*3.1. Modelling Experiments*

A series of modelling experiments have been conducted to achieve objectives 1 and 2. The models are partitioned into one-dimensional (1D) modelling or two-dimensional (2D) modelling. For the 1D modelling, the variable B has e ffectively been set to zero. For numerical models, the whole of the upper surface is irrigated and the right-hand boundary has zero lateral flux of water. The degree to which lateral transport is important for the 2D modelling is dependent on the parameter *B*. This has been set to one for this paper.

Either (or both) the PerTy3 and numerical models have been used. The PerTy3 semi-analytical model has been designed to satisfy the above theory. This does not use a mesh, but rather is designed to estimate time delays. Fluxes are generally estimated at annual time-steps. For transmission of pressure through the unsaturated zone, the time delays are estimated for steps in soil suction and then interpolated to provide recharge at annual time-steps.

The numerical modelling is undertaken using FEFLOWTM [22]. FEFLOW is an acronym of Finite Element subsurface FLOW simulation system and solves the governing flow equations in porous media for variable saturation. Richards' equation is solved for a single dominant fluid phase (in this case water) with an assumed stagnant air phase that is at atmospheric pressure everywhere. FEFLOW implements a number of empirical and spline models for variable saturation and in this work the empirical Mualem–Brooks–Corey model is used [20,21]. Fine mesh refinement is used to achieve stable numerical solutions for the adopted choices of the Mualem–Brooks–Corey model parameters. The set-up for both 1D and 2D modelling is shown in Figure 2. For the 1D modelling (Figure 2a), the third layer has a thickness of 15 m, while for the 2D modelling, it has a thickness of 5 m. The vertical mesh size for both is 10 cm (250 (1D) or 150 (2D) elements), while for the 2D modelling, the horizontal mesh size is 10 m (200 elements).

**Figure 2.** Discretisation for the FEFLOW (Finite Element subsurface FLOW) modelling of (**a**) one-dimensional (1D) situations and (**b**) two-dimensional (2D) situations.

The models have mostly been parameterized using values relevant to the Mallee region of Southeastern Australia [23]. These default values are shown in Table 1. In addition to the parameters in the Tables, the following default values were used:



**Table 1.** Default soil parameters used in the modelling.

Table 2 lists the modelling experiments, with non-default parameters and whether the semi-analytical and/or numerical model is used. These modelling experiments can be categorized as follows:



**Table 2.** Parameter values that vary between modelling experiments. 'y' or 'n' indicates whether that model has been used for that experiment.
