Optimization of Irrigation Water Depth under Water Limiting Condition

5 Water productivity is a major challenge in all agricultural regions and despite the use of 6 pressurized irrigation system, it has not increased as expected in Iran. In addition, in spite of 7 water shortage in Iran, gardeners because of lack of knowledge in economic consequences do 8 not welcome deficit irrigation and irrigation scheduling. To this end, optimization of irrigation 9 water depth in an orange orchard was conducted for two irrigation scheduling methods (with 10 and without 4 days irrigation frequency) under water and land limitations conditions by 11 mathematical analysis of production and cost functions. Then, their effect on the net income by 12 changing in water and fruit price was assessed. Production and cost functions were developed 13 based on two scenarios of applied water including only irrigation water depth and irrigation 14 water depth plus rainfall. According to results, when water is limiting, by using the optimum 15 water depth (Ww), 26% of irrigation water use can be saved that causes only 3% to 4% decrease 16 in the net income per unit of land and 16% increase in the net income per unit of irrigation 17 water. In addition, when water limiting is serious, using 46% deficit irrigation (Wew) is more 18 useful and resultes the highest water productivity, even though it causes 14% to 17% decrease 19 in the net income per unit of land. However in water limiting condition, if land is not limiting, 20 using Wew causes the maximum net income per unit of land even 50% to 60% more than full 21 1 Postdoc Fellow, Water Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran. 2 Professor, Water Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran. (*_Corresponding Author, Email: Ansary@um.ac.ir) 3 Associate Professor, Department of Civil, Construction And Environmental Engineering, University of Alabama at Birmingham 2 irrigation. Moreover, using the optimum water depths in water limitation conditions (Ww and 22 Wew) increases the water productivity 26% to 47% relative to full irrigation. On the other side, 23 the net income and the amount of optimum water depths are not sensitive to the price of water 24 at the present value of water. However, they are highly sensitive to the price of fruit. 25 Furthermore, having an irrigation schedule causes 27% increase in the net income per unit of 26 land. According to positive effects of deficit irrigation and irrigation scheduling on the water 27 productivity and the income, they are highly recommended for addressing water scarcity in 28 Iran. 29


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Increasing need to food production in Iran that has limited water resources and is subject to 35 water risks remains a major challenge in the recent years. In addition, water shortage in Iran 36 threatens its environment, food security and economic that without further action would be a 37 hotspot region with domestic and global repercussions. Groundwater as the largest available 38 source of freshwater is under natural and anthropogenic pressures in Iran (Ashraf et sl., 2021). 39 Intensive groundwater use for agriculture depletes aquifers so that the total and annual 40 groundwater deficit in Iran is 131.1 and 5.2 bm 3 (Iran cabinet approval, 2021). Since agriculture 41 is the biggest using sector of water and highly water-dependent in Iran, agricultural water 42 productivity must be improved. Although Iran is known as an arid to semi-arid country, 43 Mazandaran province located in the north of Iran has an average annual rainfall about 620 mm. 44 as well. The 20-year rainfall in Mazandaran shows that only 30% of the annual rainfall occurs 48 from April to September and 18% of the annual rainfall occurs in 4 months from June to 49 September (that is the important time for orange fruit set). Whereas, the evaporation during 50 these periods are 814 and 623 mm, respectively. In addition, according to National Adaptation 51 Plan for Water Scarcity report (Iran cabinet approval, 2021), the 10-year precipitation decreased 52 10% compared to 50-year precipitation in the north of Iran such as Mazandaran province. 53 Therefore, water supply especially during April to September is a big challenge that lie ahead 54 for farmers and deficit irrigation coupled with irrigation scheduling are important pathways to 55 address this problem. A study in the humid climate of Uruguay showed that despite having an 56 average annual rainfall of 1150 mm, irrigating increased orange and lemon trees yields by 41% 57 and 29% compared to non-irrigated trees (Petillo, 1995). 58 On the other side, to increase the irrigation efficiency and water productivity in Iran, the 59 government has financially supported gardeners to use the drip irrigation in orchards so that 60 from 1991 to 2017, more than 30,000 hectares of orchards in Mazandaran province were 61 equipped. However, despite using the drip irrigation system, water productivity have not 62 increased as expected. One of the main problems is irrigating without scheduling. Irrigation 63 experts suggest 3 to 4 days irrigation frequency, however, many gardeners irrigate the trees 64 without a proper irrigation schedule. 65 Furthermore, the total and annual groundwater depletion in Mazandaran province is around  Ginestar and Castel., 1996) and the economic profit (English 75 and Raja, 1996).

