## 1 Introduction  
Irrigation is an essential agricultural practice for food, pasture and fibre production in semiarid and arid areas. In many countries including Australia, efficient water use and management are today's major concerns. The bulk of the irrigation water is sourced from rivers and dams and conveyed via open channels or pipelines to irrigated farms for storage before use or direct application to root zones. Irrigators who use groundwater often have storage tanks on their properties. At the farm level, irrigation systems or methods commonly in use may be broadly classified as sprinkler, surface, and drip or trickle systems. In sprinkler systems (e.g., solid sets, centre pivots and travelling irrigators), water is delivered in form of sprays using overhead sprinklers. In drip or trickle systems, water is delivered in small amounts via small nozzles installed in pipes or tapes, which can either be above the ground or underground. The sprinkler and drip/trickle systems are also referred to as pressurised systems, as they operate under low pressure which often involves some form of pumping. In surface systems (e.g., furrow and basin/border), water is conveyed over the field surface by the gravitational force. The furrow system is the most common method for the irrigation of row crops in Australia and in the world. Globally, it is estimated that about 70% of fresh water abstracted is used to irrigate 25% of the world's croplands (399 million ha) which supply 45% of global food [1]. Water used for industrial and domestic purposes account for approximately 20% and 10% of the total global water usage, respectively. In Australia, for instance, in the year 2016-2017, 9.1 million mega litres were used to irrigate 2.2 million ha [2]. The demand for fresh water resources is on the increase, and the trend is likely to continue with the increasing population that comes with increased demand for food and fibre, and the predicted negative impacts of climate change. There is also increased awareness of the need to provide sufficient water to serve other ecological services. There appears to be consensus that irrigated agriculture in general is up against a future with less water. This, therefore, calls for increased effectiveness in the utilisation of the scarce water resources, a concept that is technically called water use efficiency (WUE) or simply irrigation efficiency. From an engineering standpoint, WUE is often defined using a volumetric or hydrological approach, simply as the proportion of the water supplied through irrigation that is productively or beneficially used by the plant (Equations (1) and (2)). This definition is predominantly used when referring to field-scale irrigation water management. However, it should be noted that WUE may also be assessed at the catchment or basin scale [3]. The two most commonly used efficiency measures of an irrigation system are (i) application efficiency (AE) and (ii) requirement efficiency (RE), which can be written as:  
\[\text{AE}=\frac{\text{volume of water stored in the root zone}}{\text{total volume of water applied}} \tag{1}\]  
\[\text{RE}=\frac{\text{volume of water stored in the root zone}}{\text{water deficit prior to irrigation}} \tag{2}\]  
The efficiency performance measures, AE and RE, are only applicable at the field scale. However, losses of water also occur in conveyance and distribution channels prior to delivery to the field. If the water is stored in dams prior to usage, then further losses may occur as a result of evaporation and seepage. Performance measures used in these cases include conveyance, distribution and storage efficiencies. On the other hand, the efficiency of irrigation water use may also be seen in a plant physiological sense, and in particular as a comparison of the yield or economic return of an irrigated crop or pasture to the total amount of water transpired by the crop or pasture. In fact, in recent literature (e.g., [4]), this is commonly referred to as irrigation water productivity and not WUE.