Traditional and microirrigation with stochastic soil moisture

Achieving a sustainable use of water resources, in view of the increased food and biofuel demand and possible climate change, will require optimizing irrigation, a highly nontrivial task given the unpredictability of rainfall and the numerous soil-plant-atmosphere interactions. Here we theoretically analyze two different irrigation schemes, a traditional scheme, consisting of the application of fixed water volumes that bring soil moisture to field capacity, and a microirrigation scheme supplying water continuously in order to avoid plant water stress. These two idealized irrigation schemes are optimal in the sense that they avoid crop water stress while minimizing water losses by percolation and runoff. Furthermore, they cover the two extremes cases of continuous and fully concentrated irrigation. For both irrigation schemes, we obtain exact solutions of the steady state soil moisture probability density function with random timing and amounts of rainfall. We also give analytical expressions for irrigation frequency and volumes under different rainfall regimes, evaporative demands, and soil types. We quantify the excess volumes required by traditional irrigation, mostly lost in runoff and deep infiltration, as a function of climate, soil, and vegetation parameters.