Upscaling of saturated conductivity for Hortonian runoff modelling

Stochastic and deterministic upscaling techniques are developed that upscale saturated conductivity at the support of 0.04 m2 to representative actual infiltration (Ib) for support units (blocks) of 101–104 m2, as a function of steady state rainfall and runon to the block, under Hortonian runoff (infiltration excess overland flow). Parameters in the upscaling techniques represent the surface runoff flow pattern and the spatial probability distribution of saturated conductivity within the 101–104 m2 block. The stochastic upscaling technique represents the spatial process of infiltration and runoff using a simple process-imitating model, estimating Ib using Monte Carlo simulation. The deterministic upscaling technique aggregates these processes by a deterministic function relating rainfall and runon to Ib. The stochastic upscaling technique is shown to be capable to upscale saturated conductivity derived from ring infiltrometers to Ib values of plots (1 m2) corresponding to measured Ib values using rainfall simulators. It is shown that both upscaling techniques can be used to estimate Ib for each time step and each block in transient rainfall–runoff models, giving better estimates of cumulative runoff from a hillslope and a small catchment than model runs that do not use upscaling techniques.