Introducing an economic agricultural water distribution in a hyper-arid region: A case study in Iran

Introducing an economic agricultural water distribution in a hyper-arid region: a case study in Iran Mehdi Yaltaghian Khiabani, Seied Mehdy Hashemy Shahdany, Yousef Hassani and Jose M. Maestre ABSTRACT Operational management of agricultural water based on an economic perspective was investigated as a sustainable approach in water shortage periods. Accordingly, an automatic water distribution system was coupled with the Positive Mathematical Programming economic model for a sustainable agricultural water operation in the Roodasht irrigation network, Iran. Operational management was carried out based on the economic value of water in each irrigated unit. According to the results, the existing operating system was able to supply 71 and 22% of farmers’water requirements under normal and water shortage conditions, respectively. However, employing the proposed automated operationaleconomic approach reduced water consumption by 14.3%, while maintaining the cultivation area by 11% and increasing farmers’net profit to 840,000 USD under water scarcity. The economic operation can reduce water losses, implement economic strategies in those districts without water marketing mechanisms, and provide sustainable management of limited water resources in hyper-arid regions. Key words |automation, irrigation district, socioeconomic, sustainable water management, water conservation HIGHLIGHTS •An operating system is proposed for districts with a lack of a market mechanism. •Surface water distribution is conducted based on the economic value of water. •The water conservation objective is fulfilled by employing an automatic control system. •An automatic operating system is developed to fulfill the economic objectives. Mehdi Yaltaghian Khiabani Department of Water Engineering, College of Aburaihan, University of Tehran, Pakdasht, Iran Seied Mehdy Hashemy Shahdany (corresponding author) Department of Water Engineering, College of Aburaihan, University of Tehran, Pakdasht, Iran and Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK, USA E-mail: [email protected] Yousef Hassani Water Accounting Regional Project in Iran, FAO, Tehran, Iran Jose M. Maestre Department of Systems and Automation Engineering, University of Seville, Seville, Spain ABBREVIATION RNB Roodasht Northern Branch MPC Model predictive controller PMP Positive Mathematical Programming ICSS Irrigation Conveyance System Simulation S-V Saint-Venant equation RMSE Root-mean-square error CRM Coefficient of residual mass ID Integrator-delay model NCO Normal Condition Operation scenario IFU Inflow Fluctuations of Upstream scenario COMR Current Operational Method of Roodasht AOE Automated Operation-Economic alternative TOE Traditional Operation-Economic alternative AOF Automated Operation-Fair alternative TOF Traditional Operation-Fair alternative This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/ licenses/by-nc-nd/4.0/). 548 © 2021 The Authors Journal of Hydroinformatics |23.3 |2021 doi: 10.2166/hydro.2021.008 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 INTRODUCTION The agriculture sector includes a significant portion of entrepreneurship, a substantial income source, and the means of support for poor rural households. People whose lives depend on agricultural activities make up about 40% of the world’s global population. In most agricultural societies, farmers’livelihood has received considerable attention from the government to ensure food security (Nourzadeh et al. ). Simultaneously, the reduction of available water resources due to climate changes, population growth, and malfunction of water distribution infrastructure in the agricultural sector has drawn attention to optimal management and operation of existing water resources (Monem & Hashemy ). The development of costeffective water distribution policies under water scarcity conditions has been a matter of interest to water managers and researchers. In this respect, the objective is to maximize farmers’net profit under unbalanced water supply and demand conditions by distributing and delivering more water to high-value economic areas (Ren et al. ). Most hydro-economy studies focus on large-scale issues (such as large basins); meanwhile, the literature on reducing irrigation losses mainly concentrates on small-scale farms. Accordingly, this study aims at filling the research gap (water delivery and distribution between suppliers and consumers) in integrated water resources management by providing effective management solutions for the economical operation of water delivery and distribution networks (Sheikhipour et al. ;Eini et al. ). The present study suggests a single operational-economic strategy under water scarcity conditions to connect macro- (basin) and micro- (farm) management of water resources in a surface irrigation network. Thus, this study aims to apply an operational-economic framework over the distribution of water among offtakes based on the weighted average of water’s economic value for agricultural products under water scarcity conditions. For this purpose, integral parts of the model, including the operational model (hydrodynamic simulation) and the economic model (farming activities), are