# Modelling the Effect of Efficiency Measures and Increased Irrigation Development on Groundwater Recharge through a Deep Vadose Zone

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- adapting the PerTy3 model and associated theory, that had previously been described [18] for application to new irrigation developments, in order to represent water use efficiency measures;
- testing the theory and the model by comparison with a numerical model; and
- implementing the model for the whole-of-life irrigation sequence, from development, to represent changes in irrigation practice, including efficiency improvements.

- trialling the principle of superposition of recharge models in response to individual actions over a whole-of-life irrigation sequence; and
- seeking simple conceptual models that can approximate the recharge distribution for individual actions and in particular the linear reservoir model.

## 2. Theory

- (1)
- Section 2.1 describes the conceptual model underlying the theory for objective 1. Section 2.2 and Section 2.3 contribute to objective 1(a); i.e., adapting the PerTy3 model and associated theory, which had previously been described [18] for application to new irrigation developments, in order to represent water use efficiency improvements. The theory is developed in two stages: (i) representation of the response of an unsaturated zone to an individual action, which reduces irrigation accession, until the system reaches a new equilibrium (Section 2.2.); and (ii) representation of a response to a series of actions, which reduce irrigation accessions (Section 2.3). The theory adapts the PerTy3 model [18] by adapting the kinematic theory [10].
- (2)
- Section 2.4 and Section 2.5 contribute to meeting the second objective; namely, to explore the application of transfer functions to estimate recharge from irrigation areas. More specifically, they contribute to objectives 2(a) and 2(b) by (1) defining transfer functions that can be tested for superposition, given the obvious nonlinearities and (2) describing the theory of the delayed linear reservoir conceptual model.
- (3)
- Section 2.5 contributes to the third objective by providing a theory for the drainage volumes in a manner to allow data on drainage volumes to be used for calibration.

#### 2.1. Conceptual Model for Theory

_{b}

_{b}is the air-entry point, λ is a fitting parameter, and the relative saturation, Θ, is given by

_{r}, is given by:

_{r}= Θ

^{m}

_{r}by the saturated hydraulic conductivity. These parameters will be different for the different layers and a subscript i will be subsequently used to distinguish layer i. The parameters are assumed to be the same for both vertical and horizontal properties, except for the saturated conductivity. A superscript h and v will be used with the saturated hydraulic conductivity to characterise anisotropy. The values given to the parameters is given in the Methods section.

_{2}, timescale S

_{2}l

_{2}/K

_{s2}

^{v}, horizontal length scale x

_{0}; where l

_{i}is the thickness of the ith layer; x

_{0}is the half-width of the irrigated area; K

_{si}

^{v}is the saturated vertical conductivity of the ith layer; and S

_{2}is the specific yield for the second layer for the initial dry conditions. The purpose of the non-dimensionalisation is to simplify as much as possible using scaling and non-dimensional variables.

#### 2.2. Modelling Individual Actions

#### 2.2.1. Kinematic Wave Theory for Unsaturated Zones

_{r1}, equals the new non-dimensional irrigation accession flux, A. The kinematic value approach follows how any particular value of vertical hydraulic flux (and associated moisture content and soil potential) between the old and new irrigation accession fluxes travels through layer one. The higher value of flux (and associated moisture content and soil potential) travels more quickly, with the fastest being that for the old irrigation accession and the slowest being that for the new irrigation accession. When the fastest value reaches a particular depth, the flux at that depth begins to gradually reduce from the old irrigation accession until the slowest value reaches that depth and flux stabilizes at the new value. Any value of flux can be followed through the three layers to the water table. The theory implies that the speed of any value in the ith layer is given by:

_{i}= m

_{i}S

_{i}K

_{si}

^{v}/K

_{s2}

^{v}

#### 2.2.2. Soil Zone Initially with Perched Water

_{eq}, under equilibrium conditions is given by:

_{eq}= (A − 1 − φ)/(1 + sqrt(B))

_{s1}

^{h}l

_{2}

^{2}/(K

_{s2}

^{v}x

_{0}

^{2})

_{r2}

^{v}(ψ) − 1 ) l

_{2})

_{b}to ∞ and φ is assumed to be insensitive to A.

