Accounting for surface roughness in a physically-based urban wash-off model

Abstract

To date, urban wash-off models have largely ignored the role of surface roughness in controlling particulate mass loss. We propose a mechanistic model in which particles are ejected by raindrops from surface cavities and travel laterally at the velocity of the overland flow until they are recaptured. In the model, cavities of differing depth and diameter have different ejection rates. The model has a similar form to multiple rate mass transfer models more commonly used to simulate solute transport in groundwater. An analytical solution for a model consisting of two possible cavity geometries is fit to breakthrough curves from sediment wash-off experiments. The experiments are conducted on a 0.8-m flume under artificial rainfall with a surface constructed of casts of asphalt. The experiments use fine sand (∼250 μm) and rainfall rates equivalent to that from a 2 year, 5-min storm in non-coastal regions of the Northeastern United States. Model parameters can be attributed to specific physical features of the surface cavities, particles, or rainfall rate and can be determined with limited calibration. At the plot scale, the model replicates an initial first flush and then settles to a more gradual loss rate which is noticeably different from the more rapid mass exhaustion implied by use of the common exponential wash-off model. Insights from this model could lead to improved design and placement of water quality management structures in urban landscapes.