Optimization model of an irrigation reservoir for water allocation and crop planning under various weather conditions

This paper develops a non-linear programming optimization model with an integrated soil water balance, to determine the optimal reservoir release policies, the irrigation allocation to multiple crops and the optimal cropping pattern in irrigated agriculture. Decision variables are the cultivated area and the water allocated to each crop. The objective function of the model maximizes the total farm income, which is based on crop–water production functions, production cost and crop prices. The proposed model is solved using the simulated annealing (SA) global optimization stochastic search algorithm in combination with the stochastic gradient descent algorithm. The rainfall, evapotranspiration and inflow are considered to be stochastic and the model is run for expected values of the above parameters corresponding to different probability of exceedence. By combining various probability levels of rainfall, evapotranspiration and inflow, four weather conditions are distinguished. The model takes into account an irrigation time interval in each growth stage and gives the optimal distribution of area, the water to each crop and the total farm income. The outputs of this model were compared with the results obtained from the model in which the only decision variables are cultivated areas. The model was applied on data from a planned reservoir on the Havrias River in Northern Greece, is sufficiently general and has great potential to be applicable as a decision support tool for cropping patterns of an irrigated area and irrigation scheduling.     

Real-time adaptive irrigation scheduling under a limited water supply

The problem of real-time irrigation scheduling under limited water supply is considered. The goal is to develop an irrigation operation policy which maximizes crop yields and is responsive to current season changes in weather and other variables. Because irrigation decisions are sequential and dependent on crop and soil water status, and also because crop yields can only be known at the end of the season, the decisions are arrived at by a two-stage process. In the first or the design stage, irrigations are planned for the entire season at weekly intervals using historical data and an optimal irrigation scheduling model. In the second stage, the decisions for the subsequent weeks are revised each week after updating the status of the system with real time data up to that week and solving the irrigation optimization model once again for the new conditions. Thus, each week an irrigation decision is made, the entire planning horizon is kept in view. The procedure is illustrated by application to a case study.     

Optimal allocation of water from a single purpose reservoir to an irrigation project with pre-determined multiple cropping patterns

A model for optimal allocation of water from a single-purpose reservoir to an irrigation project with pre-determined multiple cropping patterns was developed. The model consisted of two modules: (I) the intra-seasonal allocation model (non-linear programming) which is used for allocation of water among different crops for a definite combination of state variables (inflow class, rainfall class, reservoir storage classes at the beginning and at the end of the season) for the non-dormant season to maximize total farm income; and (II) the seasonal allocation model (stochastic-dynamic programming) which is used for the convergent operating policy over seasons for optimal expected farm income over a year. The model was applied to Ardak reservoir dam (I.R. Iran) in an arid region. Low river inflow in the dormant season at the study area could not admit the reservoir class changes for specific combinations of state variables, and therefore resulted in a non-usable result. Imposing a fictitious positive relative net benefit for all possible combinations of reservoir class changes eliminated this problem. It was also shown that rainfall did not play a marked role in the study area, which is an arid region, and its stochastic nature can be removed from the model.     

A model for regional optimal allocation of irrigation water resources under deficit irrigation and its applications

It is important to promote efficient use of water through better management of water resources, for social and economical sustainability in arid and semi-arid areas, under the conditions of severe water shortage. Based on the developments in deficit irrigation research, a recurrence control model for regional optimal allocation of irrigation water resources, aiming at overall maximum efficiency, is presented, with decomposition-harmonization principles of large systems. The model consists of three levels (layers). The first level involves dynamic programming (DP) for optimization of crop irrigation scheduling. The second level deals with optimal allocation of water resources among various crops. The last level concerns optimal allocation of water resources among different sub-regions. As a test, this model was applied to the combined optimal allocation of multiple water resources (surface, ground and in-take from the Weihe river) of Yangling, a semi-arid region on the Loess Plateau, China. Exemplary computation showed that not only are the results rational, but the method can also effectively overcome possible “dimensional obstacles” in dynamic programming of multiple dimensions. Furthermore, each sub-model is relatively independent by using various optimization methods. The model represents a new approach for improving irrigation efficiency, implementing water-saving irrigation, and solving the problem of water shortage in the region studied. The model can be extended in arid and semi-arid areas for better water management.     

