Sediment Transport In Shallow Overland flow

Understanding the size distribution of soil particles is very important for predicting how both sediment and agricultural chemicals move through the environment. However, most erosion models are limited because they only use a few broad size groups. While the Hairsine-Rose (HR) model can handle many different sizes, there is a trade-off between having a large number of size classes for accuracy, versus a smaller number for computational efficiency.  There is very little, if any, discussion in the literature about how many size classes are needed, or how fall velocities should be chosen to reliably represent the corresponding size class ranges.

We address both these questions through developing a model for a continuous, rather than the commonly used discrete settling velocity distribution. By integrating over discrete ranges of the settling velocity distribution, an equivalent discrete model can be obtained. This then provides conditions on how the discrete settling velocities need to be chosen in order to minimise the associated error in representing the overall distribution.  We then show how this error varies under both steady and unsteady flow conditions.