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To economically assess the applied water use and determine the optimum water depth, 77 English (1990) presented a proper method. This method is developed based on production, cost 78 and income functions. The production function is a quadratic function that has been proven by 79 other researchers (Sepaskhah and Kashefipour, 1994;Capra et al., 2011;Hughes, 2011;Yasin 80 and ghazal, 2020). In this method, optimum water use is calculated by mathematical analysis 81 and the net income then would be determined. This method was used to find optimum irrigation 82 water management of wheat in the northwestern USA, cotton in California (USA), and corn in 83 Zimbabwe that showed 15 to 59 percent reduction in water use was economically acceptable 84 (English and Raja, 1996). In addition, economic analysis of seasonal and intra-seasonal models 85 of deficit irrigation of sorghum (Sepaskhah et al., 2006) and corn (Ghahraman et al., 2001) were 86 conducted and results showed that intra-seasonal method (decision making based on water 87 allocation at different stages of plant growth) produces more reduction (23%) of optimal water.

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Economic evaluation of deficit irrigation on 20 citrus orchards in Italy showed that the 89 appropriate amount of deficit irrigation for land and water limitation conditions is 12.7% and 90 25.6% of full irrigation (Capra et al., 2011). In a study on orange in Spain, deficit irrigation up 91 to 30% increased 47% net income per unit of water use (Pérez-Pérez et al., 2010). Another study in Spain on tangerine also showed that irrigation up to 80% tree water requirement did 93 not reduce gross income (Ballester et al., 2011). In a study, the optimal applied water for sugar land. In addition, under water limiting condition, the net income per unit of water was 98 maximized and increased the net income by 12%. In a study in Iran, optimum water use for 99 citrus were obtained by English method (Ebadi et al., 2016). In this study, water use for 100 maximum yield was obtained 199.8 mm, which did not differ significantly from the water use 101 when land is limiting. Results showed by using optimum water depth in water limiting 102 condition, water use was decreased by 36% and water productivity and net income per unit of 103 water use was increased by 42% and 23%. Economic assessment of deficit irrigation and its  The production function was determined by using English method when the price of sugar beet

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To determine the soil characteristics, the soil was sampled ( Figure 1) and the soil texture was 142 determined by hydrometer method. It showed that topsoil had clay loam texture and bulk 143 density was 1.34 gr/cm 3 and subsoil had loam texture and its bulk density was 1.38 gr/cm 3 .

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Water productivity (WP) was also obtained using Equation 4. For economic assessment, English (1990) method was used in which the optimum water use 149 for growing season is obtained by mathematical analysis of production-water and cost-water 150 functions. In this method, production (y(w)), cost (c(w)), and net income (iL(w)) functions are 151 as equations 5, 6, and 7, respectively. The total irrigated area and net income for the total 152 irrigated area were also calculated by equations 8 and 9.
Where, y(w) is yield per unit of land (kg/ha), w is water use depth (mm), c(w) is cost per 172 Based on this optimization, six optimum water depth (OWD) were determined as follows.

3.Optimum water depth when water is limiting (Ww):
188 When water is limiting, the derivative of the total area with respect to the water use depth is 189 as equation 16 and the optimal function of net income is as equation 17. Therefore, the optimum 190 water use when water is limiting is as equation 18.
Where Wm is the water depth for full irrigation and WOWD is other optimum water depths.

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WS is the water, which can be saved when OWD is used, compared to when Wm is used.
Where Y and Y OWD are the yield values when Wm and other OWD are used, respectively.

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YR is yield reduction when OWD is used compared to when Wm is used.

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Technoeconomic analysis when only irrigation water depth is considered (W= I) 255 In order to economic assessment, production and cost functions for each irrigation 256 management were obtained by equations 5 and 6 (Table 1 and Figure 3). In this scenario, only 257 the irrigation water depth was considered as the applied water. Then, the optimum irrigation 258 water depths for two irrigation scheduling methods were calculated (Table 2).   respectively. This condition has almost no significant change on water use, yield and water 287 productivity. The highest net income per unit of land was obtained from this case, which is the 288 same with full irrigation. This result is almost the same when wel is used. These findings  For water productivity, the best beneficial water productivity was obtained from Wew and 291 Ww. When Wew was used, the water productivity were 51.2 and 44.3 kg/m 3 and when Ww was 292 used, they were 43.9 and 38.8 kg/m 3 for A1 and A2, respectively. In addition, the lowest water 293 productivity was obtained from full irrigation (Wm).

