Introduction

Since agriculture is the largest consumer of water among different sectors, optimal water usage in agriculture has the most significant effect on water management. To overcome the water shortage and make maximum use of the limited available water, the allocation and scheduling of irrigation water should be done optimally (Kanooni & Monem, 2014). The optimal allocation and irrigation scheduling have been conducted based on two approaches: fixed demand (Monem and Namdariyan., 2005; Mathur et al., 2009) and variable demand (Kanooni & Monem, 2014; Oad et al., 2009). In the first approach, irrigation is scheduled with the assumption of constant demand and without knowing the water needs of the irrigation unit and based on the consumers’ request. However, in the second approach, crop type, climatic conditions, and soil moisture are influential, and optimal irrigation scheduling is determined based on actual demands (Li et al., 2020).

The simulation models used in irrigation programs provide the possibility of checking and predicting the system’s behavior in the face of various variables, saving costs and making more appropriate decisions. They also reduce the limitations of field research, including time-consuming and lack of human resources (Bastiaanssen et al., 2007). The AquaCrop model has been evaluated for irrigation scheduling in different climatic conditions (Guo et al., 2021; Li et al., 2018; Linker et al., 2016). In recent years, irrigation scheduling has been optimized using plant simulation models such as AquaCrop instead of extracting experimental production functions (Kheir et al., 2021; Martinez-Romero et al., 2021). Meta-heuristic algorithms, such as genetic algorithm, has been used for various optimizations, including irrigation scheduling. The Genetic algorithm has led to reasonable outcomes in different fields (Rath et al., 2018; Wabela et al., 2022; Yao et al., 2019). The single-objective optimization for irrigation scheduling has been gradually replaced by multi-objective procedures, which have conflicting objectives without a unique optimal solution (Guo et al., 2021). The AquaCrop model was used to optimize the winter wheat irrigation schedule under dry, normal, and wet hydrological scenarios. The optimization objectives in their research included crop yield, irrigation water use efficiency (WUE), and economic benefit (EB). The results showed that the optimal irrigation scheduling performed better than the usual farmers’ schedule. It also led to an increase in crop yield, EB, and WUE (Guo et al., 2021). This study was conducted only for one crop in various hydrological scenarios. García-Vilaa and Fereres (2012) used AquaCrop and a farm-scale optimization model to optimize the water consumption of some selected crops. They showed that using crops with lower water consumption freed up water to produce crops with more water consumption and higher economic value. They used the AquaCrop model to extract the production functions of the crops, and the AquaCrop model was not combined with the optimization model for successive executions. The crop yield, EB, and water charge were among determining factors for irrigation scheduling and water resource allocation that should be considered during optimization (Rath et al., 2018; Wang et al., 2008).

Past research shows that the drained water salinity of rivers (Somlyody, 1998; McBride, 2002), and soil salinity (Connor et al., 2012; Nemoto & Sasakuma, 2002) are factors that affect crop yield and optimal water resources allocation.

The increase in the environmental pollutants loaded into rivers through industrial, urban, and agricultural activities has resulted in changing the rivers’ water quality indices (Jahin et al., 2020). Salinity is one of the primary indices of rivers’ water quality, which quantifies water-soluble salts (Quinn, 2011). Enhancing water quality and reducing its salinity requires efficacious efforts to manage water resource utilization (Somlyody, 1998; McBride, 2002). To this end, managing farms drained water entering the rivers is one of the most effective practices to preserve long-term cropping yield benefits.

Water and soil salinity are environmental hazards leading to soil deterioration and a reduction in agricultural efficiency, especially in arid and semi-arid regions such as Iran (Connor et al., 2012; Alizade Govarchin Ghale et al., 2017). Furthermore, salinity is a major factor in limiting crop growth by reducing root water and nutrient uptake (Wilkinson, 2000). The increase in soil electrical conductivity brings about salt stress and crop biochemical and physiological changes, which reduces crop growth and yield (Nemoto & Sasakuma, 2002). Hence, soil physical and chemical properties, irrigation water quality, and their management play an important role in long-term farm management (Douaik, 2006).