Water balance of centre pivot irrigated pasture in northern Victoria, Australia

The irrigated dairy industry in Australia depends on pasture as a low-cost source of fodder for milk production. The industry is under increasing pressure to use limited water resources more efficiently. Pasture is commonly irrigated using border-check but there is growing interest amongst dairy irrigators to explore the potential for overhead sprinklers to save water and/or increase productivity. This paper reports on a detailed water balance study that evaluated the effectiveness of centre pivot irrigation for pasture production. The study was conducted between 2004/2005 and 2005/2006 on a commercial dairy farm in the Shepparton Irrigation Region in northern Victoria. More than 90% of supplied water (irrigation plus rainfall) was utilized for pasture growth. Deep drainage of respectively 90 and 93 mm was recorded for the two observation seasons. During the 2004/2005 season, deep drainage resulted from large unseasonal summer rainfall events. Over the 2005/2006 season, deep drainage resulted from excess irrigation. The cumulative pasture dry matter (DM) production was 15.5 and 11.3 tonnes DM ha⁻¹ for the two irrigation seasons, with an agronomic water use efficiency (WUE) of 16 and 12 kg DM ha⁻¹ mm⁻¹ respectively. The farmer's intuitive irrigation scheduling was found to be very effective; the pattern of irrigation application closely matched measured pasture water use, prevented water stress and resulted in high irrigation efficiency.     

下级渠道流量不等时渠系优化配水模型与算法研究

目前国内外现有的渠道优化配水模型,都是在下级渠道配水流量相等这一假定条件的基础上建立的,这与绝大多数渠系实际配水要求不相符合。针对这一问题,建立了下级渠道引水流量不等情况下的渠道优化配水模型,研究了模型的遗传算法的编码及适应度设计方法,编制了VC程序,并用于冯家山灌区北干十一支共24条斗渠道的实际配水过程中进行了对比验证。结果表明,渠系优化配水过程较原配水过程斗渠配水时间搭配合理、支渠配水流量均匀,符合优化配水原则,渠系渗透损失水量比原方案可减少17.8%。表明模型及其求解算法是可行的,可为下级引水渠道流量不等时的渠系优化配水决策提供理论和技术支持。     

Optimal rotation of peanuts and cotton to manage soil-borne organisms

Damage from the root-knot nematode (Meloidogyne arenaria) and Southern blight (white mold) fungus (Sclerotium rolfsii) are principal yield-limiting factors in the production of peanuts (Arachis hypogaea) in the USA. Both are widespread in the southeastern USA and yield losses caused by them can be severe. Both organisms can be suppressed by pesticides, but both can also be suppressed by rotation with cotton and certain other crops. This article presents a stochastic dynamic programming model that maximizes the expected present value of profit over a multi-year planning horizon with production of peanuts and cotton, accounting for: (1) the stochastic population dynamics of the peanut root-knot nematode, Southern blight fungus, and beneficial microbivorous nematodes; (2) the stochastic market prices for cotton and peanuts; and (3) land use in each of the previous 2 years. Expected profit from this seven-state variable dynamic programming model is compared to expected profit for monoculture peanuts, monoculture cotton, three fixed rotations, and a myopic, but flexible, rotation. Comparison of expected returns for these decision models indicates that an information-based strategy—the optimal dynamic strategy or the myopic strategy—is better than any of the fixed rotations. The myopic strategy results in expected profits almost as high as the optimal strategy for this particular problem. Since a myopic strategy is much more easily computed and more easily explained to producers, it has much more promise for adoption than difficult-to-understand results from a stochastic dynamic programming model.     