_{1}/l

_{2}> (A − 1 − φ)/(1 + sqrt(B))

_{1}to S

_{2}; and s

_{1}is the specific yield of layer 1 after wetting front has already passed through. This has the solution:

_{eq}+ exp( − t (1 + sqrt(B))/β) (h

_{0}− h

_{eq})

_{eq}and h

_{0}are respectively the new equilibrium head and the old equilibrium head. This shows that perched head reduces exponentially to the new equilibrium conditions. The effect of two-dimensional flow is indicated by the dimensionless parameter B, where B = 0 corresponds to one-dimensional flow and large B corresponds to significant lateral movement. The effect of B is to not only reduce the steady-state ponded head, but to also quicken the rate at which the new equilibrium is attained. To understand this better, we consider the dimensioned time scale in the exponential function:

_{s}= l

_{2}S

_{2}β/((1 + sqrt(B)) K

_{s2}

^{v})

_{s}becomes in dimensioned variables:

_{s}~x

_{0}s

_{1}/sqrt(K

_{s1}

^{h}K

_{s2}

^{v})

_{eq}:

_{eq}− (q

_{eq}− q

_{0}) exp( − (t − t

_{0}) (1 + sqrt(B))/β)

_{0}is the vertical flux at initial equilibrium and is related to h

_{0}by:

_{0}= 1 + h

_{0}+ φ

_{eq}and h

_{eq}.The extent of the wetting outside of the irrigation field, x

_{1}, also decreases exponentially under the assumptions used from the original equilibrium value, x

_{10}, to the new equilibrium value, x

_{1eq}, in parallel with the ponded head.

_{1}(t) = x

_{1eq}− (x

_{1eq}− x

_{10}) exp( − (t − t

_{0}) (1 + sqrt(B))/β)

_{10}is related to h

_{0}by:

_{10}= h

_{0}sqrt(B) + 1

#### 2.2.3. Change from Perched Water Table to None

_{eq}substituted by (A − 1 − φ)/(1 + sqrt(B)). This allows the time for the perched head to go to zero to be estimated. After that time, layers 2 and 3 begin to drain; and Equations (5) and (6) apply.

#### 2.2.4. Initial State with Rejected Recharge

#### 2.3. Modelling of Multiple Actions

_{0}. Taken together, the methodology across the range of situations described in Section 2.2.1, Section 2.2.2, Section 2.2.3 and Section 2.2.4 does not change under multiple actions, which reduce irrigation accession.

#### 2.4. Transfer Function and Superposition

_{n}− IA

_{o})

_{n}* − IA

_{o}*)

_{o})/(IA

_{n}** − IA

_{o}**)

_{o}is the original drainage rate, IA** is the maximum of IA and the maximum irrigation accession that occurs without rejected recharge.

_{j}(IA*

_{j+1}− IA*

_{j}) TF’

_{j+1})/(IA*

_{p+1}− IA*

_{0})

_{j}is a sequence of modified irrigation accessions that occur from j = 0 to j = p + 1 and TF’

_{j+1}is the modified transfer function that applies for a change of irrigation accession from IA*

_{j}to IA*

_{j+1}.

#### 2.5. Theory for the Linear Reservoir Model

^{*}is the irrigation accession, adjusted for rejected recharge, if it occurs. If R is linear with respect to M i.e.,

_{5}))), t > t

_{6}

_{5}and t

_{6}become fitted parameters. While the theory in previous sections give physical meaning to parameters c and t

_{l}or fitted to model outputs, they can be also fitted to groundwater responses.

#### 2.6. Criteria for Rejected Recharge

_{s2}

^{v}(1 + φ + l

_{1}/l

_{2}+ sqrt(K

_{s1}

^{h}/K

_{s2}

^{v}) l

_{1}/x

_{0})

_{s2}

^{v}(1 + φ + l

_{1}/l

_{2}+ sqrt(K

_{s1}

^{h}/K

_{s2}

^{v}) l

_{1}/x

_{0})

## 3. Methods

- trialling the principle of superposition of recharge models in response to individual actions over the irrigation whole-of-life; and
- seeking simple conceptual models that can approximate the recharge distribution for individual actions and in particular the linear reservoir model.