The EB function is considered the main objective function in most studies related to irrigation scheduling (Rath et al., 2018; Kumar & Yadav., 2019), while the economic utility function (EU), which in addition to EB, considers the long-term environmental effects and the production sustainability, has not been evaluated. In this study, the heuristic EU function is used instead of the EB for optimal irrigation water allocation. This heuristic function is proposed instead of the EB function by applying two coefficients of soil salinity and the salinity of drained water to the river. By applying the two coefficients, in addition to maximizing the EB in the same year, the long-term environmental effects caused by the cultivation of different crops, soil quality preservation, river water quality variation, sustainable agriculture, and long-term benefits are also evaluated. To evaluate crop yield response to water, the AquaCrop plug-in model has been used instead of experimental production functions such as Doorenbos and Kassam (Doorenbos et al., 1979). Therefore, the present study aims to maximize the EU and optimal water and land allocation for five main crops in a part of the Moghan irrigation network in the northwest of Iran using the genetic algorithm optimization method incorporated with the AquaCrop model.

Materials and Methods

Study Area

The Moghan Plain is located in the northwest of Iran. The Moghan irrigation network is fed by the Aras River and irrigates 72,000 ha of the Moghan Plain agricultural lands, as shown in Fig. 1. According to the statistics and information of the regional water company of Ardabil, a part of Aras River water extracted by the Moghan network, the other part enters the Mil network of Azerbaijan, and the rest overflows the diversion dam and flows back to the Aras River and finally leads to the Caspian Sea. The volume of and salinity of water transferred back to the Aras River, for the years 2011–2020 are shown in Fig. 2 and Fig. 3. The study site is part of this network, located in the Pars-Abad region and irrigated by canal M with a covered area of about 2000 ha and 3 m3/s capacity. This area was considered an irrigation analysis unit (IAU). In the 2020 agricultural year (Sep. 2020–Aug. 2021), the main cultivated crops in the study area were wheat, grain maize (first cultivation maize, second cultivation maize), soybeans, and alfalfa. In this research, mean long-term data (20 years) of the Pars-Abad weather station were used to prepare meteorological information (Fig. 4). Table 1 shows some information related to the studied crops. The information about the crops in the region was obtained from the Agricultural Organization of Ardabil Province. The unit price of the crops was also collected from the reports of the Iranian Statistics Center. According to the Agricultural Water Price Stabilization Law, average water charge from modern networks is 3% of the crop yield.

Fig. 1
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Location of Moghan irrigation network

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Fig. 2
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The monthly volume of Aras River water after the diversion dam for the years 2011–2020

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Fig. 3
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Aras River seasonal water salinity after diversion dam for the years 2011–2020

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Fig. 4
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Average long-term minimum, maximum, and mean daily temperature values (a) and average long-term values of monthly rainfall and evapotranspiration (b) in the Pars-Abad weather station

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Table 1 Characteristics of the main crops of the Moghan irrigation network in 2020
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AquaCrop Model

The AquaCrop model is an advanced program published by the World Food and Agriculture Organization (FAO). The development of this model is based on biophysical interactions in the plant-soil-atmosphere system (Sandhu & Irmak, 2019). Evapotranspiration calculation in this program is based on the dual crop coefficient method (Steduto et al., 2012). This model simulates the crop yield as a function of water consumption in different irrigation regimes. It also connects crop yield to crop water consumption and estimates the amount of biomass resulting from actual crop transpiration through normalized water productivity, which is the core of AquaCrop’s growth engine (Steduto et al., 2012). In the AquaCrop model, the yield is calculated based on the product of crop dry matter (B) and the harvest index (HI) (Eq. 1). Separation of yield (Y) into the dry matter and harvest index distinguishes the relationship between environment and dry matter production with the relationship between environment and harvest index. Therefore, the effect of water stress on dry matter and harvest index is investigated separately. The applied changes have led to the development of the following Eq. in this model:

$$\text{B=WP}\sum {\text{Tr}}$$
(1)
$$Y = HI \times B$$
(2)

where WP is water productivity (in units of kg (biomass) m−2 (land area) mm−1 (water transpired)) and Tr is plant transpiration (mm).

