Crop Water Production Function Research Articles

Modeling Tomato Yield and Quality Responses to Water and Nitrogen Deficits with a Modified Crop Water Production Function

Increasingly severe crises, such as climate change, water scarcity and environmental pollution, pose significant challenges to global food security and sustainable agricultural development. For efficient and sustainable tomato cultivation management under resource constraints, quantitatively describing the relationship between yield-quality harvest and water-nitrogen application is practically beneficial. Two successive greenhouse experiments with three irrigation levels (1/3 FI, 2/3 FI, and full irrigation (FI)) and four nitrogen fertilizer treatments (0 FN, 1/3 FN, 2/3 FN, and full nitrogen (FN)) were conducted on tomatoes during the whole phenological stage. The tomato evapotranspiration and nitrogen application amount, yield, comprehensive quality, solid–acid ratio, and lycopene content were measured. Based on crop water production functions, three equation forms of water-nitrogen production functions containing 20 models were established and evaluated to predict tomato harvest parameters. The results show that water increased tomato yield while decreasing fruit quality, and the effect of nitrogen was primarily contrary. Water most significantly impacted tomato formation, and the interaction of water and nitrogen changed among different harvest parameters. Tomato yield and quality formation was more sensitive to water and nitrogen at the flowering and fruit maturation stages. Model Singh-2 outweighed other models for yield estimates, with an R2 of 0.71 and an RMSE of 0.11. Singh-Log, Singh-sigmoid and Rao-Root models were effective models for comprehensive quality, solid–acid ratio, and lycopene content prediction, with an R2 of 0.41, 0.62, and 0.42, and an RMSE of 0.33, 0.50, and 0.16, respectively. Finally, models in the form of f(ETi)·f(N) were ideal for tomato harvest prevision and are recommended for water and nitrogen management in tomato cultivation.

Effect of Deficit Irrigation on Wheat (Triticum aestivum L.) Yield and Water Use Efficiency in the Semi-Arid Region of Awash Basin, Ethiopia

Crop production is largely limited by water availability in arid and semi-arid regions of Ethiopia. Changing climate conditions and declining water resources demand appropriate approaches to improve crop yield and water use efficiency through a reduced and more reliable water supply. A field experiment was conducted to evaluate the effect of limited irrigation water use on bread wheat production and water use efficiency under the semi-arid climate conditions of Awash basin of Ethiopia. Five irrigation levels, that is, full irrigation (100% ETc/control), 85% ETc, 70% ETc, 55% ETc, and 40% ETc, were evaluated using a randomized complete block design (RCBD) with four replicates. Statistical analysis has shown a significant effect of irrigation levels on wheat grain yield, water use efficiency, economic profit, wheat grain quality, and aboveground biomass. The highest grain yield (5,085 kg ha−1) was obtained from 100% ETc irrigation application (i.e. 417.2 mm of water), and the lowest grain yield was obtained from 40% ETc (i.e. 223.7 mm of water) application. A deficit level of 85% ETc resulted in a yield that was comparable to that of full irrigation. Compared to other treatments, the 70% ETc application produced the highest water use efficiency (1.42 kg m−3). Using the saved water obtained from 70% ETc deficit irrigation application, 23.4% more wheat could be produced on 1.38 ha of land, resulting in the highest profit (US$2,563.9) and higher MRR (137%). The yield response factor and crop-water production function indicated that maintaining irrigation at optimal levels can prevent potential yield reductions. Consequently, a 70% ETc deficit irrigation application was found to be optimal for increasing wheat grain yield, water use efficiency, and economic benefits from irrigated wheat production. These results suggest that deficit irrigation for wheat under semi-arid climatic conditions is a viable irrigation management option for enhancing water use efficiency.

Water production function and optimal irrigation programme for drip irrigated castor (Ricinus communis L.)

