An alternative method for deriving a USLE nomograph K factor equation

Soil erodibility (K factor) is an important component of the Universal Soil Loss Equation (USLE) / Revised USLE (RUSLE) and is used in many erosion models. A soil erodibility nomograph developed by Wischmeier et al. (1971) allows for a simple and repeatable method for calculating a K factor based on five key soil attributes. These attributes include the percentage of silt + very fine sand, sand and organic matter to calculate a first approximation of K. A value for soil structure and a value for permeability can then be used to complete the nomograph where a first approximation is insufficient. Following the development of the nomograph, an equation was created to bypass the otherwise tedious and time consuming manual process. This classical soil K factor equation can emulate the nomograph with some accuracy, but has shown to lack the required precision in certain circumstances. In this research a new method for deriving an equation directly from the soil erodibility nomograph is demonstrated and tested against the classical K factor equation. The main aims of this work are to: 1. Test a method for deriving a K factor equation that facilitates graphical modification to the nomograph prior to generating an equation. 2. Compare the results against those achieved using the classical K factor equation. 3. Create resources (including open-source scripts and a custom toolbox for ESRI ArcGIS) to allow ease of access to these methods for researchers and landscape managers alike. The method assumes that by segmenting the nomograph into zones according to the percentage of silt + fine sand, the relationship between key soil properties and erodibility can then be considered as a series of linear equations and can hence be solved within a linear systems framework. This method allows for iterative creation of new equations to fit any graphical changes made to the nomograph, and results show it can produce equations that emulate the nomograph solution with higher accuracy than the classical K factor equation. When tested on 100 randomly generated theoretical soil samples, this method achieves an average difference of just 25% from the nomograph solution. The classical equation achieves an average difference of 38% from the nomograph solution when tested on the same set of theoretical soil samples. Furthermore, where the classical equation is limited to soil samples with < 70% silt + fine sand, this new method can solve the full range of values taken by the nomograph and does not require additional equations for edge cases. This work shows that alternatives methods can solve the soil erodibility nomograph with higher accuracy than the classical equation, and the method is not restricted to the soil erodibility nomograph, it can also be applied to other biophysical nomographs. A custom toolbox is developed for ESRI ArcGIS software to allow use of the equations developed here without the need to replicate the methods. A range of open-source scripts written in the Python programming language are also available.