Progress on relationships between horizontal and vertical dust flux: Mathematical, empirical and risk-based perspectives

Aeolian processes driving sediment flux and corresponding erosion are inherently 3-dimensional, but are primarily studied either with respect to the horizontal flux component, or to a lesser extent the vertical component. Understanding the relationship between horizontal flux and the vertical component of sediment and dust is critical to predicting fundamental processes such as erosion, and to assessing human and environmental risks associated with contaminated sediment and dust. Multiple mathematical approaches to calculate vertical flux of dust exist but are limited in their ability to predict vertical flux across a wide variety of landscapes and soil conditions. To address these issues, here we explore the relationship between horizontal and vertical fluxes from three perspectives: mathematical, based on existing equations; empirical, based on existing and new data; and risk-based, based on translating the former two into a risk context. Mathematical derivations suggest, depending on the approach, the two components could either be a constant ratio or that the vertical flux could be more dependent on the shear stress and particle size than horizontal flux. Empirical data highlight a wide range of ratios, varying by more than two orders of magnitude, though the ratios can be relatively similar within a given site and set of conditions. Risk-based assessment indicates the vertical flux component is relatively important in dose calculations, and consequently further improvement in mathematical and empirical relationships is needed. Collectively, these three perspectives expand insights on horizontal and vertical sediment fluxes and could aide future risk assessment from dust contaminants.