Optimal deficit irrigation using AquaCrop model: a methodology study

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.