Study area
The Moghan Plain is located in the northwest of Iran. The Moghan irrigation network is fed by the Aras River and irrigates 72000 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.
Table 1
Characteristics of the main crops of the Moghan irrigation network in 2020
Crop characteristics | Units | Wheat | Maize_1 | Maize_2 | Soybean | Alfalfa |
A | (ha) | 1495 | 585 | 882 | 280 | 155 |
Ymax | (Kg ha− 1) | 6500 | 9800 | 7200 | 3800 | 15000 |
Yave | (Kg ha− 1) | 4200 | 7400 | 5000 | 2500 | 12000 |
P | (RI Kg− 1) | 36400 | 36000 | 36000 | 56000 | 25000 |
C | (RI 104 ha− 1) | 3200 | 4050 | 3750 | 3440 | 3570 |
Pw | (RI ha− 1) | 4586400 | 7992000 | 5400000 | 4200000 | 8975520 |
A: Cultivated area, Ymax: Maximum crop yield, Yave: Average crop yield, P: Market price in Rial, |
C: Production cost, Pw: Water charge in the network, 1:Spring, 2: Summer |
Figure 1 Location of Moghan irrigation network
Figure 2 The monthly volume of Aras River water after the diversion dam for the years 2011–2020
Figure 3 Aras River seasonal water salinity after diversion dam for the years 2011–2020
Figure 4 Average long-term minimum, maximum, and mean temperature values (a) and average long-term values of rainfall and evapotranspiration in the Pars-Abad weather station
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., 2018; 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)
Crop parameters | Unit | Wheat | Maize_1 | Maize_2 | Soybean | Alfalfa |
Growth factors | | | | | | |
Base temperature | ˚C | 0 | 8 | 8 | 5 | 0 |
Cut-off temperature | ˚C | 26 | 30 | 30 | 30 | 30 |
Crop water productivity | g/m2 | 15 | 33.7 | 33.7 | 15 | 17 |
Expansion upper threshold | - | 0.2 | 0.14 | 0.14 | 0.15 | 0.2 |
Expansion lower threshold | - | 0.65 | 0.72 | 0.72 | 0.65 | 0.7 |
Morphologic factors | | | | | | |
Initial canopy cover | % | 6.75 | 0.49 | 0.49 | 0.1 | 1.8 |
Maximum canopy cover | % | 88 | 89 | 89 | 77 | 87 |
Canopy growth coefficient | %/day | 3.9 | 12.7 | 12.7 | 13.6 | 21.9 |
Canopy decline coefficient | %/GDD | 0.38 | 0.56 | 0.56 | 0.15 | 0.8 |
Maximum root depth | m | 1.5 | 2.3 | 2.3 | 2 | 1.5 |
Phenology factors | | | | | | |
Time to emergence | GDD | 150 | 96 | 120 | 162 | - |
Time to reach full canopy | GDD | 1203 | 901 | 766 | 998 | 75 |
Time to reach senescence | GDD | 1704 | 1664 | 1443 | 1609 | 362 |
Time to reach harvest | GDD | 2414 | 2165 | 1723 | 2001 | 376 |
Planting and harvest factors | | | | | | |
Harvest index | % | 48 | 48 | 48 | 40 | 85 |
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. Eq. 3 represents the EB for each crop:
EB = benefit per crop per hectare = (crop sales per hectare - costs per hectare)\(=\left({\text{Y}}_{\text{i}}\text{×}{\text{P}}_{\text{i}}\right)\text{-}\left({\text{C}}_{\text{i}}\text{+}{\text{P}}_{\text{w}}\text{×}{\text{IR}}_{\text{i}}\right)\) | (3) |
The amount of irrigation depth (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:
$$\text{EB=}\left(\sum _{\text{i=1}}^{\text{n}}{\text{A}}_{\text{i}}\text{×}\left({\text{Y}}_{\text{i}}\text{×}{\text{P}}_{\text{i}}\text{-}{\text{C}}_{\text{i}}\text{-}{\text{P}}_{\text{w}}\text{×}{\text{NIR}}_{\text{i}}/\text{E}\right)\right)$$
4
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,
$$\text{EU=}{\alpha }^{{\prime }}\left(\sum _{\text{i=1}}^{\text{n}}{{\text{γ}}_{\text{i}}\text{×A}}_{\text{i}}\text{×}\left({\text{Y}}_{\text{i}}\text{×}{\text{P}}_{\text{i}}\text{-}{\text{C}}_{\text{i}}\text{-}{\text{P}}_{\text{wi}}\text{×}{\text{NIR}}_{\text{i}}/\text{E}\right)\right)$$
5
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), NIRi is net irrigation depth (mm), E is irrigation efficiency, and Ai is the cultivated area (ha). 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).
$$\sum _{\text{i=1}}^{\text{i}}{\text{A}}_{\text{i‚d}}\text{≤AT}$$
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- 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:
$$\text{0.75×}{\text{NetIrri}}_{\text{i‚d}}\text{≤}{\text{NIR}}_{\text{i‚d}}\text{≤1.25×}{\text{NetIrri}}_{\text{i‚d}}$$
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).
$${\text{V}}_{\text{d}}\text{=}\sum _{\text{i=1}}^{\text{i}}{\text{IR}}_{\text{i‚d}}\text{×}{\text{A}}_{\text{i}}$$
8
$${\text{V}}_{\text{d}}\text{≤}{\text{W}}_{\text{d}}$$
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 salinity of the drained water to the river should not increase the river water salinity. 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:
$${\text{ECdrain}}_{\text{d}}\text{=}\frac{\sum _{\text{i=1}}^{\text{i}}{\text{ECdrain}}_{\text{i,d}}\text{×}{\text{Vdrain}}_{\text{i,d}}}{\sum _{\text{i=1}}^{\text{i}}{\text{Vdrain}}_{\text{i,d}}}$$
10
$${\text{ECriver}}_{\text{d}}\text{-mod}\text{=}\frac{\left({\text{ECriver}}_{\text{d}}\text{×}{\text{Vriver}}_{\text{d}}\right)\text{+}\left({\text{ECdrain}}_{\text{d}}\text{×}{\text{Vdrain}}_{\text{d}}\right)}{{\text{Vriver}}_{\text{d}}\text{+}{\text{Vdrain}}_{\text{d}}}$$
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.
$$\text{C}\text{=}\frac{{\text{ECriver}}_{\text{d}}\text{-mod -ECriver}}{\text{ECriver}}$$
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
̍α | C |
1 | ≤ 0 |
0.95 | 0-0.1 |
0.85 | 0.1–0.3 |
0.7 | 0.3–0.7 |
0.5 | 0.7< |
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.
$$\text{γ=}{\text{γ}}_{\text{1}}\text{×}{\text{γ}}_{\text{2}}$$
13
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.
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).