The USLE soil erodibility nomograph revisited

Abstract

The nomograph by Wischmeier et al. (1971) for calculating the K-factor in the USLE was extremely useful when there was low access to calculators. However, the generalised calculation of this factor requires the development of analytic procedures. This paper presents a detailed analysis of the nomograph and its underlying equation, which is applicable only when the silt plus very find sand fraction does not exceed 70%. We also examined the quality of fit on the nomograph of the adaptations to the equation that have been proposed, as a means of dealing with those areas where the original equation is not applicable. All models are shown to have areas where the fit is deficient or even unacceptable. Besides, the family of curves on the nomograph for the various values taken by the organic matter are not coincident with the mathematical function from which they presumably derive. The study also identifies those areas of the textural triangle in which the soils originally used in developing the USLE are located, with a view to according a lower predictive value to the contrasting areas in which calculations of the K-factor will necessarily be extrapolations. Finally, a new equation for calculating the K-factor is presented, which accurately reproduces the different sections of the nomograph, and allows the poorly functioning graph to be dispensed with. The paper ends with a link to a tool in R for simplifying the procedure for calculating the K-factor, taking into account varying situations of data availability.