Ref: C0033

Optimal deficit irrigation using AquaCrop model: a methodology study Ilya Ioslovich and Raphael Linker, Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, 32000 Haifa, Israel Georgios Sylaios, Department of Environmental Engineering, Democritus University of Thrace, 12 Vasilissis Sofias str., Greece

Abstract Both developing and developed countries have problems with availability of water to increase agricultural productivity. The importance of improving water efficiency in agriculture has been the subject in many research papers. The usual approach to limit water consumption in agriculture at the district and farm level is to apply water quotas. These quotas may be either for the whole season or for specific months. In this situation farmers have to use an optimal irrigation scheduling that maximizes the yield within these quota constraints. The same problem is of interest for the water authority managers in order to show anticipated results of the water quota allocation between farms, districts or crops. This is a constrained optimization problem where the decision variables are the daily irrigation amounts for each day of the season and the objective function, which is nonlinear and non-smooth, is the expected yield calculated with the use of a model. The model used in this study is Aquacrop developed by FAO which has been proved to be a very useful tool in many previous studies, and a cotton crop in Greece during 2009 is used as case study. This optimization problem is far trom trivial because of the non-smooth behavior of the objective function and the fact that it involves multiple integer variables. We have used the TOMLAB library in Matlab environment and have tested different solvers. The most effective results were obtained with the OQLNP solver with the glcAssign procedure of TOMLAB. OQNLP is a multistart heuristic algorithm to find global optima of constrained nonlinear programs (NLPs) in cooperation with optimal methods. To use it more effectively we have applied some problem-oriented additional pre-filters like scaling of the variables and randomized rounding of the integer variables. We achieved significantly better results for yield (400 kg/ha increase) with approximately the same irrigation water compared to the automatic scheduling determined by Aquacrop. After gradually increasing the value of the water quota and storing our best solutions, convex hull points were fitted with a third order polynomial curve, which describes yield as a function of irrigation water - IWE irrigation water efficiency. A more detailed investigation shows that the constraint for August when the water demand of the cotton is known to be maximal is one that is violated systematically. Therefore we have derived a specific IWE function for the irrigation in August keeping the other months schedule unchanged. This function may be very useful for the farmers in order to use irrigation water optimally according to the given quota and for water authority in order to manage the monthly quotas correctly.

Proceedings International Conference of Agricultural Engineering, Zurich, 06-10.07.2014 – www.eurageng.eu

1/8

The methodology is not crop specific and could be used for other crops for which an Aquacrop model is available. Keywords: irrigation, cotton, optimization, AquaCrop model

1. Introduction

Increasing competition for water use in agriculture and other sectors leads to growing importance of deficit irrigation. In countries with water scarcity water use for agriculture has been reduced and farmers are limited by legislative constraints. Moreover, water allocation for agriculture in these countries is constantly reduced. For example, (Amir & Fisher, 2000) have mentioned that in Israel one of measures used by the Water Commissioner to cope with water shortage was to limit certain crops, of which the most significant one for the Jezreel Valley was cotton, which was replaced by less water-demanding crops. They have presented and analyzed the optimization linear model in order to choose optimal crops mix at the regional level. The available agricultural area and water resources were constrained while the water requirement of each crop was fixed for water of given quality. The overall importance of irrigation modeling has increased during last decades. Irrigation modelling in agriculture is substantially based on water production functions. Outputs (yield or profits) are results of water use and other factors. A useful review of water use efficiency can be found in (Boutraa, 2010). Different aspects of irrigation management under water scarcity are discussed in (Pereira et al., 2002). Optimal control solutions for peanut irrigation based on PNUTGRO model were found by (McClendon et al., 1996). The results were then mimicked by neural networks to provide some sort of feedback scheme. Model-based optimal irrigation scheduling was investigated in (Shani et al., 2004) and in (Ioslovich et al., 2012). Here an aggregated model was used. The use of water production functions have been considered in (Shani et al., 2009). The optimized deficit irrigation in Spain based on AquaCrop model of cotton has been presented in (Garcia-Vila et al., 2009). Here the irrigation strategy was chosen based on knowledge of cotton response to irrigation in semiarid climates. Irrigation was withheld during vegetative phase and application of water was concentrated during flowering and early fruit set. Then a regression approach was used to derive a yield response function to seasonal applied irrigation water (AIW). An optimal amount of AIW was found from one-dimensional nonlinear optimization problem for maximizing the total gross margin per unit area. In our research we take a different approach by considering multi-dimensional optimization for all days of the irrigation water applications and maximizing the seasonal yield. Thus each value of a water production function IWE corresponds to a full seasonal schedule of irrigation and a corresponding seasonal accumulated value. This value may be chosen from existing constraints (quotas). In this way influence of the quota on the yield production is clearly demonstrated.

1.1

Problem formulation

The considered formulation of the problem of optimal deficit irrigation of cotton is as follows: J=IWE(w1,w2, …, wi,…, wn) [t/ha] => max wi,k + wi+1,k +…+wi+m,k