considered, respectively, to examine water distribution alternatives by which water conveyance along the canal fulfills the offtake demands and reproduces the farmer attempts from an economic point of view (Hashemy Shahdany & Roozbahani ). Definitely, farming units with better efficiency (such as low irrigation losses, high production yields and use of better fertilizers) would have more water value and, subsequently, acquire more share during circumstances of water shortage. Additionally, because of water scarcity, some agricultural products are partially removed (mainly low-value crops are cut down) to offer an effective crop pattern with maximum benefit. Linking the above-mentioned elements creates a state-of-the-art platform whereby decisions on managing water can be investigated from various operational and economic perspectives. This, in turn, directs water shortages to low-value units, ultimately leading to an increase in the net profit in the irrigation district (Rosegrant et al. ). The implementation of this strategy should be supported by the delivery and the distribution system of the irrigation network in a scale that has never been investigated in formerly done researches. The selected case study is the main canal of the Roodasht Northern Branch (RNB) irrigation network in central Iran. This canal includes a traditional delivery and distribution system and fixed duck-bill water regulating structures. Due to inefficient operation and poor performance of the water delivery and distribution system, especially in regions located at the downstream part of the canal, farmers face inadequate water supply for their agricultural units. On the other hand, water shortages and fluctuations of inflow to the canal headgate have negatively affected the irrigation network operation. For this reason, intelligent operational management of the water conveyance, distribution, and delivery systems, provided by optimal control systems, can significantly increase the flexibility of water distribution and reduce the operational water losses within the canals’networks related to the inflow fluctuations derived from drought periods. To this end, the function of the suggested framework was modeled in RNB (by gathering real data on canal operation and agricultural area for 2015) for coping with the canal inflow fluctuations and managing the water scarcity given the economic principles to find if this is an effective alternative for handling the water deficit (Shahdany et al. ). The centralized configuration of a model predictive controller (MPC) has been widely applied in studies related to canal automation, and this controller has shown promising 549 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 performance since it employs optimal control to provide a highly intelligent operational performance of the canal network (van Overloop et al. a;Zafra-Cabeza et al. ; Maestre & Negenborn ). Thus, automated adjustment structures equipped with MPCs have been proposed as an alternative to fixoverflow regulating structures for distributing water among offtakes based on their economic value. Practically, water’s economic value in agricultural units determines the tasks of MPCs in supplying water to offtakes under defined water scarcity scenarios. Under this circumstance, each tertiary farming unit acquires a dedicated water share from the operation model wherein the economic model estimates the high-profit crop pattern. However, the MPC (an operation model) receives economic signals that change it into a water management plan and then, actually, prioritize the farming units. Water delivery and distribution activities were simulated by an opensource hydrodynamic model (Hashemy Shahdany et al. a) under different operational scenarios, including fluctuation and normal inflow. To investigate the desirability of operation scenarios, the performance assessment criteria, introduced by Molden & Gates (), were employed. The Positive Mathematical Programming (PMP) economic model was used for simulating the agricultural activities of farmers and predicting their reaction to water shortage scenarios based on their assumption of the highest benefit. The economic value of water for crops was considered as the economic criteria (Graveline ). By combining the PMP economic model and the MPC operation model, an operational-economic structure was developed to maximize network profits, while reducing operational losses under water scarcity circumstances. The results obtained from different delivery and distribution alternatives were compared. MATERIALS AND METHODS Study area The Roodasht irrigation network located in the middle part of Iran is the study area of this research. Figure 1 shows a plan view of the irrigation canal networks in the irrigation district. Table 1 shows the hydraulic and physical characteristics of the trapezoidal RNB main irrigation canal. The conventional farming produce, including the existing cropping pattern, in Roodasht district, are wheat, barley, alfalfa, safflower, and sugar beet, and the whole cultivated area of crops is shown in Table 2. The study area, located in central Iran’s arid region, suffers dryness strictly and water scarcity while extracting water from the Zayandeh-Rood River. The study area aims to get the latest priority for extracting