Water shortage for crop production necessitates adequate knowledge of the crop water production function to make decisions on water allocation for optimum returns from castor crop under surface drip irrigation. The study was conducted in rabi 2009-10 at Agricultural college farm, Rajendranagar, Hyderabad. The different drip irrigation schedules at 40, 60 and 80 per cent pan evaporation replenishment levels either kept constant throughout the crop life or combinations at vegetative, flowering and development stages were compared with surface check basin at (0.8 IW/CPE ratio) irrigation. The results showed that drip irrigation at 0.6 Epan replenishment up to flowering and 0.8 Epan later on registered comparable seed yields with drip irrigation scheduled at either at 0.6 or 0.8 Epan and was significantly superior over other treatments and the best fit water production function was quadratic (R2= 0.99). The optimum quantity of water (ETc) for maximum net returns under prevailing prices (water and castor @ `10 and 30 ha/mm and kg/ha, respectively) was 381.4 ha mm with a resultant seed yield of 3611 kg/ha. The gross returns, net returns and net return/rupee invested varied from ` 72194 to 144447/ha, ` 36808 to 108018/ha and 1.040 to 3.049, respectively.

Developing a Crop Water Production Function for Alfalfa under Deficit Irrigation: A Case Study in Eastern Colorado

Recent Colorado, USA water law provisions allow a portion of irrigation water to be leased between agricultural and other users. Reducing consumptive use (CU) through deficit irrigation while maintaining some crop production could allow farmers to earn revenue from leasing water rights. This observational study aimed to determine if deficit irrigation of alfalfa (Medicago sativa L.) can be used to reduce CU, provide parameters for an alfalfa crop water production function (WPF), and evaluate the potential for improved farm income by leasing water. Soil water balance, evapotranspiration (ET), and dry matter yield from eight commercial fields (1.70 to 2.14 ha zones), growing subsurface drip-irrigated alfalfa, were monitored for five seasons (2018–2022) at Kersey, Colorado. Four irrigation treatments [Standard Irrigation (SI) = irrigate when soil water deficit (D) exceeds management allowed depletion (MAD); Moderate Deficit Irrigation (MDI) = 70% of SI; Severe Deficit Irrigation (SDI) = 50% of SI; and Over Irrigation (OI) = 120% of SI] were applied, with two zones per treatment. Reductions in CU ranged from 205 to 260 mm per season. The shape of the alfalfa WPF (dry biomass yield vs. ET) was concave, indicating that water use efficiency (WUE) could be optimized through deficit irrigation. The average WUE was 0.17 Mg ha−1 cm−1 and tended to increase with greater deficits. Deficit irrigation also increased the relative feed value. If conserved CU from deficit irrigation can be leased into a transfer water market, farmers could profit when the water lease revenue exceeds the forgone profit from alfalfa production. We found incremental profit from deficit irrigation and water leasing to be positive, assuming 2020 prices for hay ($230 bale−1) and water prices above $0.50 m−3.

Optimal allocation of agricultural water resources in Yanghe watershed considering blue water to green water ratio.

Yanghe Watershed has low annual rainfall, uneven spatial and temporal distribution, extreme shortage of water resources in some areas. The contradiction between supply and demand of water for agricultural production is prominent and the expected production value cannot be achieved. Therefore, it is necessary to investigate the supply and demand of agricultural water resources and the impact of green water on agricultural crops in Yanghe Watershed. This article proposes a new crop economic model for increasing the green-water footprint to blue-water footprint ratio (GWF:BWF) in accordance with the regional characteristics, alleviating agricultural water shortage in irrigation areas, optimizing water resource allocation, and achieving sustainable agricultural development. The proposition is based on a study of five crops in eight districts and counties in the Yanghe River watershed. By combining the economic model F with a crop water production function, we achieved 89.3%, 88.9%, 97.1%, 81.5%, and 87.0% of the optimal water demands of the five crops, respectively, and effectively improved the underground irrigation of crops and the water resource utilization efficiency. The GWF:BWF threshold interval was subsequently selected based on the temporal changes in the BWF and GWF in the study area. This enabled significant reduction of the planting area of blue-water crops and increase in the proportion of green-water crops, while also improving the agricultural economy of the Yanghe Watershed. The proposed model promises to afford enhanced management of agricultural irrigation areas that experience rainfall shortage. © 2023 The Authors. Journal of The Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Adaptabilities of Water Production Function Models for Rice in Cold and Black Soil Region of China