AquaCrop Plug-in Program

FAO has developed the AquaCrop plug-in program, whose calculation methods are similar to the standard AquaCrop program (Raes et al., 2012). It provides the simulation possibility without a user interface. The plug-in program runs consecutive projects and saves each project’s simulation results (daily, 10-day, monthly, and quarterly) of each project in an output file that includes information about the simulation period, climate, soil, and water balance, and crop yield. (Raes et al., 2012). The plug-in program makes it possible to include the AquaCrop model in other programs and makes consecutive runs possible without a user interface. The AquaCrop plug-in version 6.0 was used in this research.

In this study, the AquaCrop model was run for each crop in net irrigation water requirement mode to find the potential crop yields. The agricultural year was divided into 36 periods of 10 days to allocate water to the different crops. The potential yield and the corresponding amount of water calculated from the model simulation were then entered into the optimization model. The optimization code (i.e., AquaCrop plug-in for irrigation scheduling) uses a specified irrigation depth based on the water content at field capacity and irrigation time based on the irrigation interval (Generation of irrigation schedule). There are some studies in the Moghan Plain for the calibration and validation of the AquaCrop model for important crops (Adabi et al., 2020; Izadfard et al., 2021). In this research, to determine the calibration parameters for the main cultivated crops in the study area, the results of Izadfard et al. (2021) were used. The calibrated parameters are shown in Table 2. For forage crops such as alfalfa, the average effect of cuttings in the growing season was considered. A standard crop coefficient curve was considered, in which only a single value for crop coefficient mid needs to be employed for the whole growing season (Allen et al., 1998).

Table 2 AquaCrop model calibration parameters for the main cultivated crops in the study area (Izadfard et al., 2021)
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Objective Function and Decision Variables

The optimal irrigation water management was carried out in the IAU under different water requirements conditions on a ten-day scale. The decision variables in this model were the amount of irrigation water depth in each of the 36 periods as well as the crop cultivation area. Equation 3 represents the EB for each crop:

$$EB = {\text{ benefitper crop per hectare }} = \, \left( {{\text{crop sales per hectare }} - {\text{ costs per hectare}}} \right) = \left( {Y_{i} \times P_{i} } \right) - \left( {C_{i} + P_{w} \times IR_{i} } \right)$$
(3)

where Yi is the yield of crop i (kg/ha), Pi is the market price (Rial/kg), Ci represents production cost (Rial/ha), Pwi is water charge (Rial/m3) and IR is irrigation depth (mm). The meaning of the production costs is: land preparation, planting, cultivating and harvesting. These costs are different for each product and for each agricultural year. The amount of IR is calculated by dividing the net irrigation depth by the irrigation efficiency (IR = NIR/E). In Eq. 4, the EB function for the crop pattern is shown:

$$EB = \left( {\mathop \sum \limits_{i = 1}^{n} A_{i} \times \left( {Y_{i} \times P_{i} - C_{i} - P_{w} \times NIR_{i} /E} \right)} \right)$$
(4)

where NIRi is net irrigation depth (mm), E is irrigation efficiency, and Ai is the cultivated area (ha). Water allocation in this model was performed to maximize the IAU’s EU for five main crops. The selected option for the objective function was assumed to include the drainage water salinity as a penalty factor in the total benefit and the effect of soil water salinity as a factor in each crop’s benefit. Therefore, considering the soil water salinity and drainage water salinity, the EU function can be calculated as follows,

$$EU = \alpha \prime \left( {\sum\limits_{i = 1}^{n} {\gamma_{i} \times A_{i} } \times \left( {Y_{i} \times P_{i} - C_{i} - P_{wi} \times NIR_{i} /E} \right)} \right)$$
(5)

The coefficient ɣ represents changes in benefit due to the soil water salinity effects, and α′ is a coefficient to consider the effect of drained water salinity in the total benefit. By applying these coefficients, the benefit obtained will not be the net benefit of that year, but the long-term environmental effects are also considered.

