**1. Introduction**

Irrigated agriculture leads to greater infiltration of water than non-irrigated agriculture, especially in semi-arid and arid regions [1]. This, in turn, leads to greater recharge to underlying groundwater systems, where it can cause salinization and waterlogging of agricultural land and salinization of water resources [2] and associated riparian zones. Where groundwater is fresh, irrigation recharge may have environmental benefits in returning fresh groundwater to streams and groundwater-dependent ecosystems and providing recharge for groundwater users [3].

The assessment and managemen<sup>t</sup> of irrigation environmental risks requires an understanding of the processes that link actions, such as irrigation development and subsequent water use measures, and the environmental impacts. This linkage is not just characterized by changes in water fluxes, but in time delays for pressure changes to move from the site of the action (irrigation fields) to the site of the impact (streams, affected land, groundwater-dependent ecosystems). Where water tables are deep, the unsaturated zone under irrigation areas is an important pathway between actions and groundwater systems, that link to impacts [4]. Yet, this zone is often poorly understood, falling between the disciplines of the agronomic engineering and hydrogeology, meaning that links between actions and impacts may be poorly understood.

Previous models of the unsaturated zone have mostly assumed that water moves under gravity towards the water tables [5,6]. This means that below the agricultural zone, fluxes do not change in magnitude from the agricultural soil zone to the groundwater. However, the larger soil water fluxes under irrigation may not be able to be transmitted by gravity [7], where soil vertical hydraulic

conductivity is low. This leads to conditions of perched water tables, with increased hydraulic gradients, saturated conditions and lateral movement of water above these low-conductivity zones [8–10]. Sub-surface drainage may be required to avoid waterlogging and land salinity and water may be lost to the land surface from the perched layer by drainage and evapotranspiration. Perched water tables may, therefore, both change the magnitude of vertical fluxes and 'smear' the movement of pressure changes over time. Modelling perched water tables is important for recharge in karstic geology [11], managed aquifer recharge [12], contaminant sites [8–10] and ecology of ephemeral streams [13,14].

Irrigation districts can be complex, with di fferent zones being developed over time over a range of soils and water table depths. Any unsaturated zone model needs to be used in conjunction with groundwater models, which are often implemented to assess irrigation risks and support the design of mitigation measures. Unsaturated zone models, therefore, need to represent the main processes in these complex irrigation districts that are important for the assessment and managemen<sup>t</sup> of risks; ye<sup>t</sup> be simple enough to be practically implemented. The unsaturated zone models are required to link managemen<sup>t</sup> actions, such as water use measures to recharge across the irrigation district as a function of time, and space.

While numerical hydrological models are able to model these processes, the implementation of such models under complex irrigation districts with perched water tables is often impractical. Simplicity of process representation may be addressed by keeping the number of parameters small, seeking data sources that may be used for the parameterization and calibration of parameters, and using algorithms that can be run relatively quickly in conjunction with the groundwater model. The models and algorithms should be capable of representing the lifetime of irrigation districts, including new developments, water-use e fficiency measures and decommissioning.

This paper describes the semi-analytical PerTy3 model, which has been developed to address issues in the western Murray Basin in southern Australia. Basin-wide strategies have been responsible for reducing river salinity in the lower reaches of the River Murray [15]. This has been possible through the combination of groundwater pumping and incentives for improving water use e fficiency of irrigation districts. Groundwater models have been implemented across the western Murray Basin to assess salt load to the river. The highest-risk irrigation areas in the western Murray Basin overlie a saline regional groundwater system, which discharges into the River Murray. The paper tests and documents the PerTy3 model, as it relates to new developments.

However, even the application of semi-analytical models can be complex and resource-intensive, so this paper also explores the application of conceptual transfer functions [16–18] for individual actions, that can be superimposed. If such functions are shown to work, it would allow a transfer function model to be used for each development and action and then added, thus simplifying the estimation of recharge. Such models have previously been used for regions in which there are frequent fluctuations of the water table in response to recharge events.

Finally, since perched water tables lead to lateral movement of water, there is a need to consider both 'greenfield' and 'brownfield' developments. A greenfield development is one for which there is no hydraulic interference from nearby irrigation areas, while the opposite is true for brownfield developments. The antecedent moisture caused by prior nearby developments is thought to reduce time lags for wetting fronts to reach the water table. If so, there would be a need to consider the configuration of irrigation developments, which would add considerable complexity to the estimation of recharge under irrigation areas. This paper will consider the e ffect of interference between irrigation fields.

The aims of this study are to:

	- (a) a conceptual model representing the main physical processes at the scale of the irrigation district and periods of seasons and years;
	- (b) continuity of modelling between conditions of perching and non-perching;
	- (a) superposition of actions; and
	- (b) conceptual approximants for transfer functions.

A further paper [19] describes the development of models for change in recharge due to water-use efficiency measures and for the whole-of-lifetime irrigation, including new development, water-use measures and decommissioning. A pilot study for the Loxton-Bookpurnong district in the western Murray Basin is described in [20]. The soil properties and other characteristics of that area will be used within this paper.
