Records obtained over the past decades have shown that there has been a gradual increase in mean temperatures. Climate models predict that such a growing tendency could not only continue but also influence other climate variables, such as frost and rainfall (IPCC, 2013). The close relationship between climate and agriculture makes agriculture particularly sensitive to the potential impacts of climate change (Moriondo et al., 2010; Iglesias et al., 2012). Climate change may lead to modifications in cropping patterns, crop water requirements and, among others, the seasonal distribution of water demand. As these are determinants of effective water demand, impact may affect the quality of irrigation (Rodríguez-Díaz et al., 2007a; Daccache et al., 2010a; Pérez-Urrestarazu et al., 2010; Maeda et al., 2011). Besides climate change, there are other determinants that could also lead to variations in the cropping pattern and modify water requirements, such as: the agricultural markets evolution, the agricultural and hydraulic policy or the introduction of new laws and standards (Berbel & Gutiérrez, 2006; Gianoccaro & Berbel, 2011; Dury et al., 2012; Rinaudo et al., 2013).

The aforementioned may adversely affect the performance of irrigation networks as a consequence of the consequent total or seasonal demand increase. One way of adapting irrigated agriculture to climate change is the design of robust infrastructure (Iglesias et al., 2011). The irrigation network design is required to consider this, given that demand greater than the existing at the design period may have to be met during the operational life. Therefore, the design should provide safety margin for backing future service changes (Granados, 2013). Such a cushion should be added during the project phase, as once the network is in operation resolving performance problems becomes more complex, inopportune and expensive (Lamaddalena & Sagardoy, 2000).

Computing of the peak design flows is one phase of the design process where safety margins should be introduced. One model designed to compute the discharges that has been widely used is that proposed by Clément in 1966. Its first generalised formula (Clément’s First Formula) has been contrasted in several studies that considered it appropriate for the design of on-demand irrigation networks, although it should be noted some of its base assumptions show certain degrees of inaccuracy (Abadía, 2003; Monserrat et al., 2004; Íniguez-Covarrubias et al., 2007; Rodríguez-Díaz et al., 2007b).

The abovementioned discharges were defined on the basis of: cropping patterns, service conditions and water requirements. All these factors are collected through the irrigation variables; that is to say, the continuous specific discharge, degree of freedom, operation quality, and safety coefficients (Granados, 1986; Labye et al., 1988; Lamaddalena & Sagardoy, 2000).

The continuous specific discharge (q) is the flow which should be supplied continuously during the total operating time of the network to provide crop water requirements. This value is usually referred to as the peak season and average cropping pattern.

The degree of freedom (DF) is the ratio between the operating time of the network (t) and the required time that the farmer has to open the hydrant to meet the demands of the average cropping pattern during the peak season (t’) (Granados, 1986) (Eq. [1]). For a DF=1, in satisfying water requirements the farmer would be obliged to irrigate continuously. Hence, this represents a level of comfort afforded to the farmers that permits them to organise their activities. The DF is usually assigned by being based on the size of the plot. Large plots have a lower DF than small plots. That is to say, farmers with small plots are granted more time to manage their irrigation.

The research was addressed in the three following phases (Fig. 1): i) Performing a sensitivity analysis to determine the effectiveness of the safety margins added by the different variables; ii) Conducting a cost-effectiveness analysis of the groups that had previously shown a better performance with the objective of studying their efficiency; iii) Analysing the variables which offered the best cost-effectiveness ratio, with a detailed study of their influence in distinct parts of the network (head, intermediate, and tail sections).

The study has some limitations that should be considered when interpreting the following discussion. It was limited to branched on-demand irrigation networks which end in hydrants that supply plots. Furthermore, it was assumed that water is billed according to consumption and flow is restricted in the hydrant. Both are considered necessary conditions for providing an organised service, namely avoidance of water wastage and imbalances in the operating pressures (Daccache et al., 2010b). In networks where these are not met, the statistical models may not fit the farmer behaviour. If water consumption is not charged, farmers may open a given hydrant for a longer time than that required. Then, if flow is uncontrolled while the most favourable plots would take greater pressure than required the unfavourable areas could suffer significant drops in pressure. Moreover, networks which serve a large number of small plots, with considerable degrees of freedom may behave like those in which the flow is uncontrolled. In such cases the application of stochastic methods for determining the flow rates is advised (Khadra & Lamaddalena, 2006; Moreno et al., 2007). In pressurised irrigation networks with hourly energy pricing, the probability of utilisation of the hydrants may be highly influenced and differ substantially from the uniform one. In such cases the probability must be computed, with it being disaggregated in homogeneous time periods according to the electricity tariffs (Pulido-Calvo et al., 2003). Furthermore, it should be noted that looped networks and networks with star topology, with several supply sources, are beyond the scope of this paper, given that they should be calculated by using other methodologies (Reca et al., 2002). Notwithstanding the above, it could be reasoned that the results provide relevant information for designing more robust irrigation networks, considering cost and stakeholder contribution.

The research shows the influence of the irrigation variables on the determination of the design discharges. The network design should always consider the possibility that, at some time during operation, water consumption may rise as a consequence of climate change or because of other circumstances that may lead farmers to grow a more demanding crop. In order to cope with such a scenario, both a robust network and the stakeholder contribution are required.

The sensitivity analysis confirms that the network could be oversized acting on the irrigation variables during the discharge determination phase. It also shows that the margins provided by each variable are not equally effective when a scenario of increasing demand arises. The results show that the coefficient of utilisation and the factor of safety are the most appropriate tools available to efficiently oversize the network. It is noticeable that networks oversized by means of these variables behave better when demands increase than those oversized with the continuous specific discharge or the DF (Fig. 2). The effectiveness of each variable as a tool used to introduce margins is related to their specific function: the continuous specific discharge aim seeks to characterise the water requirements of the cropping pattern, the DF offers comfort to farmers, and the safety factors include a surplus in design to address unexpected events.

