Scale dependence of Hortonian rainfall‐runoff processes in a semiarid environment

Scale dependence of Hortonian rainfall-runoff processes has received much attention in the literature but has not been fully resolved. To further explore this issue, a recently developed model was applied to simulate rainfall-infiltration-runoff processes at multiple spatial scales. The model consists of the coupling between a two-dimensional runoff routing module and a two-layer infiltration module, thus accounting for spatial variability in soil properties, soil surface sealing, topography, and partial vegetation cover. A 76 m2 semiarid experimental plot with sparse cover of vegetation patches and a sealed soil surface in inter-patch bare areas was used as a representative elementary area (REA). A series of four larger artificial plots of different areas was created based on this REA to examine the scale dependence of rainfall-runoff relationships in the case of stationary heterogeneity. Results show that runoff depth (or runoff coefficient) decreases with increasing scale. This trend is more prominent at scales less than 10 times the REA length. Power law relationships can quantitatively describe the scaling law. The major mechanism of the scale effect is run-on infiltration. However, rainfall intensity and soil properties can both affect the scaling trend through their interaction with run-on. Higher intensity and less temporal variability of rainfall can both reduce the scale effect. Temporally intermittent rainfall may produce spatially oscillating infiltration rates at large scales. Vegetation patterns are another factor that may affect the scaling. Random-vegetation patterns, compared with regular patterns with similar statistical properties, change the spatial distributions, but do not significantly change either the total amount and statistical properties of infiltration and runoff or the scale dependence of the rainfall-runoff process.