Conditions Governing the Optimization Model

Using the optimization model, the appropriate combination of cultivation is selected among the common crops of the region. The crops’ sowing date, harvest date, total cost, and market price are entered into the optimization model. The following constraints limit the optimization:

1- The total cultivated area of different crops in each period should not exceed the area of arable land in the region (Eq. 6).

$$\sum\limits_{i = 1}^{i} {A_{i,d} } \le AT$$
(6)

where Ai,d, and AT are the cultivated area of crop i in period d and the total area of arable land in the region. d is considered to be ten days in this study.

2- A mild water deficit is optimal and can reduce water consumption without reducing yield (Wang et al., 2022). In this study, deficit irrigation of less than 25% and over-irrigation of more than 25% (to meet the leaching requirement) were prohibited. The net irrigation depth variation was limited to:

$$0.75 \times NetIrri_{id} \le NIR_{id} \le 1.25 \times NetIrri_{id}$$
(7)

where, NetIrrii,d and NIRi,d are, the crop irrigation requirement and the irrigation depth for crop i in period d.

3- The total volume of irrigation water used for crops in each period should not exceed the available water volume in that period (Eqs. 8 and 9).

$$V_{d} = \sum\limits_{i = 1}^{i} {IR_{i,d} } \times A_{i}$$
(8)
$$V_{d} \le W_{d}$$
(9)

where IRi,d, and Vd are the depth of gross irrigation water for plant i in period d and the total volume of water used for all crops in period d. Wd is the volume of available irrigation water in period d.

4- The discharge of drainage water should not lead to an increase in the salinity of the river water more than the permissible limit. Drained water volume and salinity for each crop can be derived from AquaCrop outputs. Thus, the salt amount coming from certain irrigation for each period of IAU which enters the river can be obtained from the average cultivated crops’ salinity in that period (Eq. 10). Furthermore, the river water salinity at output location in a certain period before the entrance of drainage water and its volume is available. Therefore, the river water salinity after the entrance of the drained water derives as follows:

$$ECdrain_{d} = \frac{{\mathop \sum \nolimits_{i = 1}^{i} ECdrain_{i,d} \times Vdrain_{i,d} }}{{\mathop \sum \nolimits_{i = 1}^{i} Vdrain_{i,d} }}$$
(10)
$$ECriver_{d} - \bmod = \frac{{\left( {ECriver_{d} \times Vriver_{d} } \right) + \left( {ECdrain_{d} \times Vdrain_{d} } \right)}}{{Vriver_{d} + Vdrain_{d} }}$$
(11)

In these equations, ECdraind is the average electrical conductivity of the drained water in period d, ECriverd –mod represents the river EC after receiving the drained water, ECdraini,d is the contribution of crop i to the salinity of drained water in period d, Vdraini,d is the volume of the drained water due to irrigation of crop i, ECriverd is the salinity of the river at the outlet before receiving drained water, Vriverd is the volume of the river water in period d at the outlet before receiving drained water, and Vdraind is the total drained volume in period d. To consider the drained water salinity as a penalty factor in the benefit, the coefficient C is calculated every day by Eq. 12.

$$C = \frac{{ECriver_{d} - \bmod - ECriver}}{ECriver}$$
(12)

In case the river water salinity after the entrance of the drainage water is lower than the river water salinity at the output location before the entrance of drainage water, C is lower than or equal to zero. In such cases, there is no need to apply a punishment coefficient (α′) (i.e., α′ equals one). In contrast, if the entered drainage water increases the river water salinity, C exceeds zero, and α′ can be applied. Moreover, the punishment coefficient intensifies according to the salinity increment. The α′ is calculated daily, and an average yearly coefficient applies to the objective function. α′ values for the Moghan region were derived based on local experts’ observations and suggestions, as shown in Table 3. Noteworthy, α′ regional coefficients can be modified depending on the initial river water salinity and its environmental effects.