#### 3.1. Modelling Experiments

- irrigation half-width, x
_{0}, 500 m for 2D modelling; - dimensionless parameter B: 0001 (1D); 1 (2D); and
- pre-irrigation accession for new development: 10 mm/year.

- (i)
- Experiments 7 (1d) and 8 (1D) model the transient behaviour from an equilibrium state to a new equilibrium state in response to a single reduction in irrigation accession. The modelling outputs of PerTy3 and FEFLOW will be compared. In addition, outputs will be used in Section 3.2 and Section 3.3 to test superposition and find approximants for the linear reservoir model.
- (ii)
- Experiments 9 (1D) and 14-1 (2D) model the transient behaviour from an equilibrium state to a new equilibrium state in response to multiple water use efficiency improvements. This includes the behaviour of the perched head and for the 2D modelling recharge under the external to the irrigated agriculture. The modelling outputs of PerTy3 and FEFLOW will be compared. The outputs of the two models will be compared to show differences between 1D and 2D situations. Moreover, the outputs will be used in Section 3.2 and Section 3.3 to test superposition, including superposition of approximants.
- (iii)
- Experiments 10 (1D) and 15 (2D) model the transient response from an equilibrium pre-irrigation state to a new equilibrium in response to irrigation development and successive irrigation efficiency improvements. Only PerTy3 is used. The modelling outputs are used to in Section 3.2 to test superposition. The outputs for 10a and 15a come from [18].
- (iv)
- Experiment 11 (1D) models the sensitivity of the recharge over time for the irrigation whole-of-life to K
_{s2}^{v}. The values of K_{s2}^{v}are chosen so that soil zone goes from no perching to perching for almost the entire modelling period.

#### 3.2. Superposition Experiments

- The first is for a series of water use efficiency improvements, using outputs from experiments 7, 8 and 9. The modelling experiment 9 represents a combination of water use efficiency changes of 230 to 100 mm/year and 100 to 50 mm/year, separated by 5 years. The numerical outputs for experiments 7 and 8, which each represent the individual transitions, but with each starting from an equilibrium state, were superimposed, using Equation (21). This superposition is compared to the semi-analytical and numerical modelling outputs for experiment 9.
- The second experiment (Experiment 10 (1D)) is for a one-dimensional irrigation whole-of-life i.e., a new development followed by a succession of water use efficiency improvements. The PerTy3 model is implemented for three 1D scenarios: 10a a new development that started in 1996; 10b is a sequence of water use measures separated by 5 years, starting in 2001 (the 1996s state of a new development starting in 1921 approximates an initial equilibrium state); and 10c, the same sequence of water use measures following a new development in 1976. The superposition of 10a and 10b (10d) is compared with 10c.
- The third experiment (Experiment 15(2D)) is for a two-dimensional irrigation whole-of-life. The PerTy3 model is implemented for three 2D scenarios: 15a, a new development starting in 1976; 15b, a sequence of water use measure separated by 5 years and beginning in 1981 (the 1981 state of a new development in 1961 approximates an initial equilibrium state); and 15c, the same sequence of water use measures following a new development in 1976. The superposition of 15a and 15b (15d) is compared with 10c.

#### 3.3. Seeking Approximants

#### 3.4. Using Drainage Outputs for Calibration

_{s1}

^{h}and K

_{s2}

^{v}as variables, keeping other variables constant. By varying K

_{s1}

^{h}and K

_{s2}

^{v}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.

#### 3.5. Whole-of-Life Modelling

_{s2}

^{v}. The PerTy3 model is implemented with the following values for K

_{s2}

^{v}: (a) 0.1 (b) 0.05 (c) 0.03 (d) 0.01 cm/day. The perching conditions show the full range of behaviour over this range of K

_{s2}

^{v}: The irrigation accession is varied from 10 to 400 to 150 to 100 to 50 mm/year, separated by 5 years. This should provide some insight on the interaction between IA and K

_{s2}

^{v}and whether the groundwater response may be able to be used to calibrate soil parameters.