water since other Figure 1 |Plan view of the Roodasht canal networks. Table 2 |Current crop pattern in the irrigation RNB network Crop Wheat Barley Alfalfa Safflower Sugar beet Cultivated area (ha) 10,343 1,941 873 530 22 Table 1 |Physical features of the RNB canal Magnitude Features 0.0003 m/m Bed slope 1.5 m/m Side slope 4.2 m Canal bottom width 2.5 m Canal normal depth 26 Number of offtakes 13 The number of water-level regulator stations 550 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 sections included the Isfahan metropolis and other five irrigation districts at the upstream of the basin, which is fulfilled before the Roodasht district. Briefly, the study area was selected by taking into account the factors that made the Roodasht Irrigation District the most vulnerable to water shortage in Iran. The logic behind this selection is as follows: 1. Unreliable supply of the required surface water by the river resulted in inflow fluctuations and water shortages in the main canal (Kaghazchi et al. ). 2. The region’s social tensions due to limited water supply (Hashemy Shahdany et al. ). 3. The improper design and the multiplicity of water-level regulating structures that have led to a significant waterlevel drop along the main canal (Shahdany & Firoozfar ). 4. The multitude of groundwater wells and a substantial reduction in the region’s aquifer (Khiabani et al. ). Irrigation Conveyance System Simulation (ICSS), on the open-source hydrodynamic model, was used to simulate the RNB main irrigation canal operation under existing conditions (Table 1). This model was first developed by Manz ()to simulate flows in open canals under steady and unsteady conditions by solving the Saint-Venant (S-V) equations. The model calibration and validation were conducted using the root-mean-square error (RMSE) and coefficient of residual mass (CRM) indices. The RMSE and CRM indices for the calibration stage were 0.003 and 0.99, respectively. The corresponding indices for the validation stage were, respectively, 0.015 and 1.01 (Kaghazchi et al. ), indicating the model’s acceptable precision in water delivery simulation and distribution. Economic-operational strategy of water distribution An essential step in achieving the study objectives is to combine the two economic and operation models and formulate an operation-economic framework to maximize the network’s net profit. As seen in Figure 2, in the first step, preparative data on hydraulic structures and relevant equipment, canal geometry, and regional hydrology served for the operation model. The economic modelling needs agricultural inputs consumption and prices of the agricultural inputs and services. Employing collected and clustered inputs to models applied a base condition of the RNB operation with normal farming activities regardless of any deficits. Then, the operation alternatives under the water scarcity scenarios were evaluated for their effectiveness, following which they were considered the leading platforms for the water supply system to be combined with an economic model. The average economic value of water was extracted through the economic model to all farming units as a leading factor for an operating model. In fact, under conditions of water scarcity, the economic component in the operation model comes into play in the matter of Figure 2 |A conceptual model of the operational-economic approach. 551 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 distributing water to agricultural units by determining the weighted average of the economic value of water at offtake headgates. In this way, high-value agricultural units will experience less water shortage than low-value units. Based on the volume of water allocated to each offtake, the new economic model then adapts to the new conditions of agricultural activities, ultimately resulting in a change in the cultivation pattern of agricultural units. The operational scenarios need to explain that canal operation consists of all activities performed on canal structures to distribute and deliver agricultural water properly. Therefore, the operational scenario represents specific conditions in the canal; accordingly, the relevant activities must be implemented. All the operational conditions of a canal can be determined in various operational scenarios to simulate the hydraulic behavior of flow and the delivery discharges to offtakes in different states. Accordingly, operational scenarios were defined using patterns that are obtained from canal inflow data over the operational period. A wide range of operational scenarios occurred in the daily operation of an irrigation canal, including ‘normal operational scenario,’‘fluctuation operational scenarios,’and ‘water shortage operational scenarios.’The first two scenarios were selected as the operational scenarios for the present study’s test case due to the frequent occurrence of these phenomena. Operational model: model predictive control The conventional method in the operation of irrigation canals is to deduct the water-level error with respect to a target level by adjusting the controllable regulators to keep the water-level error near zero (Schuurmans et al. ). In this paper, an MPC is utilized, a technique that has become famous due to its ability to manage the variable