Crop water production function models (WPFMs) are required methods to study the relationships between yield and water consumption under regulated deficit irrigation (RDI). In this study, a pot experiment was established to study the effect of water deficit during both individual growth stages and across two consecutive growth stages of rice on yield, water consumption, and water use efficiency (WUE) in 2017 and 2018. Light, medium, and severe water deficits were set as 80~90%, 70~80%, and 60~70% of saturated soil moisture content, respectively. The accuracies of five WPFMs were tested based on the experimental results. The results showed that yields and WUE of a light water deficit were higher than those of medium and severe water deficits at each growth stage. The yields and WUE of light drought stress treatments in the flowering and milky stages were higher than the saturated soil moisture control by 4~7.4% and 5.3~20.6%, respectively. Water consumption decreased with increasing water deficit across two consecutive growth stages. The Minhas model had the highest simulation accuracy of the five WPFMs, with relatively lower AE, RMSE, Cv, CRM, and higher R2, which were 0.0002, 0.0634, 6.9965, 0.0002, and 0.9951 in 2017 and 0.0110, 0.0760, 8.9882, 0.0131, and 0.9923 in 2018, respectively. The sensitivity indices for the Minhas model more accurately reflected the sensitivity of rice yield to water deficit at different growth stages in 2017 and 2018, compared with the Jensen model, Stewart model, Blank model, and Singh model. Rice yield was most sensitive to water deficit at the jointing and booting stage. The results indicate that the Minhas model is the most suitable WPFM for guiding rice irrigation practices in cold and black soil regions of China.

Crop yield estimation and irrigation scheduling optimization using a root-weighted soil water availability based water production function

The crop-water production function (CWPF) is widely used to quantitatively describe relationships between crop water deficit and yield, and evaluate the effects of different irrigation strategies in agro-hydrological models. In order to reasonably and reliably estimate crop yield and optimize irrigation scheduling , a novel CWPF was proposed by combining the plant water deficit index (PWDI), estimated based on root-weighted soil water availability, with a daily water sensitivity index derived from a sigmoidal cumulative function. Parameterized using data from a two-year winter wheat field lysimetric experiment conducted in the North China Plain and from a previously published two-year spring maize field drip irrigation experiment in Inner Mongolia, China, the CWPFs provided reasonable estimation of different crop yields with different water stress response characteristics under different field environments. Through coupling the genetic algorithm with the integrated simulations of soil water dynamics, PWDI and CWPF in the soil-wheat system, an optimization procedure was developed to determine PWDI threshold combinations to timely trigger irrigation according to pre-designed crop water deficit status. Crop yield and water use efficiency (WUE) of winter wheat were estimated and compared under different optimized constant and variable PWDI threshold combinations. In addition, the effects of climate change on the optimized variable PWDI threshold combinations were investigated using 38 years of historic meteorological data . The results showed that regulated deficit irrigation (RDI) with a variable threshold combination, in which the sensitivity characteristics to water deficit were considered for the crop at different growth stages, was superior to a constant threshold in enhancing crop yield and WUE. Irrespective of the number of irrigation events (1, 2, 3 or 4) during the growing season, the coefficients of variation (CV) of optimized PWDI thresholds for different combinations of irrigation sequence and events were not very large under the same kind of hydrological year (wet, normal or dry), with CV < 0.39 and a median of 0.21. When the mean (MN) of the optimized PWDI threshold combinations for different irrigation sequence and events was used to schedule RDI of winter wheat in terms of various hydrological years, up to 91% of the estimated relative yield was found to be higher than 90% of the corresponding maximum values. Therefore, the MN can be valuable in formulating rational irrigation management strategies of winter wheat to achieve relatively high yields with limited water under changing climatic conditions.