## 4. Results

#### 4.1. 1D and 2D Modelling

#### 4.2. Superposition Experiments

#### 4.3. Use of Drainage Data to Calibrate the Transfer Function

_{s1}

^{h}= 0 and K

_{s2}

^{v}= 0.0212 cm/day. The drainage volumes for other values of IA in Table 3 leads to the same contour. The relationship between the two conductivities for this contour is shown as a solid line in Figure 8b.

_{s2}

^{v}> 0.025 cm/day for high values of K

_{s1}

^{h}or >0.045 cm/day (low values of K

_{s1}

^{h}). Soil properties can then only be further constrained by fitting to the groundwater response.

#### 4.4. Approximants

#### 4.5. Whole-of-Life Modelling

_{s2}

^{v}. The highest value of K

_{s2}

^{v}(01.1 mm/day) produces the earliest and highest peak value, equalling IA after five years. For other values of K

_{s2}

^{v}, the peak values occur later and have lower values, with the lowest value of K

_{s2}

^{v}(0.01 mm/day) having a barely discernible peak. For K

_{s2}

^{v}= 0.1 mm/day, the shape mirror that of IA, but with a delay varying from 3 to 8 years. For the next highest value of K

_{s2}

^{v}, 0.05 mm/day, recharge reduces exponentially until there is no perched head and then falls to match the recharge for 0.1 mm/day. For the third highest value of K

_{s2}

^{v}, 0.03 mm/day, recharge also falls, more or less, exponentially (but more slowly than for K

_{s2}

^{v}= 0.05 mm/day), to where the perched water disappears and then falls to the final value only two years after the previous curves, and with a time delay of up to twelve years after IA. Reduction of K

_{s2}

^{v}and the presence of perched water leads to lower peak recharge values, greater time delays. When perched water disappears, the difference between the recharge disappears.

## 5. Discussion

#### 5.1. Accuracy of the Model

- (1)
- model-to-model comparison;
- (2)
- comparison of assumptions with past literature; and
- (3)
- testing with field data.

#### 5.2. Sensitivity and Calibration

_{s2}

^{v}, but much less so to K

_{s1}

^{h}. The equilibrium perched head is also very sensitive to K

_{s2}

^{v}, but K

_{s1}

^{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 K

_{s2}

^{v}suggests that groundwater responses could be used to calibrate K

_{s2}

^{v}. Because of the spatial variability of K

_{s2}

^{v}and the difficulty in measuring K

_{s2}

^{v}in the field, it is difficult to provide an independent value of K

_{s2}

^{v}within an order of magnitude, yet the impact on recharge can be very dramatic.

#### 5.3. Superposition and Approximants

#### 5.4. Learnings from the Modelling

- The 2D modelling for both new developments and water use efficiency measures: while the current modelling does capture some aspects consistently with the numerical modelling, it underestimates the overall time delays between a change in IA and a change in recharge.
- Drainage from unsaturated soils: The current model underestimates the time for drainage to occur from an unsaturated soil.
- Testing of superposition and approximants: The work so far shows that superposition and simple approximants has promise in simplifying the modelling of recharge from irrigation areas. However, it does need to be tested across a broader range of parameters and situations before regular use.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Conceptual model for theory development. The darker brown layer (layer 2) represents the impeding layer. The blue layer represents the saturated zone. The base of layer 1 is the base of the agricultural zone, while the two lighter brown layers represent higher permeability zones. Saturated conditions build up on the base of layer 1 and top of layer 2 (i.e., perching). The irrigation field extends over the horizontal axis, x, from x = 0 to x = 1. The model dimensions extend beyond the irrigation field (i.e., x > 1) to investigate the lateral effects of perching that extend to x

_{1}.

**Figure 2.**Discretisation for the FEFLOW (Finite Element subsurface FLOW) modelling of (

**a**) one-dimensional (1D) situations and (

**b**) two-dimensional (2D) situations.

**Figure 3.**The 1D modelling outputs for Experiments 7 (red), 8 (yellow) and 9 (green). (a) Transfer function (TF). Solid lines indicate FEFLOW (num-erical) outputs, while dashed line shows PerTy3 (semi-analyt-ic) outputs. The superposition for the transfer function (Experiment 9) is denoted by dotted line (super).

