Increasing water and fertilizer productivity stands as a relevant challenge for sustainable agriculture. Alternate furrow irrigation and surface fertigation have long been identified as water and fertilizer conserving techniques in agricultural lands. The objective of this study was to simulate water flow and fertilizer transport in the soil surface and in the soil profile for variable and fixed alternate furrow fertigation and for conventional furrow fertigation. An experimental data set was used to calibrate and validate two simulation models: a 1D surface fertigation model and the 2D subsurface water and solute transfer model HYDRUS-2D. Both models were combined to simulate the fertigation process in furrow irrigation. The surface fertigation model could successfully simulate runoff discharge and nitrate concentration for all irrigation treatments. Six soil hydraulic and solute transport parameters were inversely estimated using the Levenberg-Marquardt optimization technique. The outcome of this process calibrated HYDRUS-2D to the observed field data. HYDRUS-2D was run in validation mode, simulating water content and nitrate concentration in the soil profiles of the wet furrows, ridges and dry furrows at the upstream, middle and downstream parts of the experimental field. This model produced adequate agreement between measured and predicted soil water content and nitrate concentration. The combined model stands as a valuable tool to better design and manage fertigation in alternate and conventional furrow irrigation.

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Alternate furrow fertigation has shown potential to improve water and fertilizer application efficiency in irrigated areas. The combination of simulation and optimization approaches permits to identify optimum design and management practices in furrow fertigation, resulting in optimum cost, irrigation performance or environmental impact. The objective of this paper is to apply 1D surface and 2D subsurface simulation-optimization models to the minimization of nitrate losses in two types of alternate furrow fertigation: a) variable alternate furrow irrigation; and b) fixed alternate furrow irrigation. For comparison purposes, optimizations are also reported for conventional furrow irrigation. The model uses numerical surface fertigation and soil water models to simulate water flow and nitrate transport in the soil surface and subsurface, respectively. A genetic algorithm is used to solve the optimization problem. Four decision variables (inflow discharge, cutoff time, start time and duration of fertilizer solution injection) were optimized to minimize the selected objective function (nitrate loss) for two fertigation events performed during a maize growing season. The simulation-optimization model succeeded in substantially reducing the value of the objective function, as compared to the field conditions for all irrigation treatments. In the experimental conditions, optimization led to decreased inflow discharge and fertilizer injection during the first half of the irrigation event. This was due to the high potential of the field experiment to lose water and nitrate via runoff. In the optimum conditions, alternate furrow fertigation strongly reduced water and nitrate losses compared to conventional furrow irrigation. The simulation-optimization model stands as a valuable tool for the alleviation of the environmental impact of furrow irrigation.

Abstract:In this study, three mathematical models in the SIRMOD package including the hydrodynamic (HD), zero inertia (ZI), and kinematic wave (KW) models were tested using the data from several field experiments for both border and furrow irrigation systems. Five data sets for borders and seven data sets for furrows were used in this assessment. The results indicated that the performance of all models was satisfactory for the prediction of the advance and recession times. There was no difference in the prediction of the advance and recession times and infiltrated and runoff volumes between the hydrodynamic and zero-inertia approaches of the SIRMOD software. The HD, ZI, and KW models predicted the recession times better than the advance times for both the experimental borders and furrows. The predicted advance and recession times were estimated by these models more accurately than the infiltrated and runoff volumes. Also the accuracy of these models for the prediction of the advance and recession times was better for the experimental furrows in comparison with the experimental borders.Keywords: border irrigation; furrow irrigation; mathematical models; SIRMOD Iran has an arid and semi-arid climate with average annual rainfall of 240 mm. It has been reported that only 35% of the total water that is utilised for agriculture in Iran is used efficiently. The poor design, implementation, and management are generally responsible for insufficient irrigation, leading to the wastage of water, waterlogging, salinisation and pollution of surface water and groundwater resources. Considering surface irrigation that covers about 90% of the total irrigated land in Iran, an accurate and suitable design of the surface irrigation systems can save more water and increase the irrigated land area.Surface-irrigation mathematical models are important for the evaluation and design purposes. Those models are classified into four main groups: (1) full hydrodynamic models; (2) zero-inertia models; (3) kinematic-wave models, and (4) volume balance models. The fully hydrodynamic model is the most complex and the most accurate. It is based on the complete Saint-Venant equations for the conservation of mass and momentum. The zero-inertia model is a slightly simplified version of the complete Saint-Venant equations that leaves out the acceleration or inertia terms in the momentum equation. The kinematic wave model uses further simplifications and uniform flow assumptions. The simplest model, i.e., one that involves the largest number of assumptions, is the volume balance model. It is based on the analytical or numerical solution of the temporally and spatially-lumped mass conservation, commonly referred to as the "volume balance '' approach (Jurriens et al. 2001).The data from the mathematical models have allowed engineers to improve systematically irrigation system design and operation which, for many years, have been mainly based on the rule of thumb, rough empirical guidelines, and approximations (Jurriens et al. 2001). Mathematical models...

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