In a previous study, the authors developed the planning of the water used in the irrigation systems of a given farmland in order to ensure that the field cultivation is in a good state of preservation. This planning was modelled and tackled as an optimal control problem: minimize the water flow (control) so that the extent water amount in the soil (trajectory) fulfils the cultivation water requirements. In this paper, we characterize the solution of our problem guaranteeing the existence of the solution and applying the necessary and sufficient conditions of optimality. We validate the numerical results obtained previously, comparing the analytical and numerical solutions.