Agriculture is a particularly sensitive sector to the potential impacts of climate change. Thus, irrigation infrastructure is required to be robust to cope with these potential threats. The objective of this research is designing more robust irrigation networks, considering cost and stakeholder contribution. To that end, the investigation was addressed in three phases: a sensitivity analysis to understand the effectiveness of the distinct variables, a cost-effectiveness analysis assessing their efficiency, and a global study of the most efficient variables to provide an insight into their function. The sensitivity analysis indicates that the networks oversized by means of the coefficient of utilisation or the factor of safety, behave better than those oversized via the continuous specific discharge; moreover, the degree of freedom has been shown ineffective. The cost-effectiveness analysis shows that the coefficient of utilisation and the factor of safety are the most efficient variables, as they introduced safety margin oversizing fewer network elements and to a lesser extent than the continuous specific discharge. It also shows that stakeholder contribution, conveyed as a reduction of the degree of freedom, plays an important role in the network’s adaptive capacity to change. The global study of these variables reveals the subtlety of the coefficient of utilisation, which is the variable that better reproduces the farmer behaviour during demand increase scenarios. In conclusion, the results identify the coefficient of utilisation as the variable which provides the safest margins and reveal the importance of stakeholder contribution in absorb the demand increase in a better manner.

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 (

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 (

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

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 (

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The safety coefficients are the variables for oversizing the network which enable it to cope with larger demand during operation. The following two safety coefficients have been traditionally used: the

The discharge determination process consists of the following: allocating the hydrant discharge, determining the probability of utilisation of the hydrants and calculating discharge by means of a statistical formula.

The first step is the determination of the flows allocated to each plot i which is the hydrant discharge (d_{i}). Allocation is established by being based on two irrigation variables: the continuous specific discharge and the DF, and the plot area (A_{i}) (

The second step is the calculation of the probability of utilisation of each hydrant (p_{i}) (

The third step consists in the computation of the design flows. Flows are computed by means of Clément’s First Formula (

where Q is the flow rate of the section under consideration, which supplies n plots downstream; and U is the standard normal variable, which is a function of the operation quality. The first term of Clément’s First Formula represents the mean (µ) and the second term the standard deviation (σ) (

Clément’s First Formula results may be directly multiplied by a factor of safety to oversize the design flows (

The application of this formula directly involved the use of two irrigation variables: the operation quality and the factor of safety.

As may be observed, all the irrigation variables intervene in the discharge determination process. Thus, all could influence the resulting design flows and all may be used for oversizing the network. Nonetheless, each variable may influence discharges in distinct ways and to a different extent. Consequently, the safety margins are added with distinct costs and varying degrees of effectiveness for meeting increases in future demand (

The objective of this research is adding knowledge of the role and influence of each variable and determining which may improve the robustness of the network effectively and efficiently. In this context,

The research was addressed in the three following phases (

A sensitivity analysis was performed to evaluate the ability of the irrigation variables for improving system robustness, that is to say, their effectiveness. The study involved calculation and analysis of eight cases: a base-case in which the network was designed without any safety margin and seven cases in which margins were introduced via distinct irrigation variables. The safety margin was considered as the relative discharge increment in design conditions with respect to the base-case (ΔQ1) (

Climate change is one of the drivers which may lead to demand increases. Several studies have evaluated the impact of climate change on irrigation water requirements.

In this study, scenario Q2 assessed the network performance under increased demand conditions. The network performance was assessed by using the deficit between the design conditions and the demand increment situation (

Here an irrigation network that supplies 100 homogeneous plots of area A has been analysed. The continuous specific discharge was q (the resulting value for the average cropping pattern during the peak season). The other irrigation variables were set within the usual ranges of design in the professional practice (

In addition, it may be also observed how the variables change as demand increases from the design conditions (Q1) to the demand increment conditions (Q2): (i) the continuous specific discharge became 1.4·q, since an increase of 40% was analysed; (ii) the DF reduces as demand rises; once the network is built and in operation, should a farmer need a greater volume of water the only alternative would be to maintain the hydrant open for a longer duration as the hydrant discharge is constant; (iii) the coefficient of utilisation of the network became equal to 1, given that the Q2 scenario analysed the network response when the safety margin was consumed; (iv) the factor of safety, in a similar way, became 1 when evaluating the Q2 scenario; (v) the operation quality remained constant in both scenarios. This is the variable that statistically characterises the service. In Clément’s First Formula it influences the standard deviation (

The sensitivity analysis shows the variables effectiveness to improve the network robustness. Apart from this, it is also necessary to assess the respective efficiency, that is to say, the economic impact of each variable in achieving a given effectiveness. For such a reason a cost-effectiveness analysis has been carried out. This consists of both a critical examination of the design process and a study based on the results of the sensitivity analysis.

The critical analysis of the design process was carried out with the aim of determining which of the network elements (trunk mains, distribution mains, service pipes and hydrant equipment) are affected by each variable. It consisted of the examination of the discharge allocation process, at the head and tail sections, in relating the variables with the design discharges of the different elements.