Optimizing planting density and irrigation depth of hybrid maize seed production under limited water availability

Improvement in seed vigor and yield of hybrid maize is required to ensure food security. Optimal planting density and irrigation depth are critical for hybrid maize seed production in arid areas. Using data from 2012 to 2017, a new integrated model optimized planting density and border irrigation depth for achieving high yield and seed vigor of hybrid maize under limited water availability. For field experiments, a planting density of 9.75 plants m−2 under full irrigation was in the control treatment. The results showed that water deficit decreased yield, evapotranspiration, and aboveground biomass per plant. The highest yield was obtained for the planting density of 12.75 plants m−2 under full irrigation. The single crop coefficient and crop water production function models were modified to simulate evapotranspiration and yield, respectively. Using kernel number per plant and plant growth rate during the flowering stage, a kernel weight model was established. The maximum yield and minimum irrigation depth were weighted and kernel weight was constrained. Three minimum relative kernel weight (RKWmin) options were considered, option 1 with RKWmin= 1.00 (control), option 2 with RKWmin= 0 (unconstrained), and option 3 with RKWmin ranged from 0.60 to 0.90. In option 1, the optimal irrigation depth during the growing season under control planting density decreased by 24.3–39.4% compared to the conventional practices. In option 2, yield increased but average kernel weight decreased by 25% than control. In the option 3, average yield and water use efficiency increased by 9.2% and 6.5% compared to option 1, respectively. The average planting density decreased by 10.2%, yield reduced by 2.0%, and water use efficiency reduced by 1.7%, but kernel weight increased by 9% compared to option 2. Thus option 3 can be recommended for hybrid maize seed production with limited water availability in arid regions of Northwest China. Our research provided a new theoretical method to improve yield, and ensure seed vigor of hybrid maize in arid regions.

Remote Sensing—Based Assessment of the Water-Use Efficiency of Maize over a Large, Arid, Regional Irrigation District

Quantitative assessment of crop water-use efficiency (WUE) is an important basis for high-efficiency use of agricultural water. Here we assess the WUE of maize in the Hetao Irrigation District, which is a representative irrigation district in the arid region of Northwest China. Specifically, we firstly mapped the location of the maize field by using a remote sensing/phenological–based vegetation classifier and then quantified the maize water use and yield by using a dual-source remote-sensing evapotranspiration (ET) model and a crop water production function, respectively. Validation results show that the adopted phenological-based vegetation classifier performed well in mapping the spatial distributions and inter-annual variations of maize planting, with a kappa coefficient of 0.86. In addition, the ET model based on the hybrid dual-source scheme and trapezoid framework also obtained high accuracy in spatiotemporal ET mapping, with an RMSE of 0.52 mm/day at the site scale and 26.21 mm/year during the maize growing season (April–October) at the regional scale. Further, the adopted crop water production function showed high accuracy in estimating the maize yield, with a mean relative error of only 4.3%. Using the estimated ET, transpiration, and yield of maize, the mean maize WUE based on ET and transpiration in the study region were1.94 kg/m3 and 3.06 kg/m3, respectively. Our results demonstrate the usefulness and validity of remote sensing information in mapping regional crop WUE.

Biogat-fert technique for maximizing water and fertilizer units productivity for potato crop

Biogat-fert technique ensure to maximizing water and fertilizer unit productivity for potato crop, Two field experiments were carried out during growing seasons 2019-2020 and 2020-2021, at research farm of National Research Centre in Nubaria region, Egypt to study management of biogat-fert technique on potato crop under drip irrigation system in sandy soil conditions. Study factors were fertigation techniques (fertigation, biogat-fert and fertilizers). The following parameters were studied to evaluate the effect of study factors: (1) mineral and biological fertilizers effect of soil, (2) microbial number, (3) NPK ratio, (4) Yield of potato, (5) water use efficiency of potato, (6) Crop water production function. The results conducted that soil fertility was enhanced greatly in bio-fertilizer treatment. The average total N, total P and total K in 0–40 cm soil layers increased to 29.17, 26.67and 36.7% respectively. The average CFU of bacteria in soil layers increased by 15 Time. After drip irrigation, the CFU of bacteria had increased further, and reached more than 7.8× 107 CFU/g dry soil in the 0–40 cm soil layers. The results showed that the application of different bio-fertilizer along with fertilizers revealed significant positive impact on crop yield.

