Scale effects in Hortonian surface runoff on agricultural slopes in West Africa: Field data and models

Abstract

This article provides an overview of both experimental and modeling research carried out over the past 15 years by the authors addressing scaling effects in Hortonian surface runoff. Hortonian surface runoff occurs when rainfall intensity exceeds infiltration capacity of the soil. At three sites in West Africa (Côte d’Ivoire, Ghana, and Burkina Faso) runoff was measured from plots of different lengths to assess scale effects. Consistently, longer plots showed much lower runoff percentages than shorter plots. There were large variations in runoff percentages from one rainstorm to the next but there were very good correlations between plots of equal length for each single event. This strongly suggests that temporal dynamics are the cause behind the observed scale effects. In the literature, spatial variability is often proffered as explanation for such scale effects without providing a mechanism that would cause consistent reduction in runoff percentages with increasing slope length. To further examine whether temporal dynamics can indeed provide the explanation, Hortonian runoff was simulated using models with increasing levels of complexity. The simplest model was already able to reproduce the observed scale effects. Also more complex models were used that accounted explicitly for spatial variability. The conclusions remained the same regarding the role of temporal dynamics. Finally, a dimensional analysis was developed that helps predict under which circumstances one can expect scale effects similar to the ones observed in West Africa.