Delineation of management zones for applying Variable Rate Irrigation (VRI) in drip irrigation presents unique challenges due to the directionality of the drip lines and the fact that the water flow rate can not be varied along a drip line. This work presents a method for optimal delineation of irrigation zones under such constraints. It is assumed that historical weather records, a soil map, a simulation model that predicts the crop development in response to weather and irrigation, as well as crop and water prices, are available. The first step consists of estimating the water productivity function of the crop for each soil type if managed optimally, using multi-objective optimization. The second step consists of estimating the water productivity function of the crop on each soil if the irrigation is managed according to another soil. Optimal delineation of the irrigation zones is then obtained by solving a non-linear optimization problem in which the decision variables are the positions of the zones boundaries. This involves an intermediate step in which the area of each soil in each irrigation zone is calculated, and the soil according to which the irrigation should be managed in each zone is determined. The procedure is illustrated on two examples involving three soils and a cotton crop in Greece. In both cases, optimal management zones delineation and management was obtained using the average weather of years 1982–1991 and performance was estimated for years 1992–2016. The results show that splitting the field into several management zones increases profit slightly via yield increase and/or water savings, depending on the relative price of water.

中文翻译：

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基于模型的滴灌管理区优化划分

由于滴灌线的方向性和水流量不能沿着滴灌线变化的事实，在滴灌中应用可变速率灌溉 (VRI) 的管理区域的划分提出了独特的挑战。这项工作提出了一种在这种约束下最佳划定灌溉区的方法。假设历史天气记录、土壤图、根据天气和灌溉预测作物生长的模拟模型以及作物和水价都是可用的。第一步包括使用多目标优化来估计每种土壤类型的作物的水分生产力函数，如果管理最佳的话。如果根据另一种土壤管理灌溉，则第二步包括估计每种土壤上作物的水分生产力函数。然后通过求解非线性优化问题来获得灌溉区的最佳划分，其中决策变量是区域边界的位置。这涉及一个中间步骤，在该步骤中计算每个灌溉区中每种土壤的面积，并确定每个区应根据何种土壤进行灌溉。该程序通过两个例子来说明，这些例子涉及希腊的三种土壤和一种棉花作物。在这两种情况下，最佳管理区划定和管理是使用 1982-1991 年的平均天气获得的，并估计了 1992-2016 年的性能。结果表明，根据水的相对价格，将田地分成几个管理区通过增加产量和/或节水略微增加利润。