Discussion of "Hydraulic Model of Transition of Transient to Steady Flows in the Vadose Zone" by Yaguo Zhang, Tonglu Li, Wei Shen, and Yu Wang

The authors wrote an interesting article dealing with a simple hydraulic model to illustrate the transition mechanism of transient to steady flows in the vadose zone. The soil behavior is described by a set of nine vertically aligned cylinders, each opened at the top and with a small outlet at the bottom. The water level dynamic of each cylinder, associated with an intermittent constant rainfall applied to the top cylinder, C0, was analyzed and numerical simulations were performed. The only objective of this discussion is to show that results similar to those proposed by the authors could be obtained by using the recently introduced Richards equation analytical solution, under gravity-driven infiltration, and the Brooks and Corey (BC) hydraulic conductivity function (Baiamonte 2020a). Indeed, before applying the BC hydraulic conductivity function, for just one water tank, the previous solution was first introduced by studying the theoretical soil behavior under Torricelli’s law, as by the authors. In this discussion, we will first briefly summarize the aforementioned solution for constant rainfall intensity and apply the solution for different parameters, including those considered in the original article. Then, the solution is extended to variable inflow intensity applied to the top of each cylinder. The analysis is performed for dimensionless groups, which make results more general than by using dimensional variables as in Zhang et al. (2019). Indeed, what makes them most useful is their ability to contract, or make more succinct, the functional form of physical relationships that are characterized by fewer dimensionless parameters.