A flow resistance model for assessing the impact of vegetation on flood routing mechanics

The specification of a flow resistance factor to account for vegetative effects in the Saint-Venant equation (SVE) remains uncertain and is a subject of active research in flood routing mechanics. Here, an nalytical model for the flow resistance factor is proposed for submerged vegetation, where the water depth is commensurate with the canopy height and the roughness Reynolds number is sufficiently large so as to ignore viscous effects. The analytical model predicts that the resistance factor varies with three canonical length scales: the adjustment length scale that depends on the foliage drag and leaf area density, the canopy height, and the water level. These length scales can reasonably be inferred from a range of remote sensing products making the proposed flow resistance model eminently suitable for operational flood routing. Despite the numerous simplifications, agreement between measured and modeled resistance factors and bulk velocities is reasonable across a range of experimental and field studies. The proposed model asymptotically recovers the flow resistance formulation when the water depth greatly exceeds the canopy height. This analytical treatment provides a unifying framework that links the resistance factor to a number of concepts and length scales already in use to describe canopy turbulence. The implications of the coupling between the resistance factor and the water depth on solutions to the SVE are explored via a case study, which shows a reasonable match between empirical design standard and theoretical predictions.