Table 3 Suggested values for determining the α′ coefficient
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5- Cultivation should not drastically affect soil salinity in the root zone to achieve sustainable agriculture and maintain soil quality. Therefore, in this study, the soil water salinity coefficient (ɣ) was determined by multiplying two salinity change coefficients in the range of in-class coefficient (ɣ1) and the class change coefficient (ɣ2) (Eq. 13). If initial soil salinity (ECso) and soil water salinity after irrigation of plant i (ECswi) are known (which are outputs of the AquaCrop model), salinity classes are also considered based on the Wilcox diagram (Table 5), and each class changes between ECmin and ECmax, ɣ1 and ɣ2 can be obtained from Table 4. It should be mentioned that the coefficient within the class is applied exponentially (Table 5).

$$\gamma = \gamma_{1} \times \gamma_{2}$$
(13)
Table 4 Classification of soil water salinity coefficients (ds m−1)
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Table 5 Salinity classes to determine the ɣ coefficient (Wilcox, 1955)
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If the soil water salinity at the end of the irrigation equals the initial soil water salinity, ɣ1 equals one. If the soil water salinity at the end of the irrigation exceeds the initial soil water salinity, ɣ1 is considered lower than one, and vice versa. Furthermore, if the amount of reduction or increase in the soil water salinity in the root zone after the end of the irrigation does not exceed ECmin and ECmax of the Wilcox index, ɣ2 equals one, which shows no change in the soil salinity class. Otherwise, ɣ2 is considered lower (ECswi > ECmax) or higher than one (ECswi < ECmin), which leads to a change in the soil salinity class. ɣ1 and ɣ2 values for the Moghan region were suggested in Table 4 based on an engineering judgment. Undoubtedly these values could be enhanced with more experience and based on economic evaluations.

Applying these coefficients (ɣ1 and ɣ2) to the objective function accounts for the crop cultivation effects on production stability and long-term benefit. To this end, an increase in soil salinity destabilizes the production and reduces the long-term benefit while a reduction in soil salinity improves the production stability and long-term benefit (although it may not affect the current year's benefit).

Genetic Optimization Algorithm

Researchers developed algorithms to optimize any alternative issue in the agriculture (Osroosh et al., 2016), being stochastic or deterministic among the most accepted algorithms. The evolutionary algorithms allow changing a result to change until receiving the optimal solution by seeking a process that simulates living beings in nature, such as genetic algorithms (Villacampa et al., 2019). Since AquaCrop software is needed to calculate the crop yield without any provided formula, it is not feasible to use the optimization software and solve the mathematical model. Genetic algorithm has been used in many studies to generate irrigation data and crop area (Guo et al., 2021; Rabie et al., 2015; Shen et al., 2021). Hence, in this research, the genetic algorithm optimization method was used to allocate water to crops in the Moghan network. A genetic algorithm is one of the intelligent methods for optimization problems. This algorithm is based on repetition. In this method, a set of decision variables or chromosomes that are effective on the objective function forms the initial population (possible solutions). Maintaining genetic operators such as selection, cross and mutation on the decision variables of the initial population leads to the production of a more competent generation. This process is repeated in different generations (Goldberg, 1989). Thus, members or better solutions evolve over generations. Then, based on the value of the objective function, it categorizes the best answers among the answers in the form of the new generation. This process is repeated until a new generation is not produced. The produced irrigation data is used as an input to AquaCrop, and the crops’ yield is derived as an output from the model. In addition to the yield, drainage water salinity for each crop is also calculated by AquaCrop. To this end, C# coding was done in Visual Studio.

Results and Discussion

Water Optimal Allocation

The optimal cultivated area of the studied crops was obtained by running the optimization program. Figure 5 shows the cultivated area of the IAU in the current conditions compared to the optimal allocation conditions. The numbers in the figure demonstrate the difference between the existing cultivated crop areas compared to the optimal allocation conditions. The model prioritized crops with more EU and less water requirement than other crops by reducing costs and complying with restrictions. In the optimal cropping pattern, the cultivated areas of wheat, first-cultivation maize, and alfalfa have increased by 2.5%, 3.2%, and 3.4%, respectively, compared to the initial cultivated area. Among the crops, wheat requires less water than other crops, whereas first-cultivation maize and alfalfa have a higher water requirement. Their cultivation area has increased more due to their higher yield and, as a result, greater economic value than the other crops. The cultivated areas of second-cultivation maize and soybean experienced a reduction of 2.3 and 1.8 percent.