Optimal Annual Allocation Model of Large Storage Based Irrigation Project by Multi Level Approach

The effective management of water available for irrigation in arid and semi-arid regions has increased in importance due to limited water supply. The need for allocation of water resources optimally in a water limiting condition has already been recognized, and much research has been carried out. In the present study, an annual irrigation planning model is formulated for Nagarjuna Sagar Project command in the semi-arid region of South India dealing with optimal allocation of annual available water among command areas of each main canal taking off from the reservoir and reallocating the available land and water of each command area to different seasons of a year and finally allocating the available land and water of each season among crops grown in that season, maximizing the total annual benefit of the project. The problem is solved in three stages. In the first stage, fortnightly crop water requirements are calculated from the evapotranspiration model by Penman – Monteith method. In the second stage, seasonal crop water production functions are developed using the single crop intraseasonal allocation model for each crop of all seasons. In the third stage, allocations of area and water are made at seasonal, interseasonal and at reservoir levels by deterministic dynamic programming, maximizing the net annual benefit from the project. Optimal cropping pattern and irrigation water allocations are made with full and deficit irrigation strategies for various levels of probability of exceedences of expected annual water available and results obtained are discussed.

Maize grain yield and crop water productivity functions in the arid Northwest U.S.

Increased water demands and drought have resulted in the need to provide data to guide deficit water management decisions in irrigated maize (Zea mays L.) for grain production. The objective of this study was to develop relationships between maize grain yield and maize water use (ETc, crop evapotranspiration) under low and high nitrogen (N) input systems on a soil type (silt loam) common to maize production in the arid Northwest U.S. The treatments consisted of two N inputs (0 and 246 kg N ha-1 year-1, -N and +N, respectively) and four water input treatments ranging from 100% to 25% of full irrigation. The full irrigation treatment was 20% less than evapotranspiration model calculated crop use (ETm), indicating that crop coefficient (Kc) values may need to be adjusted for maize in the arid Northwest U.S. There were no grain yield response differences between N input treatments in 2017 but during 2018 and 2019 (treatments on same plots), ETc versus grain yield relationships were different for the -N and +N treatments. Crop water production functions were developed using quadratic relationships between ETc and maize grain yield. The range of grain yield across all years and treatments were 15.03–7.23 Mg ha-1. The range of crop water productivity (CWP) across all years and treatments were 1.6–2.6 kg m-3. The ETc at maximum CWPs across all years and treatments had a range of 60–71% of ETm. These relationships are valuable to understanding maize response over a range of water availability and in developing tools to assess future production under water shortages.

An interval multi-objective fuzzy-interval credibility-constrained nonlinear programming model for balancing agricultural and ecological water management