optimization goals, delays, uncertainties, and constraints in a systematic manner (Backman et al. ). An MPC is a control system that benefits from a feedback and feedforward control method, an optimization method for calculating the output controller variable and water levels in the water distribution system. The controller is responsible for making the water level reach the offtake’s target level by regulating the regulator’s degree of openness located upstream of every canal reach. The MPC uses the mathematical model of the controlled system (the internal model) to predict hydraulic variables (water levels adjacent to each offtake) within a specific time interval. This interval, which is named ‘Horizon’in this controller, is defined following the automated control system’s design goal. In this study, the interval was considered 24 h based on the recommendation of Maestre et al. (). The control commands were determined in each time step based on the simulated hydraulic conditions (in the internal controller model) along the canal’s temporal horizon and real-time measurements. The measured water levels adjacent to each offtake (state variables) are transmitted to the central dispatching office via the remote terminal units. After the control commands are determined (separately for each regulator) by the controller, they are sent to executors located at each regulator’s site to be executed. Therefore, thanks to the controller’s perfect foresight, using the Horizon component, any variation in water extraction by the water holders is taken into account 24 h before water distribution. The mentioned ability makes this automated system robust enough to fulfill water conservation and reallocate water to different clients. The mathematical model is based on the MPC system that is referred to as an internal model and demonstrates the system dynamics. In addition to the MPC model, control goals should be determined mathematically to form an objective function, and the process of water distribution and structure flow limitations should be considered. The MPC solves at any time step the Equation (1) optimization problem to compute the optimal control action (Shahdany et al. ): U¼arg min UJ(U,x0) (1) where U¼(u(0), u(1), ...,u(Nh1)) is the sequence of values of the manipulated variables on the perspective (N h ), and x 0 is a present state. According to the model and the operational and structural limitations, Equation (1) is solved at any sample time, and only the first response of the sequence of control actions is used. For utilizing the control problem with automated control algorithms, the system must be defined as a mathematical form involving controlled variables, state variables, and control action variables (Aydin et al. ). The water levels and flows in an open irrigation canal can be fully expressed by the 552 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 nonlinear S-V equations (van Overloop et al. b). Water management’s control theory applications are mainly based on linear systems, and simple linear models, such as the Muskingum model (Cunge ), integrator-delay (ID) model (Schuurmans et al. ), and Hayami model, and reduced S-V models (Xu et al. ) have been suggested to estimate the canal dynamics until a base is created to develop control procedures. In this study, the ID model is used as an internal model of the MPC system in water management for irrigation networks (Kamrani et al. ). The ID model considers that a canal reach is divided into a backwater section and a uniform flow. The delay time (T c ) and the storage area (A s ) are the two main parameters of any canal’sreach in the model. Then, the discrete time-invariant canal’s reach model utilized in this research is: h(kþ1) ¼h(k)þTc As qin(kkd)Tc As qout(k) Tc As qofftake(k) (2) where q out (k) is the control flow in time step kthat gate-con- ducts it to the downstream one (m 3 /s), his the level of water (m), q in (k) is the inflow rate, qin(kkd) is the inflow rate (m 3 / s) to the backwater part, with k d being the delay time step between control action and the change in the water level of middle downstream, T c is the control time step (s), A s is the average storage area (m 2 ), and qofftake(k) is the outflow of the disturbance offtake rate (m 3 /s). This disturbance originates from a predefined water distribution schedule. By alleviating a constant h ref from Equation (2), waterlevel error can be derived. Therefore, the internal model includes the state-space representation that will be used in the MPC. This type of representation based on inputs, states, and outputs allows direct matrix manipulations. Equation (3) defines the linear time constant state-space representation of the MPC system (van Overloop ): x(kþ1) ¼A(k)x(k)þBuu(k)þBdd(k), (3) where dimensional state vector containing water-level errors and all delayed flows; kis a discrete time step; dimensional uequals to dimensional control input vector containing the flow variations of the control structures; Ais the dimensional state matrix; B u is a dimensional control input matrix; dis a disturbance matrix consisting of the offtake flows grouped per reach; and B d is the matrix of dimensional disturbance. The MPC utilizes hard constraints on the control system input and soft constraints on waterlevel