Role of run-on for describing field-scale infiltration and overland flow over spatially variable soils

This study examines the role of run-on process on field-scale infiltration and one-dimensional overland flow over spatially heterogeneous hillslopes. Because of the high degree of heterogeneity exhibited by the soil parameters that govern the mechanisms of infiltration and overland flow on slopes, the analysis of hillslope hydrological processes requires a stochastic approach. The saturated hydraulic conductivity Ks is considered to be the only random quantity and is represented by a lognormal random field in the horizontal directions, and the soil is assumed to be homogeneous in the vertical direction. The analysis is performed by comparing the behavior of field-scale ensemble mean and variance of infiltration and overland flow rates for cases with and without run-on. The Green–Ampt model is used to describe infiltration at the local scale as it has parameters that can be easily estimated for a wide range of soils. An extensive set of Monte-Carlo simulations for all cases is supplemented with supporting theoretical analysis for the case when run-on is negligible. Field-scale mean and variance of infiltration as functions of time are computed for different parameters of the random Ks field. Results reveal that in the presence of run-on, mean field-scale infiltration increases, which in turn has a significant influence on hillslope hydrograph. Non-dimensional formulation of the ensemble averaged mean and variance of infiltration and overland flow is presented with the aid of scaled variables. Two dimensionless numbers γ and β expressing the characteristic time scales that govern infiltration and overland flow are developed.