Laboratory and field infiltration data exhibit a degree of erratic variability usually associated with measurement errors and uncertainties in the phenomenon of unsaturated porous media flow. Traditionally, these uncertainties are ignored and averaged soil characteristic curves are used in the inverse and direct modeling problems. However it is desirable to develop models capable of reproducing the inherent variability of soil moisture in order to study the erratic physics of flow at the laboratory level and to reproduce infiltration data in natural watersheds. In the present article, two exploratory models are tested as to their ability to replicate the erratic variability of experimental horizontal infiltration data. The first is based on the full partial differential equation of infiltration, and the second on the Boltzmann‐reduced differential equation. Both models are subject to a space or a time and space random soil‐water diffusivity defined as uncertainty term. The solution of the equations is presented, statistical properties of the water content function are described and verification of the models is conducted. Both models satisfactorily reproduced the statistical properties of the experimental data. While the first model easily relates to real space and time variables, the second required less computer time. As an application of the methodology, a third model is introduced as a new approach to predict vertical infiltration in hysteretic soils in natural watersheds. For this purpose, the effect of time variability of point rainfall is represented as a shot noise process, the hysteretic loops resulting from the natural wetting and drying cycles generate a correlated random soil‐water diffusivity process, and a solution of the vertical infiltration equation is presented along with statistical properties of the water co
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