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Technoeconomic analysis when irrigation water depth plus rainfall is considered (W= 296 I + R) 297 In this scenario, the applied water was considered as the sum of irrigation water depth and 298 the effective rainfall depth during the irrigation season. Then, production and cost functions for  (Table 4 and figure 4). The irrigation season in the study 302 area is April to September and the effective rainfall during this period was 129.1 mm. For the 303 rainfall lower than 5 mm, the effective rainfall was considered zero.
304   respectively. This condition has almost no remarkable change on water productivity and yield.

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The net income per unit of land in this status is the same with full irrigation.

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Overall, when irrigation water depth plus rainfall is considered to obtain production and cost 331 functions, using the optimum water depths has the weaker effect of the net income.  in water availability, using Wew is much better.

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It is worthy of note that although for the maximum yield, 45% more irrigation water is 379 applied by using Wm, the net income per unit of land is increased 14% to 17%. This is due to In addition, the changes in the net income relative to the applied water at the base water 389 price, 100% and 300% increase in the water price for 4 days irrigation frequency was plotted 390 in the figure 6. According to this figure, although by increasing the price of water, the applied 391 water for the maximum yield (Wm) is reduced, this reduction is not significant. On the other 392 hand, the net income is not sensitive to the water price and by increasing in the water price even 393 up to 300%, there is no remarkable change in the net income. On the other side, the changes in the net income relative to the applied water at the base fruit 398 price, 10% and 50% increase in the fruit price for 4 days irrigation frequency was plotted in 399 figure 7. This figure shows that 50% increase in the fruit price causes a remarkable increase 400 (more than 100%) in the net income. These issues show that the yield plays a greater role than 401 the water on the net income. The water and wastewater price in Iran compared to other countries (Figure 8) shows that 406 water price in Iran is much lower than other countries. In developed countries, however, higher 407 water price encourages farmers to use more advanced irrigation and water management 408 methods. When water is limiting and there is no land limitation, the highest net income per unit of 413 land was obtained by using Wew (45% deficit irrigation). Whereas, in the previous studies, Ww 414 was expressed. As it is shown in figure 9, when the irrigation water plus rainfall is considered 415 to obtain the equivalent irrigated area (IA), Ww has the most beneficial results. However, as it 416 was mentioned in the current study, only the irrigation water must be considered and in this 417 situation, when Wew is used, the larger areas of the orchard can be put under irrigation by 418 applying the saved water that results in the highest net income per unit of land. The following conclusion can be drawn from the current study is that having an irrigation 424 schedule causes 27% increase in the net income per unit of land. In addition, if water is not 425 limiting, using Wm causes the highest net income per unit of land. In water and land limiting 426 condition, if there is minor to moderate water limiting, using the optimum water depth (Ww) 427 can save 26% of irrigation water use that causes 3% to 4% decrease in the net income per unit 428 of land but 16% increase in the net income per unit of irrigation water. Whereas, when there is 429 sever water limiting condition, using Wew is more useful that although it causes 14% to 17% 430 decrease in the net income per unit of land, it saves 46% of irrigation water use.

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Based on results, when rainfall occurs, the irrigation water plus rainfall must be considered 432 to obtain production and cost functions. However, to assess the effect of deficit irrigation, only 433 the irrigation water must be considered to determine the equivalent irrigated area (IA).

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Therefore, when there is water limiting condition with no land limiting, using Wew (46% deficit 435 irrigation) causes the maximum net income per unit of land even 50% to 60% more than full 436 irrigation. Because by using Wew, the larger areas of the orchard can be put under irrigation.

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Moreover, the maximum water productivity was obtained from the optimum water depth in 438 water limitation conditions (Ww and Wew). On the other side, at the present price of water and 439 fruit, the net income and the amount of optimum water depths are not sensitive to the price of 440 water. However, they are highly sensitive to the price of fruit. It was due to the big difference 441 in the price of unit of fruit compared to the price of unit of water which causes the yield to play 442 a greater role than water on the net income.

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Overall, this study points out that having an irrigation schedule and using 25% and 45% 444 deficit irrigation in water limiting condition are proper solution to address water scarcity in Iran.

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In addition, economic return is a key factor doubled with technical analysis that experts should 446 consider to have the irrigation scheduling acceptable by farmers. Moreover, it is necessary to 447 focus on efforts that highlight the water value among water users. The policy makers also can 448 assist in addressing this challenge by realistic pricing of water and removing the regulations 449 that support excessive use of water to move agriculture toward sustainable production.