The cost-effectiveness study is based on cases 2, 3 and 8 of the previous sensitivity analysis, in which design discharges were oversized by means of the coefficient of utilisation, continuous specific discharge and factor of safety, respectively. These cases were selected because they provided the same network performance when demand increased. Not a single case in which the DF was used for adding a safety margin was selected for the study, since this variable was shown to be ineffective in addressing the demand increase, as further explained in the results and discussion sections.

In line with the objective of the study, the results of the sensitivity analysis (design discharges at the head section) were complemented with the calculation of the design discharges at a terminal section which supplied one plot, and with the determination of a parameter which characterised the stakeholder contribution to adaptation, named

The coefficient of utilisation and the factor of safety are shown as the most effective and efficient variables in increasing network robustness. In order to acquire deep knowledge of the specific function performed by each, their effect has been evaluated in various cases and sections located along the network from head to tail.

Therefore, this study analysed a network that supplies water to 400 homogeneous plots, evaluated under the following two scenarios: the first having resulted from oversizing the network by using the coefficient of utilisation (Qr); and the second having arisen from oversizing it with the factor of safety (Qk). Accordingly, calculations were performed for three cases: Case ‘a’ in which both variables were selected so that the introduced margin matches in the head section (the section which supplies the 400 plots); Case ‘b’ in which the variables were selected in order to include the same margin at an intermediate section (with supply to 100 plots); and Case ‘c’ in which the variables were adjusted at the tail (supply of 10 plots). The relative discharge variation (ΔQ_{rel}) among the abovementioned scenarios was also determined (

The rest of the variables were selected by using the same criteria as in the sensitivity analysis. Therefore, it was assumed that the plots have an area A=A, the continuous specific discharge is q=q, the DF=3 and the operation quality is OQ=96% (U=1.75).

The results of the eight cases studied in the sensitivity analysis are shown in

The results of cases 2, 3, 5 and 7 (each with an irrigation variable modified by 20%), show that discharges under design conditions (scenario Q1) are greater than that of Case 1-base; with increases that range from 2.7% to 20.0%. This indicates that all the irrigation variables could be used to oversize the network to different extents. It is also noted that the margins helped to relieve the rise in demand, reducing the 33.2% deficit of Case 1-base to values to 11% (Case 7). Nonetheless, Case 5 (with the DF increased by 20%), did not produce any benefit to the network, with the deficit being 33.1%.

Cases 2, 4, 6, and 8 analysed networks with the same Q1 (

The critical analysis of the calculation process gives a first approximation of how the variables intervene in the design discharge determination at distinct network points, directly related with the sizing of the network components and the cost.

As a result of this analysis it has been observed that the use of the continuous specific discharge or the DF affects the hydrant discharge allocation directly and linearly (

The design discharges, for cases in which the network was oversized by means of the coefficient of utilisation, continuous specific discharge or factor of safety, under the condition that a certain performance is required for a given demand increase, are presented in

Focussing on the terminal section, it can be seen that the use of the coefficient of utilisation or the factor of safety do not oversize the network elements (

All the outcomes indicate that improving the network safety through the coefficient of utilisation or the factor of safety is more economical than by means of the continuous specific discharge, as they oversize fewer elements of the network and do so to a lesser extent. This efficiency is not only related to the use of the coefficient of utilisation or the factor of safety, but also to stakeholder contribution. The farmer collaboration required to address the demand increase scenario is 28.7% for Case 2 and Case 8, and 14.3% for Case 3. This result also concurred with the critical analysis findings, since the variables that do not affect the hydrant allocation and provide no more comfort to farmers, require their collaboration when demand increases. Such collaboration is conveyed as a reduction of the DF.

_{rel}).

It can be observed that the margins provided by each variable vary from one part of the network to another. The margins increased by around 50% from head to tail in all cases. This effect responds directly to the statistical adjustment carried out by Clément’s First Formula (

The results also show that the margins behave differently in the various points of the network depending on which variable has been used. The relative discharge variation between the scenarios is zero (Qr=Qk) at the head in Case ‘a’, the intermediate section in Case ‘b’ and the tail in Case ‘c’, because the variables were selected to introduce the same margins in those points. However, the relative discharge variation diverges from the set-point, with the difference being greater as the distance increases. In addition to this, it should be noted that the differences do not have the same sign when they near the head or the tail. The differences are negative upstream from the set-point, which indicates that for a significant number of plots the coefficient of utilisation provides a greater margin than the factor of safety. In contrast, the differences are positive downstream which means that for a small number of plots the coefficient of utilisation introduces a smaller margin than the factor of safety.

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 (

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 (

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 (_{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 (

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 (

Some authors have identified the use of the coefficient of utilisation as an adjustment parameter of farmer behaviour in statistical distribution (

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 (

On another note, the safety factor is unable to match this behaviour. As can be seen in

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.

The authors wish to thank Professor Luis Garrote and Professor Francisco Laguna for their reviews and comments. Acknowledgement is also given to Andrew Selby for his help with the English edition.