Policies to support economic and environmental goals at farm and regional scales: Outcomes for rice farmers in Southern India depend on their resource endowment

Improving water use and nitrogen efficiencies is of overall importance to society at large - to conserve scarce water resources and prevent environmental pollution. Efficient cultivation practices for rice which had no yield penalty were not adopted by farmers because of the open access to water free of charge. Well-chosen combinations of policy measures are thus needed to stimulate adoption of new cultivation practices. We developed a multi-objective linear programming (MGLP) model to explore the impact of: (i) modified rice cultivation including water-saving irrigation on farm profit; (ii) water pricing and water quota government policies on adoption of modified rice cultivation by farmers; (iii) a combination of (i) and (ii) to achieve the objectives of both farmers and society at large, and (iv) to study the trade-offs between income, water and nitrogen use. The analysis was carried out on four rice-based farm types for the state of Tamil Nadu, South India. Model results showed that observed farm profit of all four farm types could be increased using current practices simply by optimizing land use for specific crops. Adoption of modified rice cultivation further increased farm profit. Water-saving practices were selected only when water pricing was introduced. Farm profits were reduced even at low water prices but were compensated by farmers through adoption of modified rice cultivation. The combination of policies that stimulate adoption of modified rice cultivation was effective in achieving both increased farm income and water savings. The required water prices differed across farm types and seasons and impacted poor resource-endowed farmers the most. Providing water quotas could protect the poor resource-endowed farmers. The model helped to identify the optimal water price and water quota for each farm type to achieve both the objectives of farmers and society at large. Opportunities for reducing water use and avoiding environmental pollution at acceptable profits are available for all farm types, but need to be tailored to the farmers’ resource endowments.     

灌溉兼防洪水库的优化调度

我国干旱半干旱地区，天然降水量少且时程及地域相差大，并有很大的随机性。对有水库调节的地区，如何处理天然降水的随机性，合理利用有限的水资源，解决人畜饮水、工业用水、林业及农业灌溉耗水，使其在各种情况下都能达到最佳的社会效益和经济效益，该文选用动态规划法，编制的电算程序，很好地解决了这一问题。     

Assessing basin irrigation and scheduling strategies for saving irrigation water and controlling salinity in the upper Yellow River Basin, China

Water saving in irrigation is a key concern in the Yellow River basin. Excessive water diversions for irrigation waste water and produce waterlogging problems during the crop season and soil salinization in low lands. Supply control and inadequate functionality of the drainage system were identified as main factors for poor water management at farm level. Their improvement condition the adoption of water saving and salinity control practices. Focusing on the farm scale, studies to assess the potential for water savings included: (a) field evaluation of current basin irrigation practices and further use of the simulation models SRFR and SIRMOD to generate alternative improvements for the surface irrigation systems and (b) the use of the ISAREG model to simulate the present and improved irrigation scheduling alternatives taking into consideration salinity control. Models were used interactively to define alternatives for the irrigation systems and scheduling that would minimize percolation and produce water savings. Foreseen improvements refer to basin inflow discharges, land leveling and irrigation scheduling that could result in water savings of 33% relative to actual demand. These improvements would also reduce percolation and maintain water table depths below 1 m thereby reducing soil salinization.     

A new stochastic optimization model for deficit irrigation

Deficit irrigation has been suggested as a way to increase system benefits, at the cost of individual benefits, by decreasing the crop water allocation and increasing the total irrigated land. Deterministic methods are common for determining optimal irrigation schedules with deficit irrigation because considering the inherent uncertainty in crop water demands while including the lower and upper bounds on soil moisture availability is a hard problem. To deal with this, a constraint state formulation for stochastic control of the weekly deficit irrigation strategy is proposed. This stochastic formulation is based on the first and second moment analysis of the stochastic soil moisture state variable, considering soil moisture as bounded between a maximum value and a minimum value. As a result, an optimal deficit irrigation scheduling is determined using this explicit stochastic model that does not require discretization of system variables. According to the results, if irrigation strategy is based on deterministic predictions, achievement of high, long-term expected relative net benefits by decreased crop water allocation and increased irrigated land may have a higher failure probability.     