This study presents an interval multi-objective fuzzy-interval credibility-constrained nonlinear programming (IMFICNP) model combined with spatial water requirement of ecological vegetation (SEWR) estimation for solving the problem of allocation of agricultural and ecological water in irrigation districts under uncertainties. Through techniques of remote sensing (RS) and geographic information system (GIS), the ecological vegetation is subdivided into three types including forest land, grassland and shrubland and the water requirement of ecological vegetation is extended from site-specific sample to spatial decision-making unit (DMU), which provides a set of spatial data for input parameters of constraints. The IMFICNP model can be formulated through combination of interval parameter programming, multi-objective programming and fuzzy-interval credibility-constrained programming, which can handle the conflicts of multiple objectives under uncertainties such as single uncertainty (interval and fuzzy parameters) and dual-uncertainties (fuzzy-interval sets), and finally generate optimal water allocation schemes for crop and ecological vegetation under different credibility levels. The interval quadratic crop water production functions (IQCWPFs) are introduced to express the nonlinear relationships between crop yield and irrigation amount. Then, this model is applied to a case study of Huangyang Irrigation District (HID) in Shiyang River Basin to demonstrate its applicability. The results indicate that a higher credibility level is accompanied by less amount of water allocation and lower system benefit. The amount of water allocation at the DMU is dominated by planting area of crops and ecological vegetation, but there are few exceptions that optimal solutions are determined by the economic value. In addition, SEWR enables to reflect spatial heterogeneity of the DMU at a larger scale. IMFICNP model can coordinate conflicts among multiple objectives and it can tackle the violation of system constraints with fuzzy-interval sets. Therefore, these results can effectively balance the agricultural and ecological water management in irrigation districts, and provide valuable basis for the sustainable development of arid and semi-arid areas.

Dry Bean (Phaseolus vulgaris L.) Crop Water Production Functions and Yield Response Factors in an Arid to Semi-Arid Climate

HighlightsDeficit irrigation negatively affected dry bean yield and yield components.Excess irrigation increased crop ETc but not dry bean yield.Soil moisture fluctuation was greater in the top 0.3 m of the soil profile compared to deeper depths.Crop water production function had a slope of 18.9 kg ha-1 mm-1 and threshold crop evapotranspiration of 171 mm.Dry bean crop was found to be sensitive to water stress (yield response factor Ky = 1.94).Abstract. Under changing climate conditions and declining water resources, understanding crop response to water stress is critical for effective irrigation management. The objectives of this study were to quantify dry bean (Phaseolus vulgaris L., cv. Othello) soil moisture dynamics, crop evapotranspiration (ETc), and yield response factor and to develop dry bean irrigation and crop water production functions (IWPF and CWPF). Five irrigation treatments, i.e., full irrigation (FIT), 75% FIT, 50% FIT, 25% FIT, and 125% FIT, were evaluated using a randomized complete block design (RCBD) with three replications for three years (2017, 2018, and 2019) in the arid to semi-arid intermountain region of Powell, Wyoming. The results showed a significant influence of irrigation on dry bean soil moisture dynamics and ETc. The dry bean crop showed a greater soil moisture fluctuation in the top 0.3 m of the soil profile compared to 0.6 m and at 0.9 m. ETc ranged from 187 to 438 mm, from 190 to 409 mm, and from 217 to 398 mm in the 2017, 2018, and 2019 growing seasons, respectively. A positive two-segment relationship was observed between dry bean seed yield and cumulative irrigation water applied. The average cumulative seasonal irrigation of 310 mm resulted in maximum seed yield. For all three years, the seed yield increased linearly with ETc. Combining the data from the three years resulted in a CWPF with a slope of 18.9 kg ha-1 mm-1 and an offset of 171 mm of ETc (i.e., the ETc required for crop establishment before any seed yield is produced, or threshold ETc). Moreover, the dry bean crop was found to be sensitive to water stress (Ky = 1.94). These results indicated that under the typical semi-arid to arid climate conditions of the intermountain region of Wyoming, deficit irrigation of dry bean may not be a viable strategy because the yield loss outweighs water-saving benefits. Keywords: Dry bean, Crop evapotranspiration, Crop production function, Irrigation water production function.

Influence of crop-water production functions on the expected performance of water pricing policies in irrigated agriculture

Agricultural economics Water Programming Models (WPM) has found that irrigators in water scarce areas have a rather inelastic response to water prices, making water pricing cost-ineffective towards water saving. We hypothesize that the predicted water saving performance of pricing is significantly underestimated by issues of model structure, due to the exclusion of deficit irrigation from the set of decision variables available to agents in conventional WPM. To test our hypothesis, we develop a model that integrates a continuous crop-water production function into a positive multi-attribute WPM, which allows us to assess agents’ adaptive responses to pricing through deficit irrigation. The model is illustrated with an application to the El Salobral-Los Llanos irrigated area in Spain. Our results show that incorporating deficit irrigation as an adaptation option makes the water demand curve significantly more elastic as compared to an alternative model setting where deficit irrigation is precluded. We conclude that ignoring deficit irrigation can lead to a significant underestimation of the cost-effectiveness of water pricing towards water saving.

