Analytical Model for Gravity-Driven Drainage

We model drainage flow by assuming gravitational regime. Central for the present paper is a fairly general analytical solution which is applicable to local (typically laboratory) scale. These results are then specified by adopting the Brooks et al (1964) model for the hydraulic conductivity curve. At field scale, we combine our analytical results with the stream tube model of Dagan et al. (1979) to derive the ensemble average of the effective saturation. This is achieved by regarding the parameters of hydraulic properties as random space functions (RSFs) with given joint density distribution. For illustration purposes, we limit to consider the spatial vari-ability of the saturated conductivity Ks, solely.