Comparing theoretically supported rainfall‐runoff erosivity factors at the Sparacia (South Italy) experimental site

Abstract

Interpreting rainfall‐runoff erosivity by a process‐oriented scheme allows to conjugate the physical approach to soil loss estimate with the empirical one. Including the effect of runoff in the model permits to distinguish between detachment and transport in the soil erosion process. In this paper, at first, a general definition of the rainfall‐runoff erosivity factor REFe including the power of both event runoff coefficient QR and event rainfall erosivity index EI30 of the Universal Soil Loss Equation (USLE) is proposed. The REFe factor is applicable to all USLE‐based models (USLE, Modified USLE [USLE‐M] and Modified USLE‐M [USLE‐MM]) and it allows to distinguish between purely empirical models (e.g., Modified USLE‐M [USLE‐MM]) and those supported by applying theoretical dimensional analysis and self‐similarity to Wischmeier and Smith scheme. This last model category includes USLE, USLE‐M, and a new model, named USLE‐M based (USLE‐MB), that uses a rainfall‐runoff erosivity factor in which a power of runoff coefficient multiplies EI30. Using the database of Sparacia experimental site, the USLE‐MB is parameterized and a comparison with soil loss data is carried out. The developed analysis shows that USLE‐MB (characterized by a Nash–Sutcliffe Efficiency Index NSEI equal to 0.73 and a root mean square error RMSE = 11.7 Mg ha−1) has very similar soil loss estimate performances as compared with the USLE‐M (NSEI = 0.72 and RMSE = 12.0 Mg ha−1). However, the USLE‐MB yields a maximum discrepancy factor between predicted and measured soil loss values (176) that is much lower than that of USLE‐M (291). In conclusion, the USLE‐MB should be preferred in the context of theoretically supported USLE type models.

A comprehensive analysis of Universal Soil Loss Equation‐based models at the Sparacia experimental area

“…Total run‐off and soil loss are measured after each erosive event, that is, an event producing measurable run‐off and sediment, or occasionally after a series of events if they are separated by a short time interval. The applied run‐off and sediments measurement procedures were described in other papers (e.g., Bagarello et al, , , ; Carollo, Di Stefano, Ferro, Pampalone, & Sanzone, ), and they were not repeated here for brevity reasons. For each event, total rainfall depth, P e (mm), is measured, and the rainfall erosivity index, EI 30 (MJ·mm·ha −1 ·hr −1 ), is calculated according to Wischmeier and Smith ().…”

“…Finally, the possibility to describe soil erodibility as a combination of a steady and a hydrological component was discussed for both the USLE‐MB and the USLE‐MM according to Bagarello et al () and Di Stefano, Pampalone, Todisco, Vergni, and Ferro ().…”

“…The rainfall‐run‐off erosivity factors corresponding exclusively to the conditions b 1 = 0 and b 2 = 1 (USLE; Ferro, ), b 1 = b 2 = 1 (USLE‐M; Di Stefano, Ferro, & Pampalone, ), and b 1 ≠ 1 and b 2 = 1 (USLE‐MB; Bagarello et al, ) were also obtained by the Π theorem of the dimensional analysis and the self‐similarity theory (Barenblatt, , ). Therefore, these three models are characterized by common measurement units of the soil erodibility factor and can be considered theoretically supported.…”

“…According to Bagarello, Di Stefano, Ferro, and Pampalone (), the event rainfall‐runoff erosivity factor, REF e , in a USLE‐based model is defined as in which Q R is the event runoff coefficient, equal to the ratio between the event run‐off volume per unit plot area, V e (mm), and the corresponding rainfall depth, P e (mm); EI 30 (MJ·mm·ha −1 ·hr −1 ) is the single‐storm erosion index (Wischmeier & Smith, ); and b 1 and b 2 are coefficients. The rainfall erosivity factor of the USLE is obtained from Equation for b 1 = 0 and b 2 = 1.…”

“…Although much work has been carried out on prediction of soil loss from bare plots at the experimental station of Sparacia (e.g., Bagarello et al, ; Bagarello et al, ; Bagarello, Di Piazza, Ferro, & Giordano, ; Bagarello, Ferro, & Pampalone, , ; Di Stefano et al, ; Di Stefano, Ferro, & Pampalone, ), the performances of all possible expressions of REF e have never been checked simultaneously. In particular, nothing is known about the soil loss predictive ability of both the USLE‐MR and the USLE‐M2.…”