Re-defining tillage erosion: quantifying intensity-direction relationships for complex terrain. 2. Revised mouldboard erosion model

Current tillage erosion models account for the influence of tillage direction in the magnitude of the soil transport coefficient. It is argued that a re-modelling of tillage erosion is preferable in which the influence of tillage direction is separated from the soil transport coefficient, which is a measure of tillage intensity. This has been achieved here by developing a two-dimensional tillage erosion model that incorporates tillage direction in the measure of slope and uses soil transport coefficients that are independent of tillage direction and based on relationships between transport and the slope in the direction that bisects tillage direction and the overturning direction. Mean tillage erosion, associated with a single pair of opposing tillage directions and pair of overturning directions, can be described by a two-dimensional diffusion-type equation if the dimensions are defined as the tillage direction and the direction perpendicular to tillage. Application of the model to a real-world case allows quantification of the potential soil conservation benefits associated with optimization of tillage direction. The scope for amelioration is related to the ratio between the coefficients for transport in the direction of tillage and perpendicular to tillage. As this ratio approaches unity, the potential for amelioration reduces towards zero. For the study site investigated, use of the experimentally derived ratio of 0.66 indicated that a 12% reduction in tillage erosion could be obtained by ploughing across the dominant field slope as compared to ploughing up and down the dominant slope. For an implement with a coefficient ratio of 0.2 the reduction in tillage erosion intensity, associated with optimizing the tillage direction, reaches 28%. Nevertheless, such benefits must be considered in the context of other management considerations. The tillage direction that minimizes erosion is associated with lateral slopes of 10o, or more, over 20% of the field. To the land-user this disadvantage may outweigh the soil conservation benefits.