The sensitivity analysis also shows that the DF plays an important role in the network’s adaptive capacity to change. Its reduction in attending the increment of demand has a beneficial effect on the network performance. It should be noted that as a network in operation cannot be easily modified this would require additional resources. Accordingly to this, when farmers increase water consumption the only way to satisfy it is by irrigating during a longer time. As a consequence of this, the probability of utilisation of the hydrant increases, which in Clément’s First Formula is reflected as an increase in the mean and a reduction in standard deviation (Eq. [6]). The mean discharge increases linearly with the consumption increment, while the standard deviation decreases exponentially as the population increases. Physically, this means that there would be an increment in farmers irrigating simultaneously and that demand will coincide in the terminal pipes. This effect would be diluted in the trunk mains where the mean increase would be partially balanced by the standard deviation reduction. Thus, as more terminals are designed in consideration of simultaneity (Q=∑d_i) the more robust the network will be.

In summary, if a farmer meets demand by irrigating for greater duration efficiency improves, given that this produces a tempering effect on the discharge rates. The increment of the irrigation time, depriving a part of the initial DF, may be assumed by the farmer if the service does not deteriorate. That is to say, the flow rate and the pressure remain adequate. Thus, this variable must be set by considering that the farmer will sacrifice time when a more demanding scenario is present.

It is clear that the potential increase could also be addressed by increasing hydrant allocation. In such a case, when demand rises the farmers would not be required to cooperate, since they would be in the original design conditions. As the hydrant allocation is a direct function of the continuous specific discharge and the DF (Eq. [3]), it could be oversized by modifying these variables, which is something usually performed in professional practice. Modification of these variables is equivalent to designing the network for a more demanding cropping pattern than that resulting from agronomic studies or affording the farmers with a greater, and unreasonable, DF. Either one case or the other alters the conditions which result in the previous studies and leads to a less effective network. Additionally, the cost-effectiveness study shows that oversizing the discharges by using the continuous specific discharge or the DF influences the entire hydraulic system: hydrant equipment, terminal pipes, distribution mains and trunk mains. Given that, the use of the coefficient of utilisation or the factor of safety affects only the distribution and trunk mains, they are a more efficient (cheaper) option.

Therefore, within the recommendations for designing a robust and efficient network, the selection of the continuous specific discharge and DF should agree with the cropping pattern provided by the agronomic study and to an appropriate and medium comfort level for the farmer.

In the study of the function of the coefficient of utilisation and the factor of safety it was observed that while the first produced an increase in the mean and a decrease in the standard deviation, the second increased both linearly and equally (Eq. [7]). The results have shown such an effect which suggests that the coefficient of utilisation could better oversize the network as it reproduces better the conditions that arise when demand increases, i.e. increment of the irrigation time and simultaneity in the terminal pipes.

Some authors have identified the use of the coefficient of utilisation as an adjustment parameter of farmer behaviour in statistical distribution (CTGREF, 1977; Clément & Galand, 1979; Lamaddalena & Ciollaro, 1993; Lamaddalena & Sagardoy, 2000). Others, such as Monserrat et al. (2004) have indicated that this variable has a physical meaning as introduced by Clément in 1966. This study provides an insight into the coefficient of utilisation, its action and its physical meaning. The coefficient of utilisation is a subtle safety factor. Such subtlety comes from the peculiar way of introducing the safety margin, correcting the probability of utilisation of the hydrants (Eq. [4]). As it oversizes the network, it can supply demand in less time than in the available operational one. This is a virtual reduction of the network operation time, as it remains functional for the total time. Hence, the margin consists of a virtual time cushion which is automatically mobilised when the water requirement increases.

This cushion has a particular way to develop in the discharge determination process, given that it is linked to the probability of utilisation of the hydrants. The coefficient of utilisation virtually reduces the network operating time which, in turn, increases the probability of utilisation of the hydrants. This increment in the probability influences the statistical adjustment of Clément’s First Formula (Eq. [5]), producing an increment in the mean and a decrement in the standard deviation (Eq. [6]). This distribution of the margin fits the network behaviour when this has to meet higher demands. In such a case, farmers are required to irrigate for more time. As the hydrant discharge is fixed and controlled by a flow limiter, more farmers would irrigate simultaneously, hence the dispersion will be reduced which would coincide with the adjustment provided by the coefficient of utilisation.

On another note, the safety factor is unable to match this behaviour. As can be seen in Figure 3, the curves that represent discharges in scenarios Qr and Qk intersect at the adjustment point and then diverge with different signs upstream or downstream from such a point. If the margin was adjusted at the tail section (Case ‘c’) the upstream sections would be undersized (meaning less effectiveness), while if the adjustment was made at the head section (Case ‘a’) the downstream discharges would be oversized (less efficiency).

In conclusion, this paper has provided an insight into the specific role of each irrigation variable. Among them the coefficient of utilisation is recommended as the best for improving network robustness towards potential demand increases. Results show that the coefficient of utilisation is the variable that offers not only the best cost-effectiveness relationship but also that which best suits statistical adjustment to the process that occurs when farmers are required to satisfy greater water requirements. Additionally, the study has highlighted the importance of farmer collaboration in the adaptation process. Such cooperation, considered a reduction of the degree of freedom, benefits the operation and abates the peak demands that are diluted over time.