**Figure 4.**(

**a**) The 2D modelling outputs for transfer function for experiment 14-1. Solid lines are outputs from FEFLOW (num-erical), while dashed lines are outputs from the PerTy3 (semi-analyt-ic) model. The red lines are for total recharge; yellow that from under irrigated agriculture (IRR) and green for external to irrigated agriculture (Ext). (

**b**) Comparison of transfer functions from Experiments 9 (1D) (dashed) and 14-1 (2D) (solid).

**Figure 5.**Modelled perched head for (

**a**) Experiments 7 (1D) (red) and 9 (1D) (green); and (

**b**) Experiment 14-1 (2D). Solid lines are FEFLOW (num-erical) outputs, while dashed lines are PerTy3 (semi-analyt-ic) outputs.

**Figure 6.**PerTy3 modelling output for Experiment 10 (1D): 10a new development (new, orange line); 10b water use efficiency (WUE, green line); 10c (whole sequence of new development and water use efficiency (whole, dashed red line); Experiment 10d recharge for superposition of 10a and 10c transfer functions (super, red solid line); Irrigation accession for Experiment 10c (1D) blue line.

**Figure 7.**PerTy3 model outputs for Experiment 15 (2D): Experiment 15a new development (new, orange line); Experiment 15b water use efficiency (WUE) measures (green line); Experiment 15c sequence of new development and water use efficiency measures (whole, red solid line); Experiment 15d recharge for superposition of transfer functions (super) for 15a and 15b. The Irrigation accession (IA) is shown in blue.

**Figure 8.**(

**a**) Contours for drainage for the 3a_1 soil type for irrigation accession of 300 mm/year. Negative values correspond to no drainage, while positive values correspond to drainage volumes (mm/year). The resultant drainage for Loxton (173 mm/year) corresponds to the contour starting at the vertical conductivity for layer 2 of 0.0212 and horizontal conductivity of layer 1 of zero. (

**b**) The blue solid line shows this same contour (3a_1 soil). Contours (dashed lines) are also shown for 3a_2 soil for IA of 150 (brown, 3a_2 150) for which there is no drainage and 317 (grey, 3a_2 317)) for which there is drainage. This means that the soil properties should lie between these contours and is consistent with the blue contour for all but the lowest horizontal conductivity. Further contours (dotted lines) are shown for 3b soils (3b_1 398; 3b_2 398; 3b_3 398; 3b_4 398). Even for IA of 398 mm/year, there is no drainage. Soil properties therefore should lie above these contours. The contour for 3b_4 forms the strongest constraint.

**Figure 9.**(

**a**) Fitted approximants for 1D FEFLOW (num-erical) transfer functions for modelling experiments (7) and (8). The approximants are respectively 1 − exp(−0.11 × (t − 0.8)) for t > 2; 1 − exp(−0.32 × (t − 3.5)) for t > 4. (

**b**) Superposition of a succession of fitted approximants (a) to reductions of irrigation accession from 350 to 200, 200 to 150 (5 years later), 150 to 100 (5 years later) and 100 to 50 (5 years later) and compared to FEFLOW (Num-erical) output for 2D modelling Experiment 14-1.

**Figure 10.**Plots of recharge with time for irrigation systems with different values of K

_{s2}

^{v}(a) 0.01 (b) 0.03 (c) 0.05 and (d) 0.1 cm/day in response to a sequence of IA shown as a solid blue line.

Parameter | Symbol | Layer 1 | Layer 2 | Layer 3 |
---|---|---|---|---|

Texture | Sandy Loam | Clay | Sand | |

Saturated volumetric water content (cm^{3}/cm^{3}) | θ_{si} | 0.35 | 0.4 | 0.38 |

Residual water content (cm^{3}/cm^{3}) | θ_{ri} | 0.03 | 0.1 | 0.04 |

Air-entry potential (cm) | h_{bi} | 12.0 | 40.0 | 8.0 |

Mualem exponent | m_{i} | 8.24 | 7 | 6.94 |

Vertical saturated hydraulic conductivity (cm/day) | K^{v}_{si} | 300 | 0.03 | 500 |

Anisotropy for saturated conductivity (horizontal/vertical) | ~0 (1D) 1 (2D) | ~0 (1D) 1 (2D) | ~0 (1D) 1 (2D) | |

