Constant Rainfall Infiltration Into Bounded Shallow Profiles

Broadbridge et al. (1988) studied constant rainfall infiltration into bounded profiles and, in particular, the dependence on profile depth Z * of R crit / K 1 . K 1 is saturated hydraulic conductivity and R crit is the critical rainfall rate for which surface ponding and profile base saturation occur simultaneously. They found for the linear soil that for lim z * →0 R crit/ K 1 ≈ 2.004. The correct value is in fact exactly 2. In the present work a shallow profile flow equation is established and used (1) to prove this result holds exactly for soils with moisture diffusivity D and hydraulic conductivity K quasi‐linearly connected but otherwise arbitrary functions of volumetric moisture content θ; and (2) to develop a physical argument indicating the result is exact in the fully general case with D (θ) and K (θ) unconnected.