deviations when exceeding the target levels. Thus, Equation (4) illustrates the irrigation canal system’s statespace model for the first canal reach. Qhg(kþ1) Qhg(k) Qhg(k1) Qhg(k2) e1(kþ1) e 1(kþ1) 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 ¼ 1000 00 1000 00 0100 00 0010 00 000Tc As 10 000Tc As 10 2 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 5  Qhg(k) Qhg(k1) Qhg(k2) Qhg(k3) e1(k) e 1(k) 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5 þ 10 00 00 00 00 01 2 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 5  ΔQhg(k) u 1(k)  þ 0 0 0 0 Tc As Tc As 2 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 5 [Qofftake1(k)], ΔQhg(k)ΔQhg,max(k) u 1(k)hmin(k)href u 1(k)hmax(k)href (4) where Q hg (k), Q hg (k1), Q hg (k2), and Q hg (k3) are inflows of the reach at time step kto k3 (the number of delay time steps in the first reach); e 1is the water level outside of the target band; e 1 is the deviation among h 1 and h ref ; and u* is the computed signal according to van Overloop et al. ()given in the following equation: u(k)¼ eh min(k)href ehmax(k)href hmax(k)href ehmax(k)href hmin(k)href ehmin(k)href 8 < : : (5) Soft constraints are performed by utilizing the virtual input signal of its constraints, and the optimization process will try to maintain running the optimization when the hard constraint is violated (van Overloop ). The future sequence of the conditions and control variables was 553 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 optimized over the future horizon in each time step by the objective function. A quadratic function for the MPC model in irrigation canals is defined in this study and can be solved with the quadratic programming function in MATLAB (Xu et al. ), which minimizes the subsequent performance criterion: Min j¼X n i¼0 [XT(K)QeX(K)þUT(K)RΔQU(K)] (6) where Q e is the penalty matrix of the state variables, which consists of penalty weight on eand e*;nis the step number of the prediction horizon; R ΔQ is the penalty matrix on the control variables containing a penalty weight on ΔQand u*.Great penalties on water-level deviations from the target are included using high values for Q e* .Moreover,R u* (the virtual signal penalty) should have too low values. The penalties are adjusted to get a weighted compound of smooth control. Primitive weighting factors of water-level error (Q e )andgate flow variations (R ΔQ ) were chosen based on the maximum permissible value of the predicted factor (Xu et al. ). The maximum error of the water level is specified by the permitted ±0.1 m bandwidth about the target band. The maximum gate flowvariationatanytimestepisassumedtobe1m 3 /s. The final penalties are decided by trial and error and separately for the individual reaches. In other words, the reaches are penalized based on their own particular physical characteristics. Economic model: PMP The economic model of PMP, developed to calibrate agricultural supply simulations (Howitt ), assumes that the total net profit is maximizing. The model reproduces information from observed farming activities to specify a nonlinear objective function such that the ultimate nonlinear model accurately reproduces the observed farmers’ behaviors. The standard method involves three stages. Stage 1 This stage involves elaborating a linear planning model to maximize farmers’gross profit concerning resource constraints and calibration (land and labor, water volume, and other limitations). Furthermore, the economic values of production inputs and the shadow prices of calibration constraints are obtained in each agricultural unit. The mathematical form of this stage is given as follows (Howitt ): Max GM ¼X n i¼1 {Xi[(PiYi)þSIiPWiWiTCi)]} Subject to: Pfijxibj∀i,j[λ] xix0þε∀i[ρ] xi0∀i (7) where TC i ,W i ,PW i ,SI i ,P i ,andX i refer to the area under cultivation, the crop price, the subsidiary incomes, the cost of using one unit of water, the amount of water consumed, and the mean total of the calculated costs of crop iin terms of a hectare, respectively, and f ij denotes the technical coefficients of the sources used in the region. Moreover, the resource constraints in the region are shown in Equation (7). These constraints include water resources, land, machinery, labor, capital, pesticides, and chemical fertilizers. In this equation, b j is the total inventory of resources in the region. Similarly, the calibration limit of the model is presented. In Equation (7), the status of activity in the base year is shown by x 0 , and εrefers to very few positive numbers included in the model to avoid linear dependencies and emergence of the zero-shadow price. λand ρrepresent the shadow price of system constraints and the calibration limit’s shadow price. Equation (8) refers to a non-negative constraint for activities (Medellín-Azuara et al. ). Stage 2 The information obtained in the first stage (the shadow prices and/or the economic values of production inputs and calibration constraints) is used to estimate the quadratic production function coefficients (vector a ij and matrix q ikj in Equation (8)) using the constant elasticity of substitution function (Howitt et al. ). Stage 3 The quadratic production function estimated in the second stage is replaced in the linear objective function of the first stage, and along with