Testing simple scaling in soil erosion processes at plot scale

Explaining scale effects for runoff and erosion improves our understanding and simulation ability of hydrological and erosion processes. In this paper, plot scale effects on event runoff per unit area (Qe), sediment concentration (Ce) and soil loss per unit area (SLe) were checked at El Teularet-Sierra de Enguera experimental site in Eastern Spain. The measurements were carried out for 31 events occurring in the years 2005 and 2007 in bare ploughed plots ranging from 1 to 48 m2. The analysis established the scaling relationship by dimensional analysis and self-similarity theory, and tested this relationship at different temporal scales ranging from event to annual scale. The dimensional analysis and the incomplete self-similarity condition allowed us to establish a power scaling relationship which was found to also be usable for the moments of k (1, 2, 3, 4) order. The power scaling relationship was theoretically deduced applying a boundary condition which is based on the hypothesis that sediment delivery processes do not occur at the selected plot scale. The simple scaling invariance condition was always verified (i.e. for each temporal horizon) for runoff and soil loss while the same hypothesis was not perfectly acceptable for sediment concentration. The analysis of the scaling relationships at event temporal scale showed that the spatial scale effects were less frequent for the composite variable (soil loss = sediment concentration × runoff) than the constituting variables. For 48% of the events, a statistically significant scale effect was detected for all tested variables. With reference to the statistically significant relationships, both runoff and soil loss always decreased and sediment concentration always increased in the passage from the reference area (1 m2) to the largest one (48 m2). The analysis at aggregated temporal scales suggested that annual scale effects for soil loss per unit area should be temporally more stable than those for both runoff and sediment concentration. Finally, at mean event scale the three investigated variables have a similar behaviour in terms of simple scaling invariance.