Modeling salinity risk response to irrigation practices for cotton production under film mulched drip irrigation in Xinjiang

Abstract Predicting the impacts of the irrigation amount (IA), water salinity (WS), and antecedent soil salinity (AS) on soil salinization, the crop yield, and water productivities (WPs) are important for precision agriculture. We used a calibrated HYDRUS − 2D model coupled with a validated crop water production function to quantitatively determine the response of a soil − cotton system to three factors (IA, WS, and AS) in 30 scenarios under film mulched drip irrigation. These scenarios included five IAs, two ASs, and three WSs. Under the same IA and WS, the transpiration, evapotranspiration, yield, and WPs were lower, whereas the evaporation, drainage, soil water storage, and leached salt were higher under higher AS (over the salt tolerance threshold of cotton) scenarios. Under lower AS scenarios, desalination processes (20.2 to 166.8 g m−2) occurred in freshwater (0.38 dS m−1) irrigation scenarios and salt accumulated (425.8 to 1,442.4 g m−2) in saline water (3.10 and 7.42 dS m−1) irrigation scenarios. Desalination processes (2,273.4 to 4,692 g m−2) occurred in the higher AS scenarios. Salinity risk warning should be the focus for cotton fields with lower AS and saline water irrigation. Our results may help to identify the salinity risk to support sustainable cotton production in Xinjiang.

Study on the Pricing of Water Rights Transaction between Irrigation Water Users Based on Cooperative Game in China

China’s water rights transaction is still in the initial stage of development. There is no systematic pricing method for water rights transactions between farmers. This paper puts forward a pricing model of water rights transactions among farmers in water-deficient areas. The price of water rights transaction consists of cost price and earnings price. The earnings price is determined by studying the crop water production function, calculating the crop’s marginal benefit of the two parties, and combining the Cooperative Game Theory. Finally, the pricing model was applied to the water rights transactions among the farmers of Hetao Irrigation District of Bayannaoer City, Inner Mongolia Autonomous Region. Results showed that under the A4 trading strategy, the overall income increased without losing the interests of any farmer. The increasing income of the three farmer households N1, N2, and N3 after the alliance was 8.14 thousand dollars, 4.66 thousand dollars, and 20.33 thousand dollars, respectively, and the water rights transaction prices of N3 and N1, N2 were respectively 0.485 $/m3, 0.565 $/m3. It is estimated that the model can provide a scientific basis for water rights trading between farmers and the efficient use of water resources.

A novel approach to dynamically optimize the spatio-temporal distribution of crop water consumption

The finite water resources are the main factors limiting agricultural sustainable development in arid and semiarid zones. In these water-scarce areas, optimizing limited water resources is an important way to reduce water consumption, increase crop yields and improve regional economic benefits. In this study, a CA-Jensen optimization model integrating cellular automata method and crop water production function into multi-objective dynamic optimization was developed and applied to the middle reaches of the Heihe River basin in the Northwest China to adjust the spatial distribution of cropland and the spatiotemporal allocation of crop water consumption. The net economic benefits of unit water, the crop water productivity and the value of the terrestrial ecosystem services represented the economic, social and ecological benefits in the objective function of the optimization model respectively. Adaptive cellular genetic algorithm was utilized to search and solve the optimization model. The obtained optimization results of the base year (2015) showed that the net benefits of unit water increased by 4.5% and the crop water productivity increased by 28.6%. In addition, for the target year (2030), although the reduction of agricultural water and cultivated land by 12.95% and 18.63% respectively led to a decrease of total economic benefits by 15.72%, the net benefits of unit water and social benefits got increased by 15.71% and 20.52%, respectively. Therefore, the optimization model can provide decision makers with guidance on the rational allocation of regional agricultural water resources in the future.