its resource constraints (regardless of 554 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 the calibration limitation), the function is exploited for simulation of the existing agricultural conditions and achieving an optimal set of inputs that maximize the gross income of farmers, as follows (Howitt et al. ): max X m j¼1 pjX n i¼1 aij 1 2X n k¼1 qijkxijxkj "# xij ! X n i¼1 wixij "# subject to X n i¼1 WCixiTW; X n i¼1 xiTA; XiMi;X n i¼1 MiXiTm X n i¼1 LiXiTL; X n i¼1 VixiTK; X n i¼1 FifXiTFf; X(XiXii)0; xij 0 (8) In this equation, WC i is the amount of water consumed for each product (m 3 ha 1 ), TW is the total surface water (m 3 ), TA is the total cultivated area (ha), M i is the area under cultivation due to market limitation (ha), M i is the machinery (h ha 1 ), T m is the total inventory of machinery in the region (h), L i is the required labor force (n/day/ha), TL is the total available labor force (n/day), V i is the cash costs per hectare of product i(monetary unit), TK is the total available cash investment (monetary unit), and f,F if , and TF f , respectively, represent the type, amount of consumption per hectare, and total available inputs of nitrogen and phosphorous fertilizers and chemical pesticides. Finally, X i and X ii represent the products that are grown alternately. A comparison of the results obtained from executing the model in this stage for the levels and combination of agricultural activities with the observed levels of these activities in the base year provides a criterion of calibration and simulation. Consequently, the economic value of water (as a dual value of constraint), farmers’incomes, and an optimal planting density of the cropping pattern will be determined. Preparing the preliminary data of the economic model Data required for the calibration and preparation of the economic model of agricultural activities were collected through interviews and questionnaires. Data were obtained from farmers, the office of management and operation of the Roodasht Irrigation Network, and government agencies. All necessary data, including the volume and cost of agricultural inputs, were collected for all 26 agricultural units. Table 3 lists the consumption of agricultural inputs per hectare and the price of inputs per agricultural unit used in the economic modeling. Table 4 shows the yield and the sales price of agricultural products collected from farmers for the fourth agricultural unit. After preparing the necessary information, the economic simulation of agricultural activities was carried out for a water scarcity of 32% (the mean water scarcity adopted from the Roodasht Irrigation Network Office) to extract the most cost-effective water distribution strategy and delivery to the offtakes. Operational performance indicator The operational performance assessment criteria introduced by Molden & Gates (), given in Table 5, were used to examine water distribution and delivery to offtakes. Table 5 also shows the definition, formulation, and standard levels of performance indices. Here, Q D is the volume of water delivered to the offtake, Q R is the required discharge to the offtake in the time horizon Tat the point R, and CV R and CV T , respectively, show the statistical parameters of spatial and time variations for the ratio Q D /Q R .P A and P F , respectively, represent Q D /Q R and Q R /Q D .IfP A and P F are more significant than 1, their value is considered to be 1. Operational test scenarios Subject to the water shortage periods, in drought conditions, that induce inefficient performance on irrigation network operations and create the inflow fluctuations from the canal’s headgate, this part only attempts to assess the functioning of suggested improvement operational options in fluctuating flow conditions. Indeed, to investigate the water’s capability to deliver to sluicesadequatelythroughthemain canal operation methods, two operational scenarios were included: first, Normal Condition Operation (NCO) and, second, Inflow Fluctuations of Upstream (IFU)’sheadgate. The normal scenario is arranged to show the conventional daily operation in the RNB main canal, given that data (Figure 3(a)) have been collected from the Roodasht 555 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 operational office. Accordingly, the average, minimum, and maximum inflow fluctuations of the canal’s headgate, respectively, are 43, 19, and 70%. Furthermore, the most reduced amount of discharge, which is 38% reduction, had reached 1.7 CMS. It is noticeable that all the demands of RNB agriculture units total 2.78 CMS. The IFU scenario, as shown in Figure 3(b) for 20 h of modeling, pertaining to 75% flow reduction, has reached even lower than 1 CMS. RESULTS Water distribution and delivery along the main canal were simulated and compared with the Current Operational Method of Roodasht (COMR), employing the developed MPC. Besides, the agricultural activities of farmers in 26 agricultural units were simulated through economic modeling. The performance of the operational-economic strategy in improving water distribution and delivery to offtakes was also evaluated. Operational performance indicator results The ICSS hydrodynamic model was used for COMR and MPC simulation under NCO and IFU scenarios. The four performance indices