Thickness (cm) | l_{i} | 500 | 500 | 1500 (1D) 500 (2D) |

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

Model Expt Number | Irrigation Accessions (mm/year) | Non-Dimensional Irrigation Accession | PerTy3 | FEFLOW |
---|---|---|---|---|

IA_{n} | A | |||

7 (1D) | 230 to 100 | 2.1 to 0.91 | y | y |

8 (1D) | 100 to 50 | 0.91 to 0.45 | y | y |

9 (1D) | 230 to150 (0y) to 100 (5y) to 50 (10y) | 2.1 to 1.36 to 0.91 to 0.45. | y | y |

10a (1D) | 10 to 230 (1996) | 0.09 to 2.1 | [18] | [18] |

10b (1D) | 10 to 230 (1921) to 150 (2001) to 100 (2006) to 50 (2011) | 2.1 to 1.36 to 0.91 to 0.45 | y | y |

10c (1D) | 10 to 230 (1996) to 150 (2001) to 100 (2006) to 50 (2011) | 0.09 to 2.1 to 1.36 to 0.91 to 0.45 | y | n |

10d (1D) | Superposition of 10a and 10b | n | n | |

11a,b,c,d (1D) | 10 to 400 (1996) to 150 (2001) to 100 (2006) to 50 (2011) | 0.09 to 3.65 to 1.82 to 0.91 to 0.45 | y | n |

14-1 (2D) | 400 to 200 (0y) to 100 (10y) to 50 (15y) | 3.65 to 1.82 to 0.91 to 0.45 | y | y |

15a (2D) | 10 to 400 (1976) | 0.09 to 3.65 | [18] | [18] |

15b (2D) | 10 to 400 (1961) to 200 (1981) to 100 (1986) to 50 (1991) | 0.09 to 3.65 to 1.82 to 0.91 to 0.45 | y | y |

15c (2D) | 10 to 400 (1976) to 200 (1981) to 100 (1986) to 50 (1991) | 0.09 to 3.65 to 1.82 to 0.91 to 0.45 | y | n |

15d (2D) | Superposition of 15a and 15b |

**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].

District L = Loxton B = Book L/B = both | Soil Type | Layer 1 Thickness l_{1} (cm) | Layer 2 Thickness l_{2} (cm) | φ | D (mm/year) | ||||
---|---|---|---|---|---|---|---|---|---|

IA (mm/year) 1920–1970 | IA (mm/year) 1970–1990 | IA (mm/year) 1990–2002 | IA (mm/year) 2002–2006 | IA (mm/year) 2006–2013 | |||||

398 | 339 | 317 | 150 | 83 | |||||

L | 3a_1 | 250 | 350 | 0.43 | D | 173 | 151 | ND | ND |

B | 3a_2 | 400 | 600 | 0.25 | D | D | D | ND | ND |

L/B | 3b_1 | 500 | 300 | 0.51 | ND | ND | ND | ND | ND |

L | 3b_2 | 1200 | 200 | 0.76 | ND | ND | ND | ND | ND |

L/B | 3b_3 | 400 | 200 | 0.76 | ND | ND | ND | ND | ND |

B | 3b_4 | 500 | 500 | 0.30 | ND | ND | ND | ND | ND |

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**MDPI and ACS Style**

Walker, G.R.; Currie, D.; Smith, T.
Modelling the Effect of Efficiency Measures and Increased Irrigation Development on Groundwater Recharge through a Deep Vadose Zone. *Water* **2020**, *12*, 936.
https://doi.org/10.3390/w12040936

**AMA Style**

Walker GR, Currie D, Smith T.
Modelling the Effect of Efficiency Measures and Increased Irrigation Development on Groundwater Recharge through a Deep Vadose Zone. *Water*. 2020; 12(4):936.
https://doi.org/10.3390/w12040936

**Chicago/Turabian Style**

Walker, Glen R., Dougal Currie, and Tony Smith.
2020. "Modelling the Effect of Efficiency Measures and Increased Irrigation Development on Groundwater Recharge through a Deep Vadose Zone" *Water* 12, no. 4: 936.
https://doi.org/10.3390/w12040936