide guidelines for the choice of the alternative expressions under flow scenarios of interest.