for both operation scenarios were calculated. The color spectrum in Figure 4, for both operational scenarios shows the adequacy of water delivery to offtakes under the NCO scenario. As shown in Figure 4(a), COMR fails to supply the water required under normal operating conditions. The farmers living downstream, midstream, and upstream of the canal received 88, 82, and 72% of their water requirement on average. According to the standards in Table 5, water supply to these offtakes is evaluated as good, fairly good, and poor, respectively, Table 3 |Statistics and information on agricultural input Land Phosphate Potassium Urea Manure Poison Job Machinery Water use Wheat Magnitude 921 ha 100 kg ha 1 50 kg ha 1 250 kg ha 1 0kgha 1 2Lha 1 9 one-day 22 h 11,180 m 3 ha 1 Cost (unit 1 ) 125 USD 0.36 USD 0.39 USD 0.25 USD 0.2 USD 27.5 USD 17.8 USD 16.1 USD 0.02 USD Barley Magnitude 176 ha 100 kg ha 1 37 kg ha 1 250 kg ha 1 0kgha 1 1Lha 1 6 one-day 16 h 8,952 m 3 ha 1 Cost (unit 1 ) 107.15 USD 0.36 USD 0.39 USD 0.25 USD 0.2 USD 27.5 USD 17.8 USD 16.1 USD 0.02 USD Alfalfa Magnitude 97 ha 150 kg ha 1 150 kg ha 1 50 kg ha 1 0kgha 1 5Lha 1 20 one-day 28 h 19,169 m 3 ha 1 Cost (unit 1 ) 142.86 USD 0.36 USD 0.39 USD 0.25 USD 0.2 USD 6.4 USD 17.8 USD 16.1 USD 0.02 USD Safflower Magnitude 71 ha 100 kg ha 1 0kgha 1 200 kg ha 1 0kgha 1 5Lha 1 7 one-day 10 h 16,596 m 3 ha 1 Cost (unit 1 ) 142.86 USD 0.36 USD 0.39 USD 0.25 USD 0.2 USD 10.7 USD 17.8 USD 16.1 USD 0.02 USD Sugar beet Magnitude 22 ha 200 kg ha 1 0kgha 1 300 kg ha 1 425 kg ha 1 6Lha 1 53 one-day 38 h 19,601 m 3 ha 1 Cost (unit 1 ) 214.29 USD 0.36 USD 0.39 USD 0.25 USD 0.2 USD 26.8 USD 17.8 USD 16.1 USD 0.02 USD Note: Based on the official price of the US dollar, announced by the Central Bank of Iran in 2015. Table 4 |Selected values from the information on the economic model of Unit 4 Production Yield (ton ha 1 ) Sale price (USD kg 1 ) Wheat 4.41 0.41 Barley 4.21 0.33 Alfalfa 11.64 0.18 Safflower 1.94 0.77 Sugar beet 44.23 0.1 556 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 method, which is about $1 million higher than that of the TOE, the $7 million net profit of AOE indicates this scenario’s superiority compared with others concerning profitability. Besides, a revenue difference of $140,000 and a net profit difference of $50,000 with the AOF show the positive impact of this strategy. The profit from equipping TOE with the economic model equals $140,000. Considering TOF as the base scenario under water scarcity conditions, the percentage of increase in revenues, cost, and the net profit of the automated control systems or those equipped with an economic model can be calculated as shown in Table 9. The results in Table 9 indicate the ability of automated operation scenarios in increasing income and network profits. The superiority of the net profit per hectare in TOE relative to AOE is due to the difference in the total cultivation area in the two methods, lower for the TOE. The financial losses due to each scenario’s reduced cultivation area are given in the last row of Table 9. Accordingly, AOE was able to maintain the net profitatthehighestpossiblelevel. By improving water supply to agricultural units, AOE reduced the financial losses caused by water scarcity and also the cultivation area to $197,162 compared with TOF. DISCUSSION The automated (MPC) and economic (PMP) operation components were combined to maximize the network’s net profit in the event of unbalanced water demand and supply. The results of economic effects are shown in Figure 11 and Table 9. The operation scenarios with an Table 9 |Amount of income, cost, and profit per hectare and their percentage changes Operational scenarios Features AOE TOE AOF TOF COMR (base state) Incomes per hectare (USD ha 1 ) 1,329.84 1,329.73 1,329.63 1,334.74 1,330.05 Percentage of increasing net revenue 13 2 12 –– Cost per hectare (USD ha 1 ) 779.90 778.06 781.68 785.45 781.43 Percentage of increasing net costs (%) 13% 1% 12% –– Profit per hectare (USD ha 1 ) 549.94 551.68 547.95 549.29 548.62 Percentage of increasing net profit14 2 12 –– Financial loss of water scarcity (USD) 1,296,741.15 3,041,425.02 1,403,059.31 3,268,363.27 No scarcity Figure 11 |Whole revenue, cost, and profit of performing different operational scenarios. 563 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 economic approach outperformed those without such an approach under similar conditions. Compared with automated operation as a modern alternative, this caused a slight increase in the net profit. It is noteworthy that the study area’s dimensions affect the net profit of the network, which is of great importance in large-scale areas like the basin in this study. In the studied network, COMR could not supply the water requirement of agricultural units under normal and fluctuating conditions. The simulation results for COMR are displayed in Figures 4 and 5. Therefore, the AOE strategy was considered an alternative to reducing water delivery and distribution losses and managing water scarcity. For better understanding, Figure 12 shows the AOE adequacy index in supplying offtakes’water needs. As shown in Figure 12, high-value units (including the first, fifth, and sixth units) received the least water shortage, while low economic units like the nineteenth