Runoff production on a slope with randomly distributed infiltrabilities

Runoff generated on one- and two-dimensional slopes with randomly distributed infiltrability is studied in the queuing theory and connectivity frameworks. The equivalence between the runoff-runon equation and the customers waiting time in a single server queue provides a theoretical link between the statistical descriptions of infiltrability and that of runoff flow rate. Different distributions of infiltrability, representing soil heterogeneities at different scales, are considered. Numerical simulations validate these results and improve our understanding of runoff-runon process. All of the quantities describing the generation of runoff (runoff one-point statistics) and its organization into patterns (patterns statistics and connectivity) are studied as functions of rainfall rate and runoff dimensionality.