Physically based probabilistic models of infiltration, soil moisture, and actual evapotranspiration

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Abstract
Real‐time control of irrigation in areas of sparse rainfall requires probabilistic description of infiltration, soil moisture, and actual evapotranspiration. This work develops the probability density function of infiltrated water volumes as a function of climatic and soil parameters. This stochastic input is used with a physical‐conceptual model of the soil moisture depletion process to derive analytic expressions for the soil moisture transition probabilities over a given time period and the first two moments of associated actual evapotranspiration. Analytic results are corroborated with a case study example. A forthcoming paper by the authors illustrates the use of the derived expressions in an optimal decision model for deficit irrigation practices.