Comparison between the USLE, the USLE-M and replicate plots to model rainfall erosion on bare fallow areas P.I.A. Kinnell Institute for Applied Ecology, University of Canberra, Canberra, Australia abstract article info Article history: Received 13 January 2016 Received in revised form 11 May 2016 Accepted 20 May 2016 Available online xxxx It has been proposed that the best physical model of erosion from a plot is provided by a replicate plot (Nearing, 1998). Event data from paired bare fallow plots in the USLE database were used to examine the abilities of rep- licate plots, the USLE and the USLE-M to model event erosion on bare fallow plots. The Nash-Sutcliffe efficiency factor as applied to logarithmic transforms of the data was used to evaluate the overall performance of models at a number of locations. The value of this efficiency factor is influenced by both systematic and stochastic differ- ences between the pairs. Systematic differences are the result of systematic differences in event runoff or event sediment concentration or both, and the degree of the impact of them varies as the regression coefficient for the relationship between the soil losses from the pairs varies from the value of 1.0. In most cases the replicate model performed better than the USLE-M that modelled event soil loss as a product of observed event runoff and event sediment concentration directly related to the EI 30 index. Generally, failure of replicates to match runoff was compensated by the ability of the replicated to determine sediment concentrations better than the USLE-M. © 2016 Elsevier B.V. All rights reserved. Keywords: USLE database Soil loss prediction USLE/RUSLE USLE-M Runoff 1. Introduction The Universal Soil Loss Equation (USLE; Wischmeier and Smith, 1965, 1978) and subsequent revisions (eg RUSLE; Renard et al., 1997) and refinements, have provided a model for predicting soil erosion loss that has been used rightly and wrongly throughout the world. The USLE operates mathematically in two steps. The first step is the pre- diction of long term (~20 years) average annual soil loss from the unit plot (A 1 ), a bare fallow area 22.1 m long on a 9% slope gradient, in terms of a rainfall runoff factor (R) and a soil dependent factor (K). A 1 ¼ RK ð1Þ where A 1 has units of mass per unit area, R is the long term product of storm kinetic energy (E) and the maximum 30-minute intensity (EI 30 ), and K is the loss of soil per unit of R. In order to predict soil losses from areas which differ from the unit plot, A 1 is multiplied in the second step by factors that account for slope length (L), slope gradient (S), crop and crop management (C) and soil conservation practice (P). A ¼ A 1 LSCP ð2Þ where L = S = C = P = 1.0 for the unit plot. Eq. (1) provides the means of taking account of spatial variations in climate and soil. Consequently, the unit plot is the primary physical model on which the USLE model- ling approach is based. However, it has been proposed that the best physical model of erosion from a plot is provided by a replicate plot (Nearing, 1998). The USLE data base contains data from replicated bare fallow plots installed at a number of locations. The objective of work reported here is to examine the concept that “the best physical model of erosion from a plot is provided by a replicate plot” by analyzing event data from individual pairs of replicated bare fallow plots contained in the USLE data base and compare the result with the ability of the USLE/RUSLE and the USLE-M (Kinnell and Risse, 1998) to model event soil losses on bare fallow areas. 1.1. Measures of model effectiveness Replicated plots show “random” (stochastic) variations in soil losses between them (Wendt et al., 1986) at the event scale that tend to be normally distributed (Nearing, 1998). The primary issue that concerned Nearing was the observation that the coefficients of variation were higher for small soil losses than high soil losses so that he perceived that the observation that models like the USLE and WEPP (Flanagan and Nearing, 1995) tended to over predict small soil losses and under predict large soil losses (Tiwari et al., 2000) was a mathematical phe- nomenon rather than a function of any bias inherent in the models themselves. Subsequently, Nearing et al. (1999) examined data from Catena 145 (2016) 39–46 E-mail address: peter.kinnell@canberra.edu.au. http://dx.doi.org/10.1016/j.catena.2016.05.017 0341-8162/© 2016 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Catena journal homepage: www.elsevier.com/locate/catena