Fig. 5
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Comparison of the existing and optimal cultivated area of the Moghan irrigation network crops

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The AquaCrop model was run for each crop in the net irrigation water requirement mode. Therefore, the maximum crop yield and the water depth calculated from the implementation of this model were considered normal conditions. Table 6 compares the allocated crops' water depth in two normal and optimal conditions. According to Table 6, the allocated water depth in the optimal conditions for all crops is lower than the allocated water depth in the normal conditions. The highest percentage of reduction in the allocated water depth is related to the alfalfa by 24%, and the lowest is related to the first-cultivation maize by 10%. A fraction of the first-cultivation maize’s water requirement, during the growing season, is supplied with rainfall. Alfalfa, a crop that grows and develops throughout the year, has received less water than other crops. For all the investigated crops, the allocated water depth in the optimal condition compared to the normal condition has saved water consumption by 17%. The optimal distribution of water in different growth periods of each crop is shown in Fig. 6. The model can run a deficit irrigation of less than 25% and an over-irrigation of less than 25%. For soybean (Fig. 6d), first-cultivation maize (Fig. 6b), and second-cultivation maize (Fig. 6c), the optimal water depth distribution in the entire growth stages has been less than the normal water depth. However, for the wheat (Fig. 6a) in the 34th and 35th growth stages (the last ten days of February and the first ten days of March), 7 and 17% over-normal water were considered. For the alfalfa (Fig. 6e) in the fourth growth stage (last ten days of April), 15% over-normal was considered. Since in the previous irrigation periods, the optimum water depth was lower than the normal water depth, it caused a decrease in the soil moisture content in the root zone. Therefore, to compensate water content, the model has chosen over-irrigation, which, in addition to compensating the soil moisture, it also helps to leaching. In the remains of the growth stages of wheat and alfalfa, the optimal water depth distribution was lower than the normal water depth.

Table 6 Comparison of the crops allocated water depth in normal and optimal conditions
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Fig. 6
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Comparison of normal and optimal water depth distribution in growth stages of wheat (a), first-cultivation maize (b), second-cultivation maize (c), soybean (d), and alfalfa (e)

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EB

The volume of water consumed by the IAU and the amount of EB for two normal and optimal conditions are given in Table 7. In the conditions of optimal water allocation, the volume of allocated water decreases by 14.7%, while EB increases by only 5.7%. Therefore, the optimal water allocation in this area encourages saving water consumption more than increasing benefit. Saving water consumption causes a slight increase in EB due to the small water charge in the Moghan network. As a result, water users consider water a worthless commodity and use it without economic considerations. Meanwhile, if the correct price for water is determined, the EB will increase to a greater extent. The former researchers' findings have shown that a water charge is an important option for saving water for farmers (Chu and Grafton., 2020). Also, if the water charge is set correctly, the farmers will be sensitive to it (Huang et al., 2010). The study by Cortignani and Severini (2009), conducted in Italy, showed that increasing water charges by 200 and 300 percent and applying five to ten percent water reduction policies are effective in reducing water consumption.

Table 7 Comparison of the EB and the volume of water consumed in normal and optimal conditions
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Water Productivity

Table 8 shows the potential crop yield values after optimization and the water productivity for each crop. The results indicate that the water productivity index has increased after optimization for all crops. Alfalfa has the most significant increase in water productivity (by 35%), with a 24% decrease in the allocated water depth. Kanooni (2013) also presented similar results for the current study area.

Table 8 Water productivity values in normal and optimal conditions
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The Effect of Soil Water Salinity Coefficient on EU