Soil water/salt balance and water productivity of typical irrigation schedules for cotton under film mulched drip irrigation in northern Xinjiang

Film mulched drip irrigation (FMDI) has clear benefits for saving water and promoting cotton production in Xinjiang, China. Due to the complicated transport processes for soil water and salt under FMDI, it is still challenging to systematically answer the questions such as the soil water and salt balance in the root zone, cotton yield and water productivity (WP) under typical planting modes and irrigation schedules. Previously, we proposed a HYDRUS-2D model with modified root water uptake (RWU) function and simulated the two-dimensional soil water flow and solute transport in cotton fields under FMDI, but we ignored the effects of the cotton yield and WP. From the perspective of smart irrigation, it is necessary to evaluate the effects of irrigation on crop production, WP, and soil environments. Thus, in the present study, our HYDRUS-2D model coupled with a validated crop water production function was applied to evaluate the effects of typical irrigation schedules and the antecedent soil salinity distributions on the soil water/salt balance, and plant water status, and leaching fraction, as well as the cotton yield and WP under FMDI in 36 scenarios. These scenarios included two antecedent soil salinity distributions (AS), six irrigation amounts (IA) and three irrigation intervals (IF). Compared with the lower AS scenarios, the higher AS scenarios obtained lower cotton transpiration and evapotranspiration but higher evaporation, drainage, and soil water storage, and the crop water status and leaching fraction were also increased due to the soil salt stress restricting RWU. The salt balance results indicated the current irrigation scheduling under FMDI leads to desalination processes in different scenarios. Moreover, the cotton yield and the corresponding WP for cotton (WPETa) and irrigation (WPI) were estimated. Under different AS scenarios, binary quadratic regression equations were developed based on IA and IF data to predict the cotton yield, WPETa, and WPI. Appropriate irrigation strategies are recommended based on the results. Our results could provide a scientific basis for optimizing irrigation schedules and improving the understanding of irrigation management under FMDI among local farmers in Xinjiang.

Irrigation water resources management under uncertainty: An interval nonlinear double-sided fuzzy chance-constrained programming approach

An interval nonlinear double-sided fuzzy chance-constrained programming (INDFCCP) approach is formulated to effectively allocate irrigation water among competing water users. The INDFCCP approach is formulated by combining inexact quadratic programming (IQP) and double-sided fuzzy chance-constrained programming (DFCCP) within a general optimization framework. This approach has the following features. (1) It’s able to handle interval and fuzzy uncertainties, and nonlinearity existing in the objective functions. (2) It’s capable of addressing these fuzzy constraints and fuzzy variables where different confidence levels and satisfaction degree levels should be satisfied. (3) Each fuzzy chance-constraint can be further analyzed with the maximum and minimum reliability scenarios, which makes it possible to reflect variations of system conditions. (4) Interval quadratic crop water production functions (IQCWPFs) are employed in place of deterministic ones to quantitatively describe the mathematical relationships between crop yields and actual crop evapotranspiration (or irrigation water applied). Then, to demonstrate its applicability and feasibility, the INDFCCP approach is applied in the Yingke Irrigation District (YID), northwest China for allocating irrigation water to three crops in three subareas under uncertainty. Finally, more flexible decision solutions regarding optimal irrigation water allocation have been generated and analyzed under different predetermined confidence levels, showing several advantages of the INDFCCP approach with respect to the deterministic one. Under the same confidence level, system benefits under the minimum reliability scenario (e.g. [499.6, 909.7] × 106 Yuan, α = 0.5) are higher than that under the maximum reliability scenario (e.g. [498.7, 908.9] × 106 Yuan, α = 0.5). From above outcomes, the INDFCCP approach provides more appropriate results and reliable scientific bases needed for better managing irrigation water in irrigated agricultural areas.