Irrigation scheduling under a limited water supply

The problem of scheduling irrigation at weekly intervals for a single crop when water supply is limited is considered. The mathematical formulation is based on a dated water-production function, weekly soil-water balance, and a heuristic assumption that water stress in the early weeks of a crop-growth stage leads to suboptimal yields. The allocation problem is solved at two levels, growth stages, and weeks. At the first level, the dated water-production function is maximized by dynamic programming to obtain optimal allocations for growth stages. At the second, the water allocated to each growth stage is re-allocated to satisfy weekly water deficits within the stage in a sequential order, beginning with the 1st week of the stage. Water delivery and soil-water storage constraints are included at both levels. The model is applied to a field problem to derive weekly irrigation programmes for cotton under various levels of seasonal water supply and initial soil moisture.     

夏玉米产量与水分关系及其高效用水灌溉制度

依据灌溉试验资料,研究了水分胁迫对夏玉米生长发育和产量形成的影响,建立了产量与水分关系的数学模型,分析给出了大田夏玉米的高效用水灌溉定额,并用动态规划技术优化得出了夏玉米的最优灌水时间和每次的灌水定额。结果表明,各生育时段的水分胁迫对夏玉米的生育和产量均会造成不利影响,其中尤以抽雄～吐丝期前后４０天左右缺水对产量影响最大,其次为拔节期缺水;在１９９７年夏玉米生育期降雨量只有１３７ｍｍ的条件下,得出其最优灌溉定额为１９６６．０８ｍ３／ｈｍ２,３次灌水时间分别为７月４日、７月２８日和８月１６日。     

Impact of irrigation timing on simulated water-crop production functions

Estimates of the effects of alternative discrete irrigation water scheduling options on consumptive use or evapotranspiration and on crop yield are developed for a northeastern Colorado case study. The analysis proceeds from the premise that farmers, rather than considering irrigation water as a continuously variable input, tend to treat irrigations as discrete events, and make scheduling decisions as choices among numbers of irrigations of approximately equal volume. The van Genuchten-Hanks model is employed to develop a transient-state water-crop production function model. Results for two crops – corn grain and edible dry beans – are presented here. Findings are that the effect of the number of irrigations on evapotranspiration and yield per hectare varies widely, depending upon the timing of applications. When farmers can choose the optimal timing of irrigations, a reduced number of irrigations has a relatively limited adverse effect on crop production until irrigations are reduced to less than four per season. However, there are many situations in which an inability to apply water can result in a very large reduction from potential maximum yield, particularly if water is withheld early in the season and/or during the rapid growth period of the crops. In many contexts of irrigation water management, water policy analysts will wish to consider the more realistic discrete-input simulation model for policy evaluation. Received: 1 November 1996     

Chance-constrained optimal windmill irrigation system design

In this work, a methodology was developed to enable decision making with regard to the reservoir size and optimal crop plan for a windmill irrigation system. Wind speed and hence the windmill discharge were treated as stochastic variables, and the water pumped by a windmill was computer for different probabilities. Considering the probability of non-availability of a given quantity of pumped water as the risk, reservoir sizes to meet various daily water demands were computed. The available water supplies were then optimally allocated among different crop activities and the profits were calculated. The annual profits were converted to the total profit over the amortization period. The solution which gave the maximum profit was considered to be the best choice. It was found that the most profitable windmill irrigation system can effectively irrigate an area of 2.76 ha and yield an assured annual profit of nearly Rs. 0.089 million ($\text{US\$}\text{1.00≜12}$ Indian rupees approximately).     