It has been shown that the AquaCrop model could be a feasible tool to predict the soil salinity change trend (Mohammadi et al., 2016; Pourgholam-Amiji et al., 2021). The soil water salinity values (ECSW) after the completion of irrigation of each crop, which are the outputs of the AquaCrop model in the optimization model, are presented in Table 9. Based on detailed soil studies, the studied area has different types of soils. However, according to the detailed soil science report of the canal a area, the dominant soil of the Pars-Abad series has a salinity of 1.8 ds/m, which is placed in the medium class of salinity (Table 5), according to Wilcox's classification. The results of Table 9 indicate that the soil water salinity for first and second-cultivation maize and soybean after the completion of irrigation has increased from the initial soil salinity. However, this value did not exceed the maximum salinity of the Wilcox classification. Therefore, the coefficient of change of class ɣ2 (Table 4) equals 1. For the wheat, due to the insignificant difference between the initial soil salinity and soil water salinity after irrigation (the difference is less than 0.1), the value of the in-class coefficient (ɣ1) and class change (ɣ2) is equal to 1. The crop yield and soil salinity could be significantly affected by rainfall conditions (Liu et al., 2019; Zhai et al., 2022). In the study area, during the growth period of crops such as wheat and the first-cultivation maize, rainfall distribution is higher, and crops obtain part of their water requirement from rainfall. During the summer season, rainfall is reduced, and the crops’ rainwater usage, such as second-cultivation maize and soybeans, which are part of their growth period in summer, is reduced. For alfalfa, the soil water salinity after irrigation is equal to the initial soil salinity, so for this crop, both the in-class coefficient (ɣ1) and class change coefficient (ɣ2) are equal to 1. Crops such as developed alfalfa that have extensive roots can be beneficial in lowering the average salinity in the root zone (Minhas & Gupta, 1993; Hanks et al., 1990). The roots of an established alfalfa can extend to a depth of 2.5 m (Vaughan et al., 2002). Therefore, the results indicate that, except for alfalfa and wheat, inappropriate crop rotation and neglect of soil salinity management (e.g., using certain fertilizers to prevent and eliminate soil salinity) increase the soil salinity over time. (The values of the soil water salinity coefficient (γ) for all the studied crops are given in Table 10).

Table 9 Salinity of soil water after completion of irrigation for studied crops
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Table 10 EB and EU for the studied crops
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EU

Table 10 presents the obtainable EB for each crop, the obtainable total EB for the entire IAU, and the amount of IAU’s EU. The results show that the IAU’s EB is equal to 790,821 million Rials. For wheat and alfalfa, the amount of EU (excluding α′) is equal to the amount of EB, but the amount of EU (excluding α′) for the first and second-cultivation maize and soybeans is 10% is lower than the value of EB. The reason for this reduction is the increase of soil salinity in the root zone due to the irrigation of these crops. The annual average value of α′ coefficient was calculated as 0.97. The value of α′ less than 1 indicates that the inflow of drained water produced by the IAU will enter the Aras River in the long term, increasing the river water’s salinity. By applying the α′ coefficient as a penalty factor in the total benefit, the EU value of the IAU was reduced by 8.2% compared to EB. Resultantly, the combination of planting the studied crops will be beneficial for the farmers in the same growing season, but in case of choosing incompatible plants for the local climate, and not considering the proper measures to prevent soil salinity and river water salinity, the EU of the IAU decreases. Furthermore, the EU can be increased by planting crops such as alfalfa and wheat, which reduce soil water salinity.

Conclusions

Sustainable agriculture should be environmentally compatible with nature and economically beneficial, and this benefit should continue in the long term. In this regard, optimization models are valuable tools that not only increase benefits but also assess the feasibility of extending the cultivation area and can be used for economic analyses. Therefore, in this study, a combination of the AquaCrop plug-in model with the genetic algorithm optimization model was used for the optimal water allocation in the Moghan irrigation network. The objective function in this study was set to maximize the EU heuristic function instead of the EB function. The results indicated that the allocated water depth to the IAU decreased by 17% in the optimal condition compared to the normal condition while the water productivity increased after optimization for all crops. Alfalfa had the highest increase in water productivity compared to other crops by reducing the allocated water depth by 24%, followed by wheat with a 20% reduction. The values of soil water salinity coefficient (γ) showed that in case of mismanagement in soil salinity prevention, maize and soybeans increase soil salinity in the long term. The α′ coefficient of 0.97 indicated that the combination of five major crop cultivation in this area increases the river water salinity in the long term. By applying all two mentioned coefficients, the EU value in the IAU was reduced by 8.2% compared to EB. Therefore, using the proposed EU, it is possible to identify crops that reduce soil salinity and river water salinity, and not only EB but also EU is increased. The result of this study can be used by the network managers for selecting the best crop pattern in a network scale. Utilizing this approach can protect the country’s limited water resources to obtain sustainable agriculture.