Optimal location of yield with the cheapest water footprint of the crop using multiple regression and artificial neural network models in GIS

Iran is located in an arid and semi-arid region of the world; however, more than 90% of Iran’s total water is allocated to agricultural sector. Owing to the climatic limitations of the country, agricultural water management has become one of the country’s greatest concerns. Therefore, the present study has attempted to identify optimal locations in terms of high yield and low total water footprint (WF) (m³/$) in the northwest and southeast provinces of the country to produce main cereals such as wheat, barley, and maize. In this regard, inverse distance weighting (IDW) method was first employed 150 sample coordinates to prepare interpolation maps of evapotranspiration (ETc) (mm), irrigation requirements (IR) (mm), nitrogen application (kg/ha), and effective precipitation (Peff) (mm). Subsequently, green WF, blue WF, gray WF, total WF (TWF) (m³/ton), and economical total WF (ETWF) (m³/$) maps were prepared for each crop. Multiple linear regression (MLR) was then applied to determine the correlation between ETWF (m³/$) and other parameters. ETWF (m³/$) was later predicted using multiple linear regression (MLR), in conjunction with artificial neural networks (ANNs) including multilayer perceptron (MLP) and radial basis function (RBF). Findings showed that IDW can be applied with a relatively low error so that an interpolation map for each parameter can be obtained and the changes can be examined. The results of MLR indicated that for assessing the yield of barley and wheat the TWF possesses and for assessing the yield of maize, the IR model had the highest rate of regression. The results of ANN indicated that the RBF (R² = 0.901), the RBF (R² = 0.882), and the MLP (R² = 0.947) were the most appropriate models for the prediction and evaluation of ETWF and yield with respect to measured estimates of ETWF (m³/$) and yield of wheat, barley, and maize (in order of appropriability).