Scaling analysis of space–time infiltration based on the universal multifractal model

There is broad interest in the space–time scaling behavior of infiltration over a watershed, but field data is lacking to identify such scaling and the controlling factors. Here, theoretical effects of rainfall and saturated hydraulic conductivity (Ks) on space–time infiltration are simulated using process-based numerical experiments in the framework of a universal multifractal (UM) model. A series of rainfall and Ks fields are generated including both random, non-scaling fields and multifractal fields produced using the UM model. By varying the UM model parameters based on physical considerations, rain and Ks fields with various scaling characteristics are obtained. These rain and Ks data are then fed into a distributed rainfall-runoff model developed for this study to produce space–time infiltration, including the effects of overland flow from upslope areas. The scaling properties of the infiltration are then analyzed to find the impact from the rain and Ks fields mainly in terms of the connections among the UM model parameters between the input and the output fields. Some of the major findings from this research are: (1) rainfall spatial characteristics determine the scaling of infiltration only at very early times; (2) Ks, rather than rain, determines if the resulting infiltration field displays scaling behavior after an adjusting period; (3) generally, the heterogeneity of a rain field and the singularity and sparseness of a Ks field have strong impacts on infiltration; (4) usually, infiltration fields are statistically non-homogeneous; and (5) if an infiltration field subject to space–time rain becomes less singular (localized large infiltration rates) in time, it tends to become less sparse and more heterogeneous, and vice versa. The relationships and sensitivities identified above help us understand some key factors controlling the potential scaling behavior of infiltration.