**5. Discussion**

This paper has built upon a semi-analytical model, PerTy3, to estimate the impact of reduced irrigation accessions on recharge, adapting an analytical model [10]. This has focused on deep vadose zones, where time delays for pressure transmission can be significant and where perching can occur. The theory allows straightforward changes in the status of perching as irrigation accession increases after development and reduces after infrastructure and water use measures. In addition, the theory has been generalized to two-dimensional situations. The use of non-dimensional parameters *A* and *B* reflect these transitions, *A* for perching and *B* for lateral flow. Perching will occur where *A* is greater than 1 + ϕ and rejected recharge occurs where A is large enough for criterion (Equation (11)) to no longer hold. One-dimensional behaviour will occur when *B* is small and lateral movement becomes significant as *B* becomes greater than one.

#### *5.1. Accuracy of the Model*

The model is conceptual in nature and simplifies the processes under irrigation areas. For example, topography is assumed to be flat and sub-surface soil layers are homogeneous in nature. The expectation is that some parameters will need to be calibrated, but the data to do this is limited. The aim is to capture the key processes, while keeping the model as simple as possible. Parameters related to the key processes can then be calibrated.

The testing of the model can occur in three ways:


Outputs from the semi-analytical and numerical models have been compared (Figures 3–5). The underlying assumptions and parameters for the models are very similar. The numerical model may not necessarily be taken as a point of truth, as it may have problems with numerical instability and dispersion, especially with the fine mesh required for modelling perched water situations. From inspection, there did not appear to be issues of instability. Closer examination of results than those shown here is possible and has been conducted. The model in this paper used a more restricted set of parameters than in [18] for the new developments and so any findings needs to be qualified that they are for the range of parameters used.

The outputs for PerTy3 and FEFLOW are generally very consistent for one-dimensional situations. Even the closer inspection of outputs shows grea<sup>t</sup> consistency. The largest discrepancy appears to be the modelling of the drainage of unsaturated zone, where the semi-analytical model predicted a quicker response than the numerical model. However, this discrepancy occurs for drier conditions, where perching is not an issue and, hence, associated with the analytical model [10]. The most likely issue is that this kinematic wave model only considers the gravity component of Richard's Equation and ignores the di ffusive component. The latter becomes more important for drier conditions [26]. The di ffusive component would lead to upward flow from the capillary fringe; thus, o ffsetting the gravity term and slowing the pressure fronts. This would lead to PerTy underestimating time lags for drier conditions.

The discrepancy between outputs from PerTy3 and FEFLOW is much greater for the two-dimensional modelling. The numerical modelling of total recharge is similar to the one-dimensional modelling [18], even for a value of B of 10. Figure 4b shows a similar result for reduced irrigation accessions, although the testing was limited to where B was one. The degree of similarity appears to be surprising, given the detailed processes are di fferent. Other indicators (irrigation accession at which rejected recharge occurs and partitioning between the recharge under the irrigated agriculture are showing significant di fferences from 1D processes. This similarity may be useful for groundwater modelling, where the total recharge is the quantity of interest.

PerTy3 outputs shows agreemen<sup>t</sup> with the numerical modelling in the partition proportions and the initial response for the perched head. However, it is predicting smaller time delays overall for recharge and perched head to reduce. A possible reason for the discrepancy is the assumption that the perched head is not a ffecting soil infiltration external to the irrigated field. This assumption di ffers from some of the literature for steady-state solutions e.g., [17]. The perched head for x slightly greater than 1 should be similar to that slightly less than 1. A fall in irrigation accession would lead to not only a change in wetted area, but also a fall in the ponded head external to irrigated agriculture. Consideration of the perched head external to the irrigated agriculture would lead to behaviour closer to the one-dimensional situation.

The large time delays and dispersion as predicted are generally consistent with model inversions to infer recharge from the groundwater response [3]. This is investigated more objectively in Ref. [19].

#### *5.2. Sensitivity and Calibration*

The paper has shown how drainage volumes and the absence or presence of drainage may be used to constrain soil properties. Drainage is very sensitive to *Ks*2 *v,* but much less so to *Ks*1 *h*. The equilibrium perched head is also very sensitive to *Ks*2 *v*, but *Ks*1 *h* can significantly reduce its value. It is possible that maps of perched head could be used to constrain both model parameters. The large variation in recharge patterns in Figure 10 for reducing *Ks*2 *v* suggests that groundwater responses could be used to calibrate *Ks*2 *v*. Because of the spatial variability of *Ks*2 *v* and the di fficulty in measuring *Ks*2 *v* in the field, it is di fficult to provide an independent value of *Ks*2 *v* within an order of magnitude, ye<sup>t</sup> the impact on recharge can be very dramatic.

#### *5.3. Superposition and Approximants*

This paper describes superposition experiments in time. The transfer function for a new development in the vicinity of an existing development will be approximately the same as that far away from any existing developments for the parameters tested [18]. This paper extends on that work by showing that the change in recharge from a superposition of independent actions is almost identical to that of the same set of actions occurring successively, within the range tested. This means that it is feasible to consider the numerous actions occurring both spatially and temporally across the irrigation district could be considered as independent actions and, hence, the total recharge could be considered as a sum of the changes in recharge from the individual actions. If this is shown to be the case through further testing, this could simplify the analysis of a complex irrigation district. Because there are thresholds with perched water tables and rejected recharge, there are limitations to the range of situations that superposition applies.

In parallel to considering superposition, it may be possible to use simpler approximants for the transfer function. Figure 9a showed that simple exponential functions with a built-in time delay provided a reasonable approximation to 1D transfer functions from numerical modelling. Figure 9b showed that the superposition of these approximants provided a reasonable approximation to modelling experiment 14-1. The delayed exponential function is consistent with linear reservoir modelling used by others for the vadose zone [6]. The modelling shows that there is some potential to use simple additions of transfer functions for individual actions. The fitted exponential decay parameter is strongly related to the vertical conductivity of the impeding layer.

#### *5.4. Learnings from the Modelling*

The modelling outputs has shown that the effect of a low conductivity layer is to lengthen time delays between changes in irrigation accession and recharge, perhaps up to fifteen years for the parameters considered here. This has implications for salinity management, as this implies that groundwater pumping or other engineering works may need to be maintained until the impacts of the water use efficiency measures are effective. Where groundwater is fresh, the delays in reduction in irrigation returns to the river from water use efficiency measures may be large. Where decommissioning is being implemented, the time delays are expected to be much longer again.

In summary, there has been significant progress towards efficient modelling of recharge from irrigation areas, especially where the vadose zone is deep and where perched water tables exist. However, the following issues would benefit from more work:

