*3.3. Seeking Approximants*

Approximants are fitted to the FEFLOW transfer function outputs for modelling experiments 7 (1D) and 8 (1D) using Equation (26).

Moreover, the superposition of the approximants for a series of water use efficiency improvements is tested by comparing to the FEFLOW output for the transfer function for modelling Experiment 14-1.

#### *3.4. Using Drainage Outputs for Calibration*

Drainage volumes can be potentially used to calibrate the PerTy3 model. To test this, drainage and soil data are obtained for the Loxton–Bookpurnong irrigation district in the Mallee region.

The soils of the district are categorised into six types. The 3a soils are those for which sub-surface drainage was required, while the 3b soils, none was required. The 3b soils are further divided based on sub-surface characteristics and 3a into two for the different irrigation districts.

Drainage volumes have been measured for the Loxton region [24,25], but not for the Bookpurnong area. For the latter, the presence or absence of sub-surface drainage was noted. The drainage volumes and estimated irrigation accessions [24] were averaged for four periods (1970–1990, 1990–2002, 2002–2006, 2006–2013). These four periods correspond to periods with different estimated water use efficiency factors [24]. The period before 1970 is largely ignored, as a comprehensive drainage scheme was not available before this time. Drainage was only assumed to occur for 3a soils.

Table 3 summarises the soil and drainage characteristics for the six soil types. Areas with no drainage for a period are denoted N/D; areas for which the drainage volume is known; while those where drainage occurs but the volume is unknown are denoted D.

To calibrate PerTy3, Equations (27) and (28) are first applied to create contours of drainage volumes using *Ks*1*<sup>h</sup>* and *Ks*2*<sup>v</sup>* as variables, keeping other variables constant. By varying *Ks*1*<sup>h</sup>* and *Ks*2*<sup>v</sup>* are then varied to best fit the drainage data in Table 3. One way to constrain non-uniqueness is to have the same values for all 3a soils and another one for all 3b soils.


**Table 3.** Soil physical properties and drainage responses for different soils across the Loxton–Bookpurnong Irrigation Districts. ND indicates no drainage and D drainage implemented. Φ is a non-dimensional parameter [18].