unit received the highest water shortage. The most essential factor in overcoming water scarcity in AOE is to reduce water delivery and distribution losses (42 million cubic meters) to offtakes. Furthermore, in-line storage, multi-objective function, and the ability to change irrigation planning by the MPC system also affected the water requirement of agricultural units. By modifying the cultivation pattern, management of water scarcity, and distribution of water shortage among agricultural units using the economic component (PMP) of the AOE method, efforts were made to increase the revenues and, ultimately, farmers’ net profit. The use of this strategy increased farmers’revenues up to $2 million when compared with the existing conditions, which distinguishes the AOE operation scenario from other alternatives. An 11% increase in the cultivation area is essential, considering the importance of food security. Other scenarios were designed to understand better the impact of both automated water delivery and distribution and economic component concerning financial aspects, the volume of consumed water, and cultivation area. The importance of both automated and economic components was identified individually. For example, automated operation increased the cultivation area by 10%. An economic approach in the operation scenario, on the other hand, increased the cultivation area by 1%. Thus, an increase of 1.3% ($0.9 million) in the net profit by AOE compared with existing operating conditions (TOF) under water scarcity conditions can be justified. It should be noted that 84% ($0.76 million) of increased profit is due to automation and the rest (16% equals to $0.14 million) is due to the economic component of the COMR. The advantages of such plans can be shown by evaluating and comparing the efficiency of traditional operation methods with modern delivery and distribution methods from different economic and operational aspects and the development of various operational-economic scenarios that are not seen in similar studies (Hashemy Shahdany et al. b). Most studies have been conducted on largescale areas such as basins. However, this study focuses on an irrigation network with direct contact with the final consumer. Perhaps, this is the connecting loop between macro and field research works because interconnected management of water resources, and water distribution and delivery to the second- and third-degree units, in fact, connect macro- and micromanagement. Figure 12 |Adequacy index results of automated operational-economic scenario in water shortage. 564 M. Yaltaghian Khiabani et al. |Economic agricultural water distribution Journal of Hydroinformatics |23.3 |2021 Downloaded from http://iwaponline.com/jh/article-pdf/23/3/548/892451/jh0230548.pdf by guest on 07 September 2021 CONCLUSION The evaluation of the RNB water network (as a case study) distribution and delivery system indicated the inefficiency of this system in meeting the water requirements of cultivated areas under normal and fluctuating inflow conditions. Water delivery to offtakes, particularly to downstream ones, will be exacerbated under water scarcity conditions. For this reason, the MPC automated system for increasing flexibility in water distribution and delivery and the PMP economic model for determining the distribution of water shortages were combined according to the economic value of water to maximize the net profit of farmers under water scarcity conditions. Accordingly, four operating management scenarios were developed. Automated operation scenarios led to a significant reduction of operational loss compared with conventional methods (COMR). This critical factor reduced the impact of water scarcity on canal operations. Compared with traditional TOE and TOF operation methods, the cultivation area experienced a smaller decrease in the AOE and AOF methods. As a result, the cultivation area, revenues, and net profit obtained from derived AOE and AOF were found to be higher than TOE and TOF. Comparing the performance of scenarios indicated the significant impact of the economic approach. Water shortage management with an economical approach for maximizing network profit led to an improvement in farmer’s livelihood through the irrigation network operating system. Even though the current study concentrated on irrigation scale, watershed (low resolution) and tertiary agricultural region (high resolution) could also be considered as fit for investigation. Moreover, different variables, such as groundwater sources, area, or other input limitations depending on the region’s potentials, could be regarded for developing models. Likewise, implementing such effective plans for the operation of irrigation networks to reduce water delivery and distribution losses and increase farmers’profit is a suitable solution for dealing with drought and migration from rural areas to cities. This is why modern operation strategies based on economic principles provide opportunities for sustainable development and increased food security, increase the economic efficiency of water, and reduce operational losses. ACKNOWLEDGEMENTS The authors are grateful to Prof. Saleh Taghvaeian from Oklahoma State University for his scientific support. 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