Performance based irrigation planning under water shortage

A linear programming (LP) based optimization model and a simulation model are developed and applied in a typical diversion type irrigation system for land and water allocation during the dry season. Optimum cropping patterns for different management strategies are obtained by the LP model for different irrigation efficiencies and water availability scenarios. The simulation model yields the risk-related irrigation system performance measures (i.e. reliability, resiliency and vulnerability) for the management policies defined by the optimization model. The alternative strategies are evaluated in terms of all performance criteria (i.e. net economic benefit, equity and reliability) simultaneously through a trade-off analysis using a multi-criteria decision making method (compromise programming). For the case study of the Kankai irrigation system in Nepal, with equal preference to the objectives, a management strategy with equal share of water among the project subareas appears to be the most satisfactory alternative under water shortage conditions. The existing water allocation policy is not economically efficient. Deficit irrigation in Early paddy appears attractive under favorable hydrologic scenario, particularly if accompanied by measures to improve existing irrigation system efficiency.     

石津灌区储水灌溉制度研究

储水灌溉是一种利用土壤水库 ,采用较大灌水定额、减少了灌水次数的一种灌溉方法。结合石津灌区现状 ,通过对灌区典型地块土壤质地的分析 ,提出了灌区适宜的储水灌溉制度。田间试验结果表明 ,利用这种储水灌溉模式 ,实现了节水、高产、增效     

引黄灌区灌溉效益优化计算模型

以引黄灌区为研究对象 ,在分析传统灌溉效益计算方法不足的基础上 ,按水资源合理配置的要求 ,基于作物的节水灌溉制度 ,提出引黄灌区灌溉效益优化计算的双层线性规划模型 ,开发了相应的计算软件。模型考虑了引黄水量在不同作物间和同种作物不同灌溉时段间的优化配置 ,使灌溉效益计算更趋合理     

On-farm performance evaluation of improved traditional small-scale irrigation practices: A case study from Dire Dawa area, Ethiopia

Field evaluation of surface irrigation systems play a fundamental role to determine the efficiency of the system as it is being used and to identify management practices and system configurations that can be implemented to improve the irrigation efficiency. This study evaluated the performance of an ‘improved’ traditional small-scale irrigation practice at Adada, a representative small-scale irrigation practice in Dire Dawa Administrative Council, Eastern Ethiopia. In order to determine numerical values of performance measures, certain parameters were measured/observed before, during and after an irrigation event while farmers are performing their normal irrigation practice. These parameters include: irrigated crop, irrigation method, stream size, cutoff time, soil moisture deficiency, and field size, shape and spacing. The results showed that the irrigation water applied to a farmer's plot during an irrigation event/turn was generally higher than the required depth to be applied per event. Since the irrigation method used was end-dyked, the major cause of water loss was due to deep percolation. The deep percolation loss was 32% in sorghum, 57% in maize, and 70% in tomato and potato fields. The type of irrigation system used, the ridged irrigation practice and the poor irrigation scheduling in the study sites were the main problems identified in the management and operations of the schemes. The following corrective measures are recommended to improve the system: (1) farmers should regulate the depth of irrigation water they apply according to the type of crop and its growth stage, change the field irrigation system and/or configuration especially for shallow rooted row crops, to furrow system, (2) guidance and support to farmers in developing and introduction of appropriate irrigation scheduling, and (3) future development interventions towards improvement of traditional irrigation practices should also focus in improving the on farm irrigation systems in addition to improving physical infrastructure of the scheme.     

模糊优选决策理论在浑蒲灌区改造中的应用

由于浑蒲灌区水源被污染，农田受到污水灌溉，对人畜造成危害。实现清水污水分流，消除水源污染，成为灌区改造的首要任务。利用模糊优先决策理论，通过4项评判指标对沈阳市浑蒲灌区清污分流与节水改造方案优选，从而找出最佳方案，为项目决策提供参考。