*2.7. Stage 5*

Once the wetting front reaches the water table, recharge rises from the pre-development flux to a new higher flux, less than the irrigation flux. The recharge rate continues to increase, exponentially asymptoting to the irrigation accession flux. The program ignores the e ffect of capillary fringe on timing. For example, for native vegetation or dryland agriculture the corresponding soil suction could be up to 10 m, while for irrigated agriculture, the corresponding suction is more likely 10s of cm. We shall assume that the bottom of layer 3 is the capillary fringe corresponding to irrigation.

If the perched head rises to the stage where it intercepts the upper boundary condition, there is no capacity for further infiltration to occur. We refer to this as recharge rejection. This occurs when:

$$h\mathbf{h}\_{\rm cl} = (A - 1 - q\mathbf{y})(1 + sq\mathbf{rt}(B)), \mathbf{h} \ge l\_1/l\_2 \tag{39}$$

Any excess water is returned to the surface as evapotranspiration. This process can lead to waterlogging and salinity and generally sub-surface drainage is required. The volume of rejected recharge can be estimated using Equations (19) and (30):

$$D/IA = (A - 1 - \varphi - h(1 + sqrt(B)))/A\tag{40}$$

In portraying outputs, a normalised transfer function is often used:

$$\text{TF}(t) = (R(t) - Ro) / (IA\_{\text{il}} - IA\_o) \tag{41}$$

A transfer function is a mathematical model of a system that maps its input to its output (or response). An analogous transfer function can be defined for drainage (or rejected recharge). Where there is no rejected recharge, *TF(t)* = 0 for *t* = 0; and approaches 1 after long periods. Hence it represents a cumulative probability distribution for time delays for pressure to travel through the vadose zone. Where there is rejected recharge, *TF(t)* is less than one after long periods but the sum of transfer functions for recharge and drainage approaches one. Transfer functions take on greater significance where they can be superimposed for a combination of actions. A modified transfer function will be defined below for application to superposition.
